Investigating the Effect of Tube Dimensions and Operating … · 2019-06-14 · Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in

Investigating the Effect of Tube

Dimensions and Operating

Conditions on Heat Transfer

Performance in a Rising Film

Vertical Tube Evaporator

Omkar Prabhakar THAVAL Bachelor of Technology (Sugar Engineering)

Master of Applied Science (Research), QUT

THESIS

Submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Chemistry, Physics and Mechanical Engineering

Science and Engineering Faculty

Queensland University of Technology

2019

Dedicated to the Sugar Research Institute

team who taught me the value of good and

reliable data.

“Without data you are just another person with an opinion”

– W. Edwards Deming.

Data Scientist

Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a

Rising Film Vertical Tube Evaporator I

Keywords

Annular Flow, Boiling Mechanism, Boiling Patterns, Brix, Bubbly Flow, Capital

Cost Model, Calandria Retrofitting, De-entrainment of Juice, Heat Transfer

Coefficient, Heat Flux, Headspace Pressure, Juice Level, Operating Costs, Optimum

Tube Dimensions, Pressure Difference, Rising Film Evaporator, Robert Evaporator,

Sucrose Degradation, Slug Flow, Temperature Difference, Tube Diameter, Tube

Dimensions, Tube Length, Vertical Tube.


Rising Film Vertical Tube Evaporator III

Abstract

This thesis reports on a study to investigate the effects of tube dimensions and

operating conditions on heat transfer performance of a vertical rising film evaporator

tube. The study is undertaken to build a foundation, on which an improved design of

the Robert-type evaporator can be developed, seeking better performance in terms of

heat transfer coefficient (HTC), and at the same time reducing the capital cost

associated with designing, fabrication and installation of the equipment. Robert

evaporators in Australian sugar factories are traditionally constructed with 44.45 mm

outside diameter stainless steel tubes of ~2 m length for all stages of evaporation.

There are a few vessels with longer tubes (up to 2.8 m) and smaller and larger

diameters (38.1 and 50.8 mm). This PhD project is undertaken to investigate the heat

transfer performance of tubes of different lengths and diameters for the whole range

of process conditions typically encountered in the evaporator set. The study was

carried out in four phases.

The first phase of the project involved the development of a capital costs model

to understand the cost implications for constructing evaporator vessels with calandrias

having tubes of different dimensions. A capital cost model was developed, which

provides a relative cost of constructing and installing Robert evaporators of the same

heating surface area (HSA) but with different tube dimensions. Evaporators of 2000,

3000, 4000 and 5000 m2 were investigated. The results showed that the conventional

evaporator, with 2 m tubes of 44.45 mm outside the diameter, is more expensive than

all the other tube arrangements, except for evaporators with 2 m tubes of 50.8 mm

outside diameter.

The second phase of the project involved the experimental investigations with a

single tube evaporator rig for different tube dimensions. The experimental program

was undertaken in two sections. Nine tubes were tested for the operating conditions of

1st, 3rd, and 5th effect positions in a quintuple evaporator set and the HTC was

determined. Tests with four of the tubes were replicated to understand the tube length

and tube diameter interaction and build confidence in the data. The results showed that

selection of tube length and tube diameter cannot be independent of each other. The

tube diameter is more important than tube length in achieving maximum HTC. The

IV


Rising Film Vertical Tube Evaporator

results showed that as the brix of the juice increases, HTC decreases. An optimum

juice level exists that corresponds to maximum HTC, and brix and tube diameter are

two factors strongly affecting the optimum juice level. It was found the optimum juice

levels were lower for smaller diameter tubes and the optimum juice level was higher

for larger diameter tubes. Empirical models were developed for maximum HTC and

optimum juice level.

The third phase of the project involved investigating the boiling patterns in the

single tube evaporator for different tube dimensions and operating conditions. Six

distinct boiling patterns were identified and the relationship to the overall HTC was

analysed. The Annular Flow boiling regime was found to not exist in the test

conditions, which reflected sugar mill evaporators. The dominant regimes were

hypothesised as being Bubbly and Slug flow regimes. Boiling patterns with uniform

HTC values along the tube length and with low HTC at the bottom of the tube were

identified as occurring when good heat transfer performance was achieved.

The fourth phase of the project involved identifying the favoured tubes based on

HTC performance and the capital and operating costs. For evaporators at effect 1st to

3rd effect of a quintuple set, cost savings of ~20% could be achieved if small diameter

(38,1 mm) and long tubes (3 or 4 m) are used instead of the traditional tubes. Operating

cost savings include the reduction in sucrose degradation losses in evaporators by

installing vessels with smaller diameter and longer tubes as these vessels have smaller

diameter and juice holds up volume, thus reducing the residence time (for juice) in the

evaporator. Replacing the calandria in an existing evaporator with a calandria

comprising smaller diameter and longer tubes could be an attractive option for

increasing the HSA and capacity of the set for a much lower cost than replacing the

whole evaporator.


Rising Film Vertical Tube Evaporator V

Table of Contents

Keywords ...................................................................................................................... I

Abstract ...................................................................................................................... III

Table of Contents ........................................................................................................ V

List of Figures ........................................................................................................... XV

List of Tables............................................................................................................. XX

Abbreviations & Symbols ...................................................................................... XXV

Statement of Original Authorship ....................................................................... XXVII

Acknowledgements .............................................................................................. XXIX

List of Publications .............................................................................................. XXXI

CHAPTER 1: INTRODUCTION .......................................................................... 1

1.1 Introductory Remarks ......................................................................................... 1

1.2 The Australian Sugar Industry ............................................................................ 1

1.3 Raw Sugar Production ........................................................................................ 1

1.4 The Evaporation Station ..................................................................................... 3

1.4.1 Overview ................................................................................................... 3

1.4.2 Multiple effect evaporation ....................................................................... 3

1.4.3 Evaporator design ...................................................................................... 4

1.4.4 Evaporator performance ............................................................................ 6

1.5 Scope of Research............................................................................................... 8

1.5.1 Research problem ...................................................................................... 8

1.5.2 Objectives .................................................................................................. 9

1.5.3 Individual contribution to the research team ........................................... 10

1.6 Overview of thesis ............................................................................................ 11

CHAPTER 2: LITERATURE REVIEW ............................................................ 13

2.1 Introductory Remarks ....................................................................................... 13

VI



2.2 Condensation Heat Transfer ............................................................................. 13

2.2.1 Introductory remarks ............................................................................... 13

2.2.2 Laminar film on a vertical surface .......................................................... 13

2.2.3 Concluding remarks ................................................................................ 16

2.3 Flow Boiling ..................................................................................................... 17


2.3.2 Regimes of boiling .................................................................................. 17

2.3.3 Two – phase flow .................................................................................... 18

2.3.4 Existing flow pattern maps ...................................................................... 19

2.4 Transition Mechanisms (Adiabatic Flows) ....................................................... 20


2.4.2 The transition from bubble flow.............................................................. 20

2.4.3 The transition from slug flow .................................................................. 22

2.4.4 The transition to annular flow ................................................................. 24

2.4.5 Flow pattern maps ................................................................................... 25


2.5 Previous Pilot Plant Investigations of Sugar Factory Evaporators ................... 26


2.5.2 Kestner evaporator .................................................................................. 26

2.5.3 Guo et al. investigations .......................................................................... 27

2.5.4 Broadfoot and Dunn investigations ......................................................... 29

2.5.5 Pennisi’s investigations ........................................................................... 31

2.5.6 The SRI design of Robert evaporator ...................................................... 36

2.5.7 Selection of tube dimensions................................................................... 37


2.6 Operational Investigations on Robert vessels ................................................... 39


Rising Film Vertical Tube Evaporator VII


2.6.2 Smith and Taylor investigations .............................................................. 39

2.6.3 Jayes’ evaporation model ........................................................................ 40

2.6.4 Watson investigation ............................................................................... 40

2.6.5 Shah and Peacock investigations............................................................. 42

2.6.6 Broadfoot and Tan investigations ........................................................... 43

2.6.7 Empirical relationships for HTC ............................................................. 43


2.7 CFD Modelling ................................................................................................. 46


2.7.2 CFD and heat transfer models ................................................................. 47


2.8 Concluding Remarks ........................................................................................ 48

CHAPTER 3: CAPITAL COST MODEL .......................................................... 51


3.2 Evaporator Designs and Costs .......................................................................... 51


3.2.2 Number of tubes ...................................................................................... 51

3.2.3 Vessel internal diameter .......................................................................... 54

3.2.4 Capital costs ............................................................................................ 54

3.2.5 Installation costs ...................................................................................... 58


3.3 Other Considerations in the Design of Evaporators ......................................... 60


3.3.2 Sucrose degradation during juice evaporation ........................................ 60

3.3.3 Buffer volume for improved juice level and syrup brix control ............. 61

3.3.4 De-entrainment of droplets of juice from the vapour stream .................. 62

VIII




3.4 Concluding Remarks ........................................................................................ 64

CHAPTER 4: EXPERIMENTAL PROGRAM ................................................. 67


4.2 Experimental Rig .............................................................................................. 67

4.3 Experimental Design ........................................................................................ 70

4.3.1 Selection of the experimental factors ...................................................... 70

4.3.2 Design of experiments ............................................................................. 73

4.4 Experimental Procedure.................................................................................... 74

4.5 Calculating HTC from Condensate Measurements .......................................... 75


4.5.2 Determining condensate flow rate (kg/s) ................................................ 75

4.5.3 Determining temperature difference ....................................................... 76

4.5.4 Example showing HTC calculation......................................................... 76

4.6 Analysis of Potential Errors with Condensate Collection ................................ 80


4.6.2 Collection of condensate from the base of the steam chest ..................... 80

4.6.3 Overflowing in a free-flowing scenario .................................................. 83

4.6.4 Overflowing due to blockage at the entrance to a drainage tube ............ 84

4.6.5 Concluding remarks on the collection of condensate from the four

sections of the heating tube ..................................................................... 85

4.7 Analysis of Potential Errors of Operating Conditions ...................................... 86


4.7.2 Analysis of variance of the operating conditions .................................... 87


4.8 The Effect of Tube Dimensions and Operating Conditions on Heat Flux and

Heat Transfer Coefficient ........................................................................................... 94


Rising Film Vertical Tube Evaporator IX


4.8.2 Review of the experimental data ............................................................. 95

4.8.3 Concluding remarks .............................................................................. 105

4.9 Concluding Remarks ...................................................................................... 107

CHAPTER 5: ANALYSIS OF HEAT TRANSFER COEFFICIENT

RESULTS ...................................................................................................... 109

5.1 Introductory remarks ...................................................................................... 109

5.2 Features of the Pilot Evaporator Rig that may affect HTC Results ................ 109

5.2.1 Influence of clean and new tubes .......................................................... 109

5.2.2 Effect of gutters on the tube .................................................................. 110

5.2.3 Effect of the downtake .......................................................................... 111

5.2.4 Comparison of industrial and pilot evaporator HTC values ................. 111


5.3 Visual Observations of Boiling Patterns ........................................................ 113

5.3.1 Introductory remarks ............................................................................. 113

5.3.2 No visible juice head above top plate.................................................... 113

5.3.3 Visible juice head above top plate......................................................... 113

5.3.4 Substantial juice head above top plate .................................................. 114

5.4 Overview of the results ................................................................................... 114

5.5 Comparison of Original432 and Replicate128 Results for the Overall HTC 115


5.5.2 HTC vs juice level results for M2 tube ................................................. 115

5.5.3 HTC vs juice level results for S2 tube................................................... 117

5.5.4 HTC vs juice level results for M3 tube ................................................. 119

5.5.5 HTC vs juice level results for S3 tube................................................... 121

5.5.6 Concluding Remarks ............................................................................. 124

5.6 Analysis of the Results of the Original432 Tests ........................................... 124

X




5.6.2 TL:TD:B:HS interaction plot .................................................................. 127

5.6.3 TD:JL interaction plot ............................................................................ 129


5.7 Analysis of HTCmax Results ............................................................................ 131


5.7.2 Method for HTCmax selection ................................................................ 131

5.7.3 HTCmax results ....................................................................................... 131


5.8 Analysis of Optimum Juice Level .................................................................. 134


5.8.2 Optimum juice level (JLopt(%)) for HTCmax ............................................ 135


5.9 Developing Empirical Relationships .............................................................. 139


5.9.2 Empirical relationship for HTCmax ........................................................ 140

5.9.3 Empirical relationship for optimum juice level (JLopt(mm)).................... 143



CHAPTER 6: BOILING PATTERNS IN THE HEATING TUBE ................ 149

6.1 Introductory Remarks ..................................................................................... 149

6.2 Comparison of Replicate Results with Original Results for the Section HTCs ...

........................................................................................................................ 150


6.2.2 Comparison of the HTC results for individual tube sections for

Brix-20 tests .......................................................................................... 151


Rising Film Vertical Tube Evaporator XI

6.2.3 Comparison of the HTC results for individual tube sections for

Brix-70 tests .......................................................................................... 155


6.3 Identification of Boiling Patterns.................................................................... 156


6.3.2 Boiling patterns ..................................................................................... 156


6.4 Determination of Factors Influencing the Boiling Pattern ............................. 158


6.4.2 Factors affecting the boiling patterns .................................................... 159


6.5 Analysis of Variance of Individual Sections HTC ......................................... 162


6.5.2 ANOVA for individual section HTC results ......................................... 162


6.6 Analysis of Variance of the HTC Values for Individual Sections Corresponding

to Overall HTCmax .................................................................................................... 172


6.6.2 ANOVA for individual section corresponding to HTCmax results ........ 172

6.6.3 Uniform boiling pattern for tests at HTCmax ......................................... 176

6.6.4 Non-uniform boiling pattern with low HTC at the top for tests at

HTCmax .................................................................................................. 177

6.6.5 Non-uniform boiling pattern with low HTC at the bottom for test at

HTCmax .................................................................................................. 178

6.6.6 Non-uniform boiling with low HTC at intermediate sections for

tests at HTCmax ...................................................................................... 179


6.7 Boiling Mechanism ......................................................................................... 181


XII



6.7.2 Review of the literature on boiling mechanisms in a rising film tube

evaporator .............................................................................................. 181

6.7.3 Proposed boiling mechanism ................................................................ 184


6.8 Boiling Patterns in the Tube that Provide Superior Heat Transfer Coefficient ....

........................................................................................................................ 186


6.8.2 Uniform boiling pattern ......................................................................... 187

6.8.3 Low HTC at the bottom of the tube ...................................................... 189



CHAPTER 7: SELECTING OPTIMUM TUBE DIMENSIONS ................... 193


7.2 Methodology for Determining the Optimum Tube Dimensions .................... 193


7.2.2 Favoured tubes based on HTCmax .......................................................... 193


7.3 Capital Costs for Constructing and Installing Evaporators ............................ 198


7.3.2 Construction costs ................................................................................. 199

7.3.3 Foundations and structural costs ........................................................... 201

7.3.4 Insulation and cladding costs ................................................................ 203

7.3.5 Design weight and design costs ............................................................ 204

7.3.6 Total costs ............................................................................................. 207


7.4 Selection of the Optimum Tube Dimensions.................................................. 208



Rising Film Vertical Tube Evaporator XIII

7.4.2 Basis of selection ................................................................................... 208

7.4.3 Estimates of capital costs savings ......................................................... 209

7.4.4 Estimates of operating costs savings ..................................................... 210

7.4.5 Selection of the optimum tube dimension ............................................. 212


7.5 Retrofitting of Calandria for Existing Evaporators ........................................ 213


7.5.2 Practical considerations of retrofitting a calandria ................................ 214

7.5.3 Retrofit options ...................................................................................... 214

7.5.4 Further design considerations................................................................ 215



CHAPTER 8: GENERAL DISCUSSIONS AND CONCLUSIONS ............... 217


8.2 Aim of the Research ....................................................................................... 217

8.3 Comments on the Experimental Program ....................................................... 218

8.4 Summary of the Research Outcomes .............................................................. 219

8.4.1 Capital cost model ................................................................................. 219

8.4.2 Heat transfer performance of different tube dimensions ....................... 219

8.4.3 Understanding the boiling patterns in the single tube ........................... 221

8.4.4 Selecting the optimum tube dimensions................................................ 222

8.5 Significance of the Research .......................................................................... 223


8.5.2 Increase in HTC .................................................................................... 223

8.5.3 Reducing capital costs ........................................................................... 224

8.5.4 Reducing operating costs ...................................................................... 224

8.5.5 Retrofitting of calandrias ....................................................................... 224

XIV



8.6 Recommendations for Future Research .......................................................... 225


BIBLIOGRAPHY .................................................................................................. 229

APPENDIX A: DESCRIPTION OF EXPERIMENTAL RIG .......................... 235

APPENDIX B: CFD MODEL–STEAM SIDE .................................................... 253

APPENDIX C: ORIGINAL432 DATA SET - EXPERIMENTAL DESIGN AND

RESULTS ............................................................................................................ 257

APPENDIX D: REPLICATE128 DATA SET - EXPERIMENTAL DESIGN

AND RESULTS ...................................................................................................... 279

APPENDIX E: HTCMAX AND VCCMAX RESULTS OF ORIGINAL432 AND

REPLICATE128 TESTS ........................................................................................ 289

APPENDIX F: INDIVIDUAL SECTIONS HTC RESULTS OF ORIGINAL432

EXPERIMENTS .................................................................................................... 295

APPENDIX G: INDIVIDUAL SECTIONS VCC RESULTS OF ORIGINAL432

EXPERIMENTS .................................................................................................... 307

APPENDIX H: INDIVIDUAL SECTIONS HTC RESULTS OF

REPLICATE128 EXPERIMENTS ....................................................................... 319

APPENDIX I: INDIVIDUAL SECTIONS VCC RESULTS OF REPLICATE128

EXPERIMENTS .................................................................................................... 325

APPENDIX J: REPLICATE128 ANOVA ........................................................... 331

APPENDIX K: COMPARISON OF INDIVIDUAL SECTIONS HTC FOR

TESTS WITH BRIX-70 ......................................................................................... 337

APPENDIX L: UNIFORM BOILING PATTERN RESULTS – ORIGINAL432

AND REPLICATE128 DATASETS ..................................................................... 343

APPENDIX M: RESULTS SHOWING LOW HTC AT TOP SECTION –

ORIGINAL432 AND REPLICATE128 DATASETS ......................................... 349

APPENDIX N: RESULTS SHOWING LOW HTC AT BOTTOM SECTION –

ORIGINAL432 AND REPLICATE128 DATASETS ......................................... 365

APPENDIX O: RESULTS SHOWING LOW HTC AT INTERMEDIATE

SECTIONS – ORIGINAL432 AND REPLICATE128 DATASETS ................. 373

APPENDIX P: ANALYSIS OF VARIANCE ...................................................... 377


Rising Film Vertical Tube Evaporator XV

List of Figures

Figure 1.1 The process of raw sugar production .......................................................... 2

Figure 1.2 Multiple effect evaporation diagram .......................................................... 4

Figure 1.3 Typical design of Robert evaporator (Neill et al., 1996) ............................ 5

Figure 2.1 Flow regimes of the film of condensate on a cooled vertical surface

(Bejan, 1993)................................................................................................ 14

Figure 2.2 Laminar film condensation, supplied by a reservoir of stationary

saturated vapour (Bejan, 1993) .................................................................... 15

Figure 2.3 Flow regimes for forced convection boiling inside a tube (Incropera

& Dewitt, 1996) ........................................................................................... 18

Figure 2.4 Flow patterns in vertical flow (Taitel et al., 1980) ................................... 19

Figure 2.5 Model of slug flow (McQuillan & Whalley, 1985) .................................. 23

Figure 2.6 Flow pattern map for vertical tubes 51 mm diameter, air-water at

100 kPa abs (Taitel et al., 1980) .................................................................. 25

Figure 2.7 Effect of liquid level on HTC (Guo et al., 1983) ...................................... 28

Figure 2.8 Effect of ΔT on HTC at selected constant liquid levels (h) (Guo et

al., 1983) ...................................................................................................... 29

Figure 2.9 Variation of HTC with operating level of juice at 15 brix

((Broadfoot & Dunn, 2007) ......................................................................... 30

Figure 2.10 HTC data for varying ΔT, calandria pressure and brix for the total

tube (Pennisi, 2004) ..................................................................................... 33

Figure 2.11 HTC values for water solution for segments of the evaporator tube

(Pennisi, 2004) ............................................................................................. 34

Figure 2.12 HTC values for Brix-20 sucrose solution for segments of the

evaporator tube (Pennisi, 2004) ................................................................... 35

Figure 2.13 HTC values for Brix-45 sucrose solutions for segments of the

evaporator tube (Pennisi, 2004) ................................................................... 36

Figure 2.14 Variation of head of juice above the calandria with operating level

Watson (1986b) ............................................................................................ 41

Figure 2.15 Variation of HTC with operating level for a conventional Robert

evaporator with mini-downtake (Watson, 1986b) ....................................... 42

Figure 3.1 Output sheet for the tube layout program for the Robert evaporator

design ........................................................................................................... 52

XVI



Figure 3.2 Number of tubes for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions ............................................................................. 53

Figure 3.3 Vessel ID for 2000, 3000, 4000 and 5000 m2 vessels with different

tube dimensions ........................................................................................... 54

Figure 3.4 Costs of materials for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions as fraction of cost of materials for vessels

with M2 calandrias ....................................................................................... 56

Figure 3.5 Total costs (ex-works) for 2000, 3000, 4000 and 5000 m2 vessels

with different tube dimensions as fraction of cost (ex-works) for

vessels with M2 calandrias .......................................................................... 58

Figure 3.6 Total mass on foundations for 2000, 3000, 4000, and 5000 m2

vessels with different tube dimensions as fraction of the total mass for

vessels with M2 calandrias .......................................................................... 59

Figure 3.7 Juice volume intensity for 2000, 3000, 4000 and 5000 m2 vessels

with different tube dimensions..................................................................... 61

Figure 4.1 Schematic representation of the single-tube evaporator rig ..................... 68

Figure 4.2 Pilot evaporator rig ................................................................................... 70

Figure 4.3 Condensate collection (mm) for individual sections (1 to 4) and for

section 5 ....................................................................................................... 79

Figure 4.4 Mean values of unaccounted section 5 condensate flow expressed as

percentage of total flow on tube surface ...................................................... 82

Figure 4.5 Mean values of measured brix for each level of each factor for the

Original432 tests with all results included .................................................. 89

Figure 4.6 B:HS:ΔP interaction plot with measured pressure difference as a

response factor ............................................................................................. 91

Figure 4.7 Actual average temperature differences for the three brix ....................... 93

Figure 4.8 Target temperature differences for the three brix ..................................... 93

Figure 4.9 Effect of tube dimensions and operating conditions on heat flux and

heat transfer coefficient for tests at Brix-20 ................................................ 96

Figure 4.10 Effect of tube dimensions and operating conditions on heat flux

and heat transfer coefficient for tests at Brix-35 .......................................... 97

Figure 4.11 Effect of tube dimensions and operating conditions on heat flux

and heat transfer coefficient for tests at Brix-70 .......................................... 98

Figure 4.12 Relationship between heat transfer coefficient and heat flux at the

optimum juice level at Brix-20 .................................................................. 100


Rising Film Vertical Tube Evaporator XVII





Figure 5.1 Schematic representation of condensate pattern on the outside of the

heating tube for experimental and industrial arrangements ....................... 110

Figure 5.2 Comparison of industrial and pilot evaporator HTC values for the

M2 tube dimension .................................................................................... 112

Figure 5.3 Relationship between HTC and juice level for the M2 tube .................. 117

Figure 5.4 Relationship between HTC and juice level for the S2 tube .................... 119

Figure 5.5 Relationship between HTC and juice level for the M3 tube .................. 121

Figure 5.6 Relationship between HTC and juice level for the S3 tube .................... 123

Figure 5.7 Mean values of HTC for each level of each factor for the

Original432 tests with all results included ................................................ 125

Figure 5.8 TL:TD:B:HS interaction plot for the Original432 dataset ....................... 128

Figure 5.9 TL:TD:B:HS interaction plot for the Original432 dataset with

separate plots for brix and headspace pressure .......................................... 129

Figure 5.10 TD:JL interaction plot for the Original432 dataset ............................... 130

Figure 5.11 TD:JL interaction for the Original432 dataset with three separate

plots for brix ............................................................................................... 130

Figure 5.12 Mean values of HTCmax for each level of each factor from the

Original432 tests (108 data points)............................................................ 132

Figure 5.13 TD:B:HS interaction for HTCmax for the Original432 dataset .............. 134

Figure 5.14 Mean values of JLopt(%) for each level of each factor from the

Original432 tests (108 data points)............................................................ 135

Figure 5.15 TL:B:HS interaction plot for the optimum juice level in the

Original432 dataset .................................................................................... 137

Figure 5.16 TD:ΔP interaction plot for the optimum juice level in the

Original432 dataset .................................................................................... 138

Figure 5.17 TD:ΔP interaction plot for Original432 dataset for three separate

plots for brix ............................................................................................... 139

Figure 5.18 Measured and predicted HTCmax .......................................................... 141

Figure 5.19 Measured and predicted optimum juice level ....................................... 144

Figure 6.1 Number of results showing uniform boiling throughout the tube for

each level of each factor for Original432 tests .......................................... 159

XVIII



Figure 6.2 Number of results showing non-uniform boiling with low HTC at

the top for each level of each factor for Original432 tests ........................ 160


the bottom for each level of each factor for Original432 tests .................. 160


intermediate sections for each level of each factor for Original432

tests ............................................................................................................ 161

Figure 6.5 TL:TD:B:HS interaction plot for HTC for section 1 ................................ 163




Figure 6.9 TL:B:ΔP interaction plot for HTC for section 1 ...................................... 165

Figure 6.10 TL:HS:ΔP interaction plot for HTC for section 2 ................................. 166

Figure 6.11 TL:B:ΔP interaction plot for HTC for section 2 .................................... 166

Figure 6.12 TL:JL:HS interaction plot for HTC for section 3 .................................. 167

Figure 6.13 TL:JL:HS interaction plot for HTC for section 4 .................................. 168

Figure 6.14 JL:HS:ΔP interaction plot for HTC for section 4 at HS1 values .......... 169

Figure 6.15 JL:HS:ΔP interaction plot for HTC for section 4 for HS2 values ........ 169

Figure 6.16 TD:JL interaction plot for HTC for section 1 ........................................ 170

Figure 6.17 TD:JL interaction plot for HTC for section 2 ........................................ 171

Figure 6.18 TD:B:HS interaction plot for HTCmax for the four sections for

Brix- 20 ...................................................................................................... 174


Brix- 35 ...................................................................................................... 175


Brix- 70 ...................................................................................................... 176

Figure 6.21 Mean values of overall HTCmax with uniform boiling pattern

(O432) ........................................................................................................ 177

Figure 6.22 Mean values of overall HTCmax with non-uniform boiling pattern

and low HTC at top (O432) ....................................................................... 178


and low HTC at intermediate section (O432) ............................................ 179


and low HTC at intermediate sections (O432) .......................................... 180


Rising Film Vertical Tube Evaporator XIX


100 kPa abs (Taitel et al., 1980) ................................................................ 183

Figure 6.26 Flow pattern map for experimental results ........................................... 184

Figure 7.1 Influence of tube length and tube diameter on HTCmax for Brix-20 ....... 195



Figure 7.4 Materials and labour costs for evaporators with favoured tubes

dimensions for 1st, 3rd and 5th effect positions ........................................... 200

Figure 7.5 Design vessel weight and design costs for evaporators with the

favoured tubes for 1st, 3rd and 5th effect positions ...................................... 206

XX



List of Tables

Table 2.1 Maximum length of evaporator tubes for different tube diameters

(Hugot & Jenkins, 1986) .............................................................................. 38

Table 2.2 Optimal tube lengths recommended for the different effect

parameters (Hugot & Jenkins, 1986) ........................................................... 38

Table 3.1 Code for different tube dimensions ............................................................ 53

Table 3.2 Tube costing based on tube diameter ......................................................... 55

Table 3.3 Cost data for construction of an evaporator ............................................... 56

Table 3.4 Maximum specific vapour rates for acceptable up-flow vapour

velocities in the headspace of vessels comprising tubes of 38.1 mm

OD and 4 m length ....................................................................................... 63

Table 3.5 Maximum specific vapour rates for LSEA II louvres in vessels

comprising tubes of 38.1 mm OD and 4 m length ....................................... 64

Table 4.1 Factors and levels explored in the experiment ........................................... 71

Table 4.2 Experimental factors investigated for juice at Brix-20 .............................. 72

Table 4.3 Experimental factors investigated for juice at Brix-35 .............................. 72

Table 4.4 Experimental factors investigated for juice at Brix-70 ............................. 73

Table 4.5 Density of saturated liquid and latent heat of condensation for the 12

steam chest pressures ................................................................................... 78

Table 4.6 Results of analysis of variance of unaccounted section 5 condensate

flow (%) with main sources (percent of total flow on tube surface) ........... 83

Table 4.7 Maximum value, mean value and standard deviation of the

unaccounted section 5 condensate rate for all levels of each factor for

tests at Brix-20 ............................................................................................. 84

Table 4.8 Maximum values, minimum values, mean values and standard

deviation of the experimental factors ........................................................... 87

Table 4.9 Analysis of variance of measured brix ....................................................... 88

Table 4.10 Analysis of variance of measured pressure difference............................. 90

Table 4.11 Analysis of variance of calculated temperature difference ...................... 92

Table 4.12 Conversions of heat flux to VCC for different calandria pressures ......... 95

Table 4.13 List of tubes showing high and low HTC for corresponding brix and

temperature difference ............................................................................... 103


Rising Film Vertical Tube Evaporator XXI

Table 4.14 Summary of the observations and comments for heat flux of three

brix ............................................................................................................. 104

Table 4.15 General observations for tube dimensions that provided higher

levels of heat transfer coefficient for the three brix levels ......................... 107

Table 5.1 Average values for overall HTC for all tube dimensions with Brix-

20, Brix-35 and Brix-70 ............................................................................. 114

Table 5.2 Comparison of data for Original432 and Replicate128 for M2 tube ....... 116

Table 5.3 Comparison of data for Original432 and Replicate128 for S2 tube ........ 118

Table 5.4 Comparison of Original432 and Replicate128 for M3 tube .................... 120

Table 5.5 Comparison of Original432 and Replicate128 for S3 tube ..................... 122

Table 5.6 Analysis of variance of HTC from Original432 tests with 4th order

interactions ................................................................................................. 126

Table 5.7 Analysis of variance of HTCmax from Original432 tests ......................... 133

Table 5.8 Analysis of variance of optimum juice level (JLopt-% tube height)

corresponding to HTCmax from the Original432 tests ............................... 136

Table 5.9 List of parameters considered for inclusion in the empirical model ........ 140

Table 5.10 Analysis of variance of regression model for HTCmax ........................... 142

Table 5.11 Typical operating conditions in factory vessels and the predicted

HTCmax from two models ........................................................................... 143


optimum juice levels (absolute and % tube height) ................................... 145

Table 6.1 Categories to define differences between the individual section HTC

values and the overall HTC........................................................................ 151

Table 6.2 Individual section HTC comparison with M2 tubes for Brix-20 juice .... 152

Table 6.3 Individual section HTC comparison with S2 tubes for Brix-20 juice ...... 152

Table 6.4 Individual section HTC comparison with M3 tube for Brix-20 juice ...... 153

Table 6.5 Individual section HTC comparison with S3 tube for Brix-20 juice ....... 153

Table 6.6 Comparison of the HTC data for individual sections between

Original432 and Replicate128 datasets for the four tubes for Brix-20

tests ............................................................................................................ 154


Original432 and Replicate128 datasets for M2, S2, M3 and S3 tubes

for Brix-70 tests ......................................................................................... 155

Table 6.8 Categorisation and description of the boiling patterns............................. 157

Table 6.9 Boiling pattern allocation for Original432 and Replicate128 datasets .... 158

XXII



Table 6.10 HTC pattern and the corresponding figure number ............................... 159

Table 6.11 Results of observations of the influence of experimental factors on

the boiling patterns ..................................................................................... 161

Table 6.12 Summary of significant factors and interactions for the individual

sections HTC values (Original432) ........................................................... 162

Table 6.13 Boiling pattern allocation for HTCmax results from Original432

dataset ........................................................................................................ 172


sections HTCmax (Original432) .................................................................. 173

Table 6.15 Factors affecting overall HTCmax for uniform boiling for three brix

levels .......................................................................................................... 177

Table 6.16 Factors affecting overall HTCmax for the boiling pattern with low

HTC at the top for the three brix values .................................................... 178

Table 6.17 Factors affecting overall HTCmax the boiling pattern with low HTC

at the bottom for the three brix values ....................................................... 179


HTC at an intermediate section for the three brix values .......................... 180

Table 6.19 Proposed boiling regimes for boiling patterns ....................................... 185

Table 6.20 Average HTCmax for different boiling patterns at three brix .................. 187

Table 6.21 Tube dimensions and operating conditions for HTCmax with uniform

boiling pattern ............................................................................................ 188

Table 6.22 Observation with uniform boiling pattern for three brix values ............ 188

Table 6.23 Tube dimensions and operating conditions for HTCmax with low

HTC at bottom ........................................................................................... 189

Table 6.24 Observations with non-uniform boiling pattern (low HTC at the

bottom of the tube) for three brix values ................................................... 190

Table 7.1 Favoured tubes based on HTCmax for 1st, 3rd and 5th effect positions ...... 198

Table 7.2 Heating surface areas of the respective vessels for the favoured tubes

for 1st, 3rd and 5th effect positions .............................................................. 199

Table 7.3 Cost data for foundations and structure to support the evaporator .......... 201

Table 7.4 Foundations and structural costs for evaporators comprising the

favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2

evaporator of 2000 m2) .............................................................................. 202


Rising Film Vertical Tube Evaporator XXIII


favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2

evaporator of 5000 m2) .............................................................................. 202

Table 7.6 Cost data for insulation and cladding of the evaporator .......................... 203

Table 7.7 Insulation area and costs for the favoured tubes for 1st, 3rd and 5th

effect positions (HSA of M2 evaporator of 2000 m2) ................................ 204


effect positions (HSA of M2 evaporators of 5000 m2) .............................. 204

Table 7.9 Details of the evaporator vessels with the favoured tube dimensions

to equate to the heat transfer performance of a 2000 m2 HSA M2

evaporator .................................................................................................. 207


to equate to the heat transfer performance of a 5000 m2 HSA M2

evaporator .................................................................................................. 208

Table 7.11 Estimate of cost savings from using S3 and M3 tubes in Robert

evaporators at the 1st effect and 3rd effect instead of using a Robert

evaporator with M2 tubes .......................................................................... 210

Table 7.12 Sucrose degradation and operating cost savings .................................... 212

Table 7.13 Evaporator heating surface details for retrofit options........................... 215


Rising Film Vertical Tube Evaporator XXV

Abbreviations & Symbols

A Heat transfer area, m2

ANOVA Analysis of variance

B Brix

BPE Boiling point elevation

DP Pressure difference, kPa

𝑔 Acceleration due to gravity, m/s2

HS Headspace pressure, kPa abs

HSA Heating surface area, m2

ℎ𝐿 Condensation heat transfer coefficient, W/m2/K

ℎ𝑓𝑔′ Latent heat of condensation (corrected with the Jakob

number), kJ/kg

JL Juice level, % tube height

𝑘 Thermal conductivity, W/m/K

𝐿 Length of the wall, m

𝑁𝑢𝐿 Nusselt number

OD Outside diameter, mm

Q Heat flux, W/m2

𝑄𝐺 Gas volumetric flowrate, m3/s

𝑄𝐿 Liquid volumetric flowrate, m3/s

𝑞′ Total heat flux per unit length, W/m

R Recirculation rate, kg/s/m

S Condensate rate, kg/s

Tj Temperature of juice, °C

Ts Temperature of steam, °C

𝑇𝑠𝑎𝑡 Saturation temperature of the liquid – vapour interface (K)

𝑇𝑤 Wall temperature, (K)

TL Tube length, m

TD Tube diameter, mm

U Heat transfer coefficient, W/m2/K

𝑈𝐺 Gas velocity, m/s

XXVI



𝑈𝐺𝑠 Gas superficial velocity, m/s

𝑈𝐿 Liquid velocity, m/s

𝑈𝐿𝑠 Liquid superficial velocity, m/s

VCC Vapour condensation coefficient, kg/h/m2

WR Wetting rate, kg/s/m

𝛼 Void fraction

λs Latent heat of steam, J/kg

𝜇 Viscosity, Pa.s

ρl Density of liquid, kg/m3

𝜌𝐺 Density of gas, kg/m3

ρv Density of vapour, kg/m3

𝜐 Kinematic viscosity, m2/s

𝑣𝑝 Absolute velocity of the gas slug, m/s

𝜎 Surface tension of liquid, N/m


Rising Film Vertical Tube Evaporator XXVII

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the best

of my knowledge and belief, the thesis contains no material previously published or

written by another person except where due reference is made.

Signature:

Date: May 2019

QUT Verified Signature


Rising Film Vertical Tube Evaporator XXIX

Acknowledgements

Firstly, I would sincerely like to thank my principal supervisor, Professor Ross

Broadfoot, for his encouragement to undertake this PhD, and for his guidance and

patience throughout the long investigation. I would like to thank my associate

supervisor, A/Prof Geoff Kent, for his guidance in designing the experiments and

analysing the data. I would also like to thank my associate supervisor, Dr Floren Plaza,

for his assistance with CFD model development.

Secondly, I would like to thank the Sugar Research Australia (SRA) and Sugar

Research Limited (SRL) for their financial support of this project. I would also like to

thank Queensland University of Technology for a tuition fee waiver scholarship.

Thirdly, I would like to thank those who assisted in the experimental

investigations of the project. Craig Cuttriss of Kaima Engineering is acknowledged for

fabricating the pilot evaporator rig. Brett Stone of Applied Project Engineering is

acknowledged for his assistance in installing the rig and the support he provided during

changing the tubes and dealing with breakdowns. The management and staff of Rocky

Point Sugar Mill (Bruce Tyson, Terry Drury, Peter Bresow, Glen McIntosh) are

sincerely acknowledged for their permission to undertake the experiments at the mill

and for their immeasurable support. I would like to thank Neil McKenzie for his

assistance in setting up the control system of the rig and the data collection system. I

would like to thank Mr David Moller and Mr Neil McKenzie for their assistance in

commissioning the pilot evaporator.

Fourthly, I would like to thank those who assisted in analysing the data and

interpreting the results. I would like to thank Dr Wim Dekkers from the School of

Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty,

QUT, for his assistance with analysing the results. I would also like to thank Dr

Anthony Mann, Dr Darryn Rackemann and Mr David Moller from the Centre for

Tropical Crops and Biocommodities (CTCB) for fruitful discussions about the results.

I would like to thank Diane Kolomeitz for professional editing and proof reading the

thesis.

XXX



Fifthly, I would like to thank the High-Performance Computing (HPC) group at

Queensland University of Technology for their assistance in the CFD model

development.

Sixthly, I wish to thank the staff and students of the Centre for Tropical Crops

and Biocommodities (CTCB), in particularly the Bioprocessing group, for their

ongoing guidance and support throughout this investigation.

Seventhly, I wish to thank my friends Chris Henderson, David Moller, Dr Darryn

Rackemann and Dr Anthony Mann for their support and patience. I also wish to thank

my family for their support during this long investigation.

Lastly, I would like to thank my wife Priya Patankar, who for reasons best known

to her, agreed to marry me, and for her support during the final months of this

investigation.


Rising Film Vertical Tube Evaporator XXXI

List of Publications

1. Thaval OP, Broadfoot, R (2014). Capital cost model for Robert

evaporators. Proceedings of the 36th Annual Conference of the Australian

Society of Sugar Cane Technologists, Gold Coast, Australia.

2. Thaval OP, Broadfoot, R, Kent GA & Rackemann, DW (2016).

Determining optimum tube dimensions for Robert evaporators.

Proceedings of the XXIX International Society of Sugar Cane

Technologists Congress, Chiang Mai, Thailand.

3. Thaval OP, Broadfoot, R & Kent GA (2017). Boiling mechanism in

rising film vertical tube evaproator. Proceedings of the Annual

Convention of Sugar Technologists Association of India, Kochi, India.

4. Thaval OP, Broadfoot, R, Kent GA & Rackemann, DW (2019).

Investigating the effects of tube dimensions and operating conditions on

HTC of rising film evaporators. Proceedings of the XXX International

Society of Sugar Cane Technologists Congress, Tucuman, Argentina.

(Accepted)

5. Thaval OP, Broadfoot, R, & Kent GA (2019). Understanding the effect

of tube dimensions and operating conditions on boiling mechanism in

rising film vertical tube evaporator. (Proposed)

XXXII



Introduction 1

CHAPTER 1: INTRODUCTION

1.1 Introductory Remarks

The sugar industry is a process industry, comprising several unit operations to

produce raw or white plantation sugar. The evaporation of juice is one of the unit

operations and has the aim to remove most of the water from the clarified juice. For

most factories, it is important that the evaporator station is economical in the usage of

process steam. Several evaporator designs have been adopted in the industry, with each

having advantages and disadvantages, depending on the application. This thesis deals

with the development of an improved design of the Robert (rising film type) evaporator

and endeavours to achieve better performance in terms of heat transfer coefficient

(HTC), while at the same time reducing the capital cost associated with fabrication and

installation of the equipment.

This chapter provides a general overview of the Australian sugar industry, the

raw sugar manufacturing process, the evaporator station, and conventional evaporator

station terminology. The chapter also covers the scope of research, defines the research

problem and the objectives of the research. The chapter concludes with an overview

of the document.

1.2 The Australian Sugar Industry

The Australian sugar industry is one of Australia’s largest and most important

rural industries and sugarcane is Queensland’s largest agricultural crop. The

Queensland sugar industry produces about 35 million tonnes of sugarcane from

400,000 hectares annually. This sugarcane crop produces approximately 4,200,000

tonnes of raw sugar, 1 million tonnes of molasses and 10 million tonnes of bagasse

annually. Approximately 85% of the raw sugar produced is exported, generating up to

AUD 1.5 billion in export earnings for Queensland (Australian Sugar Milling

Council).

1.3 Raw Sugar Production

Figure 1.1 shows the raw sugar manufacturing process.

2 Introduction

Figure 1.1 The process of raw sugar production

The cane grown in the field is harvested using mechanical harvesters and

transported to the sugar mill. The cane billets are passed through a shredder to open

the fibrous cells and make the juice to be extracted more accessible. After exiting the

shredder, the prepared cane is passed on to the milling train. The milling process

essentially involves the removal of juice from sugarcane by squeezing the cane

between pairs of large cylindrical rolls in a series of milling units collectively called a

milling train. To aid in the extraction process, water is added to the final milling unit

and juice is recirculated in a counter-current fashion. This is commonly known as

compound imbibition. The extracted juice is sent to the clarification station to remove

the insoluble solids and some of the soluble impurities. The clarified juice is passed to

an evaporator supply juice (ESJ) tank, from which the ESJ is fed to the evaporator

station. The aim of the evaporator station is to boil off excess water contained in the

juice. Multi-stage evaporation is employed to achieve high steam economy. The syrup

leaving the final evaporator vessel is boiled in a crystallisation pan operating under

vacuum. The syrup is super-saturated and seed crystals are added to the liquid to

initiate crystal growth. The resulting mixture of crystals and liquor, called massecuite,

is sent to the centrifugal station to separate the crystals from the liquid by spinning the

massecuite at high speed in perforated baskets. The raw sugar crystals are dried in a

Introduction 3

rotary drum, through which air is passed in counter-current flow to the sugar. The raw

sugar is sent to storage to wait for shipment to refineries in Australia and overseas.

1.4 The Evaporation Station

1.4.1 Overview

The concentration of clarified juice or ESJ from 15 brix to 70 brix is undertaken

in a multiple effect evaporator set having due regard for saving of steam (energy

efficiency) and for efficiency in the use of the installed heat transfer area (capital). The

evaporator station is the single largest consumer of low pressure (LP) steam (typically

at 200-250 kPa abs) in the sugar factory. Factories have identified the need to reduce

the energy requirements of the evaporator station, so that larger quantities of energy

can be used for co-generated electricity production and for other purposes.

1.4.2 Multiple effect evaporation

Norbert Rillieux, in 1844, developed the multiple effect evaporation system for

the Louisiana sugar industry in order to achieve more efficient usage of steam. Using

the graduated pressure difference between the process steam and vacuum in the

headspace of the final vessel as a driving force for heat transfer, the vapour generated

in the first evaporator is used to evaporate water from juice in the second evaporator,

and so on, till the vapour from the final vessel is condensed in a barometric condenser.

Typically, four, five or six stages of evaporation are used.

Figure 1.2 shows the typical layout of a multiple effect evaporation set. A

temperature difference is required to transfer the heat from the steam chest (calandria)

to the boiling juice, and so the temperature of the vapour at the outlet of the vessel will

always be lower than that of the vapour used as the heating source.

The magnitude of the temperature difference is a measure of the thermal

efficiency of the vessel. Low pressure steam is used as the heat source in the first effect

and is typically at 118 °C to 125 °C in the saturated condition or very slightly

superheated, while the temperature of the vapour at the outlet of the final effect is

usually about 50 to 58 °C at saturated conditions. The saturation temperature of the

vapour at the outlet of the final effect vessel is regulated by controlling the headspace

pressure (vacuum) in the final effect. With the vapour pressure being controlled by the

4 Introduction

two extremes, at the first and the final effect of the set, the pressure of the vapour

streams in the remainder of the effects in the set are left to equilibrate naturally.

Many factors influence the equilibrium pressures and these include the

distribution of heat transfer area among the effects in the set, the heat transfer

coefficient (HTC) of the individual effects, the vapour flow rates, and rates of

withdrawal of vapour from individual vessels for other heating duties e.g. for juice

heating, pan boiling.

Figure 1.2 Multiple effect evaporation diagram

1.4.3 Evaporator design

The sugar industry uses both the plate type and tubular type evaporators, and

these can operate as either rising film or falling film mode. The rising or falling film

designation is in reference to the direction of juice flow, e.g. the juice in a rising film

type evaporator enters the vessel beneath the heating element and rises up through the

vertical heating tubes or plates, due to the boiling action of the juice inside the tubes

(Pennisi, 2004). As this study is considering the tube type evaporator, in particularly

the Robert type, which is used almost universally in the Australian sugar industry, only

the tube-type evaporator is described below.

The tube-type evaporator consists of a series of vertical tubes packed into a

heating element called a calandria. Saturated LP steam or vapour condenses on the

outside of the tubes while the juice boils on the inside. Tube-type evaporators are

available in two forms viz., falling-film and rising-film types. In falling-film tube

evaporators the juice is pumped onto a perforated plate located above the tops of the

Introduction 5

tubes and the juice flows downwards as a film on the inside of the tubes. Vapour also

passes down the tubes. In rising-film tube evaporators the juice is fed into the space

beneath the calandria, boils inside the tubes and the concentrated juice is removed from

either the top or bottom of the vessel. Vapour passes up the tubes and into the

‘headspace’ of the vessel. Figure 1.3 shows a typical design of the tube-type, rising-

film evaporator known as the Robert evaporator.

Figure 1.3 Typical design of Robert evaporator (Neill et al., 1996)

Several variations of juice entry and exit locations above and below the calandria

have been adopted in the Robert evaporator. This gave rise to the terms under and over,

when describing the location of the juice entry and outlet locations, e.g. an under-over

configuration has the juice entry below the calandria and the juice exit above the

calandria. By far the most common evaporator in the Australian industry is the tube-

type, rising-film evaporator in the under-under configuration.

The new Robert evaporators installed in the industry in the past decade have

incorporated a central downtake, which preferentially removes the juice from above

the top tube plate and passes it to the base of the vessel via the central downtake. The

tubes in the Robert-type evaporators are commonly 44.45 mm outside diameter, 2.0 m

in length and 304 stainless steel. Tubes of these dimensions have traditionally been

6 Introduction

used in the Australian industry for all stages of evaporation. There are only a relatively

few vessels with different tube lengths or diameters.

The main advantages of the Robert evaporator, compared with other designs

such as falling-film evaporators, are the low maintenance costs, good access to all

sections of the vessel for repair, the ease of cleaning including chemical and

mechanical/hydraulic cleaning and the robust control, due to the large buffer volume

of juice held in the base of these vessels. The main disadvantages are the longer

retention time for juice, which can result in sucrose inversion and increased colour

formation in the juice, and the large footprint for a given heating surface area. The

design is relatively simple and can be made by several local heavy engineering

suppliers. Robert evaporators are relatively expensive (AUD 1200 per 1 m2 of heating

surface area, fully installed) but service life is typically more than 30 years.

1.4.4 Evaporator performance

The performance and operating conditions of an evaporator can be assessed in

terms of the coefficient of evaporation, overall heat transfer coefficient and vapour

condensation coefficient (VCC).

Coefficient of evaporation

The coefficient of evaporation (COE) is commonly used for estimating the

required size of an evaporator. It is a measure of the vapour-producing performance of

an evaporator and is expressed as the mass rate of vapour passing to the headspace per

unit area of heat transfer. A maximum value for Australian evaporators is typically

40 kg/h/m2, which corresponds to a heat flux of about 25 kW/m2. Generally, the COE

is of limited value in assessing multiple-effect evaporator performance, as it measures

how hard the evaporator is being worked, which is often not the limiting factor. It is

found that the temperature difference (i.e. the driving force) is often the rate

determining factor Watson (1986a).

Overall heat transfer coefficient

A better indicator of performance when the temperature difference is restricted

is the overall heat transfer coefficient. This is defined as:

HTC =

Q

A ΔT

1.1

Introduction 7

where 𝐻𝑇𝐶 is the heat transfer coefficient (W/m2/K),

Q is the heat flux (W),

A is the heat transfer area (m2),

ΔT is the temperature difference available for heat transfer i.e. between

the vapour and the juice, K.

The heat flux Q is calculated by:

Q = S λs 1.2

where S is condensate rate (of condensed steam), kg/s

λs is the latent heat of condensation for the steam in the calandria as

determined from the measured pressure within the calandria, J/kg.

The temperature difference ΔT for heat transfer is calculated by:

ΔT = Ts − Tj 1.3

where Ts is the saturation temperature of steam in the calandria steam chest as

determined from the measured pressure within the calandria, °C.

Tj is the boiling temperature of the juice, as estimated from the saturation

temperature of the vapour in the headspace of the evaporator plus the

boiling point elevation of the juice (as determined from the saturation

temperature of the vapour and the average brix of juice within the

evaporator), °C.

The boiling point elevation (Batterham et al., 1973) is calculated by:

𝐵𝑃𝐸 =

(𝑇𝑗 + 273.2)2

((100 + 273.2)2

𝐵𝐶 + (100 − 𝑇𝑗))

1.4

𝐵𝐶 = −0.138 + 2.23

𝐵𝑥

(100 − 𝐵𝑥)+ 0.119 (

𝐵𝑥

100 − 𝐵𝑥)

2

1.5

where 𝐵𝑥 is the juice brix

In practice, the temperature of juice varies along the length of the tube. The juice

at the bottom of the tube has a higher boiling point due to the head of the juice above

8 Introduction

it. As a simplification a single value for the boiling temperature of the juice is used, as

defined above.

In practice, the values for HTC decrease with each stage farther down a multiple-

effect evaporator set, owing to the increasing viscosity of the juice, which results from

the higher brix and lower temperature in the later stages of evaporation. Larger

temperature differences exist for subsequent stages down the set to compensate for the

lower HTCs and ensure the required heat transfer for each effect is achieved.

Vapour condensation coefficient

The vapour condensation coefficient (VCC) defines the vapour rate entering the

calandria of the evaporator and is condensed. The VCC is obviously closely related

to heat flux at the surface of the heating tube. The VCC is the condensed vapour rate

per m2 of heating surface area (Broadfoot & Dunn, 2004).

VCC = 3600

S

A

1.6

Hence, HTC can be defined in terms of VCC as:

HTC =

VCC λs

3600 ΔT

1.7

For normal operating conditions, the VCC is considered to be the controlled

variable, as set by the steam rate supplied to the first stage of evaporation. Hence to

achieve this condensation rate, the ΔT is a dependent, interrelated variable. The heat

transfer coefficient of the evaporator is then set by the magnitude of Q and ΔT.

However, if there is inadequate ΔT available across the vessel, then the steam rate that

is condensed within the calandria will decrease. The ΔT for a given VCC value will

primarily depend on (Broadfoot & Dunn, 2004):

➢ Juice properties (brix, temperature, viscosity, surface tension); and

➢ Surface properties on the juice side of the tubes (nucleation sites, scale)

1.5 Scope of Research

1.5.1 Research problem

There are two main types of rising film tube evaporator viz., Kestner evaporators

of 6 to 7 m tube length and the Robert evaporator. Kestner evaporators are used in

several overseas factories but are only suited to the evaporation of low brix juice e.g.,

Introduction 9

in 1st and 2nd effects. Robert evaporators are suitable for all stages of juice evaporation.

Australia has traditionally used stainless steel tubes of 44.45 mm outside diameter;

1.9-2.2 m long in all vessels throughout the set.

New evaporation plant for Australian factories is very expensive. During the

past 10 years the Australian sugar industry has installed eight Robert evaporators with

a total surface area of 34,000 m2 and cost more than AUD 40 m (2011 dollars). The

installation of several more evaporators is likely over the next two decades, as factories

need to replace old equipment and upgrade factories for increased energy efficiency.

At present, the optimum tube dimensions (based on minimum capital cost for a defined

evaporation duty) are not known, and the selection of the tube dimensions is currently

based on historical experience and tradition. Depending on the heat transfer

coefficient that can be achieved, there may be scope for considerable cost savings if

tubes of different dimension than the traditional dimensions are used.

Some Brazilian sugar factories have installed 4 m, 3.5 m, 3.0 m and 2.5 m for 1st

effect, 2nd effect, 3rd effect and 4th effect respectively, with the tubes mostly being

38.1 mm outside diameter. Comments from Brazilian technologists suggest that the

HTC is quite poor for the 4 m Robert vessels, although no comprehensive HTC data

are available in the literature. Poor HTC values could be attributed to many factors,

including the heating surface not being fully wetted by juice or scale deposits on the

tubes as the result of ineffective chemical cleaning procedures. It would appear that

the use of longer, small-diameter tubes would allow substantial savings in the capital

cost to be realised and also result in reduced sucrose inversion. However, the effect of

tube dimensions on the heat-transfer performance at different stages of evaporation is

not known. This information must be known before a particular tube dimension could

be recommended for a specific evaporation duty.

1.5.2 Objectives

The prime objectives of the project are to develop an increased understanding of

the heat-transfer performance of rising-film evaporator tubes of different dimensions

and to have a better understanding of the influence of tube dimensions on the

mechanism of rising film evaporation. The specific aims and outcomes of the project

are to

10 Introduction

• Develop a capital cost model to determine the costs of designing, fabricating

and installing Robert vessels of the same heating surface area but different

tube dimensions.

• Determine the HTC of tubes with different lengths and diameter operating at

different conditions.

• Determine the optimum tube dimensions and operating conditions favouring

maximum heat transfer coefficient.

• Determine the HTC at different sections of the tube in order to understand

the boiling patterns.

• Postulate a theory on boiling mechanism based on the boiling patterns

• Select the optimum tube dimensions for a particular evaporation duty by

considering the heat transfer performance, the capital costs and the operating

costs collectively.

1.5.3 Individual contribution to the research team

The project was funded by Sugar Research Australia (SRA) and Sugar Research

Limited (SRL).

The design of the single tube evaporator rig was quite complex owing to the need

to be able to test tubes of different diameters and different lengths. A drafter was

contracted to work with the student and the Principal Supervisor to develop the design

of the experimental rig.

The project provided an opportunity for the PhD student to develop design,

experimental and modelling skills and to gain experience in the process area of juice

evaporation.

The experimental rig was installed at Rocky Point Sugar Mill adjacent to factory

evaporators. The Engineering and Production staff at the factory provided excellent

support to the student in installing the rig and in replacing a tube between tests. A

tradesman was also contracted to assist with the procedure of dismantling the

apparatus, installing a replacement tube of different dimension and reassembling the

apparatus in readiness for the next series of experiments.

Introduction 11

1.6 Overview of thesis

Chapter 1 provides a general overview of the Australian sugar industry and raw

sugar production. The chapter describes multiple effect evaporation, general principles

in evaporation, different evaporator designs, and assessment of evaporator

performance in terms of coefficient of evaporation, overall heat transfer coefficient

and vapour condensation coefficient. Chapter 1 also describes the scope of the

research and the objectives of the project.

Chapter 2 reviews the previous research in evaluating and increasing the heat

transfer performance of evaporators. The chapter discusses the different tubed

evaporators’ designs (climbing and rising film), boiling mechanism in rising film and

previous investigations on pilot plant and factory evaporators. The CFD models

developed for predicting the evaporator performance are also discussed. The chapter

concludes with discussions on the poor understanding of the boiling mechanism in

Robert evaporators, selection of tube dimensions for different effects, the interaction

of tube dimensions and operating conditions and their effect on heat transfer

performance.

Chapter 3 describes a capital cost model for Robert evaporators developed for

2000, 3000, 4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and tube

outside diameters of 38.10 mm, 44.45 mm, and 50.80 mm. The results show that the

conventional evaporator with tubes of 2 m length and 44.45 mm outside diameter is

more expensive than evaporators having calandrias with the other tube dimensions,

except for evaporators with 2 m tubes of 50.8 mm outside diameter. Cost savings of

~15% are shown to be available by using tubes of 3 m length and 38.1 mm diameter.

Chapter 4 describes the experiments conducted on the single-tube evaporator

rig with tubes of different lengths and diameters. Heat transfer performance data are

obtained for all the tubes across the full range of industrial processing conditions.

Analysis of potential errors of condensate collection showed that the measured

condensate flow rates on the heating tube were reliable for determining the heat

transfer coefficient and vapour condensation coefficient. Analysis of potential errors

of operating conditions showed that the values of the operating conditions utilised

during the test program were in close agreement with the target values. This analysis

demonstrated that the experimental program was well structured, and the operating

12 Introduction

conditions were sufficiently different from each other to affect the heat transfer

performance.

Chapter 5 details the analysis of the HTC measurements. Analysis of variance

was undertaken for the HTC measurements to determine the effects of tube dimensions

and operating conditions along with interactions on HTC. The maximum HTC

(HTCmax) was determined at the optimum juice level. The effects of tube dimensions

and operating conditions along with the interactions on HTCmax and optimum juice

level were determined. Empirical models for HTCmax and the optimum juice levels

were developed.

Chapter 6 describes the boiling patterns in the heating tubes. Six different boiling

patterns were identified from the HTC data for different sections of the heating tube.

A boiling mechanism was postulated based on the boiling mechanism theory and the

measured HTC results for the different sections of the tube. The boiling patterns in the

tube corresponding to the maximum HTC values were identified and the effects of

tube dimensions and operating conditions on these boiling patterns were determined.

Chapter 7 details the selection of optimum tube dimensions based on capital cost,

operating cost and HTC. The suitability of retrofitting tubes into existing vessels is

discussed and a case is detailed.

Chapter 8 discusses the conclusions from the study and applications of the work

in industry, research and consultation. The chapter provides recommendations for

further work in understanding the boiling mechanism in rising film evaporators.

Literature Review 13

CHAPTER 2: LITERATURE REVIEW


In the previous chapter, evaporation concepts were introduced. This chapter

discusses previous investigations of the performance and operation of factory and pilot

plant evaporators. The chapter details the condensation and boiling heat transfer theory

in the literature. The chapter concludes with a discussion of the limitations of the

previous investigations in understanding the effect of tube dimensions and operating

conditions on the heat transfer coefficient of sugar juice evaporators.

2.2 Condensation Heat Transfer

2.2.1 Introductory remarks

The overall heat transfer coefficient consists of individual heat transfer

coefficients. It is known that different flow regimes occur inside the tube and present

different resistances to heat transfer. Similarly, the condensation on the outside of the

tube has a different profile along its length. It is therefore important to understand the

resistances offered by the condensation in order to understand the influence on the

overall HTC. This section describes the condensation heat transfer theory.

2.2.2 Laminar film on a vertical surface

The simplest convection phase change process is the condensation of vapour on

a cold vertical surface as shown in Figure 2.1 (Bejan, 1993). On the left side of Figure

2.1, three distinct regions of condensation are shown. The laminar section occurs at

the top of the wall where the film of condensate is the thinnest. The condensate flows

downward and enters the wavy section as more steam condenses on the wall and the

condensate film is thicker. Finally, if the wall is long enough, the condensate film

enters and remains in the turbulent flow regime. On the right side of Figure 2.1, the

laminar film region, which is the simplest of the three regions, is shown. The flow of

the liquid film interacts with the descending boundary layer of the cooled vapour. The

temperature of the liquid – vapour interface is the saturation temperature that

corresponds to the local pressure along the wall, Tsat. The saturation temperature is

sandwiched between the temperature of the isothermal vapour reservoir, T∞ and the

14 Literature Review

wall temperature Tw. Through the shear stress at the liquid–vapour interface, the

downward flow the liquid film is instigated. The vapour in the descending jet that aids

in the downward flow of liquid is cooler than the vapour reservoir and warmer than

the liquid in the film attached to the wall.

This two–phase flow is considerably more complicated in the wavy and turbulent

sections of the wall. In some applications, where the film is sufficiently long to exhibit

all three regions, the overall heat transfer rate from the vapour reservoir to the wall is

dominated by the contributions made by the wavy and turbulent sections (Bejan,

1993).

Figure 2.1 Flow regimes of the film of condensate on a cooled vertical surface

(Bejan, 1993)

Figure 2.2 shows the two–dimensional laminar film in which the distance y

measures the downward length of the film. This flow is much simpler than that shown

in Figure 2.1, as in this case the entire reservoir of vapour is isothermal at the saturation

pressure, Tsat. The simplification focuses exclusively on the flow of the liquid film and

neglects the movement of the nearest layers of vapour.


Figure 2.2 Laminar film condensation, supplied by a reservoir of stationary

saturated vapour (Bejan, 1993)

The overall Nusselt number based on the L-averaged heat transfer coefficient is

given by:

NuL =hLL

kl= 0.943 × [

L3hfg′ g(ρl − ρv)

klvl(Tsat − Tw)]

14

2.1

where NuL is the Nusselt number,

hL is the condensation heat transfer coefficient (W/m2/K),

L is the length of the wall (m),

kl is the thermal conductivity of the condensate (W/m/K),

hfg′ is the latent heat of condensation (corrected with the Jakob number),

(kJ/kg),

g is acceleration due to gravity (m/s2),

ρl is the density of liquid (kg/m3),

ρv is the density of vapour (kg/m3),


vl is the kinematic viscosity of the liquid (m2/s),

Tsat is the saturation temperature of the liquid – vapour interface (K),

Tw is the wall temperature, (K).

The total condensation rate ΓL (kg/s/m) is proportional to the total cooling rate

provided by the vertical wall:

ΓL =

q′

hfg′

=kl

hfg′ (Tsat − Tw)NuL

2.2

where q′ is the total heat flux per unit length (W/m).

The laminar film equations discussed above were developed by Nusselt (1916)

based on the assumption that the effect of inertia is negligible in the momentum

balance (Bejan, 1993). The complete momentum equation was used by Sparrow and

Gregg (1959). Their solution for NuL is lower than that determined by Nusselt equation

(2.1) when Prandtl1 number is smaller than 0.03 and the Jakob2 number is greater than

0.01.

2.2.3 Concluding remarks

It is often assumed that the condensation of vapour presents very little resistance

to the heat transfer compared to the juice side resistance in sugar juice evaporators.

For both the laminar film regime and turbulent film regime, the length of the wall has

a negative impact on the condensation heat transfer. This seems logical as the film of

the condensate on the wall adds another barrier to heat transfer, owing to its low

thermal conductivity. This effect is more profound in laminar film regime than in

turbulent, as in the turbulent regime the film thickness is not uniform along the length

of the tube. However, Peacock (2001) concluded that condensation heat transfer was

constant up to tube length of 6 m and for tubes above 6 m, the condensation heat

transfer increased. The evaporators used in the sugar industry in recent times have

1 Prandtl number is a dimensionless number approximating the ratio of momentum

diffusivity to thermal diffusivity.

2 𝐽𝑎 =𝑐𝑝(𝑇𝑤−𝑇𝑠𝑎𝑡)

ℎ𝑓𝑔 Jakob number represents the ratio of sensible heat to latent heat

absorbed (or released) during the phase change process.


longer tubes and some claim to have high overall heat transfer coefficient. The

condensation heat transfer coefficient is not recorded.

2.3 Flow Boiling


In section 2.2, heat transfer theory was described for condensation that occurs

with a change of phase from vapour to liquid. Boiling heat transfer is defined as a

mode of heat transfer that occurs with a phase change from liquid to vapour. There are

two types of boiling: pool boiling and flow boiling. Pool boiling is boiling on a heating

surface submerged in a pool of initially stagnant liquid. Flow boiling is boiling in a

flowing stream of fluid, where the heating surface may be the channel wall confining

the flow. A boiling flow is composed of a mixture of liquid and vapour and usually

comprises two-phase flow. Since evaporators in the sugar industry have flow boiling

in vertical channels, the heat transfer mechanism of flow boiling is discussed below.

2.3.2 Regimes of boiling

The existence of different boiling regimes has been documented by several

authors. Figure 2.3 shows the flow regimes for forced convection boiling inside a

vertical tube. Heat transfer to the subcooled liquid that enters the tube is initially by

forced convection. Once boiling is initiated, bubbles that appear at the surface grow

and are carried into the liquid mainstream. There is an increase in the convection heat

transfer coefficient associated with this bubbly flow regime. As the volume fraction of

the vapour increases, bubbles begin to coalesce, forming slugs of vapour. The regime

is termed as slug flow, which is followed by an annular flow regime, in which the

liquid is moving as a thin film along the inner surface of the tube. The vapour moves

at a larger velocity through the core of the tube. The heat transfer coefficient increases

through the bubbly flow regime and increases further to the annular flow. It is believed

that as annular flow gives way to mist flow, the maximum heat transfer coefficient is

achieved. The transition regime is identified by the growth of dry spots, until the

surface is completely dry, and all remaining liquid is in the form of droplets appearing

in the vapour core. The convection coefficient continues to decrease through the mist

flow regime (Incropera & Dewitt, 1996).


Figure 2.3 Flow regimes for forced convection boiling inside a tube (Incropera

& Dewitt, 1996)

2.3.3 Two – phase flow

When gas-liquid mixtures flow upward in a vertical tube, the two-phase mixture

may distribute in several patterns. Each of these patterns is characterised by the radial

and/or axial distribution of liquid and gas Taitel et al. (1980). There are four basic flow

patterns for up flow as shown in Figure 2.4 as described by Taitel et al. (1980). These

patterns are:

1. Bubble flow: The gas phase is approximately uniformly distributed in the

form of discrete bubbles in a continuous liquid phase.

2. Slug flow: Most of the gas is located in large, bullet-shaped bubbles, which

have a diameter almost equal to the pipe diameter. They move uniformly

Increasing


upward and are sometimes designated as “Taylor bubbles”. Taylor bubbles

are separated by slugs of continuous liquid, which bridge the pipe and

contain small gas bubbles. The liquid flows downward in the form of a thin

falling film between the Taylor bubble and the pipe wall.

3. Churn flow: Churn flow is similar to Slug flow; however, it is more chaotic,

frothy and disordered. The bullet-shape Taylor bubbles become narrower

and their shape is distorted. The continuity of the liquid in the slug between

successive Taylor bubbles is constantly destroyed by a high local gas

concentration in the slug. The accumulating liquid forms a bridge and is

again lifted by the gas. The oscillatory or alternating direction of motion of

liquid is typical of churn flow.

4. Annular flow: Annular flow is characterised by the continuity of the gas

phase along the core of the pipe. The liquid phase moves upwards partly as

liquid film and partly in the form of droplets entrained in the gas core.

Figure 2.4 Flow patterns in vertical flow (Taitel et al., 1980)

2.3.4 Existing flow pattern maps

There are a variety of flow-pattern maps for vertical flow proposed in the

literature. These maps propose transition boundaries in a two-dimensional co-ordinate


system. The selection of co-ordinates for the published maps has been of two basic

types.

1. The first group uses dimensional co-ordinates such as superficial velocities

𝑈𝐺𝑠 and 𝑈𝐿𝑠 (Sternling, 1965; Wallis, 1969) or superficial momentum flux,

𝜌𝐺𝑈𝐺𝑠2 and 𝜌𝐿𝑈𝐿𝑠

2 (Hewitt & Roberts, 1969). For a given pipe size and set of

fluid properties, the transition of the flow patterns can be mapped.

2. The second group represents the results by dimensionless co-ordinates in an

attempt to apply the results to line sizes and fluid properties other than those

of the data used to locate the curves. Taitel et al. (1980) suggested that the

use of dimensionless co-ordinates is more general than the use of

dimensional ones, since there was no theoretical basis.

Taitel et al. (1980) compared the various maps and found differences both as to

absolute value and trend. They stated that in most cases, the transition boundaries are

empirically located and do not rest in suitable physical models. Taitel et al. (1980)

concluded that a theoretical basis under the transition relationships was required to

improve both the prediction and classification of experimentally observed flow

patterns.

2.4 Transition Mechanisms (Adiabatic Flows)


In order to predict the conditions under which transition between flow patterns

occurs, it is required to understand the physical mechanism of the transition. In this

section, each transition is analysed, and the physical mechanism is described. The

reported experimental and modelling work on the transition of flow patterns in most

cases is for adiabatic (no heat addition) flows. The transitions described in this section

are for adiabatic flows.

2.4.2 The transition from bubble flow

Transition from the dispersed bubble condition observed at low gas rates to slug

flow requires a process of agglomeration or coalescence. The discrete bubbles combine

into the larger vapour spaces growing in diameter to that of the tube, which are

observed at the transition to slug flow. As the gas rate increases, the bubble density

increases and the closer bubble spacing results in an increased coalescence rate.


However, as the liquid rate increases, the turbulent fluctuations associated with the

flow can destroy the larger bubbles formed from the agglomeration. If the fluctuations

are quite intense, the breakup will prevent re-coalescence and the dispersed bubble

pattern is maintained.

The gas phase is distributed into discrete bubbles when initiated at low flow rates

into a large diameter vertical pipe of liquid (flowing at low velocity). Studies of bubble

motion showed that if the bubbles are very small, they behave as rigid spheres rising

vertically in rectilinear motion. Above a critical size (about 1.5 mm for air-water at

low pressure) the bubbles begin to deform, and the upward motion of the bubbles

results in a zig-zag path with extensive randomness. The bubbles randomly collide and

coalesce forming larger individual bubbles with the spherical cap similar to that of

Taylor bubbles of slug flow. However, the bubbles have not reached the diameter of

the pipe. Hence, bubble flow is characterised by smaller bubbles moving in zig-zag

motion and the occasional appearance of large Taylor-type bubbles. With further

increase in gas flow rate, with the liquid flow still being low, the bubble density

increases and reaches a point where the dispersed bubbles become so closely packed

that collisions and agglomeration occur, leading to larger bubbles. This results in a

transition to slug flow (Taitel et al., 1980).

If the gas bubbles rise at a velocity 𝑈𝐺, this velocity is related to the superficial

gas velocity 𝑈𝐺𝑠 by

𝑈𝐺 =

𝑈𝐺𝑠

𝛼

2.3

where α is the void fraction

Similarly, the average liquid velocity 𝑈𝐿 is given in terms of liquid superficial

velocity 𝑈𝐿𝑠 as:

𝑈𝐿 =

𝑈𝐿𝑠

1 − 𝛼

2.4

Designating 𝑈𝑂 as the rise velocity of the gas bubbles relative to the average

liquid velocity, equation 2.3 and 2.4 yield

𝑈𝐿𝑠 = 𝑈𝐺𝑠

1 − 𝛼

𝛼− (1 − 𝛼)𝑈𝑂

2.5


The rise velocity of relatively large bubbles has been shown by Harmathy

(1960)to be insensitive to the bubble size and given by the relation

𝑈𝑂 = 1.53 [𝑔(𝜌𝐿 − 𝜌𝐺)𝜎

𝜌𝐿2 ]

14

2.6

where 𝜌𝐺 is the density of gas (kg/m3),

𝜎 is the surface tension of liquid (N/m),

Substituting equation 2.6 into 2.5 and considering the transition to slug flow to

occur when 𝛼 = 𝛼𝑇 = 0.25 results in equation 2.7. This equation characterises the

transition for conditions where the dispersion forces are not dominant (Taitel et al.,

1980).

𝑈𝐿𝑠 = 3.0 𝑈𝐺𝑠 − 1.15 [𝑔(𝜌𝐿 − 𝜌𝐺)𝜎

𝜌𝐿2 ]

14

2.7

For the transition from non-dispersed bubble flow to dispersed bubble flow

𝑈𝐿𝑠 − 𝑈𝐺𝑠 = 4 [

𝐷0.429𝑔0.446 𝜎0.089

𝜌𝐿0.017 µ𝐿

0.072 ] 2.8

where 𝐷 is the tube diameter (m)

µ𝐿 is the liquid viscosity (Pa.s)

McQuillan and Whalley (1985)used 𝛼 = 0.52 on the assumption that dispersed

bubble flow would become unstable if the void fraction became sufficient to indicate

a cubic lattice of bubbles. McQuillan and Whalley (1985)stated that the formation of

a closely packed lattice was assumed to limit the stability of dispersed bubble flow and

hence the transition from dispersed bubble flow occurs when 𝛼 = 0.74.

Mishima and Ishii (1984)made no distinction between dispersed bubble flow and

non-dispersed bubble flow and stated that bubble flow would become unstable at void

fraction of 𝛼 = 0.3.

2.4.3 The transition from slug flow

The bubble flow regime becomes unstable due to the formation of large vapour

spaces within the flow. As a result of this process, slug flow may be formed. In some

circumstances (at high liquid flow rates) slug flow may also be unstable and therefore


the bubble flow may change directly to churn flow or annular flow. If the conditions

are favourable for slug flow to form, the large vapour spaces will assume the

characteristic bullet shape. For further increases in gas flow rate, a transition between

slug flow and churn flow will occur (Taitel et al., 1980).

Figure 2.5 shows the model of slug flow (McQuillan & Whalley, 1985).

Consecutive gas slugs rise in a vertical tube, separated by regions of liquid flow. If the

slug flow occurs as a development of bubble flow, the regions of liquid flow will be

bubbly. The small amount of gas that flows as bubbles in the liquid slugs is neglected.

As shown in Figure 2.5, the gas slug rises at an absolute velocity 𝑣𝑝. The liquid film

adjacent to the gas slug flows downward as a free-falling film at a velocity 𝑣𝑓.

Figure 2.5 Model of slug flow (McQuillan & Whalley, 1985)

Nicklin and Davidson (1962) proposed the following equation, which may be

used to determine the rise velocity of the gas slug.

𝑣𝑝 = 1.2 (𝑄𝐺 + 𝑄𝐿

𝐴) + 0.35 [

𝑔𝐷(𝜌𝐿 − 𝜌𝐺)

𝜌𝐿]

12

2.9

where 𝐴 is the cross-sectional area (m2),


𝑣𝑝 is the absolute velocity of the gas slug (m/s),

𝑄𝐺 is the gas volumetric flowrate (m3/s),

𝑄𝐿 is the liquid volumetric flowrate (m3/s).

The second term on the r.h.s. of equation 2.9 gives the rise velocity of a large

bubble in stagnant liquid and was derived theoretically by Davis and Taylor (1950).

The first term on the r.h.s. adds the liquid velocity at the centre line, since 1.2 is the

approximate ratio of centre line to average velocity in fully developed turbulent flow.

2.4.4 The transition to annular flow

When gas flow rates are high, the liquid flows upwards adjacent to the wall and

gas flows in the centre carrying entrained liquid droplets, termed as Annular Flow. The

upward flow of liquid against gravity, results from the forces exerted by the fast-

moving gas core. The liquid film, having a wavy interface, tends to shatter and enter

the gas core as entrained droplets. The interfacial shear and the drag forces on the

waves and the droplets cause the liquid to move upwards. On the basis of the idea put

forward by Turner et al. (1969). Taitel et al. (1980) suggested that annular flow cannot

exist, unless the gas velocity in the gas core is sufficiently high to lift the entrained

droplets. When the gas rate is insufficient, the droplets fall back, accumulate, form a

bridge and churn and slug flow takes place.

Taitel et al. (1980) proposed an inequality which must be satisfied if the annular

flow is to exist. This equation balances the drag and gravity forces acting on the

droplet and assumes that the entrained droplets are gradually accelerated as they move

into the gas core.

𝑣𝐺𝑠 ≥ 3.2 [𝑔𝜎(𝜌𝐿 − 𝜌𝐺)

𝜌𝐿2 ]

14

2.10

McQuillan and Whalley (1985)disagreed with Taitel et al. (1980) and proposed

a simple inequality to predict the existence of annular flow:

𝑣𝐺𝑠∗ ≥ 1 2.11

where 𝑣𝐺𝑠∗ is the modified Froude number.


The modified Froude number represents a comparison between the inertial and

gravitational forces. The critical value of unity was observed empirically for air-water

(McQuillan & Whalley, 1985).

2.4.5 Flow pattern maps

Figure 2.6 shows the flow pattern map for vertical tubes of 51 mm diameter for

air-water at 100 kPa abs (Taitel et al., 1980). The bubbly flow, plug (slug) flow, churn

flow and annular flow regions are characterised by the gas and liquid superficial

velocities. At low gas superficial velocity (<0.08 m/s), bubbly flow regime is observed.

At gas superficial velocities in the range of 0.08 – 1 m/s and corresponding liquid

superficial velocities in the range of 0.02 – 1 m/s slug (plug) flow regime is observed.

Annular flow is only seen to exist for gas superficial velocities above 10 m/s.


100 kPa abs (Taitel et al., 1980)


The transition mechanism from bubbly flow, slug flow and to annular flow, was

discussed in this section. The theory used to determine the gas and liquid superficial

velocities that define each mechanism was described. The formation of large slugs


(Taylor bubbles) and the velocity of slugs were discussed. It was found that annular

flow only existed when gas superficial velocities are above 10 m/s for the case of air–

water mixture at pressure of 100 kPa abs. Although the churn flow is shown in Figure

2.6, the formation of churn flow is a subject of debate. Mao and Dukler

(1993)concluded that there is little evidence for considering churn flow to be a separate

and distinct flow pattern. Several authors have stated that churn flow is in fact a

manifestation of slug flow and no transition actually occurs.

2.5 Previous Pilot Plant Investigations of Sugar Factory Evaporators


Previous investigations play an important part in understanding the evaporation

process. This section explores the investigations undertaken on factory vessels and

pilot plant evaporator rigs. These investigations have been undertaken to better

understand the unit operation of juice evaporation, to develop reliable heat transfer

coefficient relationships based on the process variables, to better understand the

boiling mechanisms in different designs and to develop a new or improved design of

industrial evaporator.

2.5.2 Kestner evaporator

James et al. (1978) used a single tube pilot plant Kestner evaporator to

investigate heat transfer characteristics when simulating different evaporator effects.

Tests carried out showed that the Kestner evaporator, which is used predominantly as

a 1st effect vessel in the South African sugar industry, would operate most favourably

at the tail of the evaporator set when compared to the conventional, Robert-type

evaporator. However, these results were based on unrealistically high juice inflow

rates. Practical experience has determined that the Kestner evaporator is suitable at

the 1st and 2nd effects.

Rama and Munsamy (2008) undertook plant trials to determine the effect of tube

wetting rate (kg/min/tube) on the performance of the Kestner evaporator with respect

to specific evaporation rate (kg/h/m2) and heat transfer coefficient (W/m2/K). The

investigations were prompted by very low HTC values for an industrial Kestner

evaporator. Increasing the wetting rate by 62% increased the specific evaporation rate

by 40%.


Walthew and Whitelaw (1996) investigated the factors affecting the

performance of the Kestner evaporator. The independent variables that were studied

were:

• Average temperature difference between the steam and the juice, ΔT

• Feed rate to the base of the evaporator

• Feed temperature

• Recycle of juice from above the top tube plate to the base of the

evaporator, either open or closed

• Brix of the feed juice

It was found that the HTC increased at higher levels of ΔT, feed rate and brix.

The increase in HTC with increased feed rate and ΔT can be explained in terms of

conventional theory and previous investigations. However, an increase in HTC at

higher brix was unexpected, since higher brix values are associated with higher

viscosities. There was significant interaction between the feed temperature and

recycle, which indicated that at high feed temperature, having the recycle open, greatly

improved the HTC. This seems understandable as at higher temperature without the

recycle, the tube may be drying out and not be fully wetted.

2.5.3 Guo et al. investigations

Guo et al. (1983) undertook pilot plant investigations on a triple tube evaporator

unit at the University of Queensland. The tubes were standard stainless-steel

evaporator tubes of 44 mm OD and approximately 1.9 m length. The tubes were

mounted through glands in a 200 mm diameter steam jacket. The vapour formed was

separated from the splashing liquor in a disengagement chamber and was then

condensed in a water-cooled surface condenser. The condensate was returned to the

base of the evaporator through a flow meter. The separated liquor was returned via an

external recirculation leg. For each run, the temperature of the steam, the splashing

liquor in the disengagement space and the vapour temperature were measured. The

effects of static liquor level in the tubes, temperature difference, boiling temperature

and the brix of juice on heat transfer performance were investigated.

Tests with boiling water at 100 °C showed the following. At low levels, the water

did not circulate so the evaporator tube was not filled, and low heat transfer coefficient


values were measured. As the level increased, the coefficient rose rapidly and as

circulation started, the HTC reached a maximum value corresponding to an ‘optimum’

level. The optimum level ranged from one-quarter to one-half of the tube height.

Increasing the level above this value caused a gradual drop in the HTC, which was

attributed to the effect of hydrostatic pressure on the boiling point. Figure 2.7 shows

the effect of liquid level (as a fraction of tube height) on HTC for the tests by Guo et

al., (1983).

Figure 2.7 Effect of liquid level on HTC (Guo et al., 1983)

The HTC curves in Figure 2.8 for water at 100 °C show the same data as for

Figure 2.7 but as a function of temperature difference (ΔT). The lower the ΔT, the

higher is the optimum level corresponding to the maximum HTC value.


Figure 2.8 Effect of ΔT on HTC at selected constant liquid levels (h) (Guo et al.,

1983)

Guo et al. (1983) found that boiling temperature, Tb had no detectable effect on

the optimum liquid level in the tube. However, HTC decreased as the boiling point

decreased (increasing vacuum). The effect was not large and the drop in HTC was 10%

for a 30 °C drop in temperature.

According to Guo et al. (1983), sugar and sugar molasses solutions show similar

trends to water in the effects of level, ΔT and Tb. The brix of the solution does not

appear to affect the location of the optimum level. However, HTC was found to

decrease with increase in brix from 3000 W/m2/K for water to a value of 2000 W/m2/K

for 65 brix syrups or molasses. These data are for boiling at atmospheric pressure.

2.5.4 Broadfoot and Dunn investigations

Broadfoot and Dunn (2004) conducted a pilot plant investigation on a 20 m2

evaporator vessel with 76 tubes of standard dimensions (44.45 mm OD and 1.985 m

length) to develop an improved correlation for HTC that would provide more reliable

simulations of evaporator stations in energy efficient configurations. Figure 2.9 shows

the variation of HTC with operating juice level at 15 brix. It is observed that the

maximum HTC was achieved for juice levels about 20% of the tube height.


Figure 2.9 Variation of HTC with operating level of juice at 15 brix ((Broadfoot

& Dunn, 2007)

The observations from the pilot plant study (Broadfoot and Dunn, 2007) were as

follows:

• The optimum juice level for the maximum HTC value was lower for juice

at lower brix and higher for juice at higher brix. The optimum level for

juice at brix below 25 was 20% – 35% of the tube height, and for juice

above 40 brix, was 35% – 45% of the tube height.

• For evaporation at higher VCC, the maximum HTC value was higher and

occurred at lower juice level.

• At higher headspace pressure, the maximum HTC value was higher than

for evaporation at lower headspace pressure. The effect is attributed to

the lower viscosity of the juice at the higher temperature;

• The influence of VCC on HTC was slightly less at a lower headspace

pressure than at higher headspace pressure;

• The influence of VCC on HTC was less for juice at 70 brix than for juice

at 15 brix. As well, for juice at 70 brix, the effect of VCC on the optimum

juice level was less than for juice at 15 brix.


2.5.5 Pennisi’s investigations

Investigations on a single tube evaporator rig were conducted by Pennisi (2004).

The single tube was 2 m long and 44.45 mm OD. The condensate was collected in four

gutters, which were located equidistantly on the outside of the tube.

The experimental program was designed to determine heat transfer performance

for four process variables (ΔT, brix, temperature and juice level in the tube) at a wider

range than normal operating conditions, which typically exist in factory evaporators.

In the normal operation of factory evaporators, a small ΔT (5 °C to 8 °C) exists in the

1st effect, which typically operates at high calandria pressures and low brix. As the

calandria pressure reduces from the first to the last effect of the multiple effect

evaporator, both the brix of juice and ΔT increase. The test rig was operated so that all

three variables (ΔT, brix, juice temperature) could be manipulated independently to

cover a broad range of conditions.

Boiling within the vessel was allowed to occur for a sufficient period of time to

stabilise before the static level was measured. The condensate from each of the four

gutters was collected in separate containers. The condensate from the inner wall of the

steam jacket was also collected. The volumes of collected condensates were

determined and the condensate rates were calculated. The HTC for each segment of

tube was then calculated from equation 1.7. The HTC for the entire tube was calculated

from the summed values of the condensate values.

The condensate rates provided vapour condensation coefficient (VCC) values

ranging between 4.3 kg/h/m2 and 87.8 kg/h/m2. Typical values for VCC in factory

evaporators are between 12 and 40 kg/h/m2.

The results from the study by Pennisi (2004) are summarised below:

• The highest value of HTC was obtained for boiling water at the highest

calandria pressure (100 kPa abs) and highest temperature difference (T =

15C).

• The lowest values of HTC were for the high brix solution (Brix-45) at the

lowest calandria pressure and lowest temperature difference (T = 5C).

These observations are in agreement with data for typical factory

operations where the HTC is lowest at the final stages of the set where the


brix of juice is highest and the boiling temperature lowest (i.e. the viscosity

of the sucrose solution is highest).

• In general, the HTC values were slightly lower than are normally measured

in factory evaporators for comparable process conditions. For example, in

a factory evaporator the HTC for Brix-20 juice at a calandria pressure of

100 kPa (abs) and T = 10 °C would range from 2500 to 2800 W/m2/K.

HTC values for the test rig were ~ 2000 W/m2/K. Also, heat transfer for

Brix-45 juice at a calandria pressure of 60 kPa abs and T = 15 °C in a

factory evaporator would range from ~600 to 1000 W/m2/K. The single-

tube rig produced values of about 200 W/m2/K.

• One substantial difference between the trials with the single-tube rig and

factory evaporator was the lack of superheat in the sucrose solution that

exists in the base of the single-tube rig. The juice entering a factory

evaporator (except for the first effect) is superheated as it is boiled at a

higher temperature and pressure in the previous effect. The flashing of

vapour from the juice on entry into a factory evaporator is thought to

enhance heat transfer performance. The temperature of the sucrose

solution in the single-tube rig did not exceed the saturation temperature of

water at the headspace pressure plus the boiling point elevation as it was a

closed recirculating system.

• For the sucrose solutions of Brix-20 and Brix-45, and a given calandria

pressure, the HTC values were generally higher for T = 15 °C than for T

= 5 °C. The higher T values corresponded to trials with higher heat flux.

Similar behaviour is thought to occur in factory evaporators, although the

effect is not well defined. The higher HTC value at the higher T is

attributed to the onset of boiling being at a lower level in the tube than

would occur for low T values.

• For juice at a given brix, the value of T appeared to have a larger influence

on the HTC values for operation at higher calandria pressures. In fact, at

the calandria pressure of 60 kPa (abs) the value of T appeared to have only

minimal influence on the HTC value.


Figure 2.10 HTC data for varying ΔT, calandria pressure and brix for the total

tube (Pennisi, 2004)

Pennisi (2004) calculated HTC for the individual segments of the evaporator

tubes. Figure 2.11, Figure 2.12 and Figure 2.13 show the HTC data for segments of

the single tube for water, Brix-20 and Brix-45 solutions respectively. Section 1 of the

trials by Pennisi (2004) is at the top of the heating tube and section 4 is at the bottom

of the heating tube. The observations from the HTC plots are summarised below:

• For water in Figure 2.11, as calandria pressure increased, HTC for all

segments increased significantly. The incremental increase in HTC for

an increase in calandria pressure was greatest for ΔT of 10 °C.

• For Brix-20 juice in Figure 2.12, the data were not consistent with

increase in calandria pressure. For ΔT of 5 °C, HTC increased from 60

to 80 kPa abs calandria pressure and dropped at 100 kPa abs. For ΔT of

10 °C, 3 out of 4 segments showed a drop in HTC with increase in

calandria pressure, then all segments showed an increase in HTC at 100

kPa calandria pressure. For ΔT of 15 °C, all segments showed an increase

in HTC with increasing calandria pressure, but the incremental increase

was much higher from 60 kPa abs to 80 kPa abs than from 80 kPa abs to

100 kPa abs.

0

500

1000

1500

2000

2500

3000

3500

4000

50 60 70 80 90 100 110

HT

C (

W.m

-2K

-1)

Calandria pressure (kPa abs)

0 brix, T diff = 5

0 brix, T diff = 10

0 brix, T diff = 15

20 brix, T diff = 5

20 brix, T diff = 10


45 brix, T diff = 5

45 brix T diff = 10



• For Brix-45 juice in Figure 2.13, the data showed an increase in HTC

with increase in calandria pressure for ΔT of 8.5 °C. For Brix-45 juice,

ΔT of 3 °C the HTC decreased from segment 1 to segment 4 for the

calandria pressure change from 60 to 80 kPa abs. For the change in

calandria pressure from 80 to 100 kPa abs the HTC increased. For ΔT of

3 °C at low calandria pressure, it is likely that the juice was not rising up

the tube and the upper part of the tube was not fully wetted.

Delta T (5 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

4000

Segment 1

Segment 2

Segment 3

Segment 4

Delta T (10 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

4000

Segment 1

Segment 2

Segment 3

Segment 4

Delta T (15 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

4000

Segment 1

Segment 2

Segment 3

Segment 4

Water

Figure 2.11 HTC values for water solution for segments of the evaporator tube

(Pennisi, 2004)


Delta T (5 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

Segment 1

Segment 2

Segment 3

Segment 4

Delta T (10 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

Segment 1

Segment 2

Segment 3

Segment 4

Delta T (15 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

Segment 1

Segment 2

Segment 3

Segment 4

Brix-20 juice

Figure 2.12 HTC values for Brix-20 sucrose solution for segments of the

evaporator tube (Pennisi, 2004)


Delta T (3 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

Segment 1

Segment 2

Segment 3

Segment 4

Delta T (8.5 oC)


50 60 70 80 90 100 110

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

Segment 1

Segment 2

Segment 3

Segment 4

Brix-45 juice

Figure 2.13 HTC values for Brix-45 sucrose solutions for segments of the

evaporator tube (Pennisi, 2004)

2.5.6 The SRI design of Robert evaporator

The Sugar Research Institute (SRI) investigated the performance of the Robert

evaporator design and presented a novel design to overcome the shortcomings of the

original Robert design.

Wright et al. (2003) describe the SRI design for the installation of a 5300 m2

vessel at 1st effect position at San Antonio factory, Nicaragua. The average HTC was

3014 W/m2/K over the whole 12-day operational testing period. These results were

claimed to be 23% higher than for the typical HTC achieved in Australian evaporators

under the same juice outlet brix and temperature conditions.

The steam, condensate and incondensable gases are arranged to move uniformly

from an annulus on the outside of the vessel radially to the centre of the vessel.

According to (Quinan et al., 1985), a small number of 150 mm diameter mild steel

downcomer tubes should be dispersed around the calandria among the stainless steel

heating tubes. These downcomers act as stay bars and importantly provide a

recirculation return path for the juice from above the top tube plate to below the bottom

tube plate.

Additionally, a large central downcomer is provided in the SRI design, with a

sealed pipe outlet for the juice through the bottom cone. Arrangements are made for


the bypass of juice from the lowest point in the vessel to the outlet pipe, as this feature

assists the control of the juice level.

The general performance and heat transfer results of the SRI design have been

superior compared with the conventional Robert design.

2.5.7 Selection of tube dimensions

The effect of tube dimensions on HTC has been detailed by previous researchers

(Gerasimenko, 1968; Hugot & Jenkins, 1986; Kroll & McCutchan, 1968; Peacock,

2001). Gerasimenko (1968) concluded that at atmospheric pressure, the maximum

HTC coefficient was obtained with 25 mm OD tubes and tubes of 57 mm OD exhibited

the lowest HTC. For high concentrations of the solution, the HTC values of 25 mm

OD tubes were lower than for 57 and 38 mm OD tubes. Tubes of 38 mm OD provided

good heat transfer performance under all conditions.

Previous investigators (Gerasimenko, 1968; Hugot & Jenkins, 1986; Kroll &

McCutchan, 1968; Peacock, 2001) have postulated that tube dimensions should be

selected based on the effect position in a multiple effect set. Hugot and Jenkins (1986)

recommended that vessels should use tubes with the same diameter but with decreasing

tube length from first to final vessel. A practical benefit of this arrangement is to reuse

the tubes, when the ends close to the tube plates wear or corrode. They provided no

heat transfer considerations for the basis of this tube selection. Hugot and Jenkins

(1986) mentioned that smaller diameter tubes give theoretically a higher heat transfer

coefficient, because the mean distance of segments of juice from the heating surface

is smaller. Additionally, tubes of smaller diameter allow installation of a larger heating

surface area in a vessel for a given vessel diameter. Hugot and Jenkins (1986) claimed

that tube length and diameter are not independent of each other. Moreover, they stated

that the choice of tube diameter for multiple effects is not of prime importance.

Table 2.1 shows the maximum length of evaporator tubes for the different tube

diameters, as recommended by Hugot & Jenkins (1986). For small diameter tubes,

long tubes can be used. For 38 mm tube diameter, Table 2.2 shows the optimal tube

lengths of the multiple effect taking into account all factors, including cost (Hugot &

Jenkins, 1986).


Table 2.1 Maximum length of evaporator tubes for different tube diameters

(Hugot & Jenkins, 1986)

Tube OD

(mm)

Maximum

length

m ft

50 2.5 8

38 3.5 11

35 4.0 13

30 4.5 15

Table 2.2 Optimal tube lengths recommended for the different effect

parameters (Hugot & Jenkins, 1986)

Effect Optimal

tube length

(m)

1 4.0

2 3.5

3 3.0

4 2.5

5 2.25


In comprehending the investigation undertaken by James et al. (1978), the

determination of HTC seems to be an error because the measured condensate rate

included the condensate from the inside walls of the shell.

The investigations conducted by Guo et al. (1983) and Broadfoot and Dunn

(2007) found that an optimum juice level exists, which maximises the HTC. Departure

from the optimum liquid level reduces the HTC. The influence of liquid level on HTC

is greater at juice levels below the optimum than above the optimum level (Watson,

1986b). The results of Guo et al., (1983) and Broadfoot and Dunn (2007) indicated

that the optimum juice level was lower for operation at higher ΔT (or VCC). The

operating parameters investigated by Guo et al. (1983) and Broadfoot and Dunn (2007)

have been investigated in this PhD study for tubes of different diameter and length.

The pilot plant investigation on a single tube by Pennisi (2004) throws some

light on the boiling characteristics inside a tube with the calculation of HTC on


different sections of the tube. The HTC calculations of the different segments of the

tubes are shown in Figure 2.11, Figure 2.12 and Figure 2.13. The plots are not

consistent and provide little information on the boiling mechanism of the rising film

evaporator. The significance of juice level and juice return is not discussed in the

thesis. The investigations were conducted for a single tube of 2.0 m length and 44.45

mm OD.

Although the SRI design is an improved version of the Robert vessel, there

remains scope for further improvements in the design, particularly by incorporating

heating tubes with the preferred dimension to maximise HTC. Several of the features

of the SRI design are likely to be adopted in the new design for Robert vessels using

the outcomes from this study.

The investigations undertaken by Broadfoot and Dunn (2004) were on a pilot

plant evaporator with 20 tubes of the standard dimensions. The trials assisted in

understanding the effect of juice properties and operational conditions on HTC for the

standard tubes. The trials did not enhance the understanding of the boiling mechanism

in the Robert evaporator.

2.6 Operational Investigations on Robert vessels


Sugar factory technologists have undertaken trials to better understand the

operation of the Robert evaporator in order to increase efficiency. Many of these

investigations have been used to develop empirical correlations for HTC and to

determine the optimum liquid level in the tubes. Although some of the results

contradict each other, the literature provides an understanding of the main factors

affecting the performance of Robert evaporator. They also highlight differences in

operating Robert vessels in different sugar mills.

2.6.2 Smith and Taylor investigations

Smith and Taylor (1981) present heat transfer data in multiple effect evaporators

covering 15 Robert vessels at three mills. HTC was plotted against brix, temperature

difference (ΔT) and viscosity. It was concluded from the experiment that the influence

of ΔT on HTC could not be deduced. HTC values from second to penultimate effect

were in the range of 1800 to 3500 W/m2/C, with no pronounced dependence on effect

number. The optimum vapour saturation temperature for the final effect was


determined to be in the range of 55 to 60 °C. A heating surface area distribution,

wherein the last effect is double the size of intermediate effects, was calculated to

provide 6% greater evaporation rate than the conventional arrangement. There is some

doubt on this conclusion, as no evaporator installations are known to have adopted this

arrangement. The problem with this conclusion is that the operation of a Robert vessel

as a final evaporator with low VCC creates serious problems with poor mixing of the

juice and high propensity to develop scale on the heating tubes.

2.6.3 Jayes’ evaporation model

Jayes (2004) developed a spreadsheet model of a multiple effect evaporation

train and the optimising routines in the spreadsheet software to find the distribution of

heating surface area along the evaporator train, which gives the highest specific

evaporation rate. The model uses a mathematical relation, which states that the ratio

of the area of the effect to the temperature difference in the effect is a constant. This

model is not suitable for the majority of evaporation stations as the extraction of bleed

vapour from individual evaporators, which is commonplace, is not addressed.

2.6.4 Watson investigation

The Fairymead Sugar Company installed downcomers in the new 1st effect

vessel of 5100 m2. The tube dimensions were 2.76 m length and 38.1 mm OD. Due to

the large diameter of the vessel it was thought that one central downcomer would not

reduce the liquid level in the tubes. Hence, multiple downcomers were evenly

distributed throughout the calandria. Watson (1986b) stated that for a commercial scale

evaporator, a considerable head of liquid above the top tube plate was required before

the maximum heat transfer coefficients were obtained. This observation contradicted

with the results of Guo et al. (1983) on the pilot scale evaporator with an external leg,

which showed that the maximum HTC was obtained just as the liquid started to appear

above the top tube plate. This difference may have been due to the non-uniformity of

liquid and steam conditions across the much larger calandria in the commercial

evaporator.

The downcomers reduce the quantity of juice collecting above the tube plate by

providing a return path. Observations on the operation of the vessel without the

downcomers were obtained by blocking the downcomers during a maintenance stop.

The results are shown in Figure 2.14, where it was concluded that the use of the


downcomers reduced the head of juice. Figure 2.15 shows the HTC measurements

over a single day when downcomers were operating. Low HTC values are evident at

low juice levels as the tubes are not fully wetted. The maximum HTC was recorded

when the static juice level was about 23% of the tube height. Increasing the juice level

above this value resulted in juice being collected above the calandria with a reduction

in HTC. At an operating level of 45% the HTC was decreased by 10% from its

maximum value.

Figure 2.14 Variation of head of juice above the calandria with operating level

Watson (1986b)


Level of juice in tubes (% tube height)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

500

1000

1500

2000

2500

3000

3500

Figure 2.15 Variation of HTC with operating level for a conventional Robert

evaporator with mini-downtake (Watson, 1986b)

2.6.5 Shah and Peacock investigations

Shah and Peacock (2013) developed a set of correlations to predict the minimum

recirculation rate and liquid level for juice of up to 65 brix, corresponding to various

temperature driving forces and the optimum heat transfer coefficient. A second set of

correlations was developed to predict the juice velocity as a function of temperature

driving force, the Reynolds number and the Grashof number. The results were

dimensionless numbers, which can be easily interpreted in terms of heat transfer

theory. Together, these correlations were used in designing a semi-sealed downtake

ensuring adequate recirculation and a sufficient liquid level within the Robert

evaporator to optimise heat transfer.

The correlations developed by Shah and Peacock (2013) are shown below:

hminimum = −0.0149 ΔT + 0.5816 2.12

where hminimum is the minimum liquid level as a fraction of the total tube height.

R = 0.008123 ΔT2 − 0.0246 ΔT + 0.4744 2.13

where R is recirculation rate, kg/min/tube.

WR = 0.001053 ΔT2 − 0.003188 ΔT + 0.0618 2.14


where WR is wetting rate, kg/s/m

Shah (2013) proposed some key principles in the design of Robert vessels and

focused on feed distribution and pipe design. The juice pressure drop associated with

the piping design alters the hydraulics within the system and results in preferential

flow, which can cause inadequate distribution of juice, the venting of incondensable

gases or condensate draining. The adequate removal of condensate and incondensable

gases maximised the area available for heat transfer and the HTC is maximised by

increased recirculation.

2.6.6 Broadfoot and Tan investigations

Broadfoot and Tan (2005) undertook juice sampling trials on a conventional

Robert evaporator and an SRI Robert evaporator. The sampling trials provided

information on brix profiles for the juice within the vessels and gave insight into the

juice flow patterns in both designs.

The juice below the calandria of the conventional Robert vessel, and the juice

entering the base of the heating tubes were within 0.5 units of the brix of the outlet

juice. For the SRI Robert vessel, the juice below the calandria was at an intermediate

brix between the brix of the juice at the inlet and the outlet. The availability of lower

brix juice at the base of the heating tubes across the calandria is beneficial to heat

transfer performance. For both the designs, the juice near the top tube plate was of

higher brix than the juice at the base of the heating tubes. As Robert evaporators

operate in rising film action, this scenario is expected. The information on juice brix

profiles and juice flow patterns within Robert vessels is useful for design

improvements.

2.6.7 Empirical relationships for HTC

Empirical relationships for heat transfer coefficients for evaporators are required

for assessing and predicting the performance of the evaporator set. Over the years,

many authors have proposed correlations for HTC. Some of these correlations are

summarised in this section.

The Dessin formula

The French engineer, Dessin, proposed a formula permitting the evaporation

coefficient to be calculated for any vessel of a multiple effect set. This formula was


modified by Hugot and Jenkins (1986) to take juice concentration as the average of the

inlet and outlet brix. A modified Dessin formula, as given by Jenkins (1966), included

a reduction in HTC (kW/m2/K) to 85% to allow for fouling:

HTC = 2.2 × 10−7 λs(100 − Bjav)(Ts − 54) 2.15

where Bjav is the average brix of the juice entering and leaving the vessel, %

Ts is the condensing temperature of the heating steam/vapour in the

calandria, °C

Sugar Engineer’s Library

Another formula for overall HTC (kW/m2/K) is provided in an online design of

Robert evaporators in the Sugar Engineers' Library (2014). It is a function of juice or

syrup temperature and brix as:

HTC = 0.465 Tj Bj−1 2.16

where Tj juice temperature (estimated as Tv + Tbpe), °C

Bj is the brix of the juice leaving the vessel.

The ‘Australian Typical’ formula

Wright (2008) recommends the use of the ‘Australian Typical’ formula to be

used for conventional Robert evaporator vessels. The formula for HTC (W/m2/K) s

shown below:

HTC = 16.94 × TJ

1.0174 × (B

86 − B)

−0.2695

2.17

The Broadfoot & Dunn correlation

Broadfoot and Dunn (2007) presented pilot plant and factory evaporator

performance results and developed a correlation for heat transfer coefficient

(kW/m2/K), which included a term for the vapour condensation coefficient (VCC).

HTC = 21.6 × 10−6 VCC0.4 λs µ−0.34 2.18

where µ is the estimated viscosity of the exit juice, Pa.s


Formulae based on regressions on the combined Australian dataset

A combined dataset was assembled to include the 67 measurements of Australian

sugar factories and 75 of the Broadfoot and Dunn (2007) measurements. With the

latter, the HTC values had to be multiplied by 0.85 to allow for the fact that they were

carried out on clean vessels, and the other data were based on factory vessels, which

were cleaned every two weeks (Wright, 2008). The combined dataset yielded the

correlation for HTC (kW/m2/K).

HTC = 0.00056 (110 − Bj)1.0025

Tj0.8294 2.19


The concept of recirculation rate proposed by Shah and Peacock (2013) is not

entirely clear. Several Robert vessels operating in Australian mills in under–under

configuration have no mini-downtake or central downtake but the performance is

satisfactory. For these evaporators, juice must flow from above the top tube plate to

below the bottom tube plate by flowing down the heating tubes. There is no alternative

defined recirculation path for the flow of juice.

The juice sampling undertaken by Broadfoot and Tan (2005) showed that the

juice throughout the vessel is of very uniform brix and the average brix throughout the

vessel is only a unit or two below the outlet brix. This situation occurs despite the

evaporator having no defined recirculation path. According to the hypothesis proposed

by Shah and Peacock (2013), the Australian design should not work or give very poor

performance but this is clearly not the case.

The optimum juice level proposed by Shah and Peacock (2013) is lower at the

tail end of the set, which contradicts the results shown by Broadfoot and Dunn (2007),

and practical experience that the preferred juice level is higher at the tail end where

juice at higher brix is boiled. The requirement for the higher juice level is attributed to

the higher viscosity of the juice at the tail end of the set. There is consensus that ΔT,

which is closely related to vapour rate, is important in determining the optimum juice

level. However, the influence of vapour rate on the optimum juice level in factory

evaporators is considered to be not as significant as suggested by Shah and Peacock

(2013).


Shah and Peacock (2013) stated that larger areas at the tail end are helpful in

reducing ΔT. This is logical theoretically but ignores the major concern that operating

a final vessel with a low vapour rate per unit area will result in poor mixing, reduce

the HTC and cause faster scaling. Poor mixing may even result in crystal forming due

to the wide variations in brix within the vessel.

The Robert design proposed by Shah (2013) is similar to the SRI design, with

the difference that even juice distribution is favoured in the former and the peripheral

feed is used in the latter. The central downtake in the SRI design is sealed and provides

recirculation, as compared to Shah (2013) where strong emphasis is given to having

adequate recirculation to produce sufficient wetting.

The Broadfoot and Tan (2005) investigations have given good insights into the

juice flow patterns within the Robert vessels. It is evident that the SRI design has

created a marked change in the juice flow patterns within the vessel, which results in

increased separation of the inlet and outlet juice, providing lower brix juice to the base

of the heating tubes across the whole cross-section of the calandria.

The ‘Australian Typical’ HTC correlation as described by Wright (2008) is

considered to be the most reliable relationship and is used to compare the HTC

correlations developed in this study.

Several of the Robert vessels in the Australian sugar industry operate without

mini-downtake and with the under–under juice flow arrangement. By necessity, the

juice rising up the tubes and above the top tube plate must also travel down the heating

tubes at some point. This phenomenon is observed as sections above the top tube plate

stop boiling for a short time.

2.7 CFD Modelling


Computational Fluid Dynamics (CFD) modelling has found a wide range of

applications in the sugar industry. Over the past two decades, CFD modelling has been

used for assessing boiler performance, designing clarifiers, evaporators and vacuum

pans (Steindl (2003); Pennisi et al. (2003); Pennisi et al. (2004); Rackemann, Plaza, et

al. (2006)). This section reviews the CFD models that have been developed for

modelling Robert evaporators. The work done in CFD modelling of boiling


massecuite in vertical calandria tubes in vacuum pans is also mentioned, due to the

similarities of the principle. The main difference in vacuum pans is the much higher

viscosity of the massecuite compared with the juice in evaporators; massecuite is

boiled under a headspace pressure of 15 kPa abs.

2.7.2 CFD and heat transfer models

Steindl (2003) developed a CFD model of the 1st vessel of the set and

investigated two alternative evaporator configurations. It was found that the optimal

flow pattern of juice inside an evaporator vessel is plug flow, with no internal

recirculation, stagnant regions or bypassing. The calculated benefits to the throughput

capacity from plug flow, range from 4% for the 1st effect to above 30% for the final

effect. CFD modelling of typical evaporators, which have three peripheral juice inlets

and a single central juice outlet (in under-under configuration), showed significant

mixing and recirculation of the juice, as well as short-circuiting of juice from the feed

inlet to the outlet. CFD modelling of the alternative evaporator configurations

indicated that the preferred configuration is a vessel with fully distributed feed and a

single central juice outlet (i.e., similar to the SRI design).

Pennisi et al. (2003) presented a numerical model for the single-phase fluid flow

inside a sugar mill evaporator. The model incorporated the effect of temperature and

sugar concentration (brix) on the fluid properties. The standard k-ε turbulence model

was used in the investigation. The governing equations for incompressible single-

phase flow with heat transfer are the unsteady Navier-Stokes equations in their

conservation form.

Atkinson et al. (2000) developed a one-dimensional mathematical model for

two-phase flow in heated calandria tubes. For a given set of geometric and thermo-

physical parameters, the model results were presented as characteristic curves,

showing the net pressure difference generated in the calandria tube as a function of

mass flow rate and applied heat.

Stephens and Harris (2002) developed an improved one-dimensional

mathematical model of two-phase flow in a calandria tube with constant wall

temperature for vacuum pans. The predicted results from the model were in agreement

with available experimental measurements. These relationships can be improved with

experimental work on heat transfer in a single tube.


Rackemann, Broadfoot, et al. (2006) detailed the development of a CFD model

to predict the circulation patterns and heat transfer occurring in natural circulation

vacuum pans. The CFD model was validated against velocity data measured in factory

pans. The predictions were in reasonable agreement with factory measurements. The

validated CFD model was then used to investigate the effects of altering the key

dimensions in batch and continuous pans.

CFD modelling investigations into the steam side operation of the calandria of

vacuum pans and evaporators was undertaken by Rackemann, Plaza, et al. (2006). The

CFD model was validated with factory measurements and was found to have

limitations in the condensation physics in that the steam cannot be fully condensed

without causing convergence issues. Two parts of the model needed improvement; the

physical part of the model to enable condensing of more than 80% of the steam and a

better correlation for heat transfer within the calandria that takes into account the

restriction caused by the resistance on the juice side.


The complicated physics associated with an evaporator can be understood with

the help of CFD models. The developed CFD models that have been used to predict

circulation patterns and heat transfer in evaporator and vacuum pans are described. A

complete CFD model of the evaporator with steam side and juice side (two-phase)

model is not available. The CFD model developed by Pennisi (2004) for a Robert

evaporator is the most advanced. However, complete mesh independence was not

achieved due to the memory hardware limitations of the computer used to solve the

problems. Simplifying assumptions were used to model the calandria section, which

was critical to the model’s ability to produce accurate predictions of the fluid flow

inside the evaporator vessel. The inclusion of the vapour flash from the juice on entry

to the vessel would significantly improve the accuracy of predictions.

A CFD model of an evaporator is not developed in the project although a CFD

model was developed for the vapour and gas flows in the steam chest of the pilot

evaporator (as discussed in section 4.6).

2.8 Concluding Remarks

Previous investigations in the field of evaporation have been discussed in the

chapter. The boiling mechanisms in Robert vessels, pilot plant studies and factory trials


that have been undertaken have been explored. Many interesting concepts and theories

have been reviewed in this chapter and will form the basis of comparison with the

experimental data acquired in this PhD study and analysed in Chapters 4, 5 and 6.

Capital Cost Model 51

CHAPTER 3: CAPITAL COST MODEL


This PhD study investigates the heat transfer performance of tubes of different

lengths and diameters for the whole range of process conditions typically encountered

in the evaporator set. Incorporation of the results from the experimental investigations

into practical evaporator designs requires an understanding of the cost implications for

constructing evaporator vessels with calandrias having tubes of different dimensions.

Cost savings are expected for tubes of smaller diameter and longer length in terms of

material, labour and installation costs in the factory. These savings must be considered

in terms of the required heat transfer area for the evaporation duty, which will likely

be a function of the tube dimensions.

In this chapter, a capital cost model is described, which provides a relative cost

of constructing and installing Robert evaporators of the same heating surface area

(HSA) but with different tube dimensions. Evaporators of 2000, 3000, 4000 and

5000 m2 are investigated.

3.2 Evaporator Designs and Costs


The main design parameters for vessels of 2000, 3000, 4000, 5000 m2 are

calculated for calandrias comprising three tube lengths (2, 3 and 4 m) and three outside

diameters (38.1, 44.45 and 50.8 mm). All tubes have a wall thickness of 1.2 mm. The

capital cost for each design and several other parameters are calculated.

3.2.2 Number of tubes

A tube layout program developed by the Sugar Research Institute (SRI) Australia

is used to calculate the vessel internal diameter (ID) given the required HSA, tube

dimensions, pitch of tubes, number of mini-downtake, incondensable gas removal and

stay bar details. A snap shot of the output sheet for the tube layout program for the

conventional tube dimensions is shown in Figure 3.1. All designs included in this

paper include a diametric join of the calandria, mini-downtakes comprising 150 mm

diameter pipes, incondensable gas removal pipes and stay bars. The evaporator design

52 Capital Cost Model

is based on the SRI evaporator design (Moller et al., 2003; Wright et al., 2003), which

includes a central downtake, steam annulus with slots for the radial inflow of steam

into the calandria, two steam entries and central off-take of condensate.

For the designs assessed in this project, the clearances between the heating tubes

and the evaporator body components e.g., the outer tube and the wall of the calandria

are the same for all designs. Each vessel is designed to have a 5 m strake height above

the top tube plate, a gap between the bottom tube plate and the base at the outer wall

of 300 mm and a W-shaped bottom.

Figure 3.1 Output sheet for the tube layout program for the Robert evaporator

design

The specification of the HSA of the evaporator is based on the internal diameter

of the tube and the length between the outer faces of the tube plates. This specification

is different from that documented in the BSES manual (Bureau of Sugar Experiment

Stations 1984), which is based on the outside diameter (OD) of the tubes and includes

all wetted areas (mini-downtake, central downtake, tube plates). The code for the

dimensions of the tubes that are considered in this project is shown in Table 3.1.


Table 3.1 Code for different tube dimensions

Tube length

(m)

Tube OD

(mm)

Code

2 38.10 S2

44.45 M2

50.80 L2

3 38.10 S3

44.45 M3

50.80 L3

4 38.10 S4

44.45 M4

50.80 L4

The number of tubes for each tube dimension is shown in Figure 3.2. It is evident

that an L4 tube dimension requires the fewest tubes. Calandrias with tube dimensions

S4 require 42 % fewer tubes than the conventional M2 calandria for the same HSA.

As a consequence, a calandria with S4 tubes will provide cost savings in drilling and

honing of the holes in the tube plates, inserting and expanding the tubes. These costs

are examined further in the chapter.

Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Num

ber

of

tubes

0

5000

10000

15000

20000

25000

2000

3000

4000

5000

Figure 3.2 Number of tubes for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions


3.2.3 Vessel internal diameter

Figure 3.3 shows the vessel internal diameter (ID) for calandrias with the

different tube dimensions. The vessel ID is the factor that determines the footprint for

the vessel, the mass of steel in the vessel, the volume of juice held in the vessel at the

normal operating level, the total mass of the vessel and contents for the design of the

supporting structure and foundations, and the cross-sectional area in the vapour space

for the up flow of vapour and housing for de-entrainment louvres. Smaller vessels are

attractive on all counts, apart from a potential impact on juice level control owing to a

reduced buffer volume of juice and higher up flow vapour velocities. The diameter of

the vessel is reduced by 33% when the S4 tube dimensions are used rather than the

conventional tube dimensions, M2.

Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Ves

sel I

D (

m)

0

2

4

6

8

102000

3000

4000

5000

Figure 3.3 Vessel ID for 2000, 3000, 4000 and 5000 m2 vessels with different tube

dimensions

3.2.4 Capital costs

The material costs of the vessels include the costs of heating tubes and carbon

steel boiler plate. The costs of the tubes of the three diameters per linear metre are


shown in Table 3.2. Also shown in Table 3.2 are the costs of the tubes per unit of HSA

(based on tube ID).

Table 3.2 Tube costing based on tube diameter

Tube OD (mm) AUD/m AUD/m2 of HSA

38.1 10.67 95.1

44.45 11.25 85.2

50.8 13.49 88.7

The cost of carbon steel boiler plate is assumed to be AUD 15000/m3 (or AUD

1910/t). Wastage in material is accounted by 3% in tubes and 25% in plate steel. The

simplifying assumption has been made that wastage is proportional to steel used i.e.,

variability in wastage due to the use of standard plate sizes is ignored. Transportation

cost for steel plate is 3% and for tubes is 5% of the material costs.

Figure 3.4 shows the costs of materials (without fabrication costs) for vessels

with calandrias of different tube dimensions. The data for each HSA are presented

relative to the material costs for a vessel of the same HSA comprising the conventional

tube dimensions, M2.

As expected, for evaporators with the same tube diameter, the material costs are

lower where calandrias of longer tubes are used as the vessel diameter is reduced. For

a fixed tube length, the calandrias comprising 44.45 mm OD tubes have the lowest

cost of materials for the vessel and heating tubes. This is partly because of the lower

cost of the 44.45 mm OD tubes per m2 of HSA than the 38.10 mm and 50.80 mm OD

tubes.


Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Fra

ctio

n of

M2 c

ost

of

mat

eria

ls

0.90

0.95

1.00

1.05

1.10

2000

3000

4000

5000

Figure 3.4 Costs of materials for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions as fraction of cost of materials for vessels with M2

calandrias

Table 3.3 shows the cost data used for the assessment of the cost of the fabricated

evaporators (ex-works). Some of these data have been obtained from discussions with

sugar factory engineers, while other data are estimated by the authors as they were not

available because of commercial sensitivities.

Table 3.3 Cost data for construction of an evaporator

Description of parameter Value

Labour requirement to manufacture vessel 70 man hours per tonne of

steel

Labour cost AUD 70 per man hour

Fitting of tubes (placement and expansion at top

and bottom tube plates)

5 min per tube

Workshop overhead costs 30% of labour costs

Project management costs 10% of material, labour and

workshop costs

Profit margin 15% of total costs


Figure 3.5 shows the capital costs (ex-works) for the evaporator with calandrias

of different dimensions. As for Figure 3.4, the data for each HSA are expressed

relative to the costs of vessels of the same HSA with calandrias of M2 tubes. As

expected, the material and labour costs are lower for vessels with long tubes and small

diameter and greater for vessels with short tubes and large diameter. Comparison of

the data in Figure 3.5 and Figure 3.4 shows the impact of labour costs in manufacturing

the vessels and inserting and expanding the heating tubes into the calandrias.

The data in Figure 3.5 show the length of tube has a strong impact on capital

costs. For example, increasing the tube length from 2 m to 3 m provides a 13 to 15%

cost saving. Incrementally, there is a larger cost saving in increasing the tube length

from 2 m to 3 m than from 3 m to 4 m. This finding is to be expected.

Smaller diameter tubes provide a capital cost saving, but this is of lesser

influence than the length of the tube. For the same length of tube, the cost saving in

using tubes of 38.10 mm OD is only 3 to 5% compared with tubes of 44.45 mm OD.

This result is strongly dependent on the cost of tube per m2 of HSA given in Table 3.2.

One clear observation from Figure 3.5 is that the evaporators with the

conventionally used tube dimensions M2 are more expensive than all the other tube

arrangements, except for evaporators with L2 tubes.


Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Fra

ctio

n of

M2 c

ost

0.7

0.8

0.9

1.0

1.1

2000

3000

4000

5000

Figure 3.5 Total costs (ex-works) for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions as fraction of cost (ex-works) for vessels with M2

calandrias

3.2.5 Installation costs

The installation costs include the costs of the foundations and structure to

support the evaporator, insulation and cladding costs, pipework, instrumentation and

control costs. The installation costs are likely to be proportional (probably not linearly)

to the weight of the vessel used for the design of the foundations and supporting

structure (i.e., weight of the vessel and both the calandria and juice side full of

condensate and juice respectively).

Figure 3.6 shows the total mass on the foundations for the vessels with different

tube dimensions. The mass of juice is calculated for juice of 40 brix. The data for

each HSA are presented relative to the values for M2. Comparing the S4 tube design

with the conventional M2 tube design, a 40% reduction in the mass on the foundations

and structure is achieved.

Another benefit with the S4 tube design, and in general for small diameter

vessels, is the smaller footprint, which gives an additional saving on installation costs.


The costs of locating a vessel within an existing factory are generally proportional to

the footprint, although these costs are very site-specific. Thus, in some situations,

considerable savings may also be obtained for the smaller footprint of vessels with

smaller body diameter.

Cranage costs for installing the vessel are affected by the mass of the vessel and

also access to the location for the vessel, which depends on the site for the new

evaporator. The data in Figure 3.4 provide a reasonable indication of the relative

masses (empty vessels) to be lifted into position.

Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Fra

ctio

n of

M2 m

ass

on

foun

dat

ions

0.6

0.8

1.0

1.2

2000

3000

4000

5000

Figure 3.6 Total mass on foundations for 2000, 3000, 4000, and 5000 m2 vessels

with different tube dimensions as fraction of the total mass for vessels with M2

calandrias


For each evaporator, the number of tubes, vessel internal diameter, cost of

materials, total costs (ex-works) and total mass on the structure and foundations are

calculated and plotted. The parameters for the different designs are compared with the

calandria, comprising 44.45 mm OD tubes 2 m long that are generally used in the


Australian sugar industry. The model shows that for the cost of materials, total costs

(ex-works) and the mass on foundations, the values for M2 calandria are significantly

higher than for the calandrias with longer tubes and smaller diameter, with the effect

of tube diameter being less than the effect of tube length. Vessels comprising S4 tubes

have the smallest vessel diameter, lowest cost ex-works and smallest mass on the

foundations.

3.3 Other Considerations in the Design of Evaporators


The Robert-type evaporator provides larger buffer volumes, which are beneficial

for level and brix control. Additionally, the potential for sucrose degradation and

entrainment of juice droplets in the up-flow vapour have to be considered when

designing an evaporator. These topics are explored in this section.

3.3.2 Sucrose degradation during juice evaporation

The extent of sucrose degradation that occurs in the juice evaporation process is

a function of the juice conditions (pH, temperature and brix) and the residence time.

The evaporation conditions that are likely to experience higher levels of sucrose

degradation are where high levels of steam economy are sought e.g., where extensive

vapour bleeding is undertaken and where the process steam supplied to the calandria

of effect 1 is at higher pressure. For these stations, large evaporation areas are provided

in the front end of the set and the boiling temperatures are high (e.g., 118 °C). These

arrangements provide longer residence times for the juice at high temperatures, thus

providing conditions conducive to higher rates of sucrose degradation.

There is potential with the use of smaller diameter vessels associated with

calandrias comprising smaller diameter, longer tubes that the juice volume per unit

heating surface area can be reduced. Figure 3.7 shows the calculated juice volume

intensity (litres per m2 of HSA) for the different calandrias. These values are

determined for the base of the evaporator having a fixed gap between the bottom tube

plate and the base of the evaporator at the outer wall (300 mm) and angles in a W-

shaped bottom of 15 degrees (outer plate) and 30 degrees (inner plate). The juice

operating level is set at 35% of the tube height. The data show that calandrias

comprising longer tubes of smaller diameter should allow operation with a shorter

residence time for the juice and hence provide reduced potential for sucrose


degradation. In this regard, the benefits of using longer tubes of smaller diameter

would be greater at the front end of the set where the rates of sucrose degradation are

faster and reductions in the residence time for juice would be very beneficial.

Of note in Figure 3.7, vessels with calandrias using the conventional tubes M2

provide the second largest juice volume intensity, second only to vessels with L2 tubes.

Vessels with S4 tubes have juice volume intensities of ~6 L/m2 compared with vessels

with M2 tubes of ~11 L/m2.

Tubes

S2 S3 S4 M2 M3 M4 L2 L3 L4

Juic

e vo

lum

e in

tens

ity (

L/m

2)

0

2

4

6

8

10

12

14 2000

3000

4000

5000

Figure 3.7 Juice volume intensity for 2000, 3000, 4000 and 5000 m2 vessels with

different tube dimensions

3.3.3 Buffer volume for improved juice level and syrup brix control

The juice volume in Robert evaporators provides a buffer volume, which is

beneficial for juice level control and the syrup brix control in the final evaporator. The

author is unaware of any study into the minimum volume (or residence time), below

which juice level control or syrup brix control would be problematic.

As stated, evaporator stations for steam-efficient operation will likely include

additional area at the front end of the set. So, at the front end of the set at least,


installing vessels with low juice volume intensity should not create an issue for juice

level control as there should be adequate juice volume.

For vessels at the tail end of the set it may be more important to consider the

volume of juice held in the vessel in order to achieve effective control of juice level

and syrup brix. Burke et al. (2014) discusses the fluctuations in vapour flows through

the evaporator set resulting from the variations in pan stage vapour demand, and the

control options for juice level and syrup brix control. It is therefore considered

important that the juice volumes and residence times in these latter vessels are

considered in selecting the appropriate evaporator design. If a small-diameter, long-

tube calandria is beneficial from a heat transfer efficiency and cost perspective, it may

be that a larger juice volume than in a conventional configuration will be required

below the bottom tube plate to provide sufficient volume of juice for control purposes.

3.3.4 De-entrainment of droplets of juice from the vapour stream

In practice, the de-entrainment of droplets of juice from the vapour stream

passing to the next vessel is achieved through:

• the provision of a large distance from the boiling level of the juice to the

de-entrainment system, thus providing the opportunity for droplets to

disengage from the up flow of vapour and fall back, and

• The de-entrainment equipment itself.

Vessels of smaller diameter produce a stronger up-flow velocity for the same

vapour rate and so the intensity of droplets impinging on the de-entrainment system is

likely to be increased. For the investigations in this paper a constant strake height

above the top tube plate of 5 m is assumed. This height is reasonably common in the

current installations of Robert evaporator.

Up flow velocities in the conventional evaporator vessels comprising calandrias

of 44.45 mm OD tubes and 2 m length for specific vapour rates from the heating

surface of 40 kg/h/m2 (considered a maximum vapour rate in current operation of the

conventional evaporators) are estimated to be ~1 m/s at the 1st effect and ~9 m/s at the

final effect. These are assumed to be the maximum acceptable up-flow velocities.

The vessel configuration comprising a calandria of small diameter, long tubes

will produce the highest vapour velocities for the same specific vapour rate. It is also


found that the vessels of larger HSA provide a higher heating surface area per cross-

sectional area of vessel and so will also produce a slightly higher up-flow vapour

velocity than vessels of smaller heating surface area, for the same specific vapour rate.

Table 3.4 shows the maximum specific vapour rates that produce acceptable

vapour up-flow velocities. The data are shown for calandrias comprising tubes of

38.10 mm OD and 4 m long, in evaporators of 2000 and 5000 m2, for vapour pressures

of 13, 80 and 160 kPa abs.

Table 3.4 Maximum specific vapour rates for acceptable up-flow vapour

velocities in the headspace of vessels comprising tubes of 38.1 mm OD and 4 m

length

Vapour pressure, kPa abs Maximum specific vapour rate*, kg/h/m2

Vessel of 2000 m2 Vessel of 5000 m2

13 18 16

80 18 17

160 20 19

* Based on a maximum allowable up flow velocity of 1 m/s for 160 kPa abs, 5 m/s for

80 kPa abs and 9 m/s at 13 kPa abs.

As a guide for calandrias of 38.10 mm OD but shorter tubes, the maximum

specific vapour rates that can be accommodated are 30% greater for 3 m tubes and

75% greater for 2 m tubes than shown in Table 3.4.

It is apparent from the data in Table 3.4 that the vapour velocities and potential

impact on entrainment must be considered when designing an installation of a

calandria with high heating surface area per unit cross-sectional area of vessel. Up-

flow vapour velocities are likely to be of greatest concern at the front end of the set

(vapour pressures of 160 kPa abs), where specific vapour rates of 22 to 30 kg/h/m2 are

usual. At the tail end of the set, specific vapour rates are often less than 18 kg/h/m2,

particularly for energy-efficient installations. As well, it is unlikely that calandrias

with tubes of 38.10 mm OD and 4 m length would be suitable for the final vessel from

the point-of-view of effectively producing rising film boiling.

Consideration has been given to the specific vapour rates that could be

accommodated by a de-entrainment system of LSEA II louvres (a common design

used in Australian factories) installed in the headspace of the evaporator comprising

calandrias of different dimensions. For the study, the louvre face was assumed to be

a square with the corners located 200 mm from the circular shell. A safety margin for


the installed louvre area of 30% above the minimum area required for breakthrough of

the droplets in the vapour stream exiting the louvres was allowed. The results show,

as expected, the vessels of smallest diameter (viz., calandria comprising 38.10 mm OD

tubes and 4 m long) have the lowest specific vapour rate that can be accommodated.

The vessels with the capacity to process the highest vapour rate comprise calandrias

of 50.80 mm OD tubes, 2 m long.

Table 3.5 Maximum specific vapour rates for LSEA II louvres in vessels

comprising tubes of 38.1 mm OD and 4 m length

Vapour pressure

kPa (abs)

Maximum specific vapour rate

kg/h/m2

13 16

80 35

160 47

The data in Table 3.5 indicate that for almost all practical operating conditions,

sufficient LSEA II louvre area can be installed in the headspace of the vessels, without

the need for increasing the diameter of the headspace or installing an external

separator. It is only at the final effect conditions that the vapour rate may exceed the

breakthrough velocity, and, for these conditions, it is unlikely that calandrias of these

dimensions would be suitable for the final vessel.


Consideration is given for the different designs of evaporator vessels with

different tube dimensions for the juice hold-up volume and de-entrainment of juice

droplets carried with the vapour up- flow in the headspace of the vessels. These

matters will need to be considered in selecting the optimal tube dimensions for the

different evaporation stages.


A capital cost model for Robert evaporator has been developed for 2000, 3000,

4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and 38.10 mm,

44.45 mm, and 50.80 mm tube outside diameter.


The results show that the conventional evaporator with 2 m tubes of 44.45 mm

outside diameter is more expensive than all the other tube arrangements except for

evaporators with 2 m tubes of 50.8 mm outside diameter.

Relative to the conventional evaporator, cost savings in the ex-works cost of

~12% are likely in using 3 m long tubes of 44.45 mm OD and ~15% if 3 m long tubes

of 38.10 mm outside diameter tubes are used. Further savings are made by the use of

4 m long tubes, but the incremental cost reduction is less than increasing the tube

length from 2 to 3 m. Longer tube vessels have smaller diameter and considerably less

mass on the structure and foundations than the conventional evaporator, and so

additional savings through reduced installation costs would be achieved.

Vessels comprising longer tubes and smaller diameter have a lower juice volume

per unit of heating surface area. This feature is likely to be important for vessels early

in the evaporator set when high process steam pressures are used.

The vapour up-flow velocities and the impact on the de-entrainment system will

need to be considered for vessels comprising small diameter, longer tubes.

The results from this analysis are used in conjunction with results for heat

transfer efficiency for calandrias of different tube dimensions, as discussed in Chapters

4 and 5. In combination, these results allow the optimum Robert evaporator vessel

design to be determined for the different evaporation duties, as discussed in Chapter

7.

Experimental Program 67

CHAPTER 4: EXPERIMENTAL

PROGRAM


In Chapter 3, the capital costs associated with the fabrication and installation of

Robert-type evaporators were discussed. It was concluded that ~12% savings can be

achieved for the same heating surface area if evaporators having 3 m long tubes with

44.45 mm outside diameter are installed, compared with using the conventional tubes

(M2 size). The saving increases to 15% if 3 m long tubes of 38.1 mm outside diameter

are used. The HTC performances of tubes with different dimensions, other than the

standard M2 size, are not known. To understand the HTC performance and boiling

mechanism in rising-film vertical tubes of different dimensions, pilot plant

investigations were undertaken. This chapter discusses the experimental program, the

design of experiments, the experimental procedure, and the analysis of the potential

errors for both the condensate collection and the operating conditions. The effects of

tube dimensions and operating conditions on heat flux and heat transfer coefficient are

also discussed. The chapter concluded that the errors associated with the condensate

collection and the operating conditions were sufficiently small to be able to provide

reliable determinations of the HTC and VCC for each of the tests.

4.2 Experimental Rig

The schematic arrangement of the single-tube evaporator developed for this

experiment can be seen in Figure 4.1. The pilot plant evaporator rig, the accessories,

the control system, the data logging system and the commissioning are described

broadly in Appendix A.

68 Experimental Program

Figure 4.1 Schematic representation of the single-tube evaporator rig

The four main components are the juice tank located below the heating tube, the

heating tube, the steam chest around the heating tube and the headspace above the

heating tube. The juice held in the vessel fills the juice tank and partly fills the heating

tube. The level of juice inside the heating tube is known to affect the heat transfer. The

juice inside the tube boils and produces vapour that passes through the headspace of

the vessel and is condensed in a plate heat exchanger, which is supplied with cooling

water. The condensed vapour flows to a separator under vacuum or atmospheric

pressure, depending on the test conditions. The condensate from the separator is heated

with an immersion heater to the boiling temperature of the juice before returning to the

juice tank.

The single stainless steel heating tube is encased in a steam chest allowing the

steam that enters the steam chest to condense on the outside of the heating tube. The

steam was distributed inside the steam chest via two pipes, which extended the full

height of the steam chest and were located on opposite sides of it. These pipes

contained equally spaced holes to distribute the steam and direct the steam away from


the heating tube. This arrangement was essential to ensure that the condensate on the

outside of the tube was not disturbed by the incoming steam that may influence the

boiling of the juice inside the tube. A CFD model was developed to investigate the

steam velocity within the steam chest. The CFD model is described in Appendix B.

The condensate on the outside of the heating tube was collected in four gutters,

which were located equidistantly along the length of the tube. The condensate from

each gutter was drained under gravity to its individual container located below the

vessel. A fifth container collected the condensate from the bottom tube plate. Each

container was fitted with a pressure transducer at its base to provide a continuous

measurement of the head (height) of condensate in the container.

Noxious (incondensable) gases were removed from the steam chest through two

pipes within the steam chest, which were connected to vacuum or atmosphere,

depending on the test conditions. The arrangement of the noxious gas removal pipes

was similar to that for the steam entry pipes, thus ensuring the noxious gases did not

accumulate within the steam chest and were withdrawn uniformly along the full height

of the steam chest.

Juice samples were taken at the beginning and end of each test to check that the

brix of the juice had not changed through the test. Experience showed that the brix

remained reasonably consistent through the course of a test.

The boiling juice that collected above the heating tube may fall back into the

heating tube or pass to the juice tank via an external juice return line called a downtake.

Figure 4.2 shows the pilot evaporator rig, control unit and the computer to log

the data.


Figure 4.2 Pilot evaporator rig

4.3 Experimental Design

4.3.1 Selection of the experimental factors

The objective of the experiment was to investigate the effect of tube dimensions

and operating conditions on the HTC of a single tube in a Robert evaporator

configuration. The experimental factors selected were tube length, tube diameter, juice

brix, juice level, headspace pressure and pressure difference between the steam chest

and the headspace. Although steam rate is an important parameter in evaporator

performance, it was not a controlled variable in the experimental procedure. Instead,

the steam chest pressure and the headspace pressure were controlled to nominated set

points and the difference in pressure between the steam chest and headspace

determined the resulting steam rate.


Table 4.1 shows the experimental factors and number of levels for each of the

factors. Three levels of tube length and three levels of tube diameter were selected.

Hence, a total of nine tubes of different lengths and diameters were tested. The tubes

that were selected are the same as those considered in the capital cost model (see Table

3.1).

Table 4.1 Factors and levels explored in the experiment

Factor Levels

Tube length (TL, m) 3

Tube diameter (TD, mm) 3

Brix, (B°) 3

Juice level, (JL,% tube height) 4

Headspace pressure (HS, kPa abs) 2

Pressure difference (ΔP, kPa) 2

The selected conditions covered the wide range of industrial operating

conditions for multiple effect evaporators in raw sugar factories. The juice level,

headspace pressure and pressure difference factors were selected to be consistent with

the brix of juice, according to where that brix is achieved in an evaporator set and to

encompass the usual parameter range achieved in Robert evaporators in Australian

sugar factories. The juice in the first effect (low brix) boils above atmospheric

pressure, and juice in the final effect (high brix) boils under vacuum. The temperature

difference in the first effect is smaller than the temperature difference in the final

effect.

Consideration was given to designing the experimental program to measure the

heat transfer performance for each tube at several brix levels under the same operating

conditions of juice level, headspace pressure and pressure difference. This approach

would include testing low brix juice at low boiling temperature and high temperature

difference and high brix juice (syrup) at high boiling temperature and low temperature

difference. This process would ensure the results were free from confounding

interactions of the operating conditions. However, the test program would have

included many tests that were not only impractical industrially, but would not have

produced a boiling regime. For example, a test using Brix-70 juice with a small

temperature difference (which is typical of industrial boiling for Brix-20 juice) would

not have initiated rising film boiling to wet the total length of tube. It was therefore


decided to structure the test program to encompass the practical operating conditions

that are typical of industrial evaporators for the 1st effect (typically Brix-20), 3rd effect

(typically Brix-35) and 5th effect (typically Brix-70) of a quintuple evaporator set.

The experimental factors, which were investigated for Brix-20, Brix-35 and

Brix-70 juices are shown in Table 4.2, Table 4.3 and Table 4.4. It should be noted that

in subsequent tables the following terminologies are used.

• HS1 and HS2: These are the two headspace pressures and HS1is the higher

of the two.

• DP1 and DP2: These are the two pressure differences and DP1 is the lower

of the two.

• JL1, JL2, JL3 and JL4: These are the four juice levels and the order from the

lowest to the highest is JL1 to JL4.

Table 4.2 Experimental factors investigated for juice at Brix-20

Factor Level 1 Level 2 Level 3 Level 4

Tube length (TL, m) 2 3 4 –

Tube diameter (TD, mm) 38.1 44.45 50.8 –

Juice level, (JL,% tube height) 20 30 40 50

Headspace pressure (HS, kPa abs) 149 126 – –

Pressure difference (ΔP, kPa) 33 45 – –
















4.3.2 Design of experiments

Since the number of levels of each factor was not the same (as shown in Table

4.1), the experiment was conducted as a full factorial experiment, to avoid the

complexity of selecting tests for a fractional factorial design. Because of the

difficulties associated with changing the tubes of different length and diameter and, to

a lesser extent, changing the brix and juice level, the experimental program was

conducted in a split-split-plot arrangement (TIBCO Spotfire, 2010) so that the tube

dimensions, brix and juice level were changed less frequently than in a fully

randomised experimental design. The tube dimensions formed the top order of the

experiment also known as the whole plot. The brix and juice level experimental factors

formed the subplot and the headspace pressure and pressure difference formed the sub-

sub-plot of the experiment. The structure of the experimental program is shown in

Appendix C.

The nine tubes were selected for testing in a random order. For each tube, the

brix and juice level combinations were selected for testing in a random order. For each

of the brix and juice level combinations, the headspace pressure and pressure

difference combinations were selected for testing in a random order.

With six experimental factors at the chosen number of levels, the design of the

experiment included 432 tests. These 432 tests henceforth are referred to as

Original432. For an analysis of variance (ANOVA) of the whole plot consisting of a

3 x 3 factorial experiment, the tests provided information on the significance of tube

length and tube diameter factors individually, but no information was available on the

interaction between tube length and tube diameter. The eight degrees of freedom for

the 3 x 3 whole-plot experiment were consumed by the length (2), diameter (2) and

residuals (4).


A replicated 2 × 2 whole-plot experiment was conducted to examine the tube

length and tube diameter interaction. The four tubes investigated in the replicate

experiment were M2, S2, M3 and S3. To reduce the number of tests in the replicates,

brix levels of 20 and 70 only were selected. Juice levels, headspace pressure and

pressure difference factors were kept the same as for the Original432 experiment. A

total of 128 tests were conducted in this second experiment. These 128 tests henceforth

are referred to as Replicate128.

4.4 Experimental Procedure

The Brix-20 and Brix-70 juice were sampled directly from the factory’s first and

final evaporators respectively. The Brix-35 juice was prepared manually by diluting

Brix-70 juice with hot water. Prior to each test conducted at the Brix-20 and Brix-35

levels, the evaporator rig was boiled with water at atmospheric pressure to preheat the

pilot evaporator from a cold start. For Brix-70 tests, the rig needed to be cooler and

water boiling at atmospheric pressure was not done. The test temperature is the set

point temperature calculated from the set point headspace pressure plus the boiling

point elevation, depending on the brix of the juice. The juice was transferred into the

rig using vacuum for tubes of 4 m length and was poured through the juice return line

for tubes of 2 and 3 m length. The use of vacuum was minimised since low pressure

caused the high temperature juice to flash in the vessel, increasing the brix of the juice.

Also, setting the required juice level was difficult with high vacuum. Once the juice

was transferred to the rig at the required level, this state was referred to in the

experiment as a boil. For each boil, four tests were conducted at two different

headspace pressures and two different pressure differences.

All the tests were conducted with the valve in the external downtake in the open

position. Also, for all tests, the condensed vapour return to the juice tank was heated

to the boiling temperature of the juice. The supply of juice at the boiling temperature

is, however, not usual in factory vessels. In the first vessel, the juice entering is often

5–10 °C lower than the boiling temperature of the juice and requires heating within the

evaporator to reach that temperature. This heating is often referred to as sensible

heating. From the second effect onwards in industrial evaporators, juice entering the

vessel is at a higher temperature than the boiling temperature of the vessel, causing the

juice to flash as it enters the vessel.


When conducting the tests, steady boiling conditions were established before

logging of the data commenced. The complete data logging system is explained in

detail in Appendix A. For each test, data were logged for all the operating conditions

and for the height of condensate collected in each reservoir. The sections of the tube

were designated section 1 to 4 with section 1 being the top section and section 4 being

the bottom section. The condensate collected from the bottom tube plate was

designated section 5. Each test was conducted for approximately 20–25 minutes,

ensuring a period of steady condensate collection was obtained before moving on to

the next test. Once the four tests for each boil were completed, the rig was brought to

atmospheric pressure and the conditions established for the next boil (randomly

selected juice brix and juice level). The process was then repeated.

4.5 Calculating HTC from Condensate Measurements


The condensing vapour on the outside of the tube is accumulated in four

equidistant gutters along the length of the tube and drained to condensate containers

located below the steam chest. The HTC was calculated using the condensate data.

This section describes the procedure and the calculations for determining HTC from

the raw data.

4.5.2 Determining condensate flow rate (kg/s)

The height of condensate (mm) collected in each reservoir was measured using

the differential pressure transducer in the base of the reservoir, logged and plotted

against time (minutes). An example of the data for condensate collection in each

reservoir is shown in Figure 4.3. A linear regression was fitted and for most cases

𝑅2~ 1 was determined, indicating steady boiling conditions had been reached. The

equation of the form (𝑦 = 𝑚𝑥 + 𝑐) where m is the slope for each plot is shown below

the label for each of the graphs. Parameter m is the condensate collection rate and has

the unit mm/min. Parameter c has the unit mm.

The internal diameter of each of the reservoirs for collecting condensate from

the heating tube (sections 1 to 4) was 70 mm and the internal diameter of the reservoir

for section 5 was 100 mm.


The condensate rate (kg/s) for each of the tube sections and for the collection on

the bottom tube plate was calculated from the rate of filling of the condensate reservoir,

the cross-sectional area of the reservoir and the estimated density of the condensate (as

a function of temperature). The condensate rates from the four sections are summed

to provide the total condensate rate formed on the outside of the heating tube.

4.5.3 Determining temperature difference

Using the total condensate rate for the heating tube, together with the latent heat

of condensation (function of calandria pressure–using Steam Tables) the heat flux for

the test is calculated using equation 1.2. The temperature difference between the

vapour temperature in the steam chest and the temperature of the juice is calculated

using equation 1.3. Based on the calculated heating surface area of the tube (outside

diameter and distance between the outer faces of the tube plates), the overall HTC for

the test is calculated using equation 1.1. The VCC for the test is calculated from the

total condensate rate for the four sections of the tube, divided by the heating surface

area of the tubes using equation 1.6. The temperature of the juice is determined from

the headspace pressure and boiling point elevation (from the brix) using the correlation

1.4 and 1.5 on page 7.

4.5.4 Example showing HTC calculation

To demonstrate an example of HTC calculation, a test from the experimental

investigations is selected. This test corresponds to the condensate collection results

shown in Figure 4.3.

Tube dimensions

Tube length – 2 m

Tube diameter – 44.45 mm

HSA – 0.07 m2 for each section, 0.28 m2 for the entire tube.

Operating parameters

Juice brix – 20

Juice level (%tube height) – 40

Steam chest pressure – 194 kPa abs

Headspace pressure – 149 kPa abs


Pressure difference – 45 kPa

Temperature difference – 7.7 (taking into account boiling point elevation at 20

brix and juice temperature of 111.49 ℃ )

Condensate rate (slope in mm/min) – Section 1 – 17.76

Section 2 – 21.28

Section 3 – 21.12

Section 4 – 17.45

Tube – 77.61

Calculations

Calculating condensate volume flow rate (m3/s) in each condensate container

Section 1 – (17.76

1000

60) 𝑥 (

𝜋

4𝑥0.072) = 1.14 𝑥 10^ − 6

Section 2 – (21.28

1000

60) 𝑥 (

𝜋

4𝑥0.072) = 1.36 𝑥 10^ − 6

Section 3 – (21.12

1000

60) 𝑥 (

𝜋

4𝑥0.072) = 1.35 𝑥 10^ − 6

Section 4 – (17.45

1000

60) 𝑥 (

𝜋

4𝑥0.072) = 1.12 𝑥 10^ − 6

Entire tube – 4.98 𝑥 10−6

Calculating condensate mass flow rate (kg/s)

�̇�𝐶 = �̇�𝐶 𝑥 𝜌

Where �̇�𝐶 is the mass flow rate of condensate, (kg/s)

�̇�𝐶 is the volumetric flow rate of condensate, (m3/s)

𝜌 is the density of saturated liquid, (kg/m3)

The density of the saturated liquid and latent heat of condensation are calculated

from the properties of the steam (Steam Table). Table 4.5 below shows the density of

the saturated liquid and latent heat of condensation for the 12 steam chest pressures.


Table 4.5 Density of saturated liquid and latent heat of condensation for the 12

steam chest pressures

Steam chest

pressure (kPa

abs)

Steam chest

temperature (℃)

Density of

saturated liquid

(kg/m3)

Latent heat of

condensation (kJ/kg)

194 119.27 943.74 2204.48

182 117.28 945.33 2210.02

171 115.35 946.85 2215.34

159 113.13 948.58 2221.44

144 110.15 950.88 2229.55

129 106.91 953.33 2238.30

122 105.29 954.53 2242.65

107 101.53 957.28 2252.63

89 96.41 960.94 2266.11

82 94.18 962.49 2271.91

71 90.33 965.11 2281.86

64 87.62 966.91 2288.82

Calculating heat flux 𝑄 from condensate flow rate and latent heat of steam using

equation 1.2.

Section 1 – 2370 W




Tube – 10356 W

Calculating heat transfer coefficient using equation 1.1.

Section 1 – 4397 W/m2/K




Tube – 4803 W/m2/K


Section 1

y=17.76x+41.21

Time (minutes)

0 2 4 6 8 10 12 14 16

Co

nd

ensa

te c

olle

ctio

n (

mm

)

0

50

100

150

200

250

300

350

Section 2

y=21.28x+2.45

Time (minutes)

0 2 4 6 8 10 12 14 16

Co

nd

ensa

te c

olle

ctio

n (

mm

)

0

50

100

150

200

250

300

350

Section 3

y=21.12x+15.57

Time (minutes)

0 2 4 6 8 10 12 14 16

Co

nd

ensa

te c

olle

ctio

n (

mm

)

0

50

100

150

200

250

300

350

Section 4

y=17.45x+29

Time (minutes)

0 2 4 6 8 10 12 14 16

Co

nd

ensa

te c

olle

ctio

n (

mm

)

0

50

100

150

200

250

300

350

Section 5

y=16.33x+10.7

Time (minutes)

0 2 4 6 8 10 12 14 16

Co

nd

ensa

te c

olle

ctio

n (

mm

)

0

50

100

150

200

250

300

350

Figure 4.3 Condensate collection (mm) for individual sections (1 to 4) and for

section 5


4.6 Analysis of Potential Errors with Condensate Collection


It is important to understand the potential errors associated with the experimental

investigation before analysing the data and interpreting the results. The heating tube

was designed to allow condensate to be collected from four sections of the tube, with

the condensate formed on a tube section being transferred to its reservoir. Three

scenarios that could occur exist within the steam chest, which would adversely affect

the measurement of condensate rates for a section of the heating tube.

1. Condensate departs the outside of the tube section and so is not collected

in the reservoir for that tube section but passes to the bottom tube plate.

2. Condensate overflows a gutter and flows to the tube section below.

3. Condensate overflows the bottom gutter to the bottom tube plate.

All scenarios would cause an error in the individual section’s HTC value and

lead to misinterpretation of the boiling mechanism, causing an error in the calculation

of the overall HTC for the whole tube. This section investigates the data for evidence

that any of these scenarios was occurring.

4.6.2 Collection of condensate from the base of the steam chest

Potential sources of condensate in the reservoir for section 5 include

i. Condensed vapour on the inner wall of the steam chest due to convective

and radiation heat losses from the outer wall of the steam chest. The

evaporator rig was lagged with Rockwool insulation with 30 mm of

insulation thickness. The insulation around the flanges was loose, as the

rig was frequently disassembled to change the tube. A section of the rig

around the support structure was not lagged due to the difficulty in being

able to place insulation around the support. These sections in particular

would contribute to heat losses and condensation on the inside of the

steam chest.

ii. Condensate that may enter the steam chest with the vapour. The quantity

of condensate from this source should be small, as a condensate trap was


placed after the steam valve to remove the condensate in the steam pipe

before the steam enters the steam chest.

iii. Condensate departing the outside of a tube section caused by the impact

of the inflowing steam.

iv. Condensate overflowing the bottom gutter.

With regard to item iii above, a CFD model of the steam side of the pilot

evaporator was developed and used to determine the velocity and flow path of the

steam entering the calandria. The steam velocity was found to be very low near the

tube surface and it was concluded that the steam entering the steam chest would not

disrupt the condensate on the tube, nor disturb the condensate pattern. The velocity

profile output from the CFD model is shown in Appendix B.

The condensate rate from the base of the steam chest was calculated for each of

the tests. The condensate rates ranged from 0.003 kg/s to 0.00012 kg/s with the low

rates being for tests at Brix-70. The highest condensate rates were for Brix-20. Heat

loss calculations were undertaken to estimate the quantity of condensate in section 5

that would be attributed to heat losses through the outer wall of the steam chest. These

rates ranged from 0.0023 kg/s (for tests with steam chest pressure of 194 kPa abs) and

0.00012 kg/s (for tests with steam chest pressure of 64 kPa abs). These estimates of

condensate rate due to heat losses were subtracted from the measured condensate rate

to provide an ‘unaccounted’ condensate rate for section 5. Unaccounted condensate

rates for section 5 ranged from 0.003 kg/s to 0.0001 kg/s.

Figure 4.4 shows the mean values of the unaccounted section 5 condensate flow

expressed as a percentage of the total flow on the tube surface, as measured from the

section 1 to section 4 condensate collections.


Figure 4.4 Mean values of unaccounted section 5 condensate flow expressed as

percentage of total flow on tube surface

Table 4.6 shows the analysis of variance of unaccounted section 5 condensate

flow as % of the total flow on the tube surface. It was found that only pressure

difference has a significant effect on the relative magnitude of the unaccounted section

5 condensate flows. It is well known and demonstrated in section 4.8 on page 94 that

higher pressure difference results in higher VCC (kg/h/m2) on the tube surface, for all

other process conditions being the same. However, Figure 4.4 shows that higher

unaccounted section 5 condensate flow (as percentage of the condensate flow on the

tube surface) was achieved at lower pressure difference. The higher unaccounted

section 5 condensate flow for tests with the lower pressure difference provides further

evidence that the large unaccounted section 5 condensate flow is not caused by

condensate being displaced from the outside of the heating tube. An explanation is

not obvious, but it may be that at lower pressure difference and subsequently lower

vapour rates, the condensation of vapour in the supply vapour lines is a greater

proportion of the total flow and this condensate flows to the base of the steam chest on

entering the steam chest. Excess condensate entering the steam chest will have no


influence on the measured condensate rates on the different sections of the heating

tube and hence on the measured VCC and calculated HTC values.

Table 4.6 Results of analysis of variance of unaccounted section 5 condensate

flow (%) with main sources (percent of total flow on tube surface)

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 78183 1.38 –

TD 2 106948 1.89 –

Residuals 4 56476

B 2 65823 2.02 –

JL 3 30509 0.94 –

Residuals 94 32557

HS 1 64263 2.58 –

ΔP 1 192009 7.72 0.006

Residuals 322 24872

4.6.3 Overflowing in a free-flowing scenario

The gutters, which were fabricated for condensate collection, were designed to

handle condensate flow rates well above those expected in the trials. Calculations show

the drain tubes should be able to transfer at 0.0065 kg/s per tube. Of all the tests, the

largest condensate rate collected for an individual tube section was 0.0015 kg/s, which

is well below the capacity of the drain tube to pass condensate to the reservoir in a

free-flowing situation. It is therefore concluded that if the entrance to the drain tube is

not restricted in any way, the condensate should drain readily from the gutter to the

reservoir.

Table 4.7 shows the maximum, mean and the standard deviation values of the

unaccounted section 5 condensate rate for all levels of each factor for tests at Brix-20.

The maximum value of unaccounted condensate rate viz. 0.0031 kg/s is observed for

headspace pressure of 149 kPa abs, pressure difference of 45 kPa, tube length of 4 m,

tube diameters of 38.1 and 50.8 mm and juice level of 30% tube height. The high value

of unaccounted condensate rate for headspace pressure and pressure difference is

explained, since they correspond to larger temperature difference. Longer tube lengths

would correspond to higher surface area of the tube and the steam chest. Juice level of

30% tube height would correspond to better heat transfer coefficient and higher

condensation rates. The not-so-readily explained result in Table 4.7 is tube diameter.


Higher unaccounted condensate rate are shown for 38.1 and 50.8 mm tube diameters

but the unaccounted condensate rate for the 44.45 mm tube diameter is 40% lower than

the other two diameters. This result is not properly understood.

Table 4.7 Maximum value, mean value and standard deviation of the

unaccounted section 5 condensate rate for all levels of each factor for tests at

Brix-20

Factor Level Maximum

value, kg/s

Mean

value, kg/s

Standard

deviation, kg/s

HS pressure (kPa

abs)

149 0.0031 0.0013 0.0006

126 0.0023 0.0011 0.0005

ΔP (kPa) 33 0.0021 0.0011 0.0005

45 0.0031 0.0013 0.0006

Tube length (m) 2 0.0020 0.0011 0.0004

3 0.0018 0.0011 0.0004

4 0.0031 0.0014 0.0007

Tube diameter

(mm)

38.1 0.0031 0.0013 0.0006

44.45 0.0018 0.0010 0.0004

50.8 0.0031 0.0013 0.0006

Juice level

(%tube height)

20 0.0018 0.0010 0.0005

30 0.0031 0.0014 0.0006

40 0.0022 0.0012 0.0005

50 0.0022 0.0013 0.0006

4.6.4 Overflowing due to blockage at the entrance to a drainage tube

If an overflow did occur from a gutter, the overflowing condensate is expected

to flow to the tube section below the gutter (due to the commonly referred to ‘teapot

effect’) and cause an increase in the measured condensate rate of the section below.

The HTC values of individual sections of the Replicate128 dataset showed good

consistency with the corresponding values for the same conditions in the Original432

dataset. This comparison is provided in section 6.2. The fact that the replicate tests

were undertaken several weeks later and showed similar HTC results for the individual

sections of the heating tubes indicates that overflowing of condensate was not

occurring due to a blockage at the entrance to a drainage tube.


4.6.5 Concluding remarks on the collection of condensate from the four sections of

the heating tube

The condensate rate from the base of the steam chest (section 5) was measured

for each of the tests and an allowance made for condensation on the inside wall of the

steam chest, due to radiation and convective heat transfer to atmosphere. After

deducting this allowance, an unaccounted condensate rate for section 5 was

determined. For several tests, the unaccounted condensate rate for section 5 (expressed

as a percentage of the total of flow on tube surface) was greater than 10%.

A comprehensive investigation has been undertaken to determine if the

measured condensate rate for any of the four sections of the heating tube may be in

error due to either condensate separating from the tube condensate and not being

drained from a gutter to the reservoir or a gutter overflowing condensate. The

investigations showed that:

• The steam velocity was found to be very low near the tube surface and

it was concluded that the steam entering the steam chest would not

disrupt the condensate on the tube or disturb the condensate pattern (see

Appendix B).

• The capacity of the drainage tube on each gutter far exceeds the

maximum condensate rate. Thus, without any physical restriction at the

entrance of the drainage tube, gutters should not overflow.

• Overflowing of a gutter could occur due to blockage of the entrance to

the drainage tube (e.g. due to a bubble or physical item lying at the

entrance). The HTC results for individual sections of tubes for the same

test conditions in the Replicate128 and Original432 series showed

similar values. Because the tests were undertaken several weeks apart

it is very unlikely a physical blockage would occur for a specific tube

section in a specific test, for both series.

As a result of these investigations it is concluded that there is no evidence of

overflowing of gutters or condensate separating from the tube.

All possible options have been explored to understand the cause of the

unaccounted quantity of condensate that collects on the base of the steam chest. There

is some indication that some condensate is entering with the steam supply and this is


a greater percentage relative to the rate condensed on the heating tube for tests at low

steam rate. However, strategic analysis by various scenarios confirmed that the

presence of the unaccounted condensate would not affect the HTC results.

4.7 Analysis of Potential Errors of Operating Conditions


The operating conditions of the experimental program were selected such that

the difference between the levels of each factor is sufficiently large to cause a change

in heat transfer response.

Juice level was set to a precision of 5 mm and the juice level measured after the

run was in close agreement to within 5 to 10 mm of the initial level, corresponding to

an error of 2.5% for the shortest tube with the lowest level. The variation of headspace

pressure from the set value was negligible for each run, since headspace pressure was

well controlled. The juice was sampled from the factory evaporators and the brix of

the sample after adjustment by dilution with water (when needed) was within 1–2 units

of the required brix. The brix of the sample was measured before and after the test and

the brix reading after the test was recorded. For most tests, the required calandria

pressure was able to be controlled closely to the set point. However, for some of the

20 brix tests, the calandria pressure of 194 kPa abs (149 kPa abs headspace pressure

and 45 kPa pressure difference) was not able to be achieved since the vapour supply

used to regulate the calandria pressure was at a lower pressure.

Table 4.8 shows the maximum, minimum, mean and standard deviation values

for the experimental factors. Because factory samples of the ESJ and syrup were taken

for the tests, the brix was difficult to tightly regulate to the desired value and standard

deviations of 1.3 to 2.3 units resulted. For the tests of brix 20 and 35 this variation in

brix should have a small influence on the HTC. The brix of the juice at brix 70 was

more difficult to regulate, as of the high brix, relatively small changes in water content

have a large influence on the brix value. The high standard deviations of ΔP2 and ΔT3

for the first effect are explained in the above section by the inability to supply vapour

at 194 kPa abs for several tests. The high standard deviations of all the four ΔTs for

5th effect conditions can be attributed in part to the sensitivity of boiling point elevation

at higher brix values and the variation in juice brix among the tests. Headspace pressure


is not included in Table 4.8, since it was well controlled, and the set point was always

achieved.

Table 4.8 Maximum values, minimum values, mean values and standard

deviation of the experimental factors

Effect Factor

Set

point

Maximum

value

Minimum

value

Mean Standard

deviation

1 B 20 21.7 14.2 18.2 1.7

ΔP1 33 33 33 33 0

ΔP2 45 45 35 40 3.2

ΔT1 5.7 5.9 5.6 5.7 0.1

ΔT2 6.5 6.7 6.4 6.5 0.1

ΔT3 7.7 7.8 6.1 7 0.5

ΔT4 8.9 8.9 8.6 8.8 0.1

3 B 35 38.5 34 36.1 1.3

ΔP1 35 35 35 35 0

ΔP2 50 50 50 50 0

ΔT1 7.9 8 7.7 7.8 0.1

ΔT2 9.8 10.8 9.6 10.2 0.2

ΔT3 11.2 11.2 11 11.1 0.1

ΔT4 13.5 13.6 13.4 13.5 0.1

5 B 70 74 65 70 2.3

ΔP1 42 42 42 42 0

ΔP2 60 60 60 60 0

ΔT1 17.2 21.7 16 18.8 1.3

ΔT2 20.9 24 19.7 21.8 1

ΔT3 23.3 24.4 22.1 23.2 0.6

ΔT4 27.4 28.5 26.3 27.4 0.6

4.7.2 Analysis of variance of the operating conditions

The following sections describe an analysis of variance of the actual operating

conditions, to identify if any other factors were inadvertently varied along with the

desired factor and could possibly have confounded the results. The analysis also helps

understand the impact that variations in operating conditions have on the calculated

values of heat transfer coefficient.

Brix

Table 4.9 presents the analysis of variance of measured brix values for the

Origianl432 tests. It is observed that brix has the most significant effect on measured


brix values. An unexpected result is the significance of tube length on measured brix

values. Figure 4.5 shows the mean values for measured brix for all the factors. For

Brix-20 and Brix-35, the maximum deviation with tube length is 1 unit. For Brix-70,

the maximum deviation with tube length is 3 units.

Figure 5.7 on page 125 shows the mean values of HTC for each level of each

factor for the Origianl432 tests. For 15 units change in brix (Brix-20 to Brix-35), the

change in HTC is ~1500 W/m2/K. Hence, each unit change in brix corresponds to

100 W/m2/K. For tests with Brix-20, a change of 100 W/m2/K is small (< 5%) of the

mean of the HTC values for Brix-20.

Table 4.9 Analysis of variance of measured brix

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 118.6 7.34 0.045

TD 2 1.5 0.09 –

Residuals 4 16.14

B 2 97838 8646 0.000

JL 3 7.82 0.7 –

B:JL 6 18.8 1.6 –

Residuals 88 11.3 – –

HS 1 9.3E-28 0.71 –

ΔP 1 4.92E-29 0.03 –

B:HS 2 3.2E-30 0.00 –

B:ΔP 2 1.9E-28 0.15 –

JL:HS 3 8.06E-28 0.62 –

JL:ΔP 3 1.38E-27 1.06 –

HS:ΔP 1 3.5E-28 0.27 –

B:JL:HS 6 2.12E-27 1.62 –

B:JL:ΔP 6 1.18E-27 0.91 –

B:HS:ΔP 2 3.38E-29 0.02 –

JL:HS:ΔP 3 1.38E-27 1.06 –

B:JL:HS:ΔP 6 1.98E-27 1.52 –

Residuals 288 1.3E-27

For 35 units change in brix (Brix-35 to Brix-70), the change in HTC is ~1000

W/m2/K. Hence, each unit change in brix corresponds to 30 W/m2/K. For tests with

Brix-35, a change of 30 W/m2/K is small (< 5%) of HTC values for Brix-35.


Figure 5.7 on page 125 shows the mean values of HTC for tests with Brix-70.

According to Figure 4.5, a change of 3 units of brix corresponds to a change in HTC

value of 250 W/m2/K. Hence each unit change in brix corresponds to 80 W/m2/K,

which is large (> 10%) compared to the mean of the HTC values for Brix-70.

Figure 4.5 Mean values of measured brix for each level of each factor for the

Original432 tests with all results included

Pressure difference

The pressure difference values were selected to generate a temperature

difference or driving force for heat transfer. For each brix, two pressure difference

values were selected, along with two headspace pressure values. The headspace

pressure values were always held at set point in the experimental program. This section

describes the analysis of variance for the measured pressure difference.

Table 4.10 shows the analysis of variance of measured pressure difference for

the Original432 tests. Three main effects (B, HS, ΔP), three 2nd order interaction

(B:HS, B:ΔP, HS:ΔP) and one 3rd order interaction (B:HS:ΔP) were identified with a

significance level less than 0.05.


Figure 4.6 shows the B:HS:ΔP interaction plot with measured pressure

difference as the response factor. It is evident that for Brix-35 and Brix-70, the

measured pressure difference coincides with the set pressure difference. For Brix-20,

the measured pressure difference is lower than the set points for headspace pressure of

149 kPa (abs). The explanation for this is that the calandria set point of 194 kPa (abs)

could not always be achieved, since the vapour source from the factory itself was at

lower pressure.

Table 4.10 Analysis of variance of measured pressure difference

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 4.8 4.36 –

TD 2 0.96 0.87 –

Residuals 4 1.1

B 2 6345.5 8212.4 0.000

JL 3 1.3 1.67 –

B:JL 6 1.5 1.97 –


HS 1 54.67 62.37 0.000

ΔP 1 21998 25098 0.000

B:HS 2 57.5 65.6 0.000

B:ΔP 2 613.2 699.7 0.000

JL:HS 3 1.56 1.78 –

JL:ΔP 3 1.38 1.57 –

HS:ΔP 1 53.8 61.4 0.000

B:JL:HS 6 1.35 1.54 –

B:JL:ΔP 6 1.43 1.63 –

B:HS:ΔP 2 57.4 65.5 0.000

JL:HS:ΔP 3 1.19 1.36 –

B:JL:HS:ΔP 6 1.6 1.83 –

Residuals 288 0.88


Figure 4.6 B:HS:ΔP interaction plot with measured pressure difference as a

response factor

Temperature difference

The temperature difference in the evaporator rig was a consequence of the

headspace pressure, the calandria pressure and the brix of the sample (and the boiling

point elevation). This section describes the analysis of variance for the measured

temperature differences.

Table 4.11 shows the analysis of variance of the measured temperature

difference for the Original432 tests. Three main effects (B, HS, ΔP) and three 2nd order

interactions (B:HS, B:ΔP, HS:ΔP) were identified, with a significance level less than

0.05.


Table 4.11 Analysis of variance of calculated temperature difference

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 10.38 6.25 –

TD 2 1.24 0.74 –

Residuals 4 1.66

B 2 9139 4476.4 0.000

JL 3 0.86 0.42 –

B:JL 6 0.64 0.31 –


HS 1 704 478.2 0.000

ΔP 1 1485 1008.7 0.000

B:HS 2 71.3 48.4 0.000

B:ΔP 2 129 87.6 0.000

JL:HS 3 0.6 0.4 –

JL:ΔP 3 1.7 1.16 –

HS:ΔP 1 27.95 18.9 0.000

B:JL:HS 6 1.3 0.88 –

B:JL:ΔP 6 1.52 1.03 –

B:HS:ΔP 2 1.98 1.3 –

JL:HS:ΔP 3 0.77 0.52 –

B:JL:HS:ΔP 6 1.6 1.1 –

Residuals 288 1.47

Figure 4.7 shows the actual average temperature differences and Figure 4.8

shows the target temperature differences for the three brix. It is evident in most cases

the actual average temperature difference was in close agreement with the target

temperature difference.

For Brix-20, the actual temperature difference corresponding to the headspace

pressure of 149 kPa abs and pressure difference of 45 kPa was not achieved. However,

the actual average temperature difference is statistically different from the other three

temperature differences for Brix-20.


Figure 4.7 Actual average temperature differences for the three brix

Figure 4.8 Target temperature differences for the three brix



The operating conditions were selected to represent typical factory conditions

for a first, third and final effect in a quintuple evaporator set. It is concluded that the

experiment was well controlled and the few disparities between the target values and

the achieved values would not substantially influence the results. The achieved values

for the operating conditions are statistically different from each other.

4.8 The Effect of Tube Dimensions and Operating Conditions on Heat Flux

and Heat Transfer Coefficient


The experimental program was designed to induce a heat flux through the

imposed temperature difference between the heating steam and boiling juice for a

given brix and operating juice level. The HTC was then calculated based on the heat

flux, the heating surface area of the tube and the effective temperature difference (see

section 1.4.4). Four temperature differences were selected for each level of juice brix

as explained in section 4.3. This section describes the initial observations of the effects

of tube dimensions and operating conditions on the heat flux and the heat transfer

coefficient.

As described in section 1.4.4, the VCC and heat flux (Q/A) are closely related

as shown

Q

A=

VCC λs

3600

4.1

Thus, the only factor influencing the relationship is the change in latent heat λs

for the different steam chest pressures. Table 4.12 shows the conversion factor

between Q/A (kW/m2) and VCC (kg/h/m2).


Table 4.12 Conversions of heat flux to VCC for different calandria pressures

Calandria

pressure, kPa abs

Latent

heat, kJ/kg

To convert heat flux (kW/m2) to VCC

(kg/h/m2) multiply heat flux by the factor

194 2204.5 1.63

182 2210.0 1.63

171 2215.3 1.63

159 2221.4 1.62

144 2229.5 1.61

129 2238.3 1.61

122 2242.6 1.61

107 2252.6 1.60

89 2266.1 1.59

82 2271.9 1.58

71 2281.9 1.58

64 2288.8 1.57

4.8.2 Review of the experimental data

Appendix C presents the detailed experimental results from the Original432 tests

and Appendix D presents the results from the Replicate128 tests.

The data from the Original432 dataset are plotted as HTC versus heat flux for

each imposed temperature difference. The plots are arranged in groups of four for

each juice brix value and are shown in Figure 4.9, Figure 4.10 and Figure 4.11. Each

plot shows the results for the nine tubes and four juice levels. These data lie on a

straight line with slope equal to 1/∆T according to equation 1.1 in section 1.4.4. As

expected, the maximum HTC occurs for a series of tests at constant ∆T when the heat

flux is greatest, and likewise the minimum HTC occurs when the heat flux is lowest.


HS 149 kPa abs/DP 33 kPa/DeltaT 5.6

Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

L2L3L4M2M3M4 S2S3S4


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


heat transfer coefficient for tests at Brix-20


HS-94 kPa abs/DP-35 kPa/DeltaT-7.9

Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

L2

L3

L4

M2

M3

M4

S2

S3

S4





Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400

L2

L3

L4

M2

M3

M4

S2

S3

S4



The data in Figure 4.9, Figure 4.10 and Figure 4.11 show several important findings:

• For all tests except for the test at Brix-20 with set points of 149 kPa abs

for the headspace and pressure difference of 45 kPa, the data lie very

tightly on a straight line with slope at the target 1

∆T . Thus, for all tests

except the ones mentioned above, the process variables for the tests were

at the set points for the headspace pressure and the steam chest pressure.

For the test at Brix-20 with the headspace pressure of 149 kPa abs and

pressure difference of 45 kPa, the plot is not completely linear. The

explanation for this was given in section 4.7.2 on page 87, where the


target steam chest pressure of 194 kPa abs was not achieved for all tests

as the vapour supply pressure from the factory evaporator was often

slightly lower than 194 kPa abs;

• For tests at the same brix and headspace pressure operation with a larger

pressure difference (steam chest pressure to headspace pressure), this

results in a higher heat flux. There is one exception to this, which is for

M2 tube at Brix-70 for the lower head space pressure of 22 kPa abs. A

higher heat flux and HTC were obtained for this test at a pressure

difference of 42 kPa compared with a pressure difference of 60 kPa.

Investigations of the boiling conditions for the test at the lower pressure

difference show high VCC on the tube. A similar result is observed for

the Replicate128 data set3;

• For each juice brix, headspace pressure and pressure difference, for each

individual tube, there is an optimum juice level, which achieved the

maximum heat flux and HTC for that tube and processing conditions;

• For each set of operating conditions and for each tube operating at its

optimum juice level, each tube was able to achieve a certain peak value

of heat flux and HTC. Thus, for each set of conditions a specific tube

operating at its optimum juice level achieved the maximum heat flux and

maximum HTC for the imposed operating conditions; and

• The maximum HTC values are much greater for the tests at Brix-20

compared with Brix-35 and likewise for Brix-35 compared with Brix-70.

Figure 4.12, Figure 4.13 and Figure 4.14 show plots of HTC versus heat flux for

each of the test conditions at Brix-20, Brix-35 and Brix-70 respectively for the juice

level that provided the maximum HTC (and heat flux) for each of the nine tubes. These

figures show the maximum HTC and heat flux that was obtained for each tube at the

nominated processing conditions, and consequently show which tube provided the

highest heat flux and highest HTC for the imposed processing conditions.

3 The Original432 and Replicate128 tests for the M2 tube for Brix-70, HS pressure

22 kPa abs and pressure difference of 42 kPa showed similar results viz. low HTC

for juice levels of 30,, 55 and 70% of tube height and high HTC values for 45% juice

level. The HTC values for the Original432 and Replicate128 are shown in

Appendices C and D.


Table 4.13 lists the tubes in the order of highest HTC first to lowest HTC last,

for the tests at the three brix values. The HTC values for the three brix values are

further divided into two categories, being for Brix-20 by HTC values above or below

4000 W/m2/K; for Brix-35 by HTC values above or below 2500 W/m2/K; for Brix-70

by HTC values above or below 500 W/m2/K.


Heat flux (kW/m2)

0 5 10 15 20 25 30 35

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

L2

L3

L4

M2

M3

M4

S2

S3

S4


optimum juice level at Brix-20



Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000


Heat flux (kW/m2)

0 10 20 30 40 50

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

L2L3L4M2M3M4S2S3S4





Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400


Heat flux (kW/m2)

0 5 10 15 20 25 30

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

1200

1400

L2

L3

L4

M2

M3

M4

S2

S3

S4



The following general comments are made for the data in Table 4.13.

• For Brix-20, tubes of smaller diameter (38.1 mm and 44.45 mm)

provided higher HTC values. Tubes of 2, 3 and 4 m provided high HTC

values;

• For Brix-35, tubes of 3 and 4 m length provided higher HTC values.

Tubes of 44.45 mm diameter provided high HTC values;

• For Brix-70, tubes of 2 m length and larger diameter (44.45 and 50.8

mm) provided higher HTC values.


More detailed investigation of the heat flux and HTC data shown in Figure 4.9

to Figure 4.14 was undertaken and the results of these observations are shown in Table

4.14.

Table 4.13 List of tubes showing high and low HTC for corresponding brix and

temperature difference

Brix Test conditions Tubes

demonstrating good

HTC

Tubes

demonstrating poor

HTC

(>4000 W/m2/K) (<4000 W/m2/K)

20 HS:149/ΔP:33/DeltaT:5.6 L3, M2, S2, S4, L2,

M3, S3

L4, M4

HS:149/ΔP:45/DeltaT:7.7 S2, M2, M3, S4 S3, M4, L2, L3, L4

HS:126/ΔP:33/DeltaT:6.5 S2, M2, L2, S4, S3 M3, M4, L3, L4

HS:126/ΔP:45/DeltaT:8.7 S2, M3, S3, M4, S4 M2, L2, L3, L4

(>2500 W/m2/K) (<2500 W/m2/K)

35 HS:94/ΔP:35/DeltaT:7.9 S3, M3, M4, M2 S2, S4, L2, L3, L4

HS:94/ΔP:50/DeltaT:11.2 M3, S3 M4, L2, M2 S2, S4, L3, L4

HS:72/ΔP:35/DeltaT:9.8 L2, M4, M3 S2, S3, S4, M2, L3,

L4

HS:72/ΔP:50/DeltaT:13.5 M4 L2, L3, L4, M2, M3,

S2, S3, S4

(>500 W/m2/K) (<500 W/m2/K)

70 HS:29/ΔP:42/DeltaT:17.2 L2, M2, S3 S2, S4, M3, M4, L3,

L4

HS:29/ΔP:60/DeltaT:23.3 M2, L2, L3 S2, S3, S4, M3, M4,

L4

HS:22/ΔP:42/DeltaT:20.9 M2, L2, S2 S3, S4, M3, M4, L3,

L4

HS:22/ΔP:60/DeltaT:27.4 S2, L3 S3, S4, M2, M3, M4,

L2, L4


Table 4.14 Summary of the observations and comments for heat flux of three

brix

Juice

brix

Observation Comments

20 Largest heat flux (for the

optimum tube and juice level)

occurs at the largest imposed ∆T

–

The maximum HTC values for

the tests at the higher headspace

pressure are higher than for the

tests at the lower headspace

pressure.

The lower viscosity of the juice at

the higher boiling temperature is

most likely the cause of the

increased heat transfer.

The two series of trials at the

higher headspace pressure (149

kPa abs) produced similar

maximum values for HTC,

although these were at

substantially different heat flux

values.

It appears the juice boiling

temperature has a strong influence

in determining the HTC values.

For some tubes and test

conditions the juice level has a

strong influence on the heat flux

and the HTC.

–



occurs at the second largest

imposed ΔT and not the largest

∆T as for the tests at Brix-20.

The reason is attributed to boiling at

a higher temperature (greater

influence on juice viscosity) having

a strong influence on the heat

transfer efficiency and this effect

being greater than the effect of

larger ∆T.


the tests at the higher headspace

pressure are higher than for the

tests at the lower headspace

pressure.

This result is similar to that for juice

at Brix-20, and for the same

reasons.



kPa abs) produced reasonably

similar maximum values for

HTC, although the maximum

HTC at the lower ∆T was higher.

As for Brix-20 and Brix-70 it

appears the juice boiling

temperature has a strong influence

on the HTC values.


Juice

brix

Observation Comments



occurs at the second largest

imposed ΔT.

This result is similar to that observed

for juice at Brix-35 and is attributed to

boiling at a higher temperature (greater

influence on juice viscosity) having a

strong influence on the heat transfer

efficiency and this effect being greater

than the effect of larger ∆T.


the tests at the higher

headspace pressure are higher

than for the tests at the lower

headspace pressure*.

This result is similar to those observed

for juice at Brix-20 and Brix-35, and

for the same reasons.



kPa abs) produced similar

maximum values for HTC,

although these were at

substantially different heat

flux values.

As for Brix-20 and Brix-35 it appears

the juice boiling temperature has a

strong influence in determining the

HTC values.



strong influence on the heat

flux and the HTC.

This result is similar to that for the tests

at Brix-20 and Brix-35.



strong influence on the heat

flux and the HTC.

This result is similar to that for the tests

at Brix-20.

*This statement is based on the bulk of the data in Figure 4.11 and excludes the apparent exceptional value for M2 at

a headspace pressure of 22 kPa abs and pressure difference of 42 kPa.


Examination of the raw data plotted as HTC versus heat flux at the various

processing conditions has shown the following:-

• The processing conditions for a test involve setting the headspace

pressure, the steam chest pressure and the brix of the juice. For these

conditions a specific temperature difference (∆T) exists between the

steam side of the heating tube and the average boiling temperature of the

juice. For the imposed processing conditions each test on a specific tube

at a selected juice level results in a certain heat flux, from which the HTC

is calculated.


As expected from the calculation of HTC, a linear relationship exists

between HTC and the heat flux that is obtained for the imposed ∆T. The

slope of the plot of HTC versus heat flux is 1/∆T. Plots were prepared

for each set of processing conditions (single values of ∆T) and included

the HTC and heat flux results for the nine tubes and four juice levels. For

all tests apart from those requiring a steam chest pressure of 194 kPa abs,

the test conditions for headspace pressure and steam chest pressure were

at (or very close to) the nominated set point. For some tests at a

nominated steam chest of 194 kPa abs, only a slightly lower pressure was

able to be achieved.

• For each tube operating at a nominated processing condition an optimum

operating level for the juice in the heating tube exists, for which the HTC

and heat flux are maximised. For many tests, for the imposed ∆T, the

juice operating level has a strong effect on the achieved heat flux and

HTC.

• For tests at specific processing conditions (e.g. a certain juice brix,

headspace pressure and steam chest pressure):

o For each tube, at the imposed operating conditions an optimum

operating level for the juice in the heating tube exists, for which

the HTC and heat flux are maximised.

o Tubes of different dimensions experienced different levels of heat

flux and hence calculated HTC values for the imposed operating

conditions. Consequently, for a given set of processing

conditions, certain tubes provide a higher level of heat transfer

efficiency than other tubes. In general terms, observations on the

effects of tube dimensions on HTC are summarised in Table 4.15.


Table 4.15 General observations for tube dimensions that provided higher levels

of heat transfer coefficient for the three brix levels

Juice brix Favoured tube length, m Favoured tube diameter, mm

20 2, 3 and 4 38.1 and 44.45

35 3 and 4 44.45

70 2 44.45 and 50.8

• For tests at Brix-20 the maximum heat flux was obtained for the test at

the highest ∆T. This corresponded to the test at the lower headspace

pressure and larger pressure difference. However, for the tests at Brix-

35 and Brix-70, the maximum heat flux was at the higher headspace

pressure and larger pressure difference. This corresponded to the second

highest ∆T. The difference in these results is attributed to the stronger

dependence of HTC on juice viscosity at higher juice brix values.

Consequently, for the tests at Brix-35 and Brix-70, the effect of juice

boiling temperature on juice viscosity has a greater effect on heat flux

and the calculated HTC than the ∆T.

• For tests at Brix-20, Brix-35 and Brix-70 the maximum HTC was

obtained for the tests at the higher headspace pressure (i.e. higher boiling

temperature).


The experimental program was designed to investigate the effect of tube

dimensions and operating conditions on heat transfer performance of a single tube in

a rising film evaporator rig. The selection of the experimental factors, the design of the

experiments and the experimental procedure are explained in detail.

An analysis of potential errors was undertaken to ensure that the measured

condensate flow rates on the heating tube were reliable, before determining the heat

transfer coefficient and vapour condensation coefficient. A thorough investigation was

carried out to determine if there was any evidence that the high condensate flow rate

to the base of the steam chest was the result of condensate departing the heating tube

or overflowing gutters. The measured data were investigated from several approaches

to determine if such evidence existed. It was concluded that there was no evidence of


overflowing gutters or condensate separating from the heating tube and falling to the

base of the steam chest.

The most likely explanation for the high condensate flow to the base of the steam

chest was condensate entering with the vapour supply. Vapour entering the steam chest

is dispersed away from the heating tube and the associated condensate would not pass

near the surface of the heating tube.

As well, replicate tests showed very good consistency in the results for the

individual sections of the heating tubes. Consequently, the measured data on the

individual sections of the heating tube are considered to be reliable and suitable for

determination of the overall HTC and investigations of the mechanism of heat transfer

occurring at the individual sections of the heating tube.

An analysis of potential errors in the values of the operating conditions was

conducted. This analysis found that the values of the operating conditions utilised

during the test program were in close agreement with the target values. The analysis

demonstrated that the experimental program was well structured, and the operating

conditions were sufficiently different from each other to allow each factor an

opportunity to alter the heat transfer performance.

Analysis of Heat Transfer Coefficient Results 109

CHAPTER 5: ANALYSIS OF HEAT

TRANSFER COEFFICIENT

RESULTS

5.1 Introductory remarks

This section discusses in detail the HTC results from the experiments described

in Chapter 4. The preliminary assessment of the results in Chapter 4 demonstrated the

existence of an optimum juice level, which provided the maximum HTC value for a

given tube and operating conditions. For a given set of operating conditions, particular

tubes provided better heat transfer performance. In this chapter, the Replicate128

results are firstly compared with the Original432 results, in order to increase the

confidence in the Original432 dataset. The Original432 dataset are analysed in detail.

For both datasets, analysis of variance was undertaken with the two response factors

HTC and VCC. The optimum juice level (JLopt %) corresponding to the maximum

HTC value for a given set of conditions (HTCmax) was selected and this new response

factor analysed. Empirical models for HTCmax and JLopt(mm) were developed4. The

section concludes with identifying the tube dimensions that provide the strongest heat

transfer performance for different effect positions in a quintuple set.

Appendix C presents the detailed experimental results from the Original432 tests

and Appendix D presents the results from the Replicate128 tests. Appendix E provides

the results for the optimum juice level, HTCmax and VCCmax values for the Original432

datasets.

5.2 Features of the Pilot Evaporator Rig that may affect HTC Results

5.2.1 Influence of clean and new tubes

Industry experience has shown that brand new tubes have higher heat transfer

performance than tubes that have been in service for some time, even after cleaning.

Chemical cleaning of evaporators with caustic soda solution is commonly undertaken

4 JLopt (%) is the juice level expressed as % of the tube height whereas JLopt (mm) is the juice level

expressed absolute length (mm).

110 Analysis of Heat Transfer Coefficient Results

with reasonably good results, but the tubes are never entirely clean. The tubes

purchased for the pilot evaporator were brand new tubes and after each day of testing,

the evaporator was thoroughly boiled with water. It was expected that the calculated

heat transfer coefficients for the pilot evaporator would be higher than for industrial

evaporators, because of the extremely clean tube surface.

5.2.2 Effect of gutters on the tube

The tubes fabricated for the experimental investigations had gutters between the

four sections to allow the condensate flow of each section to be collected separately.

This arrangement changes the film thickness of the condensate when compared to a

tube of the same length without the gutters, such as for an industrial tube. Figure 5.1

shows the schematic representation of condensate pattern for tubes in the experimental

configuration and for industrial tubes.

Figure 5.1 Schematic representation of condensate pattern on the outside of the

heating tube for experimental and industrial arrangements

Industrial tube

condensate

collection Experimental Rig

tube condensate

collection

L

l


The average film thickness on an industrial tube would be thicker than on the

tube in the experimental rig for the same vapour condensation rate. The thinner

condensate film in the experimental rig will reduce the resistance to heat transfer on

the steam side and slightly enhance the overall heat transfer efficiency. However, the

effect is likely to be relatively small, as the resistance to heat transfer for the

condensate film is much lower than the thermal resistance on the juice side (Peacock,

2001).

5.2.3 Effect of the downtake

All tests were undertaken with the downtake line open. There was no facility for

measuring the flowrate of juice returning to the juice tank through the external

downtake.

As discussed in section 2.6.4, mini-downtakes in sugar mill evaporators reduce

the liquid head above the top tube plate and increase HTC (Watson, 1986b; Wright et

al., 2003). Industrial evaporators typically have one mini-downtake for ~400 tubes and

for a calandria comprising M2 heating tubes, the average distance from a heating tube

to the edge of the downtake is ~200 mm and the ratio of downtake cross-sectional area

to total heating tube cross-sectional area is 0.034. The pilot evaporator had one

downtake for one tube. For the M2 tube in the pilot evaporator, the distance from the

edge of the heating tube to the edge of the downtake is ~55 mm and the ratio of

downtake cross-sectional area to total heating tube cross-sectional area is 0.14. As a

consequence, it is likely that, compared with an industrial evaporator, a greater

proportion of the pool of juice above the top tube plate returned to the juice tank

through the downtake line, as opposed to running down inside the heating tube. These

changes are expected to have a positive effect on the heat transfer performance.

5.2.4 Comparison of industrial and pilot evaporator HTC values

In this section, the HTC results from the single-tube evaporator rig are compared

with industrial results. The Australian industry predominantly uses M2 tube dimension

for all stages of evaporation. Hence the HTC data for other tube dimensions for

industrial vessels are not readily available.

Figure 5.2 shows the industrial and pilot evaporator HTC values for the M2 tube

dimension. The industrial evaporator HTC values are acquired from Broadfoot (2013).


It is to be noted that the industrial HTC values are for different evaporator sets

operating under different conditions e.g. vapour bleeding schemes.

It is evident from Figure 5.2 that the pilot evaporator HTC values are slightly

higher than for the industrial vessels, especially for 1st effect conditions. For the 3rd

and 5th effect conditions, HTC values for both the pilot evaporator and industrial

vessels are in close proximity. Most importantly, the HTC values for both the

evaporators show the same trend with brix, temperature difference and juice

temperature.

Effect number

0 1 2 3 4 5 6

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Industrial

Pilot evaporator

Brix

10 20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Temperature difference (oC)

0 10 20 30 40 50 60 70

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Juice temperature (oC)

20 40 60 80 100 120 140

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Figure 5.2 Comparison of industrial and pilot evaporator HTC values for the

M2 tube dimension



The HTC results achieved with the single tube evaporator are expected to be

higher than those calculated in industrial evaporators owing to the positive effects on

heat transfer efficiency of using new tubes, removing condensate at four sections from

the tube, the closeness of the downtake and having a relatively larger cross-sectional

area of the downtake. Of these factors, it is likely that the closeness and larger relative

downtake area would affect the boiling mechanism inside the tube to the greatest

extent.

While the HTC and VCC results for the tube in the experimental rig are expected

to be greater than an industrial tube of the same dimensions operating under the same

processing conditions, the relative performance data of the tubes with different

dimensions are expected to be valid and transferrable to performance in industrial

evaporators.

5.3 Visual Observations of Boiling Patterns


The headspace of the single tube evaporator was fitted with a sight glass, which

allowed the movement of juice and froth above the top tube plate to be observed. In

industrial evaporators, the preferred boiling conditions generally show a vigorous

boiling juice and froth layer above the top plate for a height of 200 to 300 mm. The

boiling behaviours in the experimental rig were noted while conducting the

experiments and are presented in Appendix C. This section describes the three boiling

patterns observed.

5.3.2 No visible juice head above top plate

For a few tests, boiling juice was not evident above the top tube plate. This

behaviour was described as ‘no visible juice head’. Analysis of the data later confirmed

that for these tests, HTC was very low. One example where this behaviour was

observed was for Brix-70 juice in a 4 m tube with low ∆T.

5.3.3 Visible juice head above top plate

When the juice was consistently slightly above the top tube plate, this scenario

was described as ‘visible juice head’. Of the three boiling behaviours, this behaviour


was observed more frequently. When this behaviour was observed, good heat transfer

performance (high HTC) was generally calculated.

5.3.4 Substantial juice head above top plate

Where the juice was consistently boiling at a height of 50 mm to 250 mm above

the top tube plate, this behaviour was defined as ‘substantial juice head’. These tests

reported the highest HTC values and often included the tests at the optimum juice level

in the tube, which corresponds to maximum HTC.

5.4 Overview of the results

The results from the experimental investigation are summarised in this section.

The section provides an overview of the HTC results for all tube dimensions, for the

three brix levels, which are known to significantly affect HTC.

The average values of the overall HTC obtained for each tube for the three brix

values are shown in Table 5.1. The data show the usual trend observed in factory

evaporators, of higher HTC values at lower juice brix and much lower values at Brix-

70 (typical of the final factory evaporator). The values are of the same magnitude as

usually experienced in factory evaporators. However, it must be remembered that

these data include HTC values for operation with non-optimum juice levels and these

would depress the HTC below those normally encountered in industrial evaporators.

Table 5.1 Average values for overall HTC for all tube dimensions with Brix-20,

Brix-35 and Brix-70

Tube Brix-20

(W/m2/K)

Brix-35

(W/m2/K)

Brix-70

(W/m2/K)

S2 ~3000 ~700 ~200

S3 ~3500 ~2000 ~350

S4 ~3500 ~500 ~200

M2 ~3500 ~1700 ~400

M3 ~2500 ~1100 ~150

M4 ~3000 ~2200 ~250

L2 ~2500 ~1500 ~400

L3 ~2500 ~1000 ~200

L4 ~800 ~400 ~100


5.5 Comparison of Original432 and Replicate128 Results for the Overall HTC


As mentioned in section 4.3, the replicates were undertaken to determine if a

tube length and tube diameter interaction was significant and to check the consistency

of data from repeat tests. The replicate tests were undertaken for four tubes viz., M2,

S2, M3 and S3 at the boiling conditions for juice at Brix-20 and Brix-70. This section

compares the results from the Original432 and Replicate128 datasets.

The results for Brix-20 and Brix-70 are discussed below. For each tube, the

boiling tests were undertaken for two headspace pressures, two pressure differences

and four juice levels. For each plot shown below, these boiling conditions are shown,

as is the ∆T.

5.5.2 HTC vs juice level results for M2 tube

Figure 5.3 shows the HTC vs juice level plots for the M2 tube for the

Original432 and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns

of HTC versus juice level for each of the tests are similar.

Table 5.2 shows the comparison of the HTCmax and optimum juice level for the

Original432 and Replicate128 datasets for M2 tube. The juice levels corresponding to

the maximum HTC are similar for the two datasets. The maximum HTC values

however, are different for some tests for the two datasets. In most cases, the

Replicate128 dataset shows lower HTC than the Original432 dataset.

One item of rate in is the high HTC value of M2 tube at Brix-70 for juice level

of 45% compared with the other three juice levels for both the Original432 and

Replicate128 datasets. This high value was discussed in section 4.7.


Table 5.2 Comparison of data for Original432 and Replicate128 for M2 tube

Brix Headspace

Pressure

(kPa abs)

Pressure

difference

(kPa)

Temperature

difference

(°C)

Optimum juice

level (% tube

height)

HTCmax (W/m2/K)

Org432 Rep128 Org432 Rep128

20 149 33 5.6 40 40 5509 4958

149 45 7.7 40 40 5663 5097

126 33 6.5 30 30 4835 2655

126 45 8.6 30 50 2639 4506

70 29 42 17.6 45 45 625 548

29 60 23.6 30 30 557 546

22 42 22.2 45 45 934 878

22 60 28.8 70 70 478 821


Original (20 brix)

Juice level (%tube height)

15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

HS:149/DP:33/DT:5.6 oC

HS:149/DP:45/DT:7.7 oC

HS:126/DP:33/DT:6.5 oC

HS:126/DP:45/DT:8.6 oCReplicate (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

Original (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

HS:29/DP:42/DT:17.6 oC

HS:29/DP:60/DT:23.6 oC

HS:22/DP:42/DT:22.2 oC

HS:22/DP:60/DT:28.8 oC

Replicate (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Figure 5.3 Relationship between HTC and juice level for the M2 tube

5.5.3 HTC vs juice level results for S2 tube

Figure 5.4 shows the HTC vs juice level plots for the S2 tube for the Original432

and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns of HTC versus

juice level for each of the tests are similar.


Original432 and Replicate128 datasets for S2 tube. The juice levels corresponding to

the maximum HTC are similar for the two datasets. There is good agreement between


the values for the HTCmax and optimum juice level values for the Original432 and

Replicate128 datasets.

Table 5.3 Comparison of data for Original432 and Replicate128 for S2 tube

Brix Headspace

Pressure

(kPa abs)

Pressure

difference

(kPa)

Temperature

difference

(°C)

Juice level (%

tube height)

HTCmax (W/m2/K)


20 149 33 5.6 30 30 4661 4772

149 45 7.7 30 30 4152 4270

126 33 6.5 30 30 4938 5075

126 45 8.6 40 40 5225 5142

70 29 42 17.6 70 70 453 482

29 60 23.6 70 70 444 477

22 42 22.2 55 55 535 539

22 60 28.8 70 70 546 589


Original (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

HS:149/DP:33/DT:5.6 oC

HS:149/DP:45/DT:7.7 oC

HS:126/DP:33/DT:6.5 oC



20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

Original (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

HS:29/DP:42/DT:17.6 oC

HS:29/DP:60/DT:23.6 oC

HS:22/DP:42/DT:22.2 oC

HS:22/DP:60/DT:28.8 oC

Replicate (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Figure 5.4 Relationship between HTC and juice level for the S2 tube

5.5.4 HTC vs juice level results for M3 tube

Figure 5.5 shows the HTC vs juice level plots for the M3 tube for the

Original432 and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns

of HTC versus juice level for each of the tests are similar.


Original432 and Replicate128 datasets for M3 tube. There is good agreement between




Table 5.4 Comparison of Original432 and Replicate128 for M3 tube

Brix Headspace

Pressure

(kPa abs)

Pressure

difference

(kPa)

Temperature

difference

(°C)

Juice level (%

tube height)

HTCmax (W/m2/K)


20 149 33 5.6 30 30 4343 4227

149 45 7.7 30 30 4084 3971

126 33 6.5 50 50 3620 3529

126 45 8.6 30 30 4459 4335

70 29 42 17.6 70 70 454 431

29 60 23.6 70 70 337 320

22 42 22.2 45 45 197 217

22 60 28.8 45 45 231 254


Original (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

HS:149/DP:33/DT:5.6 oC

HS:149/DP:45/DT:7.7 oC

HS:126/DP:33/DT:6.5 oC

HS:126/DP:45/DT:8.6 oC Replicate (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

Original (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

HS:29/DP:42/DT:17.6 oC

HS:29/DP:60/DT:23.6 oC

HS:22/DP:42/DT:22.2 oC

HS:22/DP:60/DT:28.8 oC

Replicate (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Figure 5.5 Relationship between HTC and juice level for the M3 tube

5.5.5 HTC vs juice level results for S3 tube

Figure 5.6 shows the HTC vs juice level plots for the S3 tube for the Original432

and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns of HTC versus

juice level for each of the tests are similar.


Original432 and Replicate128 datasets for S3 tube. There is good agreement between




Table 5.5 Comparison of Original432 and Replicate128 for S3 tube

Brix Headspace

Pressure

(kPa abs)

Pressure

difference

(kPa)

Temperature

difference

(°C)

Juice level (%

tube height)

HTCmax (W/m2/K)


20 149 33 5.6 40 40 4221 4010

149 45 7.7 40 40 3749 3561

126 33 6.5 20 20 4133 3846

126 45 8.6 20 20 3867 3598

70 29 42 17.6 70 70 539 593

29 60 23.6 55 55 427 448

22 42 22.2 45 45 466 443

22 60 28.8 55 55 385 404


Original (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

HS:149/DP:33/DT:5.6 oC

HS:149/DP:45/DT:7.7 oC

HS:126/DP:33/DT:6.5 oC



20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

Original (70 brix)


20 30 40 50 60 70 80

HT

C (

W/m

2/K

)

0

200

400

600

800

1000

HS:29/DP:42/DT:17.6 oC

HS:29/DP:60/DT:23.6 oC

HS:22/DP:42/DT:22.2 oC

HS:22/DP:60/DT:28.8 oC

Replicate (20 brix)


15 20 25 30 35 40 45 50 55

HT

C (

W/m

2/K

)

0

1000

2000

3000

4000

5000

6000

Figure 5.6 Relationship between HTC and juice level for the S3 tube

Figure 5.3 to Figure 5.6 shows very strong replication of the profiles of HTC

versus juice level in the two datasets.

For many tests, the variation of HTC with juice level was not a consistent,

gradually changing variation, but often quite discontinuous. This result is unexpected

but interestingly, is replicated closely in the two datasets.


Two interesting observations are made:

• Brix-20 and M2 tubes: The general pattern is a faster decline in HTC at

juice levels below the optimum compared with juice levels above the

optimum. This pattern agrees with the observations of Broadfoot and

Dunn (2007) for their work on M2 tubes.

• Brix-20 and S2 tubes: The general pattern is a faster decline in HTC at

juice levels above the optimum compared with juice levels below the

optimum i.e. opposite behaviour than for the M2 tubes at Brix-20.

5.5.6 Concluding Remarks

Comparisons of the HTC versus juice level patterns for the Original432 and

Replicate128 datasets show very similar patterns for the four tables and test conditions

at Brix-20 and Brix-70.

The juice levels corresponding to the maximum HTC are the same for the two

datasets for the S2, M3 and S3 tubes and for all except one set of conditions for the

M2 tube. There is good agreement for the values of HTCmax between the two datasets

for S2, M3 and S3 tubes. For some unknown reasons, the HTCmax value for the M2

tube is more variable than for the S2, M3 and S3 tubes.

The good repeatability of the HTC patterns shown in replicate datasets increases

the confidence in the results obtained. The consistency of the results between the two

datasets suggests that juice properties, such as surface tension variation, were not

influencing the heat transfer performance and the boiling juice pattern to a large extent.

It is noted from the HTC versus juice level patterns that headspace pressure and

pressure difference (and corresponding ∆T) also affect the optimum juice level and the

maximum HTC. The effects of operating conditions on HTCmax and optimum juice

level are investigated further in the chapter.

5.6 Analysis of the Results of the Original432 Tests


This section describes the analysis of variance for the Original432 tests for HTC.

The section details the main effects and interactions affecting the HTC for the nine

tubes.


Figure 5.7 shows the mean values of HTC for each of the experimental factors

at each level. It was found that tube length and tube diameter alone do not affect the

HTC significantly. The most important factor affecting HTC was brix of the juice. As

expected from industrial experience, higher HTC was achieved at lower brix and HTC

was lower at higher brix.

Figure 5.7 Mean values of HTC for each level of each factor for the Original432

tests with all results included

Table 5.6 presents the analysis of variance of HTC. The ANOVA is undertaken

for split-split-plot design, with whole plot for tube dimensions, sub-plot for brix and

juice level and sub-sub-plot for headspace pressure and pressure difference. The same

procedure is applied for all ANOVA for all datasets. Significant interactions were

achieved up to 4th order. Two main factors (B, HS), three 2nd order interactions (B:HS,

TD:B, TD:JL), two 3rd order interaction (TL:TD:B, TL:TD:HS) and one 4th order

interaction (TL:TD:B:HS) were identified with a level of significance less than 0.05.

The lower order interaction identified as significant is included in the higher order

interaction.


Table 5.6 Analysis of variance of HTC from Original432 tests with 4th order

interactions

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 6562399 0.69 –

TD 2 21762038 2.28 –

Residuals 4 9548502

B 2 230647154 245.15 0.000

JL 3 2569618 2.73 –

TL:B 4 1868540 1.99 –

TL:JL 6 890671 0.95 –

TD:B 4 9562815 10.16 0.000

TD:JL 6 3354494 3.57 0.011

B:JL 6 2106656 2.24 –

TL:TD:B 8 3278353 3.48 0.008

TL:TD:JL 12 1005306 1.07 –

TL:B:JL 12 789134 0.84 –

TD:B:JL 12 1666036 1.77 –

Residuals 24 940844

HS 1 5271514 15.17 0.000

ΔP 1 264281 0.76 –

TL:HS 2 947255 2.73 –

TL:ΔP 2 65834 0.19 –

TD:HS 2 96601 0.28 –

TD:ΔP 2 96802 0.28 –

B:HS 2 3138628 9.03 0.000

B:ΔP 2 858313 2.47 –

JL:HS 3 273703 0.79 –

JL:ΔP 3 46677 0.13 –

HS:ΔP 1 46190 0.13 –

TL:TD:HS 4 1389868 4.00 0.004

TL:TD:ΔP 4 179391 0.52 –

TL:B:HS 4 564882 1.63 –

TL:B:ΔP 4 1091752 3.14 –

TL:JL:HS 6 748109 2.15 –

TL:JL:ΔP 6 166142 0.48 –

TL:HS:ΔP 2 832428 2.40 –

TD:B:HS 4 1148956 3.31 –

TD:B:ΔP 4 383181 1.10 –

TD:JL:HS 6 467756 1.35 –


Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:ΔP 6 187437 0.54 –

TD:HS:ΔP 2 281050 0.81 –

B:JL:HS 6 404672 1.16 –

B:JL:ΔP 6 74783 0.22 –

B:HS:ΔP 2 76723 0.22 –

JL:HS:ΔP 3 565762 1.63 –

TL:TD:B:HS 8 1172778 3.38 0.002

TL:TD:B:ΔP 8 298091 0.86 –

TL:TD:JL:HS 12 360754 1.04 –

TL:TD:JL:ΔP 12 164010 0.47 –

TL:TD:HS:ΔP 4 286797 0.83 –

TL:B:JL:HS 12 244066 0.70 –

TL:B:JL:ΔP 12 242668 0.70 –

TL:B:HS:ΔP 4 384196 1.11 –

TL:JL:HS:ΔP 6 96163 0.28 –

TD:B:JL:HS 12 320568 0.92 –

TD:B:JL:ΔP 12 258218 0.74 –

TD:B:HS:ΔP 4 455442 1.31 –

TD:JL:HS:ΔP 6 497655 1.43 –

B:JL:HS:ΔP 6 613441 1.77 –

Residuals 116 347431

5.6.2 TL:TD:B:HS interaction plot

Figure 5.8 presents the TL:TD:B:HS interaction plot. The headspace pressure

“HS1” represents boiling at higher headspace pressure and “HS2” represents boiling

at lower headspace pressure. The headspace pressures corresponding to the brix are

presented in Table 4.2, Table 4.3 and Table 4.4.


Figure 5.8 TL:TD:B:HS interaction plot for the Original432 dataset

It is observed from Figure 5.8 that higher brix results in lower HTC. It is known

that higher boiling temperature (higher headspace pressure) results in higher HTC

(Broadfoot & Dunn, 2007). The results from the Original432 dataset show that there

is an effect of headspace pressure on HTC, but the effect is not consistent through the

full dataset. The choice of headspace pressure values for the three brix values could be

the possible cause for the inconsistency.

Figure 5.9 shows TL:TD:B:HS interaction with the dataset split in brix values and

headspace pressure. The rows show the three brix values and the columns show the

two headspace pressure. The following conclusions are drawn from Figure 5.9:

• 2 m tube length, higher HTC was achieved at 44.45 mm OD




Figure 5.9 TL:TD:B:HS interaction plot for the Original432 dataset with

separate plots for brix and headspace pressure

5.6.3 TD:JL interaction plot

Figure 5.10 shows the TD:JL interaction plot. The four juice levels for the three

brix values were different. Given the inconsistency in the effect of headspace pressure,

it makes sense to look at the juice level effects for different brix.

Figure 5.11 shows the TD:JL interaction plot for each of the three brix values on

separate plots. It is observed that for Brix-20, the highest HTC is achieved at 30% juice

level for 38.1 and 44.45 mm tube diameter tubes. For 50.8 mm tube diameter, the

highest HTC is achieved at juice level of 40% tube height (10% higher than for 38.1

and 44.45 mm).

For Brix-35, juice level does not show a strong effect on HTC for 38.1 mm tube

diameter up to 45% juice level. There is drop in HTC for juice level higher than 45%.

The data for the 50.8 mm tube diameter tube show the highest HTC occurs at 35%

juice level. The 44.45 mm tube diameter shows the highest HTC at juice level of 60%

tube height.


For Brix-70, highest HTC is achieved at a juice level of 70% tube height for all

the tube diameters.

Figure 5.10 TD:JL interaction plot for the Original432 dataset

Figure 5.11 TD:JL interaction for the Original432 dataset with three separate

plots for brix



The analysis of variance of HTC for the Original432 dataset has been discussed

in this section. It was found that brix is the most dominating factor affecting HTC.

Tube length and tube diameter interaction was found to be significant. It was

concluded that for 2, 3 and 4 m tube length, 44.45, 38.1 and 44.45 mm tube diameters

respectively showed higher HTC than the other tube dimensions. The effects of juice

level and headspace pressure on HTC were not consistent amongst the dataset.

5.7 Analysis of HTCmax Results


For each brix, HTC was calculated at four juice levels, of which one juice level

was found to be the optimum juice level. This optimum juice level corresponds to

HTCmax. Two methods were used in determining the HTCmax. This section details the

methods used for determining HTCmax, the ANOVA and the significant interactions

for HTCmax for the Original432 and Replicate128 datasets.

5.7.2 Method for HTCmax selection

With Method 1, the HTCmax was selected by identifying the maximum HTC

value on the graphs. With Method 2, polynomial regressions were plotted with the

HTC and VCC against the juice level to identify the curve of the regression. The

polynomial regression was used to determine the HTC at juice level values not tested

(below 20% and above 70%). The results between both methods were similar. An

analysis of variance was undertaken to test the differences, and this showed the same

conclusion. Hence, Method 1 was selected in determining the HTCmax results.

5.7.3 HTCmax results

The HTCmax results are presented for the Original432 dataset. The Original432

dataset contains 108 HTCmax results. Figure 5.12 shows the mean values of HTCmax

for all the experimental factors at each level. It is evident from Figure 5.12 that brix

has the most significant effect on HTCmax.


Figure 5.12 Mean values of HTCmax for each level of each factor from the

Original432 tests (108 data points)

Table 5.7 shows the analysis of variance of HTCmax for the Original432 dataset.

Two main effects (B, HS) and one 3rd order interaction (TD:B:HS) were identified with

significance level less than 0.05.


Table 5.7 Analysis of variance of HTCmax from Original432 tests

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 7605799 4.31 –

TD 2 9027073 5.12 –

Residuals 4 1763889

B 2 96679890 62.58 0.000

TL:B 4 1356587 0.88 –

TD:B 4 3724704 2.41 –

Residuals 8 1544845 – –

HS 1 1284893 4.38 0.043

ΔP 1 794988 2.71 –

TL:HS 2 471666 1.61 –

TL:ΔP 2 132652 0.45 –

TD:HS 2 735357 2.51 –

TD:ΔP 2 29695 0.10 –

B:HS 2 774050 2.64 –

B:ΔP 2 442284 1.51 –

HS:ΔP 1 16133 0.05 –

TL:TD:HS 4 509971 1.74 –

TL:TD:ΔP 4 169562 0.58 –

TL:B:HS 4 222860 0.76 –

TL:B:ΔP 4 356036 1.21 –

TL:HS:ΔP 2 947662 3.23 –

TD:B:HS 4 1087098 3.70 0.013

TD:B:ΔP 4 263404 0.90 –

TD:HS:ΔP 2 31442 0.11 –

B:HS:ΔP 2 24413 0.08 –

Residuals 36 293421

Figure 5.13 presents the TD:B:HS interaction plot. For Brix-20 higher HTC is

achieved for tubes of 38.1 and 44.45 mm diameter. For Brix-35 and Brix-70, higher

HTCmax is achieved for tubes of 44.45 mm diameter.

For tubes of 38.1 mm OD, the headspace pressure has negligible influence on

the HTCmax whereas for the tubes of 44.45 mm and 50.8 mm OD, the higher headspace

pressure provides substantially higher values of HTCmax. The one exception to this is

the tube of 50.8 mm OD at 35 brix.


In the ANOVA for HTC with the Original432 dataset, TL;TD:B:HS interaction

was found to be significant. However, for the HTCmax tube diameter is identified to be

significant. This concludes that tube diameter is a more important dimension than tube

length in influencing HTCmax.

Figure 5.13 TD:B:HS interaction for HTCmax for the Original432 dataset


The HTCmax results are presented and the interactions of operating conditions on

HTCmax are discussed. It was concluded that higher brix results in lower HTCmax. Tube

diameter is more important than tube length in influencing HTCmax. For tubes of

38.1 mm diameter, headspace pressure has little influence on HTCmax. For tubes of

44.45 and 50.8 mm diameter, higher headspace pressure generally provides

substantially higher values of HTCmax.

5.8 Analysis of Optimum Juice Level


The operation of the evaporator with optimum juice level is imperative in order

to achieve maximum heat transfer performance. Sugar factory staff usually operates


the vessel with a certain dynamic head (juice level above the top tube plate) to ensure

that the tube is fully wetted. This does not necessarily mean that HTCmax is being

achieved. In setting this level, the actual optimum juice level may not be set, but it

ensures that the minimum requirement to fully wet the top of the tube is achieved.

This section describes the interaction of optimum juice level with tube

dimensions, headspace pressure and pressure difference.

5.8.2 Optimum juice level (JLopt(%)) for HTCmax

The optimum juice level corresponding to HTCmax is presented in Appendix E.

Figure 5.14 shows the mean values of the optimum juice level (% tube height) results

for the Original432 tests. It is observed that optimum juice level is lower for lower

brix and increases with increase in brix. This observation agrees closely with practical

experience with industrial Robert evaporators.

Figure 5.14 Mean values of JLopt(%) for each level of each factor from the

Original432 tests (108 data points)

Table 5.8 shows the analysis of variance of optimum juice levels corresponding

to HTCmax from the Original432 dataset. One main source (B), one 2nd order


interaction (TD:ΔP) and one 3rd order interaction (TL:B:HS) were identified with

significance level than 0.05.

Table 5.8 Analysis of variance of optimum juice level (JLopt-% tube height)

corresponding to HTCmax from the Original432 tests

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 41.89 0.26 –

TD 2 46.06 0.28 –

Residuals 4 163.77

B 2 5381.48 18.27 0.001

TL:B 4 110.65 0.38 –

TD:B 4 587.73 2.00 –


HS 1 75 0.84 –

ΔP 1 237.03 2.66 –

TL:HS 2 4.86 0.05 –

TL:ΔP 2 100.23 1.13 –

TD:HS 2 0.69 0.01 –

TD:ΔP 2 321.06 3.60 0.037

B:HS 2 202.77 2.28 –

B:ΔP 2 195.37 2.19 –

HS:ΔP 1 0.92 0.01 –

TL:TD:HS 4 173.26 1.95 –

TL:TD:ΔP 4 24.88 0.28 –

TL:B:HS 4 284.72 3.20 0.024

TL:B:ΔP 4 46.06 0.52 –

TL:HS:ΔP 2 264.12 2.97 –

TD:B:HS 4 190.97 2.14 –

TD:B:ΔP 4 52.31 0.59 –

TD:HS:ΔP 2 143.28 1.61 –

B:HS:ΔP 2 250.92 2.82 –

Residuals 36 89.07

Figure 5.15 shows the TL:B:HS interaction plot for optimum juice level. It is

observed that tube length and headspace pressure do not show consistency in the

results. Hence the effect of tube length and headspace pressure on optimum juice level

is not completely clear.


Figure 5.15 TL:B:HS interaction plot for the optimum juice level in the

Original432 dataset

Figure 5.16 shows the TD:ΔP interaction plot. At higher pressure differences,

optimum juice level was higher for 38.1 and 50.8 mm tube diameters. However, for

44.45 mm tube diameter, higher pressure difference resulted in lower optimum juice

level. This result is in agreement with factory experience with calandrias of 44.45 mm

tube diameter.

Figure 5.17 shows the TD:ΔP interaction plot with three separate plots for brix. The

data in Figure 5.17 show the following:

For 38.1 mm tube diameter;

• Pressure difference has no effect on optimum juice level at Brix-20

• Optimum juice level increases with increase in pressure difference at Brix-

35 and Brix-70


• Optimum juice level decreases with increase in pressure difference for Brix-

20 and Brix-70


• Optimum juice increases slightly with increase in pressure difference for

Brix-35


• For all three brix values, optimum juice level increases with increase in

pressure difference.

The reason for the variability in the effect of pressure difference for the different

tube diameters and different juice brix values is not known. However, the effect of

juice level when nominated in terms of the absolute level (in mm) shows a more

consistent pattern of lower optimum juice level for higher pressure difference.

Figure 5.16 TD:ΔP interaction plot for the optimum juice level in the

Original432 dataset


Figure 5.17 TD:ΔP interaction plot for Original432 dataset for three separate

plots for brix


The optimum juice level (as % of tube height) corresponding to maximum HTC

was analysed. It was found that juice at higher brix required higher optimum juice

levels. The effect of tube length and headspace pressure on optimum juice level was

not consistent across the full dataset. It was found that in general, for tubes of 38.1 and

50.8 mm diameter, the optimum juice level increases with increases in pressure

difference while for 44.45 mm tube diameter, optimum juice level decreases with

increase in pressure difference. Among these results there was some variability in the

effect for the different brix values.

5.9 Developing Empirical Relationships


Empirical relationships for HTC and optimum juice level were developed by

previous investigators. The relationships have been discussed in section 2.6. This

section describes the empirical relationships developed for HTCmax and optimum juice

level from the Original432 dataset.


5.9.2 Empirical relationship for HTCmax

An empirical relationship for HTCmax was developed that takes into account

different processing conditions, allowing more reliable simulations of evaporator

stations for energy efficient scenarios to be undertaken. It is to be noted that some

HTCmax results were omitted from the data to develop a regression model valid over a

wide range of operating conditions. For example, HTCmax results of L4 tube were

below average (very poor) for Brix-20 tests. Inclusion of these results would result in

poor regression and lessen the applicability of the regression to industrial scenarios.

Hence these results were not included in the regression model. Table 5.9 shows the list

of parameters considered in the step-wise regression of the model.

Table 5.9 List of parameters considered for inclusion in the empirical model

List of parameters Symbol

Tube length (mm) TL

Tube diameter (mm) TD

Brix B

Headspace pressure (kPa abs) HS

Pressure difference (kPa) ΔP

Tube length × Tube diameter TL:TD

Tube length × Brix TL:B

Tube length × Headspace pressure TL:HS

Tube length × Pressure difference TL:ΔP

Tube diameter × Brix TD:B

Tube diameter × Headspace pressure TD:HS

Tube diameter × Pressure difference TD:ΔP

Brix × Headspace pressure B:HS

Brix × Pressure difference B:ΔP

Headspace pressure × Pressure difference HS:ΔP

Latent heat of steam (kJ/kg) 𝜆𝑆

Temperature of steam (°C) TS

Temperature of juice (°C) TJ

Viscosity of juice (Pa.s) 𝜇

Temperature difference (°C) ΔT

Vapour condensation coefficient (kg/h/m2) VCC


Step-wise regression was undertaken to determine the parameters in the

empirical model. The best empirical relationship for HTCmax was found to be:

𝐻𝑇𝐶𝑚𝑎𝑥 = 𝐵−0.4901 𝑇𝑗1.3582 𝑉𝐶𝐶0.8877 5.1

where 𝐵 is the brix of the juice,

𝑇𝑗 is the temperature of the juice, °C

𝑉𝐶𝐶 is the vapour condensation coefficient, kg/h/m2

It is important to understand the significance of each of the parameters in the

equation when developing an empirical relationship. As mentioned in section 5.7.3,

brix is the most dominating factor affecting HTCmax followed by headspace pressure.

The temperature of the juice is a function of the headspace pressure in the vessel. As

vapour bleeding changes, VCC values of the effects change and the developed

equation takes this into account when predicting the HTC of the effect. The analysis

of variance of the regression model is shown in Table 5.10.

Figure 5.18 shows the measured and predicted HTCmax. The predictions from the

empirical model provide a good match with measured HTCmax (R2 = 0.94) and are in

agreement with industry values.

Measured HTCmax

(W/m2/K)

0 2000 4000 6000

Pre

dic

ted H

TC

max

(W

/m2/K

)

0

2000

4000

6000

Figure 5.18 Measured and predicted HTCmax


Table 5.10 Analysis of variance of regression model for HTCmax

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

B 1 869 109278 0.000

Tj 1 71.26 8959 0.000

VCC 1 2.66 334 0.000

Residuals 89 0.008

It is evident from equation 5.1 that as brix increases, HTCmax decreases and as

temperature of juice and VCC increase, HTCmax increases. Table 5.11 shows examples

of the typical operating conditions in factory vessels and the predicted empirical

HTCmax from two models viz. (Equation 5.1 and Australian Typ as discussed in section

2.6.7 on page 43). The ‘AusTyp’ formula is extensively used for predicting HTC when

undertaking evaporator simulations. The ‘AusTyp’ does not contain the VCC

parameter and shows higher HTC than ‘Equation 5.1’ correlation.

The incorporation of VCC into equation 5.1 is an important inclusion in the

correlation to allow improved simulations of evaporator stations, which incorporate

extensive bleeding of vapour (i.e. for stations that often experience very low VCC

values).



HTCmax from two models

Brix Temperature of

juice (°C)

VCC (kg/h/m2) HTCmax (W/m2/K)

Equation

5.1

AusTyp

17 115 25 2734 3086

20 115 25 2524 2918

25 115 25 2263 2690

17 110 20 2111 2949

17 110 25 2574 2949

17 110 35 3469 2949

17 110 40 3906 2949

35 105 25 1696 2134

35 100 25 1587 2031

35 95 25 1480 1928

35 100 15 1008 2031

35 100 20 1302 2031

35 100 25 1587 2031

70 60 10 250 733

70 60 15 359 733

70 60 20 463 733

65 60 15 372 805

70 65 15 400 795

70 75 15 486 920

5.9.3 Empirical relationship for optimum juice level (JLopt(mm))

As expected from the assessments of the factors influencing the optimum juice

level (section 5.8.2), the development of a satisfactory empirical relationship for

optimum juice level was difficult. Developing an empirical relationship for juice level

(% tube height) did not give a robust correlation and the model either over-predicted

or under-predicted optimum juice level. However, the empirical relationship

developed with absolute juice level (mm) resulted in a better correlation. The list of

parameters shown in Table 5.9 was considered for inclusion in the model.

Step-wise regression was undertaken to determine the parameters in the

empirical model. The best empirical relationship for optimum juice level (𝐽𝐿𝑜𝑝𝑡 mm)

is given by:

𝐽𝐿𝑜𝑝𝑡 (𝑚𝑚) = 𝑇𝐿0.7253 𝐵0.4544 ΔT−0.1122 5.2


where 𝑇𝐿 is the tube length, mm

𝐵 is the brix of the juice,

ΔT is the temperature difference between the steam and juice, °C

Figure 5.19 shows the predicted and measured values of JLopt (mm). The data

are differentiated for tubes of 2, 3 and 4 m lengths. The correlation coefficient R2 for

the match of the predicted values is 0.61. The R2 values for 2, 3 and 4 m tube length

are 0.31, 0.36 and 0.39 respectively.

Measured optimum juice level (mm)

0 500 1000 1500 2000 2500 3000

Pre

dic

ted o

ptim

um j

uice

leve

l (m

m)

0

500

1000

1500

2000

2500

3000

Tube length - 2 m

Tube length - 3 m

Tube length - 4 m

Figure 5.19 Measured and predicted optimum juice level

Table 5.12 shows the typical operating conditions in factory vessels and the

predicted optimum juice levels (absolute and %tube height). The predictions for tube

length of 2 m are above the accepted values in the Australian industry but are still in

range. The predictions are in agreement with observations in industrial evaporators.

For example, operation at a higher juice brix given a higher juice level and operation

at a higher temperature difference gives a slightly lower optimum juice level.


It is noted that the correlation incorporates a tube length term, such that for

longer tubes the optimum juice level (mm) is higher. This result is logical.


optimum juice levels (absolute and % tube height)

Tube

length (m)

Brix ΔT

(°C)

Optimum juice

level (mm)

Optimum juice level (%

tube height)

2000 20 5 807 40

2000 35 6 1020 51

2000 20 7 777 39

2000 35 7 1002 50

2000 70 20 1221 61

2000 70 12 1293 65

3000 70 20 1638 55

3000 70 12 1735 58

3000 15 5 950 32

3000 20 6 1061 35

3000 20 7 1043 35

3000 35 8 1325 44

4000 15 5 1171 29

4000 35 8 1633 41

Despite the confounding results from the analysis for optimum juice level (mm)

in section 5.8.2, the correlation for optimum juice level (mm) has provided

dependencies for brix and ΔT that are in general agreement with the expression in

industrial evaporators with M2 tubes.


The empirical equation developed for HTCmax is valid for different tube

dimensions (S2, S3, S4, M2, M3, M4, L2 and L3) over a wide range of operating

conditions. The HTCmax correlation is shown to be a function of brix, juice temperature

and VCC. The predicted HTCmax values are in close agreement to the measured

HTCmax values. The predicted HTCmax values for M2 tubes are in general agreement

with HTCmax values for industrial evaporators with M2 tubes.

An empirical model for optimum juice level (mm) was developed. The optimum

juice level is a function of tube length, brix and temperature difference. The optimum

juice level increases with increase in tube length and brix and decreases with increase


in temperature difference. The predictions for optimum juice level are also in general

agreement with the experience with industrial evaporators with M2 tubes.


In this study, an experimental investigation was undertaken to determine the

HTC of different tube lengths and diameters (nine tubes) for different operating

conditions corresponding to those typically experienced at the 1st, 3rd and 5theffects.

Replicates were undertaken for four tubes to understand the tube length and tube

diameter interaction and to determine the consistency in the results.

The replicate HTC results showed very good agreement with the original results,

thus providing confidence in the data for which replicates were not undertaken.

Analysis of the HTC results from the Original432 dataset showed the tube length

and tube diameter interaction to be significant. In other words, the selection of tube

length and tube diameter is not independent of each other in relation to achieving good

heat transfer performance. This result confirms the conclusion made by Hugot and

Jenkins (1986). The replicate analysis confirmed the result. It was concluded that as

brix increases, HTC decreases. For 2, 3 and 4 m tube lengths, tube diameters of 44.45,

38.1 and 44.45 mm respectively gave higher HTC values. The effects of juice level,

headspace pressure and pressure difference on HTC were not consistent through the

complete dataset, although the results indicate that juice level and headspace pressure

influence the HTC.

For many tests, the variation of HTC with juice level was not a consistent,

gradually changing variation, but often quite discontinuous. This result is unexpected

but interestingly replicated closely in the two datasets.

Two interesting observations are made:

• Brix-20 and M2 tubes: The general pattern is a faster decline in HTC at juice

levels below the optimum compared with juice levels above the optimum;

• Brix-20 and S2 tubes: The general pattern is a faster decline in HTC at juice

levels above the optimum compared with juice levels below the optimum i.e.

opposite behaviour than for the M2 tubes at Brix-20.

HTCmax results were determined from the Originla432 dataset. It was concluded

that tube diameter is more important than tube length in affecting HTCmax. This result


contradicts the statement by Hugot and Jenkins (1986). As brix increases, HTCmax

decreases. For Brix-20, higher HTCmax is achieved for tubes of 38.1 and 44.45 mm

diameter. For Brix-35 and Brix-70, higher HTCmax is achieved for tubes of 44.45 mm

tube diameter. For tubes of 38.1 mm diameter, headspace pressure has little influence

on HTCmax. For tubes of 44.45 and 50.8 mm diameter, higher headspace pressure

generally results in substantially higher values of HTCmax.

Analysis of optimum juice level corresponding to HTCmax showed that as brix

increases, optimum juice level increases. The effect of tube length and headspace

pressure on optimum juice level was not completely clear. There was also large

variability in the effect of pressure difference on the optimum juice level for the

different tube diameters and the different juice brix.

Empirical relationships were developed for HTCmax and optimum juice level

(mm). The empirical relationship for HTCmax showed good agreement with measured

result and industry values for M2 evaporators. The empirical relationship for optimum

juice level showed satisfactory agreement with measured results and the trend of the

predictions from the model was in agreement with industry practice for M2

evaporators.

The analysis of HTCmax assisted in understanding the effect of tube dimensions

and operating conditions on HTCmax. The selection of optimum tube dimensions for

maximum heat transfer coefficient is detailed in Chapter 7. However, it is interesting

enough to state here that the traditional tube dimension M2 was determined to provide

good heat transfer performance for the three effect positions.

Boiling Patterns in the Heating Tube 149

CHAPTER 6: BOILING PATTERNS IN

THE HEATING TUBE


In Chapter 5, the heat transfer coefficients of the tubes of different lengths and

diameter were analysed. The effects of tube length, tube diameter, juice brix, juice

level, headspace pressure and pressure difference, along with the interaction of these

parameters on HTC, were discussed. It was determined that an optimum juice level

exists, which corresponds to the maximum HTC for each set of test conditions.

The HTCmax results differ with tube length, tube diameter, headspace pressure

and pressure difference for a given juice brix. In order to understand the influence of

operating conditions on the HTCmax results, the HTC values of the individual sections

of the heating tube were investigated in this chapter. This chapter describes the

different patterns of HTC values for the individual sections of the heating tubes and

proposes different boiling mechanisms that may be associated with those HTC

patterns. For example, a test may show low HTC at the bottom section of the tube

while the rest of the tube was boiling with a higher HTC, say close to the overall HTC.

The HTC pattern may provide an insight into the boiling pattern inside the tube.

The variations of the HTC results for the different tube sections and the possible

boiling patterns were examined through a staged process:-

1. The consistency of the HTC patterns was examined by analysing the

results for the corresponding tests in the Original432 and Replicate128

datasets.

2. Identification of the HTC patterns that existed and determination of

which patterns were more common, and under which test conditions.

3. Qualitative determination of the factors influencing the boiling patterns.

4. Analysis of variance of the HTC and HTCmax for the individual sections

of the tubes.

150 Boiling Patterns in the Heating Tube

5. Determination of the predominant boiling pattern when HTCmax values

were achieved and the influence that the various factors have at these

conditions.

6. Postulation of the boiling mechanism in the tube corresponding to the

different HTC patterns.

7. Determination of the boiling patterns in the tube that provides superior

heat transfer performance.

Appendix F presents the HTC results and Appendix G the VCC results for the

individual sections of the tubes for the Original432 dataset. Corresponding results for

the Replicate128 dataset are given in Appendix H and I.

6.2 Comparison of Replicate Results with Original Results for the Section

HTCs


In section 5.5, the Replicate128 test results were compared with the Original432

test results. It was found that the overall HTC vs juice level trends for both datasets

were similar. These results very likely indicate that the boiling behaviour inside the

tube was similar for the two datasets at the same test conditions. However, this

assumption needs to be checked by comparing the HTC values for the individual

sections of tubes in the Original432 and Replicate128 datasets.

For each test, the difference between the overall HTC for the whole tube and the

HTC value for each individual section was calculated and allocated to one of three

categories, as shown in Table 6.1. A colour code and number code were assigned to

each category to facilitate the analyses of the data. The 15% variation from the overall

HTC value, which was chosen to define the category, was selected based on the

average error of HTC for 20 Brix, 35 Brix and 70 Brix juice tests. The error was

calculated from the square root of the mean square of the residuals in Table 5.6 and

the highest average HTC from Table 5.1. Section 1 is the top part of the heating tube

and Section 4 is the bottom part of the heating tube.


Table 6.1 Categories to define differences between the individual section HTC

values and the overall HTC

Factor Higher (>15%

above overall

HTC)

Lower (>15%

below overall

HTC)

Within (15% of

overall HTC)

Colour

Number +1 -1 0

6.2.2 Comparison of the HTC results for individual tube sections for Brix-20 tests

The individual HTC results for tests of four different tubes (M2, S2, M3, S3)

from the Original432 and Replicate128 datasets were assigned to the categories of

Table 6.1. These results are shown in Table 6.2, Table 6.3, Table 6.4 and Table 6.5 for

M2, S2, M3 and S3 tubes respectively for the Brix-20 juice tests. The operating

conditions for each test number shown in the tables are detailed in Appendix C and

Appendix D.

Comparison of the HTC patterns for the Original432 and Replicate128 data for

the same test conditions allows the consistency of the boiling behaviour for each test

to be determined. In each table, the percentages of results lying in each of the three

categories are shown.

For each test at the same operating conditions, the HTC values for each tube

section for the Original432 and Replicate128 datasets were assigned to one of the

categories defined in Table 6.1. If the individual section of the tube had the same

boiling category for the Original432 and Replicate128 datasets, then consistency was

good. If the individual section had boiling category one level apart (either from 0 to 1,

1 to 0, 0 to -1 and -1 to 0), consistency was assumed to be satisfactory. If the individual

section had boiling category two levels apart (either from -1 to 1 or 1 to -1) consistency

was assumed to be poor.

This analysis allowed the consistency of the individual HTC values, relative to

the overall HTC values, to be compared.

Table 6.6 summarises the results from the Brix-20 juice tests for M2, S2, M3,

and S3 tubes (based on the data in Table 6.2, Table 6.3, Table 6.4 and Table 6.5).


Table 6.2 Individual section HTC comparison with M2 tubes for Brix-20 juice

Test Original432 Replicate128 Test Section

1

Section

2

Section

3

Section

4

Section

1

Section

2

Section

3

Section

4

241 -1 0 1 0 -1 0 1 0 5

242 -1 -1 1 1 -1 -1 1 1 7

243 0 0 1 0 0 0 1 0 6

244 0 -1 0 1 0 -1 0 1 8

277 1 -1 -1 -1 1 -1 -1 -1 25

279 0 0 0 0 0 0 0 0 27

278 0 1 0 -1 0 1 0 -1 26

280 -1 0 0 1 -1 0 0 1 28

260 0 0 0 0 0 0 0 0 9

259 0 0 0 0 0 0 0 0 10

258 0 0 0 0 0 0 0 0 11

257 -1 -1 1 1 -1 -1 1 1 12

284 0 0 0 0 -1 -1 0 1 1

281 0 0 0 0 -1 0 0 1 3

283 -1 0 1 0 -1 0 1 1 2

282 -1 0 0 1 -1 -1 0 1 4 Category Comparison of results (%)

Individual section HTC in same zone 89 Individual section HTC one zone apart 11

Individual section HTC two zones apart 0

Table 6.3 Individual section HTC comparison with S2 tubes for Brix-20 juice


1

Section

2

Section

3

Section

4

Section

1

Section

2

Section

3

Section

4

230 -1 -1 -1 1 -1 -1 -1 1 37

231 -1 -1 0 1 -1 -1 0 1 38

232 -1 1 -1 0 -1 1 -1 0 40

219 0 -1 0 1 0 -1 0 1 39

218 0 1 -1 0 0 1 -1 0 57

217 0 1 -1 0 0 1 -1 0 59

220 0 1 -1 0 0 1 -1 0 58

215 -1 0 0 1 -1 0 0 1 60

213 1 0 -1 1 1 0 -1 1 33

214 -1 0 -1 1 -1 0 -1 1 35

216 0 1 -1 0 0 1 -1 0 34

194 0 0 0 0 0 0 0 0 36

193 -1 0 0 1 -1 0 0 1 63

196 -1 -1 -1 1 -1 -1 -1 1 62

195 -1 1 0 0 -1 1 0 0 64

239 -1 -1 0 1 -1 -1 0 1 61 Category Comparison of results (%)




Table 6.4 Individual section HTC comparison with M3 tube for Brix-20 juice


1

Section

2

Section

3

Section

4

Section

1

Section

2

Section

3

Section

4

121 -1 1 -1 1 -1 1 -1 1 69

122 -1 -1 -1 1 -1 -1 -1 1 70

124 -1 -1 1 1 -1 -1 1 1 72

123 -1 -1 1 1 -1 -1 1 1 71

102 1 1 0 -1 1 1 0 -1 89

104 0 0 0 -1 0 0 0 -1 91

101 0 1 0 -1 0 1 0 -1 90

103 0 0 0 -1 0 0 0 -1 92

118 -1 0 1 1 -1 0 1 1 65

120 -1 0 -1 1 -1 0 -1 1 67

117 -1 -1 1 1 -1 -1 1 1 66

119 -1 -1 0 1 -1 -1 0 1 68

100 1 1 -1 -1 1 1 -1 -1 95

98 1 1 0 -1 1 1 0 -1 94

97 0 1 0 -1 0 1 0 -1 96

99 0 0 0 -1 0 0 0 -1 93 Category Comparison of results (%)



Table 6.5 Individual section HTC comparison with S3 tube for Brix-20 juice



1

Section

2

Section

3

Section

4

Section

1

Section

2

Section

3

Section

4

80 1 0 -1 0 1 0 -1 0 101

79 1 0 -1 0 1 0 -1 0 102

77 0 1 0 -1 0 1 0 -1 104

78 0 0 0 -1 0 0 0 -1 103

93 0 1 -1 0 0 1 -1 0 121

96 0 1 -1 0 0 1 -1 0 123

95 1 1 -1 -1 1 1 -1 -1 122

94 1 1 -1 -1 1 1 -1 -1 124

74 0 1 -1 0 0 1 -1 0 97

73 1 1 -1 -1 1 1 -1 -1 99

76 1 1 -1 -1 1 1 -1 -1 98

75 1 1 0 -1 1 1 0 -1 100

51 1 1 0 -1 1 1 0 -1 127

52 1 1 -1 -1 1 1 -1 -1 126

49 1 1 -1 -1 1 1 -1 -1 128

50 0 0 1 -1 0 0 1 -1 125 Category Comparison of results (%)




Original432 and Replicate128 datasets for the four tubes for Brix-20 tests

Tube Percentage of data for individual section HTC values

In the same

category

One category

apart

Two categories

apart

M2 89 11 0

S2 100 0 0

M3 100 0 0

S3 100 0 0

Average across all

tubes

97 3 0

Analysis of the two datasets showed that 97% of the results had similar

individual section HTC values relative to the overall HTC. Only 3% of results were

found to have individual section HTC values at categories one level apart and no tests

showed a section of the tube that was two categories apart.

Overall it was concluded for the trials with these four tubes with Brix-20 juice

that the HTC patterns along the length of the tubes were very similar. This result most


likely indicates that the boiling behaviour in the tubes was also consistent between the

Original432 and Replicate128 datasets for tests at the same operating conditions.

6.2.3 Comparison of the HTC results for individual tube sections for Brix-70 tests

Appendix K contains tables that compare the HTC patterns for M2, S2, M3 and

S3 tubes for tests with Brix-70 juice. Table 6.7 summarises the results to compare the

HTC values for the individual tube sections for the Brix-70 juice tests for M2, S2, M3

and S3 tubes. Analysis of the two datasets showed that 57% of the individual section

HTC values belonged to the same category. Of the remainder, 28% of the individual

HTC values were found at categories one level apart and 15% of the dataset two levels

apart.

Obviously, the HTC patterns for the tests on the four tubes with Brix-70 juice

were not as consistent between the Original432 and Replicate128 datasets as for the

tests with Brix-20 juice.


Original432 and Replicate128 datasets for M2, S2, M3 and S3 tubes for Brix-70

tests

Tube Percentage of data for individual section HTC values

In the same

category

One category

apart

Two categories

apart

M2 58 34 8

S2 63 28 9

M3 61 20 19

S3 47 28 25

Average across all

tubes

57 28 15

The data in Table 6.7 with Brix-70 juice do not show that any of the four tubes

provided a markedly greater level of consistency or inconsistency.


The HTC of the individual sections of the four tubes in the replicate dataset were

compared to the HTC of the individual sections from the corresponding original

dataset.

Tests with Brix-20 juice demonstrated a high level of consistency in the results

for the two series of tests. The results showed 97% of the individual section HTC


values in the two datasets were within 15% of each other. No test conditions produced

HTC values for an individual section of tube, two categories apart.

Tests with Brix-70 juice showed a much lower level of consistency; only 56%

of the individual sections HTC values were within 15% of each other. Of the

remainder of the tests, 15% of the individual sections of tube produced HTC values

two categories apart.

The reason for the Brix-70 tests demonstrating a much lower level of consistency

in HTC for the individual sections between the Original432 and Replicate128 datasets

is not known. The conclusions in section 5.5.6 on page 124, demonstrate that the juice

properties, such as surface tension, were not affecting the overall HTC values for the

whole tube. It may be that variations in juice properties such as surface tension had a

greater influence on the boiling behaviour in industrial sections for juice at Brix-70

than for juice at Brix-20. Also, as shown in the test data (see section 4.7.2), the

variation in brix among the Brix-70 juice tests was greater than the variation in brix

among the Brix-20 juice tests. The effect of the variation in brix on HTC was

proportionally much greater for the Brix-70 juice tests than for the Brix-70 juice tests.

6.3 Identification of Boiling Patterns


It is evident from Table 6.2 to Table 6.5 and the tables in Appendix K that the

patterns defining the variation of HTC among the individual sections of the tubes are

different for the different operating conditions. The different HTC for the different

tube sections indicates that different boiling patterns were present for the different test

conditions. This section categorises the boiling patterns observed for the Original432

and Replicate128 datasets.

6.3.2 Boiling patterns

Six boiling patterns were identified in the Original432 and Replicate128 datasets

and these patterns are presented in Table 6.8. Of the six boiling patterns, one has HTC

values for all four sections of the tube within 15% of the overall HTC value–designated

Uniform Boiling. For the other five boiling patterns, a low HTC region exists at some

part of the tube while the rest of the tube is boiling within or higher than 15% of the

overall HTC. Appendices L, M, N and O present the data for the two datasets for

Uniform boiling, Non-uniform boiling–low HTC at top; Non-uniform boiling–low


HTC at bottom; Non-uniform boiling–low HTC at an intermediate section

respectively. Table 6.9 shows the percentage of the tests in the Original432 and

Replicate128 datasets that aligned with the different boiling patterns.

As shown in Table 6.9, four of the boiling patterns represent more than 10% of

the data.

Table 6.8 Categorisation and description of the boiling patterns

Category of HTC pattern Description of category

Uniform boiling along the

tube

HTC of all the four sections of the tube are

within 15% of the overall HTC

Non-uniform boiling; low

HTC at the top section

HTC at top section >15% below the overall

HTC; HTC for other tube sections within 15%

or >15% above overall HTC


HTC at the bottom section

HTC at bottom section >15% below the overall

HTC; HTC for other tube sections within 15%

or >15% above overall HTC


HTC at the top and bottom

section

HTC at top and bottom section >15% below the

overall HTC; HTC for other tube sections

within 15% or >15% above overall HTC


HTC at an intermediate

section (i.e. section 2 and/or 3)

HTC at intermediate section (section 2 and/or

3) >15% below the overall HTC; HTC for other

tube sections within 15% or >15% above

overall HTC


HTC at top and intermediate

section (i.e. section 1 and 2 or

3)

HTC at top and intermediate section (section 1

and 2 or 3) >15% below the overall HTC; HTC

for other tube sections within 15% or >15%

above overall HTC

The same percentage of tests demonstrating the same boiling pattern would not

be expected in Table 6.9 for the Original432 and Replicate128 datasets. One factor

contributing to this difference is that the Original432 dataset incorporated nine tubes

and the Replicate128 dataset incorporated only four tubes.

It is evident from Table 6.9, that Non-uniform boiling–low HTC at the top of the

heating tube is the most common of all the boiling patterns followed by Non-uniform

boiling–low HTC at bottom, for both the Original432 and Replicate128 datasets.


Table 6.9 Boiling pattern allocation for Original432 and Replicate128 datasets

Boiling pattern Location of

data

Percentage of data in this

category

Original432

dataset

Replicate128

dataset

Uniform Appendix L 9.5 5.5

Non-uniform; low HTC at

top

Appendix M 49.5 43.7


bottom

Appendix N 19.9 27.3


intermediate section

Appendix O 10.2 18


top and bottom

– 1.9 1.6


top and intermediate

– 4.4 1.6

No particular pattern – 4.6 2.3


The analysis of the individual section HTC results identified that several

different boiling patterns were experienced in the single-tube pilot evaporator during

the experiments. Six distinct boiling patterns were identified, which included uniform

boiling and non-uniform boiling throughout the tube. The non-uniform boiling–low

HTC at the top of the heating tube was found to be the most common boiling pattern

for both the Original432 and Replicate128 datasets. Non-uniform boiling with low

HTC at the bottom section was found to be the next most common pattern. It is

hypothesised that each of these HTC patterns is associated with a different boiling

mechanism occurring in the tube.

6.4 Determination of Factors Influencing the Boiling Pattern


This section provides a qualitative analysis to understand the influence that tube

dimensions and operating conditions have on the formation of the different boiling

patterns. For each pattern of HTC values, the number of tests with that pattern was

divided among the different levels of each factor. The Original432 dataset was

analysed to determine which factors are most influential in establishing each HTC

pattern.


6.4.2 Factors affecting the boiling patterns

Figure 6.1, Figure 6.2, Figure 6.3 and Figure 6.4 show the distribution of the

number of tests for each level of each factor for the Original432 dataset for the four

dominant HTC patterns, as summarised in Table 6.10. The non-uniform boiling with

low HTC at both the top and bottom simultaneously and with low HTC at the top and

intermediate sections, are not shown due to their low prevalence.

Table 6.10 HTC pattern and the corresponding figure number

Figure number HTC pattern

Figure 6.1 Uniform

Figure 6.2 Non uniform; low HTC at top

Figure 6.3 Non uniform; low HTC at bottom

Figure 6.4 Non uniform; low HTC at intermediate section

Figure 6.1 to Figure 6.4 provide information on which levels of specific factors

are most prevalent for each pattern of boiling. Also, it is clear that variations in the

levels of some factors have minimal influence on the boiling patterns. The results of

these observations are summarised in Table 6.11.

Experimental factors

TL TD B JL HS DP

Num

ber

of

resu

lts

0

5

10

15

20

25

30

TL-2 m

TL-3 m

TL-4 m

TD-38.1 mm

TD-44.45 mm

TD-50.8 mm

Brix-20

Brix-35

Brix-70

JL1

JL2

JL3

JL4

HS1

HS2

DP1

DP2

Figure 6.1 Number of results showing uniform boiling throughout the tube for

each level of each factor for Original432 tests



TL TD B JL HS DP

Num

ber

of

resu

lts

0

20

40

60

80

100

120

TL-2 m

TL-3 m

TL-4 m

TD-38.1 mm

TD-44.45 mm

TD-50.8 mm

Brix-20

Brix-35

Brix-70

JL1

JL2

JL3

JL4

HS1

HS2

DP1

DP2

Figure 6.2 Number of results showing non-uniform boiling with low HTC at the

top for each level of each factor for Original432 tests


TL TD B JL HS DP

Num

ber

of

resu

lts

0

10

20

30

40

50

60

TL-2 m

TL-3 m

TL-4 m

TD-38.1 mm

TD-44.45 mm

TD-50.8 mm

Brix-20

Brix-35

Brix-70

JL1

JL2

JL3

JL4

HS1

HS2

DP1

DP2

Figure 6.3 Number of results showing non-uniform boiling with low HTC at the

bottom for each level of each factor for Original432 tests



TL TD B JL HS DP

Num

ber

of

resu

lts

0

5

10

15

20

25

30

TL-2 m

TL-3 m

TL-4 m

TD-38.1 mm

TD-44.45 mm

TD-50.8 mm

Brix-20

Brix-35

Brix-70

JL1

JL2

JL3

JL4

HS1

HS2

DP1

DP2


intermediate sections for each level of each factor for Original432 tests

Table 6.11 Results of observations of the influence of experimental factors on

the boiling patterns

HTC patterns Factors which have a strong influence on

the HTC pattern

Uniform 2 m tube length

Brix-20

Higher juice levels

Higher headspace pressure

Non uniform; low HTC at top Brix-35 and Brix-70

Lower juice levels

Non uniform; low HTC at bottom 4 m tube length

44.45 mm tube diameter

Brix-20 and Brix-70

Higher juice levels

Non uniform; low HTC at

intermediate section

2 m tube length

38.1 mm tube diameter

Lower headspace pressure


The factors affecting the boiling patterns are discussed in this section. It was

concluded that different tube dimensions and different operating conditions affect the

HTC patterns.


6.5 Analysis of Variance of Individual Sections HTC


This section details the analysis of variance of individual section HTC values.

6.5.2 ANOVA for individual section HTC results

Analysis of variance was undertaken for the individual section HTC values to

determine the experimental factors affecting the HTC values of the individual sections.

The ANOVA tables are shown in Appendix P (Tables P.1 to Table P.4). Table 6.12

shows the single parameters and interactions that were found to have a significant

effect on the HTCs for the four sections. The 4th order interaction (TL:TD:B:HS) was

found to be significant for all four sections.


sections HTC values (Original432)

Tube

section

Factor identified with significance level less than 0.05

Single

parameter

2nd order

interaction

3rd order

interaction

4th order

interaction

Section 1 B, HS TD:B, TD:JL,

TD:HS

TL:TD:B

TL:TD:HS

TL:B: ΔP

TL:TD:B:HS

Section 2 B, JL,HS, ΔP TD:B, TD:JL,

B:JL, B:HS,

B:ΔP

TL:TD:B

TL:TD:HS

TL:B:ΔP

TL:HS:ΔP

TL:TD:B:HS

Section 3 B, HS TD:B, TD:JL TL:TD:B

TL:TD:HS

TL:JL:HS

TD:B:HS

TL:TD:B:HS

Section 4 B, HS TL:B, TD:B,

TL:HS, B:HS,

B: ΔP

TL:TD:B

TL:TD:HS

TL:JL:HS

TD:B:HS

TL:B:HS

JL:HS:ΔP

TL:TD:B:HS

Figure 6.5 to Figure 6.8 show the TL:TD:B:HS interaction plot for sections 1 to

4. It is observed that as brix increases, HTC of the individual sections decreases.

Although there are a few anomalies, S3, M4 and L4 tubes show higher HTC for Brix-

35 than for Brix-20 for sections 3 and 4. The reason for this is not clear.


Figure 6.5 TL:TD:B:HS interaction plot for HTC for section 1






Figure 6.9 shows the TL:B:ΔP interaction plot for section 1. It is evident that

there is no consistency in the behaviour for the three brix values. The effect of tube

length and pressure difference on section 1 HTC is not clear.

Figure 6.9 TL:B:ΔP interaction plot for HTC for section 1

Figure 6.10 shows the TL:HS:ΔP interaction plot for section 2. It is observed that

HTC is generally higher for the HS1 and DP1 combination for all tube lengths. HTC

reduces from HS1 to HS2 with one exceptions viz. for 4 m tube length and higher

pressure difference.

Figure 6.11 shows the TL:B:ΔP interaction plot for section 2. There is no

consistency in the results. The effects of tube length and pressure difference on section

2 HTC values are not clear.


Figure 6.10 TL:HS:ΔP interaction plot for HTC for section 2

Figure 6.11 TL:B:ΔP interaction plot for HTC for section 2


Figure 6.12 and Figure 6.13 show the TL:JL:HS interaction plot for sections 3

and 4 respectively. For section 4 it is observed that an increase in tube length results

in a decrease in HTC for all the juice levels at both the headspace pressures. This can

be explained by the increased hydrostatic head at the bottom of the longer tube

increasing the saturation temperature and suppressing the formation of vapour bubbles.

However, for section 3, no consistency is observed in the results.

Figure 6.12 TL:JL:HS interaction plot for HTC for section 3


Figure 6.13 TL:JL:HS interaction plot for HTC for section 4

Figure 6.14 shows the JL:HS:ΔP interaction plot for HTC for section 4 for HS1

values. Pressure difference has an effect on section 4 at lower juice levels (JL1 and

JL2). Similarly, the JL:HS:ΔP interaction plot for HTC for section 4 at HS2 values is

shown in Figure 6.15. Pressure difference has an effect on HTC at lower juice level

(JL1).


Figure 6.14 JL:HS:ΔP interaction plot for HTC for section 4 at HS1 values

Figure 6.15 JL:HS:ΔP interaction plot for HTC for section 4 for HS2 values


Figure 6.16 and Figure 6.17 show the TD:JL interaction plot for sections 1 and

2. For 44.45 and 50.8 mm tube diameter, the sections 1 and 2 show similar trends.

However, for 38.1 mm tube diameter, juice level corresponding to the highest HTC

has shifted from JL3 for section 2 to JL2 for section 1.

Figure 6.16 TD:JL interaction plot for HTC for section 1


Figure 6.17 TD:JL interaction plot for HTC for section 2


The ANOVA for the individual section HTC was analysed. The ANOVA shows

that tube length, tube diameter, brix and headspace pressure have significant effects

on the HTC of the individual sections.

As a general trend, headspace pressure seems to have little influence on section

1 and 3 HTC for all the three brix for S2, M2, M4 and L4 tube dimensions. For section

2 HTC, headspace pressure has little influence for all three brix for S2 and L4 tube

dimensions. For section 4, headspace pressure has little influence for all three brix for

S2, M3 and L4 tube dimensions. The findings show that a decrease in headspace

pressure for these tube dimensions would be less likely to cause a drop in overall HTC.

As a general trend regarding brix, it is observed that as brix increases, HTC

decreases. The S3, M4 and L4 tubes show higher HTC for Brix-35 than for Brix-20

for sections 3 and 4.


6.6 Analysis of Variance of the HTC Values for Individual Sections

Corresponding to Overall HTCmax


Of great interest is to understand the patterns of HTC for the individual sections

for operation at the optimal juice levels, that is, for the HTCmax results for the nine

tubes and test conditions of juice brix, headspace pressure and pressure difference.

The boiling patterns discussed in section 6.3.2 were identified for the HTC

results. Table 6.13 shows the boiling pattern allocations for the HTCmax results from

the Original432 dataset. The same four common boiling patterns, which were

identified as being most prevalent in the Original432 results for HTC, were also

common for HTCmax. However, for the conditions providing HTCmax there is a greater

percentage showing uniform boiling pattern and non-uniform boiling pattern–low

HTC at bottom. There are fewer results in the non-uniform boiling pattern–low HTC

at top section category, indicating that selection of the optimal juice level reduces the

likelihood of this particular boiling pattern.

Table 6.13 Boiling pattern allocation for HTCmax results from Original432

dataset

Boiling pattern Percentage of data in this

category

Uniform 18.5

Non-uniform; low HTC at top 30.6

Non-uniform; low HTC at bottom 28.7

Non-uniform; low HTC at intermediate

section

11.1

Non-uniform; low HTC at top and bottom 1.9

Non-uniform; low HTC at top and

intermediate

5.6

No particular pattern 3.7

6.6.2 ANOVA for individual section corresponding to HTCmax results

Analysis of variance was undertaken for individual section HTC values

corresponding to the overall HTCmax to determine the experimental factors affecting

the HTC values of individual sections of the tube at these conditions. The ANOVA

tables are shown in Appendix P (Tables P.5 to P.8). In order to simplify the

descriptions, these section HTC values will be referred to as section HTCmax.


Table 6.14 presents a summary of the factors and interactions for the individual

section HTCmax that were found to be significant. Brix is identified as a significant

factor for all the sections. TD:B:HS is identified as significant for sections 1, 2 and 3.


sections HTCmax (Original432)

Tube section Factor identified with significance level less than 0.05

Single parameter 2nd order

interaction

3rd order

interaction

Section 1 B, HS TD:B, TD:HS TD:B:HS, TL:HS: ΔP

Section 2 B, HS, ΔP TD:B TL:HS:ΔP, TD:B:HS

Section 3 B - TD:B:HS

Section 4 TL, B -

The HTCmax results for the whole tube are discussed in section 5.7.3 on page

131. The TD:B:HS interaction was found to be significant for HTCmax. The individual

section HTCmax values show TD:B:HS as significant for three-out-of-four sections,

implying that tube diameter affects the HTC of the individual sections. Since the effect

of brix on HTCmax is known, tube diameter and headspace pressure are for the four

sections for each of the three brix values. Figure 6.18, Figure 6.19 and Figure 6.20

show the TD:B:HS interaction plots for Brix-20, Brix-35 and Brix-70 respectively.

For Brix-20, Brix-35 and Brix-70, the results show that headspace pressure has

close-to-no effect on section 1, 2 and 4 HTC for 38.1 mm tube diameter. Headspace

pressure has a slight effect on section 3 HTC, for all the three tubes’ diameter.

For the four sections of the tube, the individual section HTCmax value was higher

for the higher headspace pressure. The only notable exception was for section 3 in the

38.1 mm diameter tube.

Also, the effect of tube diameter for the individual section HTCmax values is

similar for sections 1 to 3 viz. HTC values similar for the 38.1 and 44.45 mm diameter

tubes but low HTC values exist for the 50.8 mm diameter tube. For section 4 of the

tube, higher HTC values are achieved for the 38.1 mm diameter than compared with

the two larger diameter tubes.



Brix- 20

Figure 6.19 shows that for Brix-35, the tubes with 44.45 mm diameter showed

higher individual section HTCmax values than for the tubes of the other diameters. As

well, the individual section HTCmax values for the tubes of 44.45 mm are substantially

higher for the higher headspace pressure for sections 1 to 3, while for section 4 there

is little influence of headspace pressure.



Brix- 35

For Brix-70 (Figure 6.20), no consistent pattern for the effects of tube diameters

or headspace pressure on individual section HTCmax values was obvious.



Brix- 70

6.6.3 Uniform boiling pattern for tests at HTCmax

In section 6.4, the apparent influence of each level of each factor from the

experimental design for the Original432 dataset was investigated for the four

predominant boiling patterns. This section investigates the effect of each level of each

factor on the overall HTCmax where a uniform boiling pattern existed. A quantitative

analysis was undertaken for uniform boiling pattern for Brix-20, Brix-35 and Brix-70.

The classification of the boiling pattern is based on brix, since brix is known to be the

most dominant factor affecting HTCmax.

Figure 6.21 shows the mean values of overall HTCmax for tests when the uniform

boiling pattern existed. Table 6.15 details the factors affecting the overall HTCmax for

uniform boiling. Juice level is shown to be a factor in Table 6.15 and Figure 6.22.

These juice levels are optimum juice levels corresponding to maximum HTC for

different tube dimensions.


Table 6.15 Factors affecting overall HTCmax for uniform boiling for three brix

levels

Brix Factors which have a strong influence on the overall HTCmax

20 Tube diameter, juice level

35 Tube diameter, headspace pressure

70 Tube length, tube diameter, juice level, headspace pressure

Figure 6.21 Mean values of overall HTCmax with uniform boiling pattern (O432)

6.6.4 Non-uniform boiling pattern with low HTC at the top for tests at HTCmax

The non-uniform boiling pattern showing low HTC at the top section of the tube

formed the largest dataset containing 34 tests. Figure 6.22 shows the mean values of

overall HTCmax for tests when a non-uniform boiling pattern showing low HTC at the

top section existed. Table 6.16 shows the factors affecting the overall HTCmax for a

non-uniform boiling pattern with low HTC at the top section.



HTC at the top for the three brix values


20 Tube length, tube diameter, juice level, pressure difference

35 Tube length, tube diameter, juice level



and low HTC at top (O432)

6.6.5 Non-uniform boiling pattern with low HTC at the bottom for test at HTCmax

The non-uniform boiling pattern showing low HTC at the bottom section of the

tube contained 31 tests. Figure 6.23 shows the mean values of overall HTCmax for tests

when a non-uniform boiling pattern showing low HTC at the bottom section existed.

Table 6.17 shows the factors affecting the overall HTCmax for a non-uniform boiling

pattern with low HTC at the bottom section.


Table 6.17 Factors affecting overall HTCmax the boiling pattern with low HTC

at the bottom for the three brix values


20 Tube length, juice level


70 Tube length, juice level, pressure difference


and low HTC at intermediate section (O432)

6.6.6 Non-uniform boiling with low HTC at intermediate sections for tests at HTCmax

The non-uniform boiling pattern showing low HTC at intermediate sections of

the tube contained 12 tests. Figure 6.24 shows the mean values of overall HTCmax for

tests when a non-uniform boiling pattern with low HTC at an intermediate section

existed. Table 6.17 shows the factors affecting the overall HTCmax: a non-uniform

boiling pattern with low HTC at an intermediate section.



HTC at an intermediate section for the three brix values


20 Tube diameter, juice level, pressure difference

35 Headspace pressure

70 Tube diameter

sin


and low HTC at intermediate sections (O432)


The ANOVA of the individual section HTC values producing the HTCmax were

analysed. It was found that brix is the most significant factor affecting the HTC values

for all individual sections at the HTCmax conditions. Both tube diameter and tube length

were found to affect the individual HTC values for conditions corresponding to the

overall HTCmax. For specific conditions, headspace pressure and pressure difference

are also important factors affecting the HTC values of the individual sections for the

tests corresponding to the HTCmax values. A third order interaction (TD:B:HS) was

found to be significant for sections 1, 2 and 3.


The influence of each factor on the four most common boiling patterns was

analysed. The factors having strong influence on the HTCmax for the different boiling

patterns are summarised in Table 6.15, Table 6.16, Table 6.17 and Table 6.18. Both

tube diameter and tube length were found to affect the HTCmax value for the various

conditions. For specific conditions, headspace pressure and pressure difference were

also important factors affecting the HTCmax values.

6.7 Boiling Mechanism


The various patterns of HTC values for the individual sections of the heating

tube are attributed to variations in the boiling patterns for the juice within the tube. In

this section, possible boiling mechanisms are proposed, which relate to the observed

effects of tube dimensions and operating conditions on the HTC values. While the

proposed boiling mechanisms relate to the single heating tube used in the experimental

rig, the proposed boiling mechanisms are likely to provide a reasonable description of

the boiling mechanisms in industrial vertical-tube rising-film evaporators. One cause

of any differences, if they exist, between the boiling patterns for the single tube and

the tubes in an industrial evaporator, is the influence of juice flow from adjacent tubes

pooling above the tube plate affecting the juice flow rising in an individual tube.

It is to be noted that the effect of gutters on the outside of the tube, although

ignored for calculation of the overall HTC, may influence the boiling patterns.

Consequently, the boiling patterns of industrial tubes when a thicker condensate layer

would exist at the base of the tube may show a slightly different boiling pattern,

resulting from a slightly lower HTC at the bottom of the tube.

6.7.2 Review of the literature on boiling mechanisms in a rising film tube evaporator

In section 2.3 on page 17, the flow regimes in vertical channels were described.

It is accepted that the different flow regimes inside the vertical tube possess different

resistances to heat transfer. Hence, in order to maximise the heat transfer for a

particular set of operating conditions, it is logical to seek to achieve a flow regime

which imposes the least resistance to heat transfer on the juice side for the maximum

length of the vertical tube. According to theory, HTC increases from bubbly flow to

slug flow to annular flow, with the latter having the least resistance to heat transfer

with a liquid film along the tube wall and vapour core. However, when the annular


flow regime gives way to the mist flow regime there is a drop in HTC in the region

with single phase vapour (Bejan, 1993).

In tests that showed a uniform boiling pattern, it would be reasonable to assume

that the annular flow regime was not reached. This assumption is based on the fact that

part of the tube is filled with liquid (dynamic liquid level5), some of which would only

have single-phase saturated liquid convective heat transfer, and/or a section of nucleate

boiling exists. The occurrence of the annular flow regime for the entire length of the

tube would be impossible.

In tests that showed a non-uniform boiling pattern with low HTC at the bottom

the conventional flow regime, as shown in Figure 2.3 on page 18, would explain the

boiling mechanism. If, for these results, annular flow exists in the top section, the HTC

of the top section would have to be higher than the HTC for the uniform boiling pattern

results, which was determined to not have an annular flow regime. The HTC results of

Section 1 (top section) for the uniform boiling pattern and the non-uniform boiling

pattern with low HTC at bottom are shown in Appendix L and N respectively. The

HTC values of the two boiling patterns at the top section of the tube are similar.

5 Dynamic liquid level is used to represent the liquid level inside the tube when the

liquid is under saturated boiling. This level is higher than the set static liquid level

owing to the presence of vapour bubbles.



100 kPa abs (Taitel et al., 1980)

Chen et al. (2006) identified seven typical flow patterns in vertical two-phase

flow for tubes ranging in diameter from 1.1 to 4.26 mm. Chen et al. (2006) concluded

that the flow patterns for the large diameter tubes (2.88 and 4.06 mm) strongly

resemble flow pattern characteristics found in normal size (above 2.88 mm) tubes.

Mishima and Ishii (1984)presented flow pattern maps for tubes of 12 mm diameter

and 1.0 m length operating at 100 kPa pressure. Their flow pattern maps clearly

indicate the existence of annular flow when gas velocities were above 10 m/s. Watson

(1987) stated that slug flow and not annular flow is expected to occur in Australian

design evaporators; although Watson (1987) did not provide any supporting results or

reference to the conclusion.

The gas and liquid superficial velocities were determined using equations 2.7

and 2.8 on page 22, and shown on the graph in Figure 6.25. Values for superficial gas

velocities have been calculated for the range of tests in the experimental program.

These values are plotted in Figure 6.26, together with the superficial liquid velocity. It

is evident from the range of values in Figure 6.26 and comparison to the locations of

the flow regimes in Figure 6.26, that all the results lie in the churn flow regime.

However, the formation of churn flow is a subject of debate. Mao and Dukler


(1993)concluded that there is little evidence for considering churn flow to be a separate

and distinct flow pattern. Several authors have stated that churn flow is in fact a

manifestation of slug flow and no transition actually occurs. Hence, it is hypothesised

that for the test conditions, bubbly and slug flow regimes (gas velocity <10 m/s) are

dominant. It is postulated that annular flow does not exist in the single tube evaporator.

Superficial gas velocity (m/s)

0.01 0.1 1 10 100

Sup

erfic

ial l

iqui

d v

eloci

ty (

m/s

)

0.01

0.1

1

10

100

TD-38.1 mm

TD-44.45 mm

TD-50.8 mm

Figure 6.26 Flow pattern map for experimental results

6.7.3 Proposed boiling mechanism

As discussed in the previous section, it was postulated that for the test conditions

that are typical of industrial Robert evaporators, annular flow did not exist in the single

tube. Hence, the presence of bubbly and slug flow is dominant in the single tube

evaporator. The presence of a sub-cooled liquid region could also be dismissed, since

the juice entering the base of the heating tube should be close to the temperature for

boiling at the headspace pressure (See Experimental Procedure - section 4.4 on page

74).


Table 6.19 presents the proposed boiling phases for the various boiling patterns

that have been identified. The term “dry out” is proposed here to describe the situation

where the tube surface is not fully wetted by liquid. This mechanism should not be

confused with mist flow, which occurs post annular flow. Descriptions and

justifications for the proposed boiling patterns are given below.

Table 6.19 Proposed boiling regimes for boiling patterns

Boiling pattern Section 1 Section 2 Section 3 Section 4

Uniform boiling Bubble/slug Bubble/slug Bubble/slug Bubble/slug

Low HTC at top Dry out Dry out Bubble Bubble

Low HTC at bottom Bubble/slug Bubble/slug Bubble Bubble

Low HTC at

intermediate

Bubble/Slug Not know Not known Bubble/slug

stated that, during the transition from bubble flow to slug flow, bubble flow is

characterised by small bubbles moving in zig-zag motion and the occasional

appearance of large, Taylor-type bubbles. With further increase in gas flow rate, the

liquid flow still being low, the bubble density increases and reaches a point where the

dispersed bubbles become so closely packed that a high frequency of collisions and

agglomeration occurs, leading to larger bubbles. Hence, the occurrence of bubble and

slug flow together could explain the uniform boiling throughout the tube.

With higher brix and lower headspace pressure (higher viscosities), the ability

of the juice to rise up the tube for a given heat flux is dampened, compared with

operation with lower brix juice at higher headspace pressure (lower viscosities). The

effects of brix and headspace pressure are found to be substantial, to the extent where

low HTC at the top section occurred even for tubes of small length (2 m). The bottom

sections of the tube showed relatively acceptable HTC and hence resemble bubbly

flow. The top section is proposed to be drying out and a steep decrease in overall HTC

is recorded.

With longer tubes and higher operating juice levels, the HTC of the bottom

section is reduced (refer to Figure 6.3). A possible explanation for this reduction is the

increased pressure on the juice at the bottom section and reduced temperature

difference between the vapour in the steam chest and the saturation temperature at the

bottom of the tube. It is postulated that the bottom sections could be under a bubble


flow (saturated nucleate boiling) regime and the top sections could be under a slug

flow regime. The interesting part is the effect of tube diameter of 44.45 mm (OD) and

brix of 20 and 70 on this boiling pattern (Figure 6.3). This effect was not entirely

understood.

The reduction of HTC at the intermediate section was the most confounding

pattern observed in the single tube evaporator. The reduction of HTC at the

intermediate section has been termed in the literature as Boiling crisis or Critical heat

flux (Hong Chae Kim et al., 2000). However, this phenomenon is normally present for

conditions of very high ΔT (e.g. >100 °C) in boilers. It is possible that a form of vapour

blanketing is occurring in these intermediate sections.


A boiling mechanism is proposed, wherein the boiling patterns identified are

related to the HTC patterns on the tubes. A boiling mechanism is proposed, wherein

Annular flow does not exist in tubes of sugar mill evaporators and Bubbly and Slug

flow regimes are dominant. The four boiling patterns, which accounted for more than

90% of the results, have been described by a possible boiling regime.

6.8 Boiling Patterns in the Tube that Provide Superior Heat Transfer

Coefficient


As discussed earlier, the preferred boiling pattern in the tube would present the

least resistance to heat transfer on the juice side. The boiling patterns identified and

related to the boiling flows are explained in the above sections. This section determines

the boiling patterns in the tube that provide superior heat transfer performance. The

tube dimensions and the operating conditions, which are most likely to provide the

proposed boiling pattern, are investigated.

Table 6.20 presents the average overall HTCmax values for the different boiling

patterns for Brix-20 (1st effect), Brix-35 (3rd effect) and Brix-70 (5th effect). The

uniform boiling pattern shows the highest HTCmax for all the three brix values. Low

HTC at the bottom and low HTC at intermediate position show similar HTCmax values

and these are lower than for the uniform boiling pattern. Of the two patterns, low HTC

at the bottom was the higher at all the three brix values. The boiling pattern with low


HTC at the top shows the lowest HTCmax values for all the three brix values. Thus,

boiling conditions that result in a low HTC at the top section are the least favoured.

Table 6.20 Average HTCmax for different boiling patterns at three brix

Boiling pattern % of

results

Brix-20 Brix-35 Brix-70

Uniform boiling 18 4593 2899 512

Low HTC at top 31 2431 1701 370

Low HTC at bottom 29 3939 2616 468

Low HTC at intermediate 10 3733 2443 475

Low HTC at top and

intermediate 4

- - -

Low HTC at top and bottom 4 - - -

No pattern 4 - - -

Further discussion of the results is undertaken for the two proposed boiling

pattern of uniform boiling and low HTC at the bottom, to determine which tubes and

operating conditions promote boiling with these two patterns.

6.8.2 Uniform boiling pattern

Table 6.21 shows the tube dimensions and operating conditions for HTCmax with

a uniform boiling pattern. The observations are summarised in Table 6.22.


Table 6.21 Tube dimensions and operating conditions for HTCmax with uniform

boiling pattern

Tube Brix JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

Achieved

ΔT (°C)

Set

ΔT

(°C)

HTC

(W/m2/K)

S2 20 800 126 45 8.8 8.8 5225

S4 20 1600 149 33 5.8 5.8 4504

S4 20 1200 149 45 7.7 7.7 4039

S4 20 800 126 33 6.5 6.5 4214

S4 20 800 126 45 8.8 8.8 3795

M2 20 800 149 33 5.7 5.7 5509

M2 20 800 149 38 6.5 7.7 5663

L2 20 800 149 33 5.7 5.7 4378

L2 20 400 149 35 6.1 7.7 3784

L2 20 800 126 33 6.5 6.5 4557

L3 20 1200 149 33 5.7 5.7 5668

L3 20 1200 149 35 6.1 7.7 3778

S3 35 1800 72 35 9.6 9.8 2161

M2 35 1200 94 35 7.9 7.9 3020

M3 35 1800 94 35 7.8 7.9 3632

M3 35 1800 94 50 11.1 11.2 3550

M3 35 1800 72 50 13.5 13.5 2134

M3 70 1350 22 60 27.8 27.4 231

L2 70 1400 29 60 23.5 23.3 797

L3 70 1650 29 60 23.0 23.3 508

Table 6.22 Observation with uniform boiling pattern for three brix values

Brix Observations

Brix-20

The S4 tube shows a uniform boiling pattern irrespective of operating

conditions (headspace pressure and pressure difference)

The M2, L2 and L3 tubes shows a uniform boiling pattern occurs more

commonly at the higher headspace pressure (149 kPa abs)

Brix-35 The M3 tube shows a uniform boiling pattern more often than the other

tubes. No operating conditions are dominant

Brix-70 Only three tubes at Brix-70 showed uniform boiling for the HTCmax

condition

No single tube nor operating condition dominates


6.8.3 Low HTC at the bottom of the tube

Table 6.23 shows the tube dimensions and operating conditions for HTCmax with

low HTC at the bottom of the tube. The observations are summarised in Table 6.24.

Table 6.23 Tube dimensions and operating conditions for HTCmax with low

HTC at bottom

Tube Brix JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

Achieved

ΔT (°C)

Set

ΔT

(°C)

HTC

(W/m2/K)

S3 20 600 126 33 6.5 6.5 4133

S3 20 600 126 45 8.8 8.7 3867

S3 20 1200 149 41 7.0 7.0 3749

M2 20 600 126 33 6.5 6.5 4835

M3 20 900 149 33 5.7 5.7 4343

M3 20 900 149 45 7.7 7.6 4084

M3 20 1500 126 33 6.5 6.5 3589

M3 20 900 126 45 8.7 8.7 4459

M4 20 1600 149 45 7.8 7.6 3725

M4 20 2000 126 33 6.6 6.5 3134

M4 20 1600 126 45 8.8 8.7 3806

M4 20 1200 149 33 5.7 5.7 3542

S2 35 400 72 35 9.7 9.8 2294

M2 35 900 72 50 13.5 13.5 2267

M4 35 1400 94 35 8.0 7.9 3530

M4 35 2400 94 50 11.2 11.2 2989

L3 35 1800 72 50 13.5 13.5 2002

S3 70 2100 29 42 17.5 17.2 539

M2 70 600 29 60 22.7 23.3 557

M2 70 600 22 60 26.9 27.4 478

M2 70 900 22 42 20.4 20.9 934

M3 70 2100 29 60 23.7 23.3 337

M3 70 2100 29 42 17.6 17.2 454

M4 70 1800 29 60 23.4 23.3 412

M4 70 2800 22 42 21.7 20.9 249

M4 70 2200 22 60 28.5 27.4 441

L2 70 1400 29 42 17.5 17.2 769

L2 70 1400 22 42 21.1 20.9 589

L3 70 2100 22 60 26.5 27.4 623

L4 70 2800 29 60 23.3 23.3 91

L4 70 2200 22 60 28.5 27.4 75


Table 6.24 Observations with non-uniform boiling pattern (low HTC at the

bottom of the tube) for three brix values

Brix Observations

Brix-20

S3, M3 and M4 tubes are the tubes that more commonly show low HTC

in the bottom section

For the M3 and M4 tubes no operating condition is dominant

Brix-35 Only five tubes showed low HTC at the bottom section and no single

tube or operating condition dominates

Brix-70 Seven of the nine tubes showed low HTC at the bottom section. Tubes

M2 and M4 were the more common. For both tubes, the higher pressure

difference dominates

Comparison of the data in Table 6.21 and Table 6.23 shows that for

Brix-70, many more of the HTCmax test conditions showed lower HTC

at the bottom than uniform boiling


The two boiling patterns in the tube, which provided superior heat transfer

performance, were identified as uniform boiling and low HTC at the bottom. Those

tube dimensions and operating conditions that are likely to promote these boiling

patterns were determined. Although it is well understood that the formation of the

boiling patterns is not directly controlled, setting the operating conditions for the

evaporator close to the optimum conditions will ensure good heat transfer performance

is achieved.


The HTC of the individual sections of the four tubes in the Replicate128 dataset

were compared with the HTC of the individual sections from the corresponding

Original432 dataset. A high level of consistency in the results of the two series of tests

was obtained for the Brix-20 tests. The consistency was not as good for the Brix-70

tests.

The HTC of the individual sections of the Original432 dataset were analysed.

Six boiling patterns were identified, of which four boiling patterns accounted for more

than 90% of the results. The four boiling patterns were

• Uniform boiling pattern

• Low HTC at the top section of the tube


• Low HTC at the bottom section of the tube

• Low HTC at the intermediate sections of the tube

These four boiling patterns were qualitatively and quantitatively analysed to

understand the occurrence of these boiling patterns and their effect on the overall HTC

of the tube.

Juice brix is identified as a significant factor affecting the HTC values for all

four sections of the tube, for the conditions corresponding to the overall HTCmax.

A boiling theory was proposed, wherein it was concluded that Annular Flow did

not exist in the single tube evaporator. The two dominant flow regimes in the single

evaporator tube and most likely in the industrial rising-film tube evaporator are bubbly

and slug flows. Low HTC at the bottom section is boiling associated with high

hydrostatic head (e.g. long tube), while low HTC at the top of the tube most likely

indicates drying out of the tube surface (i.e. insufficient wetting). No mechanism has

been proposed to describe the circumstances with low HTC at the intermediate sections

of the tube.

After examining the HTC patterns for those tests that provided the overall

HTCmax results, it was determined that Uniform boiling and Low HTC at bottom were

the boiling patterns in the tube that provided superior heat transfer performance.

Of the two boiling patterns, uniform boiling pattern provided the higher HTC.

However, the formation of boiling patterns is not essentially a matter of control.

Operating the evaporator close to the optimum conditions might result in formation of

these boiling patterns and good heat transfer performance can be achieved.

In general terms, uniform boiling conditions are more likely to be established for

boiling at Brix-20 with headspace pressure. Uniform boiling appears to form in the

tubes of all three diameters. For tubes of 38.1 mm diameter, tubes of 4 m length

produced uniform boiling, whereas for tubes of 44.45 mm and 50.8 mm diameter,

uniform boiling was more likely to be achieved with the shorter tubes.

The second favoured boiling pattern with low HTC at the bottom was likely to

be established for all three brix values, and particularly for Brix-20 and Brix-70. Tubes

S3, M3 and M4 were shown to be more likely to produce this boiling pattern at Brix-

20. For Brix-70, tubes with diameter 44.45 mm and 50.8 mm appeared more likely to


produce this boiling pattern than the 38.1 mm tube. A higher pressure difference also

enhanced the formation of this boiling pattern.

.

Selecting Optimum Tube Dimensions 193

CHAPTER 7: SELECTING OPTIMUM

TUBE DIMENSIONS


In Chapter 3, the costs associated with designing, fabricating and installing a

Robert evaporator with different tube dimensions were calculated. The heat transfer

performances of the tubes of different dimensions for the typical range of operating

conditions were analysed in Chapter 5.

Chapter 7 provides the selection of the tube dimensions that provide good heat

transfer performance for different effect positions in a quintuple effect set, taking into

account the heat transfer performance (HTCmax) in addition to the capital and

installation costs and the operating costs for the 1st, 3rd and 5th effects in a quintuple

set.

7.2 Methodology for Determining the Optimum Tube Dimensions


Chapter 5 details the HTCmax results for the nine tube dimensions for the 1st, 3rd

and 5th stages of evaporation in a multiple effect set. Although capital cost is an

important criterion when procuring a new vessel, higher heat transfer coefficients

allow reductions in the HSA required to achieve the same rate of evaporation, achieve

higher juice processing rates for the installed areas, or extend the period of operation

between cleans. In addition, an important benefit of increased HTCs is the ability to

achieve the required rate of evaporation with a smaller temperature difference. This

benefit is of particular interest to factories seeking to reduce their process steam

consumption and fuel usage (Moller et al., 2003; Rose et al., 2009).

7.2.2 Favoured tubes based on HTCmax

The analysis undertaken in section 5.8 on page 134 determined the tubes that

provided good heat transfer performance for the typical operating conditions in the 1st

effect, 3rd effect and 5th effect of a quintuple evaporator set.

194 Selecting Optimum Tube Dimensions

In order to determine which tubes are most suitable for a particular evaporation

duty, three aspects need to be considered. These three aspects include:

• The HTC data for the tubes;

• The capital costs to construct and install an evaporator with these tubes; and

• The operating costs of using an evaporator with a particular tube. Operating

costs are associated with sucrose loss through hydrolysis and potential for

juice entrainment into the discharged vapour.

These matters are considered in the following sections, to determine the most

suitable tubes (optimum tubes) for each effect position.

Figure 7.1, Figure 7.2 and Figure 7.3 show the HTCmax results for the nine tube

dimensions for Brix-20, Brix-35 and Brix-70 respectively. Each data value shown in

Figure 7.1 to Figure 7.3 is the average of the HTCmax values for two headspace

pressures and two pressure differences, i.e., the average of the four ∆T values for the

tests at the nominated juice brix. These figures therefore show which tubes provide

good and poor heat transfer performance for the typical conditions for the 1st, 3rd and

5th effect positions in a quintuple set.

It is evident from Figure 7.1, that tubes of small and medium diameter (38.1 and

44.45 mm) show high HTCmax values and tubes M2, S2, M3, S3 and S4 provide

HTCmax values close to or above 4000 W/m2/K). It is seen that tubes with large

diameter (50.8 mm) provide consistently lower HTCmax values than tubes with 38.1

and 44.45 mm tube diameter, for all the tube lengths. The lowest HTCmax value is for

the L4 tube size.


Figure 7.1 Influence of tube length and tube diameter on HTCmax for Brix-20

Figure 7.2 shows the HTCmax results for Brix-35. This result is an interesting and

unexpected finding from the study. The reason for the variable data for the tubes of

38.1 mm diameter with different length is not known. Compared to the M2 tube

dimensions (traditional), M3, S3, and M4 tube dimensions show higher HTCmax.

Tubes S4 and L4 show very poor heat transfer performance.



Figure 7.3 shows that for Brix-70, tube dimensions giving the highest HTCmax

are M2 and L2. Tube lengths of 3 and 4 m result in very low HTCmax. Tube L4

provides very poor heat transfer performance for juice at Brix-70.



Table 7.1 shows those tube dimensions that provided good heat transfer

performance for each effect position. The average HTCmax value for each case is also

shown in Table 7.1, as is the ratio of HTCmax to the HTCmax value for M2.

Examination of the data in Table 7.1 shows that for the 1st effect, M2 and S2

have the highest HTCmax, for the 3rd effect M3 and M4 have the highest HTCmax and

for the 5th effect, M2 and L2 have similar HTCmax values. Each of the tubes shown in

Table 7.1 is considered appropriate to achieve good heat transfer performance at the

nominated processing conditions.


Table 7.1 Favoured tubes based on HTCmax for 1st, 3rd and 5th effect positions

Effect

number

Tube with good heat

transfer performance

Average HTCmax

value (W/m2/K)

Ratio of HTCmax

to HTCmax for

M2

1 M2 4660 1.00

S2 4740 1.02

M3 4240 0.91

S3 3990 0.86

S4 4140 0.81

3 M2 2620 1.00

M3 3030 1.16

S3 2800 1.07

M4 2950 1.13

5 M2 650 1.00

L2 640 0.98


The favoured tube dimensions based on the HTCmax results are presented in this

section. It was found that for the 1st effect position, five different tube dimensions had

good heat transfer performance, including the traditional M2 dimensions. For the 3rd

effect position, three tube dimensions were identified with heat transfer performance

better than M2. It was concluded that for the final effect position, M2 and L2 tube

dimensions had the highest (and similar) heat transfer performance, while tubes of

other dimensions had substantially worse heat transfer performance.

7.3 Capital Costs for Constructing and Installing Evaporators


The capital costs of the vessels comprising the favoured tube dimensions are

described in this section. The cost model (Chapter 3) was used to determine the

construction and installation costs of each of the evaporators in Table 7.1. In order to

account for the differences in heat transfer performance as defined by HTCmax, the

areas of the vessels was selected so that HTCmax x heating surface area (HSA) is

constant for a nominated HSA for an M2 evaporator. Thus, the evaporators with the

different tube dimensions would have the same evaporation capacity, for a given ∆T.

The cost analysis was undertaken for evaporators of 2000 m2 and 5000 m2

comprising M2 tubes. The areas of the respective vessels for the favoured tubes,


having the same HTCmax x HSA as for the M2 evaporator, are shown in Table 7.2 for

M2 evaporators of 2000 and 5000 m2.

Table 7.2 Heating surface areas of the respective vessels for the favoured tubes

for 1st, 3rd and 5th effect positions

Effect

number

Tube with good heat transfer

performance

HSA for

2000 (m2)

HSA for

5000 (m2)

1 M2 2000 5000

S2 1960 4900

M3 2200 5490

S3 2330 5810

S4 2250 5620

3 M2 2000 5000

M3 1720 4310

S3 1870 4670

M4 1770 4420

5 M2 2000 5000

L2 2040 5100

The basis of costs for labour, materials, designs etc. are given in Chapter 3.

7.3.2 Construction costs

In this section, the construction costs of evaporators comprising the favoured

tube dimensions for the 1st, 3rd, and 5th effect positions are discussed.

Figure 7.4 shows the materials and labour costs for evaporators with the favoured

tubes for the 1st, 3rd and 5th effect positions relative to the M2 evaporator at these effect

positions. The material costs for the 1st effect position are higher for small diameter

and long tubes. This result is due to the increased heating surface areas of the vessels

with small diameter and long tubes, compared with the M2 tube dimensions. However,

the labour costs are reduced up to 20% for vessels comprising small diameter and long

tubes, due to the smaller vessel diameter and fewer tubes to be installed.

For the 3rd effect position, the materials and labour costs both show a reduction

of ~20% for vessels with medium diameter and long tubes. For the 5th effect position,

the M2 tube dimensions show lower materials and labour costs than for an evaporator

with the L2 tube dimensions.


Tubes

M2 S2 M3 S3 S4

Mat

eria

ls c

ost

s (f

ract

ion

of

M2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1st

effect position

Tubes

M2 S2 M3 S3 S4

Lab

ou

r co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Area-2000

Area-5000

1st

effect position

3rd

effect position

Tubes

M2 M3 S3 M4

Mat

eria

ls c

ost

s (f

ract

ion

of

M2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

3rd

effect position

Tubes

M2 M3 S3 M4

Lab

ou

r co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

5th

effect position

Tubes

M2 L2

Mat

eria

ls c

ost

s (f

ract

ion

of

M2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

5th

effect position

Tubes

M2 L2

Lab

ou

r co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Figure 7.4 Materials and labour costs for evaporators with favoured tubes

dimensions for 1st, 3rd and 5th effect positions


7.3.3 Foundations and structural costs

The foundations for the vessels were assumed to comprise a square pad of N32

concrete, with sides equal in length to the diameter of the vessel plus one metre and a

depth of 0.5 m. The reinforced steel mesh in the pad was set at three levels, with

spacing in each direction of 200 mm. The vessels are supported on universal beam

pillars of dimensions 200 mm by 200 mm (weight 41 kg/m of length). The number of

pillars required was based on each pillar being capable of supporting 96 t. The vessel

weight used to calculate the number of supporting pillars was the mass on the

foundations when the juice side is full of 40 brix juice and the calandria is full of

condensate (see section 3.2.5). The minimum number of pillars used was six,

irrespective of weight of the vessel. For heavier vessels, the number of pillars was

increased according to the calculation method above. The design weights for

evaporators with the favoured tubes are provided in section 7.3.5.

Table 7.3 shows the cost data for foundations and structure to support the

evaporators. It was assumed that wastage of concrete, reinforced steel and pillars

would be 6%. The labour requirement for preparation of the foundations, laying

reinforced steel and filling with concrete, was taken to be three man hours/tonne of

steel.

Table 7.3 Cost data for foundations and structure to support the evaporator

Description of

parameter

Value

N32 concrete for

foundation

AUD 250 per m3

Reinforced steel AUD 4 per m

Universal beam pillar AUD 240 per m

Wastage 6%

Labour requirement 3 man hours/tonne steel (preparation, laying reinforced

steel and filling)

Labour cost AUD 70 per man hour

Table 7.4 and Table 7.5 show the foundations and structural costs (materials and

labour) for evaporators with the favoured tubes for the 1st, 3rd and 5th effect positions

with equivalent evaporation performance to evaporators with M2 tubes for HSA of

2000 and 5000 m2 respectively.



favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2 evaporator of

2000 m2)

Effect

number

Tubes N32 concrete

for

foundation

cost (AUD)

Reinforced

steel cost

(AUD)

Steel

pillars

cost

(AUD)

Total

foundation &

structural

costs (AUD)

1 M2 6043 5882 7560 19485

S2 5275 5145 7560 17980

M3 4757 4642 7560 16959

S3 4423 4316 7560 16299

S4 3481 3414 7560 14455

3 M2 6043 5882 7560 19485

M3 3956 3873 7560 15389

S3 3757 3680 7560 14997

M4 3301 3235 7560 14096

5 M2 6043 5882 7560 19485

L2 6804 6622 7560 20986


favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2 evaporator of

5000 m2)

Effect

number

Tubes N32 concrete

for

foundation

cost (AUD)

Reinforced

steel cost

(AUD)

Steel

pillars

cost

(AUD)

Total

foundation &

structural

costs (AUD)

1 M2 12851 12468 10080 35399

S2 11109 10780 10080 31969

M3 9866 9592 10080 29538

S3 9096 8833 10080 28009

S4 7014 6834 7560 21408

3 M2 12851 12468 10080 35399

M3 8088 7873 7560 23521

S3 7621 7412 7560 22593

M4 6551 6374 7560 20485

5 M2 12851 12468 10080 35399

L2 14609 14171 12600 41380

For 2000 m2 HSA, there is a reduction in N32 concrete and reinforced steel costs

of 20, 30 and 40% with M3, S3 and S4 tube dimensions respectively as compared to


M2 tube dimensions. The cost savings are higher, with 5000 m2 HSA. For 2000 m2

HSA, there is no reduction in the costs for the steel pillars when using tubes of smaller

diameter or longer. As mentioned earlier, the minimum number of pillars is taken to

be six; hence vessels with longer tubes than M2 have the same number of pillars,

despite having lower vessel diameter and foundation weight. For the 5000 m2 HSA,

the number of pillars varies among the vessels between 6 and 10, depending on the

mass on the foundations.

7.3.4 Insulation and cladding costs

The vessel is insulated and clad at the top cone, the strake and the steam annulus.

Table 7.6 shows the cost data for insulation and cladding of the evaporator. The

scaffolding costs include the labour and materials and increase with the height of the

vessel (Bundaberg Walkers Engineering Ltd, 2015).

Table 7.6 Cost data for insulation and cladding of the evaporator

Description of parameter Value

Insulation and cladding costs AUD 340 per m2

Scaffolding (including labour and materials) AUD 30000 for 2 m calandria

AUD 35000 for 3 m calandria

AUD 40000 for 4 m calandria

Table 7.7 and Table 7.8 show the insulation and cladding costs of the favoured

tubes for the 1st, 3rd and 5th effect positions to equate to the M2 HSA of 2000 and

5000 m2 respectively. It was observed that although there is a 15–20% reduction in

the area for insulation with S3 and S4 tube dimensions, the overall insulation and

cladding cost savings are negligible. This effect is due to the increased scaffolding

costs for taller vessels.



effect positions (HSA of M2 evaporator of 2000 m2)

Effect

number

Tubes Area for insulation

(m2)

Insulation and cladding costs

(AUD)

1 M2 189 100584

S2 171 93774

M3 176 100872

S3 167 97450

S4 155 98024

3 M2 189 100584

M3 154 92535

S3 148 90387

M4 149 100584

5 M2 189 100584

L2 206 107142


effect positions (HSA of M2 evaporators of 5000 m2)

Effect

number

Tubes Area for insulation

(m2)

Insulation and cladding costs

(AUD)

1 M2 333 154602

S2 298 141555

M3 301 147454

S3 283 140927

S4 257 136143

3 M2 333 154602

M3 260 132168

S3 249 128021

M4 245 154602

5 M2 333 154602

L2 367 167411

7.3.5 Design weight and design costs

The design weight was calculated when the entire juice side of the vessel is filled

with juice (density–1.2 kg/m3) and the steam side is entirely filled with condensate.

This weight, plus the weight of the empty vessel, is the total weight on the foundations.

The juice side volume includes all tubes, mini-downtakes, central downtake, vapour

space and one-third of the top cone. These considerations are essential to ensure the


support columns can withstand the weight of the vessel if the condensate pump or the

juice valve fails, and the vessel fills with juice and/or condensate. Figure 7.5 shows

the design weight for the evaporators, with the favoured tubes for the 1st, 3rd and 5th

effect positions relative to the M2 evaporator at these effect positions.

The design costs include the project management costs and profit margin. The

calculation methodology for determining the project management costs and profit

margin are detailed in Table 3.3 on page 56. As shown in Figure 7.5, there is a

substantial reduction in design costs for small and medium diameters and long tubes

for the 3rd effect positions.


Tubes

M2 S2 M3 S3 S4

Des

ign

ves

sel w

eig

ht

(t)

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1st

effect position

Tubes

M2 S2 M3 S3 S4

Des

ign

co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Area-2000

Area-5000

1st

effect position

3rd

effect position

Tubes

M2 M3 S3 M4

Des

ign

ves

sel w

eig

ht

(t)

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

3rd

effect position

Tubes

M2 M3 S3 M4

Des

ign

co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

5th

effect position

Tubes

M2 L2

Des

ign

ves

sel w

eig

ht

(t)

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

5th

effect position

Tubes

M2 L2

Des

ign

co

sts

(fra

ctio

n o

f M

2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Figure 7.5 Design vessel weight and design costs for evaporators with the

favoured tubes for 1st, 3rd and 5th effect positions


7.3.6 Total costs

Table 7.9 and Table 7.10 provide details of the evaporators with the favoured

tube dimensions, which provide equivalent heat transfer performance to 2000 m2 and

5000 m2 evaporators with M2 tubes. The juice level in the tubes is the optimum level

determined from the experimental investigations (section 5.8). The optimum juice

level affects the juice level intensity (juice volume per m2 of HSA).

The data in Table 7.9 and Table 7.10 show that, at the 1st and 3rd effect positions,

the diameter of the vessel is reduced by ~18% and the mass on foundations reduced

by ~20% when S3 tube dimensions are used, compared to the conventional M2 tube

dimensions. The juice level intensity is reduced by ~40% with S3 tube dimensions.

These reductions are even greater when S4 tube dimensions are used.

For the 1st effect position, cost savings of between 4 and 10% are indicated by

suing the favoured tube dimensions compared with the M2 tube. Larger cost savings

(of 18 to 20%) are indicated for the favoured tubes at the 3rd effect position, because

of the superior HTCmax values of these tubes relative to the M2 tubes. For the 5th effect

position, the M2 evaporator is the lower cost option.

Table 7.9 Details of the evaporator vessels with the favoured tube dimensions to

equate to the heat transfer performance of a 2000 m2 HSA M2 evaporator

Effect Code Area

(m2)

No.

of

tubes

Vessel

ID (m)

Optimum

juice level

in tubes

Design

vessel

weight

(t)

Juice

intensity,

(L/m2)

Total

cost

(M

AUD)

1 M2 2000 7590 5.78 35% 322 9.27 1.28

S2 1960 8770 5.34 33% 278 7.56 1.21

M3 2200 5574 5.02 35% 279 7.34 1.21

S3 2330 6986 4.80 30% 259 5.76 1.23

S4 2250 5024 4.15 28% 221 4.71 1.14

3 M2 2000 7590 5.78 56% 322 11.65 1.28

M3 1720 4354 4.49 60% 225 10.07 1.03

S3 1870 5578 4.35 50% 214 7.58 1.05

M4 1770 3374 4.01 47% 205 7.72 1.01

5 M2 2000 7590 5.78 40% 322 9.83 1.28

L2 2040 6718 6.20 70% 366 15.24 1.37



to equate to the heat transfer performance of a 5000 m2 HSA M2 evaporator

Effect Code Area

(m2) No. of

tubes Vessel

ID (m) Optimum

juice

level in

tubes

Design

vessel

weight

(t)

Juice

intensity,

(L/m2)

Total

cost

(M

AUD)

1 M2 5000 18986 8.89 35% 762 10.35 2.58

S2 4900 21900 8.20 33% 652 8.40 2.46

M3 5490 13890 7.67 35% 642 7.91 2.39

S3 5810 17304 7.32 30% 593 6.20 2.44

S4 5620 12576 6.31 28% 496 4.99 2.22

3 M2 5000 18986 8.89 56% 762 12.73 2.58

M3 4310 10920 6.85 60% 512 10.53 1.99

S3 4670 13924 6.62 50% 485 7.98 2.06

M4 4420 8432 6.06 47% 453 7.96 1.89

5 M2 5000 18986 8.89 40% 762 10.91 2.58

L2 5100 16814 9.55 70% 874 16.59 2.80


The various costs associated with the design, fabrication and installation of the

evaporator vessels with the favoured tube dimensions for the 1st, 3rd, and 5th effect

positions were determined. Estimates of the total costs for the evaporator installations

with the favoured tube dimensions are provided.

The total cost was calculated from the materials, labour, freight of material,

wastage, workshop costs, support structure and foundations, insulation and cladding,

project management costs and profit margins.

7.4 Selection of the Optimum Tube Dimensions


This section discusses the selection of optimum tube dimensions based on

HTCmax measurements, calculated costs for an installation and operating costs.

7.4.2 Basis of selection

Many factors are considered by factory management in selecting the appropriate

tube dimensions including heat transfer performance, installed cost, access to site for

installing the evaporator (crane hire etc.), availability of replacement tubes, potential


sucrose degradation, potential entrainment of juice in the vapour flow and perceived

risk in departing from previously used tube dimensions. If the assessment is based

largely on installed cost, given appropriate heat transfer is achieved and the other

factors are acceptable, then the data in Table 7.9 and Table 7.10 indicate that

evaporators with S4, M4 and M2 tubes are preferred for the 1st effect, 3rd effect and 5th

effect respectively. This result applies to both the 2000 m2 and 5000 m2 vessels.

Discussions with Australian factory staff indicate that there is stronger interest

in using 3 m long tubes rather than 4 m long tubes in future installations of Robert

evaporators. There are two main reasons for this, viz., (1) use of 4 m long tubes would

be a major departure from the traditional 2 m long tubes, and (2) the up-flow vapour

velocity for the same VCC will be more than double compared with that for the M2

tube, which is likely to cause overloading of the juice de-entrainment louvres within

the vessel, as discussed in section 3.3.4 The industry already has a few Robert

evaporators with 38 mm diameter tubes after 1st effect position (Watson, 1986b) and

at Millaquin and Rocky Point mills (Broadfoot, 2017) and so the use of smaller

diameter tubes at the 1st effect and 3rd effect positions is likely to be perceived as low

risk.

It is for these reasons that the interest from the industry for future installations

into Robert evaporators will be in comparing S3 and M3 tubes with the traditional M2

tubes.

7.4.3 Estimates of capital costs savings

Table 7.11 shows the cost savings in using S3 and M3 tubes in the 1st and 3rd

effect positions relative to using evaporators with M2 tubes. For the 5th effect, the M2

tube dimensions are preferred, based on both the HTC and capital costs.


Table 7.11 Estimate of cost savings from using S3 and M3 tubes in Robert

evaporators at the 1st effect and 3rd effect instead of using a Robert evaporator

with M2 tubes

Tube

dimensions

Saving in installed cost relative to cost of M2 evaporator

(AUD)

1st effect 3rd effect

2000 m2 HSA

S3 48,000 222,000

M3 61,000 245,000

5000 m2 HSA

S3 139,000 519,000

M3 188,000 591,000

The cost savings for the S3 and M3 tubes, relative to the M2 tubes, are

substantially greater for the 3rd effect than for the 1st effect because the heat transfer

performance of S3 and M3 tubes in the 3rd effect is superior to that for the M2 tubes.

For the 1st effect, the S3 and M3 tubes provide slightly inferior heat transfer

performance than the M2 tubes, but overall the savings on installation costs of the S3

and M3 tubes outweigh the influence of slightly inferior heat transfer performance.

The cost savings from using S3 tubes instead of M2 tubes are ~5% for the 1st effect

and ~20% for the 3rd effect. The cost savings are greater for the M3 tubes than for the

S3 tubes at both the 1st and 3rd effect positions. As expected, the cost savings are greater

for the evaporator of larger HSA.

7.4.4 Estimates of operating costs savings

For the use of S3 and M3 tubes at the 1st and 3rd effects, de-entrainment of juice

from the up-flow vapour should be able to be effectively achieved using conventional

louvre systems located within the head space of the evaporator. Hence, for most

practical applications, the de-entrainment of juice should be managed adequately for

similar costs compared to the M2 evaporator.

Under certain circumstances, sucrose degradation during juice evaporation can

be a major operational cost, resulting in a loss of revenue for the factory.

The extent of sucrose degradation that occurs in the juice evaporation process is

a function of the juice conditions (pH, temperature and brix) and the residence time

(Vukov, 1965). The evaporation conditions that are likely to experience large sucrose


losses are where high levels of steam economy are sought, e.g., where extensive

vapour bleeding is undertaken and where the process steam pressure is high. Several

studies have shown that under these conditions, the majority of sucrose degradation

that occurs during evaporation is in the first evaporation stage (Purchase et al., 1987;

Schaffler et al., 1985). Sucrose losses should be low (<0.1% of sucrose in clarified

juice) when minimal vapour bleeding is undertaken and the process steam pressure is

200 kPa abs or lower (Rackemann & Broadfoot, 2016).

As noted in Table 7.9 and Table 7.10, Robert evaporators with different tube

dimensions have markedly different juice hold-up volumes per m2 of HSA (juice

intensity as described in section 3.3.2 on page 60). Evaporator vessels with lower juice

volume intensities will provide shorter residence times for the juice and hence

experience reduced sucrose loss through hydrolysis.

Using the correlation developed by Vukov (1965), the sucrose losses in a 1st

effect evaporator have been calculated for evaporators with the favoured tube

dimensions, based on the evaporation capacity being equivalent to that of a 5000 m2

M2 evaporator. The results and the assumed processing conditions are shown in Table

7.12. For the assumed conditions, the vapour loading would be 24 kg/h per m2 of

HSA. The average juice residence time in each evaporator is calculated for operation

at the optimum juice level (see Table 7.10). In all cases, due to the smaller juice holdup

volume than for an M2 evaporator, the calculated sucrose loss is less than for the M2

evaporator.

Table 7.12 also shows the estimated increase in annual revenue that would be

expected for an Australian factory utilising a 5000 m2 evaporator at the 1st effect in an

energy efficient plant. It was assumed that the cane/sugar mass ratio is 7 (typical of

Australian factories), the annual crop is 1.3 million t of cane, sugar price is AUD 400

per t, molasses price is AUD 120 per t, and final molasses is of 45 purity and 78 dry

substance. The values of the discounted increases in revenues (using a discount rate

of 15% for a 10 year period), from reduced sucrose losses relative to using a M2

evaporator, are also shown in Table 7.12.

These results demonstrate that for a factory intending to use Robert evaporators

at the 1st effect in a situation where a large HSA is required to suit vapour bleeding

arrangements and a high boiling temperature will be used, serious consideration should

be given to using smaller diameter and longer tubes than M2, e.g., S3 or S4.


Table 7.12 Sucrose degradation and operating cost savings

Process conditions for 1st effect:

Juice inflow: 425 m3/h, 90 purity, 16 brix

Conditions in vessel: 22 brix, 119 °C and pH 6.8 at 20 °C

Parameter M2 S2 M3 S3 S4

Residence time, min 10.1 8.0 8.4 7.0 5.4

Predicted sucrose degradation

(%)

0.40 0.32 0.34 0.28 0.22

Annual saving in reduced sucrose

loss relative to the loss for a M2

evaporator (AUD)

75,000 56,000 112,000 168,000

Discounted value* over 10 years

of increased revenue due to

reduced sucrose loss relative to

the loss for an M2 evaporator

(M AUD)

0.45 0.34 0.67 1.01

* Discount rate of 15% per annum

7.4.5 Selection of the optimum tube dimension

New Robert evaporator vessels, comprising S3 and M3 tubes, provide

installation costs savings of 5 to 7% at the 1st effect and 20 to 22% at the 3rd effect

compared with an M2 Robert evaporator, for the same evaporation capacity. While

S4 tubes at the 1st effect and M4 tubes at the 3rd effect are well suited to these

applications, providing good heat transfer performance and would provide greater cost

savings, Australian mills are unlikely to utilise a 4 m long tube in a Robert evaporator.

Thus, S3 and M3 tubes are the favoured tubes for the 1st and 3rd effects from a cost and

heat transfer point-of-view.

For the installation of a Robert evaporator at the 1st effect in a factory seeking to

reduce the process steam consumption to a low level, major operational cost savings

are achieved for evaporators with S3 and M3 tubes compared to an evaporator with

M2 tubes, owing to the lower juice volume intensity of the evaporators with the S3

and M3 tubes. Reduced sucrose degradation would occur in the 1st effect vessel as a

result of the shorter residence time for the juice at the high boiling temperature. Use

of an evaporator with S3 tubes provides a larger increase in revenue compared with

the use of the M3 tubes, because of the lower juice volume intensity of the S3 tube.

For the 5th effect, a Robert evaporator with the traditional M2 tube is favoured.



The selection of optimum tube dimensions is discussed in this section. Robert

evaporators comprising calandrias of S3 and M3 tubes are recommended for the 1st

and 3rd effect positions, compared with using the traditional M2 tube. This assessment

is based on the heat transfer performance of the different tubes, cost analysis for

fabricating and installing the evaporators, operating costs associated with sucrose

losses through hydrolysis and reduced risk compared with installing 4 m long tubes.

The S3 and M3 tubes are also recommended for the 2nd effect on the basis that

the operating conditions for the 2nd effect are intermediate between the conditions for

the 1st and 3rd effects.

At the 1st effect in a factory, which operates to reduce the process steam

consumption to a low level (typically requiring a large area allocation and high boiling

temperature at the 1st effect), a Robert evaporator comprising S3 tubes is

recommended. An evaporator with S3 tubes has a much lower juice volume intensity

than the M2 evaporator and would experience a large reduction in the extent of sucrose

hydrolysis. The evaporator with the S3 tubes also has a lower juice volume intensity

than the M3 evaporator.

The heat transfer investigations and cost analysis determined that for the 5th

effect, a Robert evaporator with the traditional M2 tube is favoured. The M2 tube is

also recommended for the 4th effect as for many evaporator stations, particularly for

the steam efficient configurations, the brix of juice in the 4th effect is quite high (e.g.

60 brix) and so the processing conditions are not markedly different from those for the

5th effect.

7.5 Retrofitting of Calandria for Existing Evaporators


When an evaporator station requires the installation of additional area, the usual

procedure is to install another evaporator at the appropriate position or to replace an

existing evaporator with a new vessel of larger HSA to debottleneck the capacity.

However, consideration should be given to whether it may be feasible to replace the

calandria comprising M2 tubes of an existing evaporator with a favoured tube being

longer, or of smaller diameter. The experimental investigations have shown that this


change could be feasible at the 1st to 3rd effect positions. Obviously, retrofitting a new

calandria is only feasible if the remainder of the vessel body has adequate service life.

7.5.2 Practical considerations of retrofitting a calandria

When factories are upgrading the evaporator station to increase the capacity

and/or changing the configuration to suit increased steam efficiency, larger heating

surface areas are required. When increased steam efficiency is being sought, the

additional area will likely be placed in the effects upstream of the effect from which

maximum vapour bleeding is undertaken. In most scenarios, the additional area is

required in one, or perhaps two, of the first three effects in a quintuple set. In these

circumstances, retrofitting of a new calandria into an existing vessel may be feasible.

If a calandria is to be replaced with one of larger area, smaller diameter and/or

longer tubes would be used. Some additional practical matters have to be considered.

When the calandria is replaced with a new calandria comprising longer tubes,

the height of the vessel will most likely be increased in order to retain de-entrainment

efficiency. It is preferable to retain the base of the vessel at its current position, and

consequently the top cone and vapour offtake pipe will be raised. These costs must be

taken into account in the financial assessment to determine the viability of the retrofit.

If the top of the headspace cannot be lifted due to height limitations, lowering the

bottom remains the only option. In most cases, this option will be feasible if the

evaporators are located at a sufficient elevation above the ground floor level.

Consideration will need to be given to the transfer of the juice from one vessel to the

next, due to the different elevation of the base of the retrofitted evaporator.

7.5.3 Retrofit options

Design calculations have been undertaken for typical 2000 m2 and 5000 m2

Robert evaporators comprising M2 tubes (internal diameters of vessels being 5.78 and

8.89 m respectively) being replaced with calandrias using S3 and M3 tube dimensions,

with the pitch of tubes set at the minimum according to Australian Standards for a

pressure vessel. For this retrofit, the top of the vessel would be 1 m higher, assuming

the strake height is unchanged. The HSAs for the retrofitted evaporators are shown in

Table 7.13.


Table 7.13 Evaporator heating surface details for retrofit options

Original HSA of M2

evaporator

Details of evaporator with

S3 tubes

Details of evaporator with

M3 tubes

Number of

tubes

HSA

(m2)

Number of

tubes

HSA

(m2)

2000 10430 3500 7590 3000

5000 26034 8740 18986 7500

The data in Table 7.13 show that using S3 tubes, the HSA is increased by 75%

and using M3 tubes the HSA is increased by 50%. These are large increases in area

and would be sufficient to suit most applications for a retrofit. If a smaller increase in

area is required, then it would be feasible to increase the pitch of the tubes (resulting

in fewer tubes being installed) or reducing the height of the tubes (e.g. use 2.8 m tubes).

7.5.4 Further design considerations

The large increases in area that can be achieved by retrofitting S3 or M3 tubes

will increase the vapour rate from the vessel substantially. Retrofitting a calandria at

the 3rd effect position with S3 tube dimensions (previous one being M2 tube) would

result in higher HTC with an enhanced area. In such cases, increasing the strake height

may be necessary to avoid entrainment of juice. If increasing the strake height is not

an option, efficient louvre designs must be installed.


Replacing a calandria of M2 tubes in an existing evaporator with a new calandria

comprising S3 or M3 tubes provides a large increase in heating surface area (up to

75% increase). This retrofitting option may be a much cheaper option than installing

a new evaporator of the larger required area. However, there are several practical

matters including the maintenance of de-entrainment efficiency that must be

considered for the retrofit options.


The experimental program determined that the traditional tube M2 provided

good heat transfer performance across the full set of processing conditions that are

typically found in a quintuple evaporation station. The experimental program also

showed that tubes of 38.1 mm outside diameter and/or longer tubes (3 or 4 m length)


provided comparable heat transfer performance to the traditional tube at the 1st effect

position, and superior heat transfer performance at the 3rd effect position. Australian

mills are unlikely to utilise 4 m long tubes in Robert evaporators and so the favoured

tubes for the 1st to 3rd effects positions are S3 and M3. For the 5th effect position, the

traditional tube is favoured.

A cost analysis determined that evaporator vessels with the traditional tube are

more expensive than evaporator vessels comprising tubes of smaller diameter and/or

greater length. Thus, cost savings of ~20% should be possible by using tubes such as

38.1 mm outside diameter and 3 m length at the 3rd effect position.

An important benefit from using smaller diameter and longer tubes is that the

juice volume is smaller than in an evaporator with the traditional tube dimensions. For

a 1st effect evaporator operating in a high steam efficiency scenario (typically at high

boiling temperature and with large HSA), the smaller juice volume and shorter

residence time would provide for reduced sucrose losses and increased revenue for the

factory.

When an increase in HSA in the 1st to 3rd effects is required in order to increase

the juice processing capacity of the set and/or to suit an upgrade for a more steam-

efficient configuration, a financially attractive option may be to replace the calandria

of M2 tubes in an existing evaporator body with a calandria comprising smaller

diameter and longer tubes. This option should be much less expensive than installing

a new evaporator. Again, tubes S3 and M3 would be recommended for the replacement

calandrias.

General Discussions and Conclusions 217

CHAPTER 8: GENERAL DISCUSSIONS

AND CONCLUSIONS


This chapter summarises the research of this thesis and highlights the main

conclusions from the research. The knowledge gained during this research, along with

the significance and benefits to the Australian raw sugar industry are described.

Recommendations are made for further work, based on the foundation of this research.

8.2 Aim of the Research

The research project aimed to investigate the effect of tube dimensions and

operating conditions on the HTC of a rising film vertical tube evaporator. The research

aims are summarised in six parts:

• Developing a capital cost model to determine the costs of designing,

fabricating and installing Robert vessels of the same heating surface area but

comprising tubes of different dimensions.

• Determining the HTC of tubes with different lengths and diameters operating

through the full range of operating conditions experienced in industrial raw

sugar factory evaporators.

• Determining the optimum tube dimensions and operating conditions that

provide the maximum heat transfer coefficient (HTCmax) at the typical

conditions for the 1st effect, 3rd effect and 5th effect positions.

• Determining the HTC at different sections of the tube, in order to understand

the boiling patterns for the juice within the tube.

• Postulating a theory on boiling mechanisms based on the variation of HTC

along the length of the tube.

• Selecting the optimum tube dimensions for industrial evaporators based on

HTCmax, capital costs and operational costs.

218 General Discussions and Conclusions

8.3 Comments on the Experimental Program

Heat transfer measurements were undertaken for nine stainless steel tubes

comprising three different diameters and three different lengths for the following range

of operating conditions, corresponding to the conditions at the 1st, 3rd and 5th effects:

three brix values, two headspace pressures, two pressure differences and four juice

levels within the heating tube. In addition, replicate tests were undertaken for four

tubes (two different diameters and two different lengths) for the operating conditions

corresponding to the 1st and 5th effects.

The designation for the diameters of the tubes was S, M and L being for

38.1 mm, 44.45 mm and 50.8 mm outside diameters respectively. The tube lengths

were 2, 3 and 4 m. Thus, a code M2 was for the tube of 2 m length and 44.45 mm

outside diameter. This M2 tube is the tube traditionally used in evaporators in

Australian factories.

Each of the heating tubes was fitted with gutters on the outside of the tube, to

collect and drain condensate to an external container. Four gutters, which were spaced

equidistantly along the length of the tube, were installed on each tube. Thus, HTC

values could be calculated from the condensate collected for the four individual

sections on the tube and overall HTC values calculated from the total condensate rate

on the tube.

The test program was undertaken at typical industrial conditions, but a few

characteristics of the rig meant that the heat transfer performance might be slightly

different from that experienced in industrial evaporators. These factors included

• the drainage of condensate on the outside of the tube being from four

positions, whereas condensate in industrial evaporators drains to the

bottom plate;

• the single tube was combined with an adjacent downtake for juice flow

to the base of the evaporator, which would likely have reduced to some

extent the flow of juice down into the top of the heating tube. In

industrial evaporators, downtakes are provided but are located slightly

more distant from the heating tube on average than in the experimental

rig; and


• the tubes being new and clean for the tests (i.e. without any scale

deposits). Industrial evaporator tubes, even after a clean, would

generally have a slight deposit of scale, which would reduce the heat

transfer.

The replicate tests with the four tubes demonstrated a high level of consistency

with the heat transfer results of the original test program with the nine tubes. This

consistency provided confidence in the determinations of the heat transfer performance

for the nine tubes at the different operating conditions.

8.4 Summary of the Research Outcomes

8.4.1 Capital cost model

A capital cost model for the Robert evaporator was developed for 2000, 3000,

4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and 38.10 mm,

44.45 mm, and 50.80 mm tube outside diameter.

The results showed that the conventional evaporator, for which Australian

factories almost universally use 2 m tubes of 44.45 mm outside diameter, is more

expensive than using all the other tubes, except for evaporators with 2 m tubes of 50.8

mm outside diameter.

Relative to the conventional evaporator, cost savings in the ex-works cost of

~12% are likely in using 3 m long tubes of 44.45 mm outside diameter and ~15% if 3

m long tubes of 38.10 mm outside diameter are used. Further savings are made by the

use of 4 m long tubes, but the incremental cost reduction is less than increasing the

tube length from 2 to 3 m. Longer tube vessels have smaller diameter and considerably

less mass on the structure and foundations than the conventional evaporator, and so

additional savings through reduced installation costs would be achieved.

8.4.2 Heat transfer performance of different tube dimensions

The experimental investigations were undertaken to determine the HTC of

different tube lengths and diameters (nine tubes) for different operating conditions,

corresponding to the typical conditions in the 1st, 3rd and 5th effects (the Original432

dataset). Replicate tests were undertaken for the M2, S2, M3 and S3 tubes, to

understand the tube length and tube diameter interaction and to determine the

consistency in the results. These replicate tests were designated Replicate128.


The selection of two headspace pressures and two pressure differences for each

set of test conditions provided heat transfer data (heat flux and HTC) for four

temperature differences between the vapour in the steam chest and the boiling juice.

Analysis of the HTC results showed tube length and tube diameter interaction to

be significant. In other words, the choice of tube length and diameter cannot be

independent of each other in selecting a high level of heat transfer performance. The

trends observed from the results of the experimental program show that for tube

lengths of 3 m and higher, small diameter tubes are preferred. The replicate analysis

confirmed the result. It was concluded that as brix increases, HTC decreases. Also, at

higher headspace pressure the HTC values were generally higher. The effect of

headspace pressure is attributed to the lower viscosity of the juice at the higher boiling

temperature when the headspace pressure is higher. For 2 and 3 m tube lengths, 44.45

and 38.1 mm tube diameters gave higher HTC. For 4 m tube length, both 44.45 and

38.1 mm tube diameters gave higher HTC.

For each tube at each set of processing conditions (juice brix, headspace pressure

and pressure difference), HTC measurements were undertaken at four juice levels. In

all cases, a particular juice level provided a maximum HTC value (HTCmax) for those

conditions.

HTCmax results were determined from the Originla432 dataset. Analysis of

variance determined that tube diameter is more important than tube length in affecting

HTCmax. As brix increases, HTCmax decreases. For Brix-20, higher HTCmax values are

achieved at 38.1 and 44.45 mm tube diameter. For Brix-35 and Brix-70, higher HTCmax

values are achieved at 44.45 mm tube diameter. For Brix-35, the tube of 38.1 mm

diameter and 3 m length (S3) also provided good heat transfer performance.

Analysis of the optimum juice levels corresponding to HTCmax showed that as

brix increases, optimum juice level increases. The effect of tube length and headspace

pressure on optimum juice level was not clear. It was found that for tubes of 38.1 and

50.8 mm diameters, the optimum juice level increases with increase in pressure

difference, while for 44.45 mm tube diameter, the optimum juice level decreases with

increase in pressure difference.


Empirical relationships were developed for HTCmax and optimum juice level

(expressed as the actual level in the tube in mm). The empirical relationship for

HTCmax was

𝐻𝑇𝐶 = 𝐵−0.4901 𝑇𝑗1.3582 𝑉𝐶𝐶0.8877 8.1

where 𝐵 is the brix of the juice,

𝑇𝑗 is the temperature of the juice, °C

𝑉𝐶𝐶 is the vapour condensation coefficient, kg/h/m2

This relationship showed good agreement with the measured results (R2 = 0.94)

and with industry values, although the experimental data are slightly higher than

typical industry values at Brix-20.

The empirical relationship for optimum juice level (mm) was

𝐽𝐿𝑜𝑝𝑡 = 𝑇𝐿0.7253 𝐵0.4544 ΔT−0.1122 8.2

where 𝑇𝐿 is the tube length, mm

ΔT is the temperature difference between the steam and juice, °C.

8.4.3 Understanding the boiling patterns in the single tube

The HTC values for the individual sections of the tube of the Original432 dataset

were analysed to determine the variations relative to the overall HTC values. Six HTC

patterns were identified, of which four patterns accounted for more than 90% of the

results. The test conditions for each of these four HTC patterns were qualitatively and

quantitatively analysed to determine which tube dimensions and operating conditions

were most common for each of these boiling patterns. The relationship between these

HTC patterns and the magnitude of the overall HTC of the tube was also investigated.

The uniform boiling pattern was determined to be bubbly/slug flow boiling for the

whole length, while the low HTC at the bottom was of similar boiling behaviour but

bubbly flow at the bottom section. The boiling pattern that provided the second highest

overall heat transfer performance was Low HTC at bottom, for which the bottom

section of the tube had HTC value more than 15% below the overall HTC value. The

other two HTC patterns were Low HTC at top and Low HTC at intermediate section.

Both these patterns resulted in a lower overall HTC than the other two patterns.


A boiling mechanism was proposed for each of the four dominant HTC patterns.

It was concluded that Annular Flow did not exist in the single tube evaporator.

A new mechanism termed as “dry out” was identified to occur in the tube for the

low HTC at the top pattern. This mechanism was observed to be more likely to occur

for long tubes and low operating juice levels, wherein insufficient juice is able to rise

to the top of the tube and boiling is restricted to the bottom section of the tube. For the

boiling pattern with Low HTC at the intermediate section, no boiling pattern was

identified. The literature suggests that a Boiling Crisis or Critical Heat Flux can exist,

whereby bubbles adhere on the inner surface of the tube and as an insulating blanket

to heat transfer. However, the behaviour is only expected for very large temperature

differences between vapour and liquid and would not be expected in an evaporator.

The formation of a specific boiling pattern cannot be independently set.

However, setting the operating conditions for the evaporator, close to the optimum

conditions, will likely ensure that boiling patterns are formed, and good heat transfer

performance is achieved.

8.4.4 Selecting the optimum tube dimensions

The traditional 44.45 mm diameter, 2 m tube provides good heat transfer

performance across the full set of processing conditions typically found in a quintuple

evaporation station. It has been found that tubes of 38.1 mm outside diameter and/or

longer tubes (3 or 4 m length) provide comparable (or perhaps slightly inferior) heat

transfer performance to the traditional tube at the 1st effect position, and superior heat

transfer performance at the 3rd effect position.

Evaporator vessels with the traditional tube are more expensive than evaporator

vessels comprising tubes of smaller diameter and/or greater length. Thus, cost savings

of ~20% should be possible by using tubes such as 38.1 mm outside diameter and 3 m

length at the 3rd effect position. Even larger savings are achieved with 4 m long tubes.

However, Australian Mills are unlikely to utilise 4 m long tubes in Robert evaporators

and so the favoured tubes for the 1st to 3rd effects positions are S3 and M3. For the 4th

and 5th effect positions the traditional tube (M2) is favoured

An important benefit from using smaller diameter and longer tubes is that the

juice volume is smaller than in an evaporator with traditional tube dimensions. For a

1st effect evaporator operating in a high steam efficiency scenario (typically at high


boiling temperature and with large heating surface area), the smaller juice volume and

shorter residence time would provide for reduced sucrose losses and increased revenue

for the factory. This aspect reinforces the benefit of using S3 or M3 tubes at the 1st

effect position.

When an increase in heating surface area in the 1st to 3rd effects is required in

order to increase the juice processing capacity of the set and/or to suit an upgrade for

a more steam-efficient configuration, a financially attractive option may be to replace

the existing calandria of 44.45 mm and 2 m tubes with a calandria comprising smaller

diameter and longer tubes. Tubes of 38.1 mm or 44.45 mm diameter and 3 m length

(S3 and M3) are recommended for the replacement calandrias. Increases in heating

surface area of 75% and 50% respectively are achievable. This option should be much

less expensive than installing a new evaporator.

8.5 Significance of the Research


For practical application within the Australian sugar industry, this PhD study

• provided the cost implications for installing new Robert evaporators with

calandrias comprising tubes of different dimensions,

• determined the tube dimensions and juice level in the tube, which

provided the best heat transfer performance for the typical operating

conditions at the different effect positions,

• provided an understanding of the boiling mechanism in the rising film

vertical tube evaporator, and

• determined, through consideration of the heat transfer performance and

the capital and operating costs of the evaporators, the optimum tube

dimensions for use at the different effect positions.

8.5.2 Increase in HTC

An increase in HTC as a result of selecting the optimum tube dimensions for the

different effect positions would

1. allow reductions in the heating surface area required to achieve the same

rate of evaporation, or


2. achieve higher juice processing rates for the installed areas, or

3. extend the period of operation between cleans, compared with the use of

tubes of the traditional dimensions.

An important benefit of increased HTCs is the ability to achieve the required rate

of evaporation with a smaller temperature difference. This benefit is of particular

interest to factories seeking to reduce their process steam consumption and fuel usage.

8.5.3 Reducing capital costs

Selecting tube dimensions with smaller diameter and longer tubes would reduce

the vessel diameter, weight of the vessel, labour costs, foundations and structural costs,

and insulation costs. The potential savings from using S3 or M3 tubes for the same

heating surface area are ~15% for S3 tubes and ~12% for M3 tubes, compared with

using the M2 tubes.

8.5.4 Reducing operating costs

Vessels with smaller vessel diameter have lower juice volume intensities, which

results in lower juice residence times in the vessels. Sucrose degradation is primarily

a function of juice residence time and juice temperature. Reducing the juice residence

time in the early effects of the set would decrease the potential sucrose degradation

and increase the revenue of the factory.

For a Robert evaporator at the 1st effect in a factory seeking to reduce the process

steam consumption to a low level (usually operating at a high juice boiling

temperature), S3 and M3 tubes are favoured compared to an evaporator with M2 tubes,

owing to the lower juice volume intensity of these evaporators leading to reduced

sucrose losses. An evaporator with 38.1 mm diameter and 3 m long tubes provides a

larger increase in revenue compared with an evaporator with M3 tubes because of the

lower juice volume intensity of the evaporator with S3 tubes.

8.5.5 Retrofitting of calandrias

For situations where additional area is required at the 1st to 3rd effect positions

and the body of an existing evaporator with calandria of 44.45 mm diameter and 2 m

long tubes is in good condition, it may be feasible to retrofit a calandria with 38.1 mm

or 44.45 mm diameter and 3 m long tubes. Increases in area up to 75% and 50%

respectively can be achieved using 38.1 mm or 44.45 mm diameter and 3 m long tubes.


The retrofit option is likely to be much cheaper than installing a new evaporator of the

required area.

8.6 Recommendations for Future Research

While the research undertaken in this PhD study is considered comprehensive,

there remain tasks to understand the following:

• Why, at Brix-35, S2 tubes produced substantially inferior HTC values

compared with S3 tubes but at Brix-20 S2 and S3 tubes produced similar

and good HTC values?

• Would tubes of 25 mm diameter provide sufficiently good heat transfer

performance at the 1st effect position (and perhaps even the 2nd and 3rd

effect positions) to be feasible? Substantial cost savings are likely with

the use of 25 mm diameter tubes, compared with the longer diameter

tubes.

• To what extent has the removal of condensate at gutters on the tubes

affected the overall HTC values?

• What further information can be obtained to better understand the boiling

mechanism in vertical rising-film evaporators?

The CFD model development was only undertaken on the steam side of the

experimental rig. Further work is required to:

• Develop a CFD model of a single rising-film vertical tube to incorporate

two-phase flow. This model may use the HTC relationship and boiling

pattern information determined in this PhD study for validation.

• Develop a CFD model of a wedge of a Robert evaporator incorporating

the CFD model of the single tube. This CFD model would specifically

need to examine the effects of juice rising from individual tubes passing

across the top tube plate and flowing down adjacent tubes. This

behaviour is known to occur in industrial Robert evaporators.

The experimental setup, although quite sophisticated could be modified for

future investigations. Few of the modifications are listed here to assist future

investigators in this area of research:


• Include a stirrer in the juice tank to ensure good mixing of condensate

return into the juice.

• Include a small flowmeter in the juice downtake line to measure rate.

The author is not sure whether a suitable and very small flowmeter is

available.

• Undertake replicate trials on juice of 35 brix. In hindsight data at 35 brix

are more important than data at 70 brix, especially with the industrial

application of long tubes (>3 m length).

• No changes to the method of measuring HTC are proposed but some

trials on tubes with only a large bottom gutter would be worthwhile to

determine the influence of condensate on the outside of the tube on HTC

performance and to align this with theory.


In conclusion, the study has contributed to the knowledge of rising film vertical

tube evaporators through the following determinations:

• Tube length and tube diameter interaction is significant in affecting HTC of

the tube. In other words, the selection of tube length and tube diameter cannot

be independent of each other in seeking to maximise the HTC performance.

• At higher brix, the HTC is lower. Also, at a higher headspace pressure the

HTC is higher. This latter effect is attributed to the lower viscosity of the

juice at the higher boiling temperature.

• Juice level and tube diameter interaction is significant in affecting the HTC

of the tube. Tube diameter should be considered when selecting the juice level

in the evaporator. Higher juice levels for small diameter tubes and lower juice

levels for large diameter tubes have a detrimental effect on HTC.

• For a given tube and boiling at certain operating conditions, an optimum juice

level in the tube exists, which provides a maximum HTC (HTCmax). The

optimum juice level and HTCmax values are functions of juice brix, tube

diameter, tube length, headspace pressure and pressure difference.

• Tube diameter is more important than tube length in affecting HTCmax.


• Empirical models were developed for HTCmax and optimum juice level.

• Six different boiling patterns were identified to exist for the nine tubes and

operating conditions of the experimental program. Among these boiling

patterns, it was postulated that the bubbly and slug flow regime are dominant,

and an annular flow regime does not exist in the heating tube for typical

conditions in sugar mill evaporators. Boiling patterns with uniform HTC

values along the tube length and with low HTC at the bottom of the tube were

identified when good heat transfer performance is achieved.

• Favoured tube dimensions were selected, based on HTCmax. For the typical

operating conditions at the 1st effect, the traditional tube M2 and tubes S2,

M3, S3 and S4 provided high values of HTCmax. At the typical 3rd effect

boiling conditions, the traditional tube M2 and tubes M3, S3 and M4 provided

high values of HTCmax. For the typical 5th effect boiling conditions, the

traditional tube M2 and tube L2 provided high values of HTCmax.

• A cost model was developed, which showed that the fabrication and

installation costs for evaporators with smaller diameter and/or longer tubes

were substantially lower than for evaporators with the traditional M2 tube.

• For evaporators at the 1st effect in a steam efficient configuration (typically

high juice boiling temperature and large heating surface areas), tubes of

smaller diameter and/or longer tubes than the traditional M2 tube have

smaller juice hold-up volumes. Consequently, the extent of sucrose

hydrolysis would be less in these evaporators than for the M2 tube evaporator

owing to the shorter juice residence time.

• Based on considerations of the HTC performance, capital costs for an

installation, operating costs (particularly related to the potential sucrose

degradation at the 1st effect) and also practical considerations, the favoured

tubes in a quintuple evaporator set are:-

• For the 1st to 3rd effects, tubes S3 and M3

• For the 4th and 5th effects, the traditional M2 tube.

• Retrofitting of a calandria comprising S3 or M3 tubes into an existing

evaporator with M2 tubes may be a financially attractive alternative to


installing a new evaporator, in circumstances where additional heating

surface area is required. The retrofitting of the S3 or M3 tubes is only

recommended for evaporators at the 1st to 3rd effect positions, owing to their

good heat transfer performance at these positions.

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Appendix A: Description of Experimental Rig 235

APPENDIX A: DESCRIPTION OF

EXPERIMENTAL RIG

In Chapter 2, heat transfer results from previous pilot plant investigations and

factory trials of Robert evaporators were discussed. A major part of this study included

the assessment of the heat transfer performance of a single evaporator tube operating

in rising-film mode. The pilot evaporator rig was constructed so as to accommodate

the installation of tubes with different lengths and diameters. The heat-transfer

performance for each tube was evaluated for the full range of process conditions

normally experienced in factory vessels. The design, construction and commissioning

of the rig were completed in 2013 and are broadly described in this Appendix. The full

experimental program was conducted during the 2014 crushing season at Rocky Point

Mill between July and November.


A.1. Designing of the single tube evaporator rig

A.1.1. Design and construction of single tube

The single tube evaporator, which was used in the PhD study by Steven Pennisi

(at James Cook University), was used as a starting point for designing the experimental

rig (Pennisi, 2004). The rig at JCU was designed with a single stainless steel tube of 2

m length and 44.45 mm OD (i.e. M2 dimension).

The scope of this PhD study was extended to investigate the single-tube

evaporator rig with tubes of different dimensions as shown in Table 3.1. For future

references to the tube dimensions, the code shown in Table 3.1 on page 53 for each

tube is used. Since the evaporator rig from JCU was used for only the M2 dimension,

the rig had to be modified significantly. A draftsman was contracted to prepare the

manufacturing drawings.

The heating sources used in the evaporator rig were vapours from the factory

vessels at the 1st, 2nd, 3rd and 4th effects. Since Rocky Point mill has cogeneration, the

exhaust steam pressure is 250 kPa (abs) and the exhaust steam connection was located

distant from the rig installation. Hence, it was decided to use vapour from the 1st effect

as the heating source when operating the rig as a 1st effect. This arrangement is logical,

as the pressure of the 1st effect vapour is ~200 kPa (abs) (120 °C), which is typical of

the exhaust steam pressure in factories without cogeneration.

The vapour rate is not a controlled parameter in the experimental setup. Based

on the run, the pressure inside the calandria is controlled by an automatic control valve

through a PID controller. This is discussed in detail in section A.2. The maximum and

minimum values of vapour condensation coefficient for Australian vessels are 40

kg/h/m2 and 12 kg/h/m2 respectively (Watson, 1986a).

When designing the single tube rig, the anticipated maximum and minimum

vapour rates were used. The vapour rates for the nine tubes are described in A.1. These

data show that the maximum condensation rate on the tube is calculated at 25.5 kg/h

and the minimum condensation rate at 2.9 kg/h.

238 Appendix A: Description of Experimental Rig

Table A.1 Highest and lowest vapour rate for tubes

Tube Vapour rate (kg/h)

VCC–12 kg/h/m2 VCC–40 kg/h/m2

S2 2.9 9.6

M2 3.4 11.2

L2 3.8 12.8

S3 4.3 14.4

M3 5.0 16.8

L3 5.7 19.2

L2 5.7 19.2

L3 6.7 22.3

L4 7.7 25.5

Each tube has four gutters attached to the outside of the tubes, which are placed

equidistantly along the heating tube to drain the condensate to separate collection

chambers. This arrangement allows the determination of the heat transfer coefficient

at the different sections of the tube and for the entire tube length. The gutters were

designed to drain the condensed vapour for the highest vapour rate, without

overflowing and causing an error in the HTC calculations. The length and area of each

section is shown in Table A.2.

Table A.2 Section length and area for all tubes

Tube Section

length (m)

Section area (m2)

Section 1 Section 2 Section 3 Section 4

S2 0.50 0.06 0.06 0.06 0.06

M2 0.50 0.07 0.07 0.07 0.07

L2 0.50 0.08 0.08 0.08 0.08

S3 0.75 0.09 0.09 0.09 0.09

M3 0.75 0.10 0.10 0.10 0.10

L3 0.75 0.12 0.12 0.12 0.12

S4 1.00 0.12 0.12 0.12 0.12

M4 1.00 0.14 0.14 0.14 0.14

L4 1.00 0.16 0.16 0.16 0.16

In designing the gutter and the pipe to drain the condensate, a check needs to be

made on the pressure losses through the pipe to the collection chamber. The longest

tube in the experimental program is L4 and this would provide the greatest frictional

loss as it has the highest condensation flow and longest drain tube from the uppermost

gutter to the container.


Figure A.1. shows a photograph of the gutters and condensate drain pipes. The

pipe used for draining the condensate from the gutters is 9.53 mm diameter pipe (1

mm thickness).

Figure A.1 View of the gutters and drain pipes on two of the heating tubes

To determine the pressure drop in the pipe, the K-Hooper equation (Hooper,

1981) was used. Frictional losses were calculated, and the resulting pressure drop is

shown below in kPa and mm of fluid, based on the conditions for L4 tube (see Table

A.1).

Fluid flow (t/h)–6.4 × 10-3

Pipe ID–7.53 mm

Pipe length–5 m


Two 45 degree bends

One entrance and one exit

Viscosity of condensate at 20 °C

Pressure drop–0.1212 kPa (12.34 mm of fluid)

This pressure loss is equivalent to 2.4 mm per metre of length of the drain pipe,

which indicates that, even for a condensation rate several times the expected maximum

condensation rate, the drain tubes should readily drain the condensate from the gutter

to the condensate container. Overflowing of the gutters due to frictional losses in the

drain pipes should not occur.

A.1.2 Fabrication of vapour lines

As mentioned earlier, the heating sources in the evaporator rig were the vapours

from factory vessels. Vapour pipes from the 1st, 2nd, 3rd and 4th effect vapour lines were

connected to a single manifold near the rig installation. A condensate reservoir was

fabricated and installed on the vapour manifold after the steam control valve, to drain

the condensate that is present with the vapour stream before the vapour enters the

steam chest of the experimental rig.

A.1.3 Headspace and sight glass arrangement

As the liquid inside the tube boils, the vapour is passed through the headspace

of the rig. The headspace was made up of two sections. The first section, which was

just above the steam chest, was 600 mm long, 200 NB SCH 40 SS pipe with a sight

glass. The second section was 450 mm long, 400 NB SCH 40 SS pipe. This section

was added to reduce the entrainment of juice in the vapour when operating at high

evaporation conditions. The headspace equipment is shown in Figure A.2.

The vapour is withdrawn from the headspace through a trap to remove entrained

liquid. The trap was a 250 NB polycarbonate container (Figure A.2), which provided

a flow reversal designed to disengage the liquid. The separated liquid is collected in

the trap and the vapour passes through to the heat exchanger.

A.1.4 Heat exchanger, condenser and vacuum arrangement

The plate-type heat exchanger condensed the vapour by heat exchange with

cooling water. By necessity, in order to ensure that the total vapour flow is condensed,

the condensate is slightly sub-cooled (by up to 10 °C).


The condensed vapour from the heat exchanger passes to a separator pot where

incondensable gases are removed. The separator pot vents the incondensable gases to

vacuum (for trials with the headspace below atmospheric pressure) and to atmosphere

(for trials with the headspace above the atmospheric pressure).

The vacuum connection is procured from the factory’s vacuum pump via a

control valve. The control system for regulating the pressure (vacuum or above

atmospheric pressure) is discussed in section A.2.

The sub-cooled condensate from the separator pot is heated using an immersion

heater located in the pipe, transferring the condensate back to the juice tank. The

amount of sub-cooling is regulated so that the heating load does not overload the

immersion heater. The control systems for regulating the temperature of the cooled

condensate and the heated condensate are discussed in section A.2.


Figure A.2 Steam chest and headspace arrangement

Headspace

Sight glass

Steam

chest Steam pipe

Headspace

pressure

transmitter

Steam

chest

pressure

transmitter

External

juice return

line

Vapour

trap

Nox gases

pipe to

vacuum


A.1.5 Condensate collection for the heating tube and condensate level measurement

The condensate from each gutter and the base of the steam chest (flowing in 10

mm pipe) passed through a cooling jacket (32 NB SS pipe with sealed ends) before

entering the respective condensate container.

The cooled condensate was collected in polycarbonate containers of 76 mm OD

and 700 mm height for each of the four gutters and in a 100 mm OD 700 mm high

container for condensate from the base of the steam chest. The base of each container

had connections for a differential pressure transmitter (ΔP cell) and a drain valve.

The measurement setup for the ΔP cell is shown in Figure A.3. The low pressure

side of the ΔP cell was connected to the polycarbonate container and the high pressure

side was connected to a stand pipe (15 NB stainless steel pipe) holding a column of

water with a constant height of 700 mm. A manifold was located level with the top of

the polycarbonate container to equalise the pressure in the headspace of the container

to that of the steam chest. Thus, condensate collected in the gutter flowed by gravity

(via the cooling jacket) to the polycarbonate container. Before the start of each run,

condensate was drained from the reservoir.

The ΔP cell on the base of each container has a constant head of 700 mm water

on its high pressure side with the pressure on the low pressure side being the head of

condensate in the container, which varied from zero (empty container) to 700 mm (full

container). Thus, the differential pressure ranges between 700 mm and 0 mm. The ΔP

cells were calibrated from 0 to 700 mm.


Figure A.3 Arrangement for measuring the pressure head of condensate in the

container

The high performance Yokogawa differential pressure transmitters EJX110A

were selected to measure the condensate level in the containers. These transmitters

feature a single crystal silicon resonant sensor with output of 4 to 20 mA DC signal

corresponding to the measured differential pressure. The EJX110A- M capsule was

selected, as its range and accuracy suited the duty. The ambient temperature limits for

the EJX110A are -30 to 80 °C. In order to suit the temperature conditions, the

condensate was cooled prior to entering the containers. Cooling water was passed

through jackets that surrounded the drain tubes.

Figure A.4 shows a photograph of the polycarbonate containers, the cooling

jackets and the DP transmitters under the experimental rig.


Figure A.4 Arrangement of the DP transmitters and polycarbonate containers

A.1.6 Juice return and take off arrangement

A juice return line was provided to transfer juice from the top tube plate to the

juice tank below the steam chest. This setup replicates a mini downtake, which is often

provided in factory evaporators.

A.1.7 Assembly of the evaporator rig

Figure 4.1 on page 68 shows the layout of the evaporator rig assembly. The juice

tank was mounted on the support frame and the 2 m steam chest was placed on top.

The tube was then inserted from the top of the steam chest and using a spirit level, the

DP cell Support

frame

Polycarbonate

container

Manifold for

pressure

equalisation

Condensate

reservoir

Condensed

vapour

Cooling

water jackets


tube was aligned vertically, and all the bolts were tightened. Anti-Seize was used on

all the bolts to avoid cramming due to high temperature in the calandria and juice tank.

As described in section 4.3 on page 70, experiments were undertaken for nine

tubes. The procedure that was followed when changing a tube is explained below:

1. Isolate all utilities from the evaporator; turn off the immersion heater and

drain all the juice from the juice tank.

2. Uncouple all the unions on pipes on the rig.

3. Disconnect the condensate drainage pipes from the containers.

4. Remove the headspace vessel and unbolt the steam chest from the juice

tank.

5. Lift the steam chest with the chain block and unbolt the top flange on the

steam chest.

6. Lift the heating tube out of the steam chest and place it safely in storage.

7. As an example, if the existing set up is for a 2 m tube and a 3 m tube is

to be installed, install the 1 m steam chest above the 2 m steam chest. [If

the tube is of 4 m length, install the two 1 m steam chests above the 2 m

steam chest.]

8. Insert the selected heating tube inside the steam chest and reinstall the

top flange

9. Place the headspace vessel back in position and reinstall all connections.

10. Ensure all the unions on the pipework are connected correctly.

11. Connect the condensate drainage pipes into the cooling jackets and

connect each drain pipe to the condensate container.

12. Fill the steam chest with water and hydro test the vessel for any leaks.

Recheck all connections if any leaks are found.

A.2 Instrumentation and Control System of the Rig

A.2.1. Introductory remarks

This section describes the instrumentation and the control systems required to

operate the rig. There are four control loops in the evaporator rig and each one is


described in detail. Figure A.6 shows the arrangement for the instrumentation and

control system for the evaporator rig.

A.2.2 Headspace pressure control system

The arrangement for the headspace pressure control is shown in Figure A.6. The

pressure within the headspace of the evaporator rig was measured by the absolute

pressure transmitter (PT1), which sends an input signal to the proportional-integral-

derivative (PID 1) controller. The output signal from the controller regulates the valve

to the vacuum source or to atmosphere. The controller is set to forward-acting when

operating above atmospheric pressure and reverse-acting when operating below

atmospheric pressure. The operator enters a pressure set point for the headspace based

on the required boiling conditions for the run.


Figure A.6 Experimental rig control system


A.2.3 Vapour pressure control

The arrangement for the pressure control of vapour within the steam chest is

shown in Figure A.6. The pressure within the calandria of the evaporator rig is

measured by the absolute pressure transmitter (PT2), which sends an input signal to

the PID 2 controller. The output signal from the controller modulates the position of

the control valve (MSV) to allow/restrict vapour flow in the manifold. The steam

valves (SV1, SV2, and SV3) valves are manual valves for different tube heights. The

operator enters a pressure set point for the steam chest, based on the required boiling

conditions of the run.

A.2.5 Temperature control of the condensed vapour leaving the heat exchanger

In order to ensure the heating duty of the immersion heater is within its power

rating, the temperature of the condensed vapour is controlled to be ~10 °C below the

headspace saturation temperature. The PID 4 controller uses the temperature reading

from RTD2 (PV) and modulates the position of the valve to allow/restrict the flow of

cooling water to the heat exchanger.

A.2.4 Temperature control of return condensed vapour

The condensed vapour needs to be reheated to the boiling temperature of the

juice before adding it back to the juice tank. The juice temperature set point is

determined from RTD1. The RTD3 measures the temperature after the immersion

heater. The PID 3 controller regulates the power input to the immersion heater to the

heat the condensate until the RTD3 signal is at the set point. An auto switch is

implemented in the immersion heater to turn off the heater when the return leg has no

fluid. The switch had to be turned on manually before the start of each run.

A.2.6 Juice level monitoring

The juice level within the heating tube of the evaporator rig was measured by

the differential pressure transmitter (PT3) mounted on the juice tank. The low pressure

side of the transmitter was connected to the headspace of the rig. A glass tube

connected to the juice tank and to the headspace was installed to provide a visual check

on the level of juice and assist in setting the conditions for a run.

The instrumentation requirements are listed in Table A.4


Table A.4 List of instruments for the control of the evaporator rig

Tag Duty Type Control system Controller

PT1 Saturated

steam/vapour

Absolute

pressure

transmitter

Headspace

pressure

PID 1

PT2 Saturated

steam/vapour

Absolute

pressure

transmitter

Steam chest

pressure

PID 2

PT3 Level

monitoring

Differential

pressure

transmitter

Juice level

monitoring

RTD1 Juice/water Resistance

temperature

detectors

Juice tank

temperature

RTD2 Condensate Resistance

temperature

detectors

Condensate

temperature

before

immersion heater

PID 4

RTD3 Condensate Resistance

temperature

detectors

Condensate

temperature after

immersion heater

PID 3

Cartridge

heater, ½” D

×10” L

A.3 Data Logging

A.3.1 Introductory remarks

The pilot plant evaporator rig contained individual PID controllers to control the

operating parameters, as described in section A.2. The process variable signals from

these controllers along with the measurements of the condensate level in the

polycarbonate containers were routed through an Automation Direct Programmable

Logic Controller (PLC). This section describes the data logging system for the pilot

plant rig.

A.3.2 Programmable logic controller (PLC)

The process variable signals were wired into the analogue input modules of the

PLC. The Automation Direct Logic PLC utilises DirectSOFT32, a proprietary

software interface program suite to allow programming of the PLC and data access.

A part of this suite is the DSData Server. DSData Server is an application that

allows the third party software applications to read and write data to the PLC. DSData

supports two different mechanisms for undertaking this:


• Dynamic Data Exchange (DEE)

• Object Linking and Embedding for process control (OLE).

The project data was logged in Microsoft Excel with a simple visual basic macro

accessing and storing data with DEE via the DSData interface.

A.3.3 Process data logging

The process data that was logged for each run included juice level, juice

temperature, calandria pressure, headspace pressure and the condensate level in the

five polycarbonate containers. All the operating values were displayed on the excel

spreadsheet on the computer screen, which was placed next to the control box. The

computer screen was checked often to make sure data was being logged.

A.4 Commissioning of the Rig

The evaporator rig was commissioned during a two week period in mid-

November 2013, prior to the factory ceasing crushing operations for the 2013 season.

Overall the evaporator rig operated and functioned well. The instrumentation

and control system in particular worked well. The main changes needed to prepare the

rig for the experimental program were:-

• Insulation of the rig needed to be completed

• Spare polycarbonate containers were required to be constructed in

readiness for failures

• The manual valves for draining the condensate from the polycarbonate

containers needed to be replaced by solenoid valves so they could be

operated remotely

• The control valve for regulating the cooling water flow to the heat

exchanger needed to be replaced with a larger valve.

For the commissioning, only the M2 tube was tested; hence the possible

problems associated with changing tubes were still unknown. It was expected that,

even with the assistance of Rocky Point tradesmen, a full day might be taken to change

a tube.


A.5 Experimental trials in 2014

The experimental trials were undertaken in the period July to November 2014 at

Rocky Point sugar factory. The trials included the Original432 and Replicate128

experiments. A total of 13 tubes were changed during the trials. Table A.5 presents the

test order for the Original432 and Replicate128 experiments.

Table A.5 Test order for the tubes for the Original432 and Replicate128

experiments

The procedure for changing a tube took approximately 7 hours. A contractor

tradesman assisted with replacing the tube and preparing the rig for the next series of

experimental trials.

A.5 Concluding Remarks

The design, construction and installation of the evaporator rig have been

described in this Appendix. The control system has also been described.

Commissioning was undertaken late in the 2013 crushing season. The modifications

that were required have been listed. These modifications were completed prior to

undertaking the experimental trials in the 2014 season.

Order Tube

Original432

1 M4

2 S3

3 M3

4 L4

5 S2

6 M2

7 L2

8 L3

9 S4

Replicate128

1 M2

2 S2

3 M3

4 S3

Appendix B: CFD Model–Steam Side 253

APPENDIX B: CFD MODEL–STEAM

SIDE

B.1 Introductory Remarks

This appendix presents the CFD model simulations on the steam side of the pilot

evaporator. The modelling demonstrates that the velocity of vapour in the vicinity of

the outer wall of the heating tube is very low. The likelihood of the vapour flow

disturbing the condensate film on the outside of the tube is negligible.

Appendix B: CFD Model–Steam Side 255

Figure B.1 CFD model showing the steam velocity profile for a 0.5 m section of

the pilot evaporator

Appendix C: Original432 Data Set - Experimental Design and Results 257

APPENDIX C: ORIGINAL432 DATA SET -

EXPERIMENTAL DESIGN AND

RESULTS

C.1 Introductory remarks

This appendix presents the results of the Original432 experiments conducted

with the evaporator rig. Nine tubes were tested with a wide range of operating

conditions. Table C.1 presents the experimental design. The HTC and VCC results of

the Original432 experiments are shown in Table C.2. Visual observations of the

boiling pattern were discussed in section 5.3 on page 113. Three boiling patterns were

identified:

• No visible juice above top plate (NV)

• Visible juice above top plate (VJ)

• Substantial juice above top plate (SJ)

Table C.2 presents the visual observations for each test. The code shown above

is used to describe the visual observations of the test.


Table C.1 Order of tests for the Original432 experiment

Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

36 4 44.45 20 20 800 149 33

33 4 44.45 20 20 800 149 45

35 4 44.45 20 20 800 126 33

34 4 44.45 20 20 800 126 45

8 4 44.45 20 30 1200 149 33

6 4 44.45 20 30 1200 149 45

5 4 44.45 20 30 1200 126 33

7 4 44.45 20 30 1200 126 45

32 4 44.45 20 40 1600 149 33

30 4 44.45 20 40 1600 149 45

31 4 44.45 20 40 1600 126 33

29 4 44.45 20 40 1600 126 45

1 4 44.45 20 50 2000 149 33

4 4 44.45 20 50 2000 149 45

3 4 44.45 20 50 2000 126 33

2 4 44.45 20 50 2000 126 45

13 4 44.45 35 20 800 94 35

16 4 44.45 35 20 800 94 50

15 4 44.45 35 20 800 72 35

14 4 44.45 35 20 800 72 50

9 4 44.45 35 35 1400 94 35

12 4 44.45 35 35 1400 94 50

11 4 44.45 35 35 1400 72 35

10 4 44.45 35 35 1400 72 50

45 4 44.45 35 45 1800 94 35

48 4 44.45 35 45 1800 94 50

47 4 44.45 35 45 1800 72 35

46 4 44.45 35 45 1800 72 50

26 4 44.45 35 60 2400 94 35

27 4 44.45 35 60 2400 94 50

25 4 44.45 35 60 2400 72 35

28 4 44.45 35 60 2400 72 50

42 4 44.45 70 30 1200 29 42

44 4 44.45 70 30 1200 29 60

43 4 44.45 70 30 1200 22 42

41 4 44.45 70 30 1200 22 60

39 4 44.45 70 45 1800 29 42

37 4 44.45 70 45 1800 29 60

38 4 44.45 70 45 1800 22 42

40 4 44.45 70 45 1800 22 60

23 4 44.45 70 55 2200 29 42

24 4 44.45 70 55 2200 29 60

21 4 44.45 70 55 2200 22 42

22 4 44.45 70 55 2200 22 60

19 4 44.45 70 70 2800 29 42

260 Appendix C: Original432 Data Set - Experimental Design and Results

Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

18 4 44.45 70 70 2800 29 60

20 4 44.45 70 70 2800 22 42

17 4 44.45 70 70 2800 22 60

80 3 38.1 20 20 600 149 33

79 3 38.1 20 20 600 149 45

77 3 38.1 20 20 600 126 33

78 3 38.1 20 20 600 126 45

93 3 38.1 20 30 900 149 33

96 3 38.1 20 30 900 149 45

95 3 38.1 20 30 900 126 33

94 3 38.1 20 30 900 126 45

74 3 38.1 20 40 1200 149 33

73 3 38.1 20 40 1200 149 45

76 3 38.1 20 40 1200 126 33

75 3 38.1 20 40 1200 126 45

51 3 38.1 20 50 1500 149 33

52 3 38.1 20 50 1500 149 45

49 3 38.1 20 50 1500 126 33

50 3 38.1 20 50 1500 126 45

86 3 38.1 35 20 600 94 35

85 3 38.1 35 20 600 94 50

88 3 38.1 35 20 600 72 35

87 3 38.1 35 20 600 72 50

70 3 38.1 35 35 1050 94 35

69 3 38.1 35 35 1050 94 50

72 3 38.1 35 35 1050 72 35

71 3 38.1 35 35 1050 72 50

81 3 38.1 35 45 1350 94 35

82 3 38.1 35 45 1350 94 50

84 3 38.1 35 45 1350 72 35

83 3 38.1 35 45 1350 72 50

68 3 38.1 35 60 1800 94 35

65 3 38.1 35 60 1800 94 50

66 3 38.1 35 60 1800 72 35

67 3 38.1 35 60 1800 72 50

62 3 38.1 70 30 900 29 42

64 3 38.1 70 30 900 29 60

63 3 38.1 70 30 900 22 42

61 3 38.1 70 30 900 22 60

59 3 38.1 70 45 1350 29 42

58 3 38.1 70 45 1350 29 60

57 3 38.1 70 45 1350 22 42

60 3 38.1 70 45 1350 22 60

91 3 38.1 70 55 1650 29 42

92 3 38.1 70 55 1650 29 60

90 3 38.1 70 55 1650 22 42

89 3 38.1 70 55 1650 22 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

53 3 38.1 70 70 2100 29 42

54 3 38.1 70 70 2100 29 60

56 3 38.1 70 70 2100 22 42

55 3 38.1 70 70 2100 22 60

121 3 44.45 20 20 600 149 33

122 3 44.45 20 20 600 149 45

124 3 44.45 20 20 600 126 33

123 3 44.45 20 20 600 126 45

102 3 44.45 20 30 900 149 33

104 3 44.45 20 30 900 149 45

101 3 44.45 20 30 900 126 33

103 3 44.45 20 30 900 126 45

118 3 44.45 20 40 1200 149 33

120 3 44.45 20 40 1200 149 45

117 3 44.45 20 40 1200 126 33

119 3 44.45 20 40 1200 126 45

100 3 44.45 20 50 1500 149 33

98 3 44.45 20 50 1500 149 45

97 3 44.45 20 50 1500 126 33

99 3 44.45 20 50 1500 126 45

139 3 44.45 35 20 600 94 35

138 3 44.45 35 20 600 94 50

137 3 44.45 35 20 600 72 35

140 3 44.45 35 20 600 72 50

130 3 44.45 35 35 1050 94 35

129 3 44.45 35 35 1050 94 50

132 3 44.45 35 35 1050 72 35

131 3 44.45 35 35 1050 72 50

128 3 44.45 35 45 1350 94 35

127 3 44.45 35 45 1350 94 50

125 3 44.45 35 45 1350 72 35

126 3 44.45 35 45 1350 72 50

107 3 44.45 35 60 1800 94 35

106 3 44.45 35 60 1800 94 50

108 3 44.45 35 60 1800 72 35

105 3 44.45 35 60 1800 72 50

142 3 44.45 70 30 900 29 42

141 3 44.45 70 30 900 29 60

143 3 44.45 70 30 900 22 42

144 3 44.45 70 30 900 22 60

115 3 44.45 70 45 1350 29 42

116 3 44.45 70 45 1350 29 60

113 3 44.45 70 45 1350 22 42

114 3 44.45 70 45 1350 22 60

136 3 44.45 70 55 1650 29 42

133 3 44.45 70 55 1650 29 60

134 3 44.45 70 55 1650 22 42


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

135 3 44.45 70 55 1650 22 60

109 3 44.45 70 70 2100 29 42

110 3 44.45 70 70 2100 29 60

112 3 44.45 70 70 2100 22 42

111 3 44.45 70 70 2100 22 60

181 4 50.8 20 20 800 149 33

183 4 50.8 20 20 800 149 45

182 4 50.8 20 20 800 126 33

184 4 50.8 20 20 800 126 45

177 4 50.8 20 30 1200 149 33

178 4 50.8 20 30 1200 149 45

179 4 50.8 20 30 1200 126 33

180 4 50.8 20 30 1200 126 45

169 4 50.8 20 40 1600 149 33

170 4 50.8 20 40 1600 149 45

171 4 50.8 20 40 1600 126 33

172 4 50.8 20 40 1600 126 45

146 4 50.8 20 50 2000 149 33

145 4 50.8 20 50 2000 149 45

148 4 50.8 20 50 2000 126 33

147 4 50.8 20 50 2000 126 45

186 4 50.8 35 20 800 94 35

185 4 50.8 35 20 800 94 50

188 4 50.8 35 20 800 72 35

187 4 50.8 35 20 800 72 50

176 4 50.8 35 35 1400 94 35

173 4 50.8 35 35 1400 94 50

175 4 50.8 35 35 1400 72 35

174 4 50.8 35 35 1400 72 50

167 4 50.8 35 45 1800 94 35

168 4 50.8 35 45 1800 94 50

166 4 50.8 35 45 1800 72 35

165 4 50.8 35 45 1800 72 50

163 4 50.8 35 60 2400 94 35

164 4 50.8 35 60 2400 94 50

161 4 50.8 35 60 2400 72 35

162 4 50.8 35 60 2400 72 50

158 4 50.8 70 30 1200 29 42

157 4 50.8 70 30 1200 29 60

159 4 50.8 70 30 1200 22 42

160 4 50.8 70 30 1200 22 60

156 4 50.8 70 45 1800 29 42

155 4 50.8 70 45 1800 29 60

153 4 50.8 70 45 1800 22 42

154 4 50.8 70 45 1800 22 60

189 4 50.8 70 55 2200 29 42

190 4 50.8 70 55 2200 29 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

191 4 50.8 70 55 2200 22 42

192 4 50.8 70 55 2200 22 60

150 4 50.8 70 70 2800 29 42

149 4 50.8 70 70 2800 29 60

152 4 50.8 70 70 2800 22 42

151 4 50.8 70 70 2800 22 60

229 2 38.1 20 20 400 149 33

230 2 38.1 20 20 400 149 45

231 2 38.1 20 20 400 126 33

232 2 38.1 20 20 400 126 45

219 2 38.1 20 30 600 149 33

218 2 38.1 20 30 600 149 45

217 2 38.1 20 30 600 126 33

220 2 38.1 20 30 600 126 45

215 2 38.1 20 40 800 149 33

213 2 38.1 20 40 800 149 45

214 2 38.1 20 40 800 126 33

216 2 38.1 20 40 800 126 45

194 2 38.1 20 50 1000 149 33

193 2 38.1 20 50 1000 149 45

196 2 38.1 20 50 1000 126 33

195 2 38.1 20 50 1000 126 45

226 2 38.1 35 20 400 94 35

225 2 38.1 35 20 400 94 50

227 2 38.1 35 20 400 72 35

228 2 38.1 35 20 400 72 50

224 2 38.1 35 35 700 94 35

223 2 38.1 35 35 700 94 50

222 2 38.1 35 35 700 72 35

221 2 38.1 35 35 700 72 50

204 2 38.1 35 45 900 94 35

203 2 38.1 35 45 900 94 50

202 2 38.1 35 45 900 72 35

201 2 38.1 35 45 900 72 50

200 2 38.1 35 60 1200 94 35

199 2 38.1 35 60 1200 94 50

198 2 38.1 35 60 1200 72 35

197 2 38.1 35 60 1200 72 50

239 2 38.1 70 30 600 29 42

237 2 38.1 70 30 600 29 60

240 2 38.1 70 30 600 22 42

238 2 38.1 70 30 600 22 60

210 2 38.1 70 45 900 29 42

212 2 38.1 70 45 900 29 60

211 2 38.1 70 45 900 22 42

209 2 38.1 70 45 900 22 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

235 2 38.1 70 55 1100 29 42

236 2 38.1 70 55 1100 29 60

233 2 38.1 70 55 1100 22 42

234 2 38.1 70 55 1100 22 60

206 2 38.1 70 70 1400 29 42

208 2 38.1 70 70 1400 29 60

207 2 38.1 70 70 1400 22 42

205 2 38.1 70 70 1400 22 60

241 2 44.45 20 20 400 149 33

242 2 44.45 20 20 400 149 45

243 2 44.45 20 20 400 126 33

244 2 44.45 20 20 400 126 45

277 2 44.45 20 30 600 149 33

279 2 44.45 20 30 600 149 45

278 2 44.45 20 30 600 126 33

280 2 44.45 20 30 600 126 45

260 2 44.45 20 40 800 149 33

259 2 44.45 20 40 800 149 45

258 2 44.45 20 40 800 126 33

257 2 44.45 20 40 800 126 45

284 2 44.45 20 50 1000 149 33

281 2 44.45 20 50 1000 149 45

283 2 44.45 20 50 1000 126 33

282 2 44.45 20 50 1000 126 45

245 2 44.45 35 20 400 94 35

246 2 44.45 35 20 400 94 50

247 2 44.45 35 20 400 72 35

248 2 44.45 35 20 400 72 50

268 2 44.45 35 35 700 94 35

267 2 44.45 35 35 700 94 50

266 2 44.45 35 35 700 72 35

265 2 44.45 35 35 700 72 50

263 2 44.45 35 45 900 94 35

264 2 44.45 35 45 900 94 50

262 2 44.45 35 45 900 72 35

261 2 44.45 35 45 900 72 50

286 2 44.45 35 60 1200 94 35

285 2 44.45 35 60 1200 94 50

288 2 44.45 35 60 1200 72 35

287 2 44.45 35 60 1200 72 50

251 2 44.45 70 30 600 29 42

252 2 44.45 70 30 600 29 60

250 2 44.45 70 30 600 22 42

249 2 44.45 70 30 600 22 60

269 2 44.45 70 45 900 29 42

272 2 44.45 70 45 900 29 60

271 2 44.45 70 45 900 22 42


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

270 2 44.45 70 45 900 22 60

256 2 44.45 70 55 1100 29 42

253 2 44.45 70 55 1100 29 60

255 2 44.45 70 55 1100 22 42

254 2 44.45 70 55 1100 22 60

275 2 44.45 70 70 1400 29 42

276 2 44.45 70 70 1400 29 60

274 2 44.45 70 70 1400 22 42

273 2 44.45 70 70 1400 22 60

314 2 50.8 20 20 400 149 33

315 2 50.8 20 20 400 149 45

313 2 50.8 20 20 400 126 33

316 2 50.8 20 20 400 126 45

295 2 50.8 20 30 600 149 33

296 2 50.8 20 30 600 149 45

294 2 50.8 20 30 600 126 33

293 2 50.8 20 30 600 126 45

310 2 50.8 20 40 800 149 33

311 2 50.8 20 40 800 149 45

312 2 50.8 20 40 800 126 33

309 2 50.8 20 40 800 126 45

292 2 50.8 20 50 1000 149 33

290 2 50.8 20 50 1000 149 45

291 2 50.8 20 50 1000 126 33

289 2 50.8 20 50 1000 126 45

324 2 50.8 35 20 400 94 35

323 2 50.8 35 20 400 94 50

321 2 50.8 35 20 400 72 35

322 2 50.8 35 20 400 72 50

304 2 50.8 35 35 700 94 35

303 2 50.8 35 35 700 94 50

302 2 50.8 35 35 700 72 35

301 2 50.8 35 35 700 72 50

320 2 50.8 35 45 900 94 35

319 2 50.8 35 45 900 94 50

318 2 50.8 35 45 900 72 35

317 2 50.8 35 45 900 72 50

299 2 50.8 35 60 1200 94 35

300 2 50.8 35 60 1200 94 50

297 2 50.8 35 60 1200 72 35

298 2 50.8 35 60 1200 72 50

332 2 50.8 70 30 600 29 42

329 2 50.8 70 30 600 29 60

330 2 50.8 70 30 600 22 42

331 2 50.8 70 30 600 22 60

333 2 50.8 70 45 900 29 42

336 2 50.8 70 45 900 29 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

334 2 50.8 70 45 900 22 42

335 2 50.8 70 45 900 22 60

328 2 50.8 70 55 1100 29 42

325 2 50.8 70 55 1100 29 60

326 2 50.8 70 55 1100 22 42

327 2 50.8 70 55 1100 22 60

308 2 50.8 70 70 1400 29 42

305 2 50.8 70 70 1400 29 60

307 2 50.8 70 70 1400 22 42

306 2 50.8 70 70 1400 22 60

379 3 50.8 20 20 600 149 33

377 3 50.8 20 20 600 149 45

380 3 50.8 20 20 600 126 33

378 3 50.8 20 20 600 126 45

347 3 50.8 20 30 900 149 33

346 3 50.8 20 30 900 149 45

348 3 50.8 20 30 900 126 33

345 3 50.8 20 30 900 126 45

373 3 50.8 20 40 1200 149 33

376 3 50.8 20 40 1200 149 45

374 3 50.8 20 40 1200 126 33

375 3 50.8 20 40 1200 126 45

351 3 50.8 20 50 1500 149 33

350 3 50.8 20 50 1500 149 45

352 3 50.8 20 50 1500 126 33

349 3 50.8 20 50 1500 126 45

364 3 50.8 35 20 600 94 35

362 3 50.8 35 20 600 94 50

363 3 50.8 35 20 600 72 35

361 3 50.8 35 20 600 72 50

384 3 50.8 35 35 1050 94 35

382 3 50.8 35 35 1050 94 50

383 3 50.8 35 35 1050 72 35

381 3 50.8 35 35 1050 72 50

356 3 50.8 35 45 1350 94 35

355 3 50.8 35 45 1350 94 50

354 3 50.8 35 45 1350 72 35

353 3 50.8 35 45 1350 72 50

357 3 50.8 35 60 1800 94 35

360 3 50.8 35 60 1800 94 50

359 3 50.8 35 60 1800 72 35

358 3 50.8 35 60 1800 72 50

344 3 50.8 70 30 900 29 42

343 3 50.8 70 30 900 29 60

342 3 50.8 70 30 900 22 42

341 3 50.8 70 30 900 22 60

340 3 50.8 70 45 1350 29 42


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

339 3 50.8 70 45 1350 29 60

338 3 50.8 70 45 1350 22 42

337 3 50.8 70 45 1350 22 60

371 3 50.8 70 55 1650 29 42

370 3 50.8 70 55 1650 29 60

369 3 50.8 70 55 1650 22 42

372 3 50.8 70 55 1650 22 60

368 3 50.8 70 70 2100 29 42

367 3 50.8 70 70 2100 29 60

366 3 50.8 70 70 2100 22 42

365 3 50.8 70 70 2100 22 60

403 4 38.1 20 20 800 149 33

401 4 38.1 20 20 800 149 45

402 4 38.1 20 20 800 126 33

404 4 38.1 20 20 800 126 45

400 4 38.1 20 30 1200 149 33

398 4 38.1 20 30 1200 149 45

397 4 38.1 20 30 1200 126 33

399 4 38.1 20 30 1200 126 45

390 4 38.1 20 40 1600 149 33

391 4 38.1 20 40 1600 149 45

392 4 38.1 20 40 1600 126 33

389 4 38.1 20 40 1600 126 45

385 4 38.1 20 50 2000 149 33

387 4 38.1 20 50 2000 149 45

388 4 38.1 20 50 2000 126 33

386 4 38.1 20 50 2000 126 45

425 4 38.1 35 20 800 94 35

427 4 38.1 35 20 800 94 50

426 4 38.1 35 20 800 72 35

428 4 38.1 35 20 800 72 50

429 4 38.1 35 35 1400 94 35

432 4 38.1 35 35 1400 94 50

431 4 38.1 35 35 1400 72 35

430 4 38.1 35 35 1400 72 50

422 4 38.1 35 45 1800 94 35

421 4 38.1 35 45 1800 94 50

424 4 38.1 35 45 1800 72 35

423 4 38.1 35 45 1800 72 50

420 4 38.1 35 60 2400 94 35

418 4 38.1 35 60 2400 94 50

417 4 38.1 35 60 2400 72 35

419 4 38.1 35 60 2400 72 50

414 4 38.1 70 30 1200 29 42

416 4 38.1 70 30 1200 29 60

415 4 38.1 70 30 1200 22 42

413 4 38.1 70 30 1200 22 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

411 4 38.1 70 45 1800 29 42

412 4 38.1 70 45 1800 29 60

410 4 38.1 70 45 1800 22 42

409 4 38.1 70 45 1800 22 60

395 4 38.1 70 55 2200 29 42

393 4 38.1 70 55 2200 29 60

394 4 38.1 70 55 2200 22 42

396 4 38.1 70 55 2200 22 60

408 4 38.1 70 70 2800 29 42

405 4 38.1 70 70 2800 29 60

407 4 38.1 70 70 2800 22 42

406 4 38.1 70 70 2800 22 60


Table C.2 Results from the Original432 experiment

Test Brix ΔP (kPa) ΔT (°C) HTC

(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

36 17.9 33 5.73 2826 26.37 VJ

33 17.9 40 6.91 2802 31.57 VJ

35 17.9 33 6.54 2969 31.48 VJ

34 17.9 45 8.76 3474 49.47 VJ

8 17.8 33 5.73 3542 33.08 SJ

6 17.8 45 7.73 3269 41.25 SJ

5 17.8 33 6.55 1751 18.58 NV

7 17.8 45 8.77 3453 49.20 SJ

32 17 33 5.76 2975 27.92 VJ

30 17 45 7.76 3725 47.19 VJ

31 17 33 6.57 3118 33.22 VJ

29 17 45 8.79 3806 54.39 VJ

1 15 33 5.83 1441 13.68 VJ

4 15 40 7.01 3596 41.10 SJ

3 15 33 6.64 3134 33.73 SJ

2 15 45 8.86 3097 44.59 VJ

13 36 35 7.86 898 11.35 NV

16 36 50 11.10 1374 24.64 NV

15 36 35 9.74 2308 35.91 VJ

14 36 50 13.49 2159 46.75 VJ

9 34 35 7.97 3530 45.24 SJ

12 34 50 11.21 2007 36.33 VJ

11 34 35 9.84 2494 39.23 VJ

10 34 50 13.59 2435 53.14 SJ

45 36.2 35 7.85 3328 42.00 VJ

48 36.2 50 11.09 1132 20.27 VJ

47 36.2 35 9.73 2628 40.85 VJ

46 36.2 50 13.48 2651 57.35 VJ

26 34.7 35 7.93 2651 33.82 NV

27 34.7 50 11.17 2989 53.93 SJ

25 34.7 35 9.81 2510 39.34 VJ

28 34.7 50 13.56 2319 50.47 VJ

42 68 42 17.70 145 4.05 NV

44 68 60 23.77 252 9.50 NV

43 68 42 21.32 146 4.90 NV

41 68 60 27.88 187 8.26 NV

39 69.5 42 17.34 186 5.08 NV

37 69.5 60 23.42 412 15.32 NV

38 69.5 42 20.98 118 3.88 NV

40 69.5 60 27.54 200 8.72 NV

23 65 42 18.30 261 7.54 NV

24 65 60 24.38 308 11.93 NV

21 65 42 21.90 71 2.44 NV

22 65 60 28.46 441 19.90 VJ

19 66 42 18.11 149 4.26 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

18 66 60 24.19 386 14.81 VJ

20 66 42 21.72 249 8.50 NV

17 66 60 28.28 409 18.35 VJ

80 17.9 33 5.73 3886 36.27 SJ

79 17.9 40 6.91 3737 42.11 SJ

77 17.9 33 6.54 4133 43.83 SJ

78 17.9 45 8.76 3867 55.08 SJ

93 21.7 33 5.59 3389 30.84 VJ

96 21.7 40 6.76 3521 38.84 VJ

95 21.7 33 6.40 2917 30.27 VJ

94 21.7 45 8.62 2978 41.74 VJ

74 20 33 5.65 4221 38.86 SJ

73 20 41 6.99 3749 42.78 SJ

76 20 33 6.47 3457 36.24 VJ

75 20 45 8.69 3445 48.64 VJ

51 16.3 33 5.79 2616 24.66 NV

52 16.3 36 6.29 2177 22.33 NV

49 16.3 33 6.60 2166 23.16 NV

50 16.3 45 8.82 3114 44.62 VJ

86 37.7 35 7.76 2020 25.20 NV

85 37.7 50 11.00 2735 48.59 VJ

88 37.7 35 9.64 296 4.56 NV

87 37.7 50 13.39 800 17.20 NV

70 38 35 7.74 3998 49.77 SJ

69 38 50 10.98 2964 52.58 SJ

72 38 35 9.62 1144 17.60 NV

71 38 50 13.38 1006 21.60 NV

81 38 35 7.74 3763 46.84 VJ

82 38 50 10.98 3231 57.30 SJ

84 38 35 9.62 1532 23.56 NV

83 38 50 13.38 1000 21.48 NV

68 38 35 7.74 840 10.46 NV

65 38 50 10.98 2041 36.20 NV

66 38 35 9.62 2161 33.24 NV

67 38 50 13.38 1806 38.78 NV

62 66.8 42 17.95 258 7.32 NV

64 66.8 60 24.03 350 13.35 NV

63 66.8 42 21.57 271 9.20 NV

61 66.8 60 28.13 325 14.48 NV

59 67 42 17.91 272 7.68 NV

58 67 60 23.99 376 14.31 NV

57 67 42 21.53 466 15.79 NV

60 67 60 28.09 246 10.94 NV

91 67.6 42 17.78 427 11.97 NV

92 67.6 60 23.86 427 16.19 NV

90 67.6 42 21.41 404 13.61 NV

89 67.6 60 27.97 385 17.05 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

53 69 42 17.47 539 14.84 NV

54 69 60 23.54 347 12.97 NV

56 69 42 21.10 346 11.48 NV

55 69 60 27.66 103 4.51 NV

121 17.9 33 5.73 1964 18.33 NV

122 17.9 40 6.91 1193 13.44 NV

124 17.9 33 6.54 1223 12.97 NV

123 17.9 45 8.76 909 12.95 NV

102 20 33 5.65 4343 39.98 VJ

104 20 45 7.65 4084 51.00 SJ

101 20 33 6.47 2016 21.13 SJ

103 20 45 8.69 4459 62.96 SJ

118 20 33 5.65 2922 26.90 VJ

120 20 45 7.65 2105 26.29 NV

117 20 33 6.47 2288 23.99 NV

119 20 45 8.69 1079 15.24 NV

100 18 33 5.73 3288 30.67 VJ

98 18 45 7.72 3530 44.51 VJ

97 18 33 6.54 3620 38.37 VJ

99 18 45 8.76 4057 57.75 SJ

139 35.9 35 7.86 126 1.59 NV

138 35.9 50 11.11 206 3.69 NV

137 35.9 35 9.74 169 2.64 NV

140 35.9 50 13.49 194 4.20 NV

130 38.5 35 7.71 548 6.79 NV

129 38.5 50 10.95 337 5.97 NV

132 38.5 35 9.59 485 7.43 NV

131 38.5 50 13.35 838 17.94 NV

128 37.5 35 7.77 900 11.24 NV

127 37.5 50 11.01 775 13.79 NV

125 37.5 35 9.65 633 9.77 NV

126 37.5 50 13.40 698 15.03 NV

107 36.5 35 7.83 3632 45.74 SJ

106 36.5 50 11.07 3550 63.48 SJ

108 36.5 35 9.71 2794 43.36 SJ

105 36.5 50 13.46 2134 46.11 SJ

142 70 42 17.22 71 1.93 NV

141 70 60 23.29 226 8.37 NV

143 70 42 20.86 104 3.42 NV

144 70 60 27.42 52 2.27 NV

115 68.5 42 17.58 138 3.84 NV

116 68.5 60 23.66 25 0.93 NV

113 68.5 42 21.21 197 6.57 NV

114 68.5 60 27.77 231 10.18 NV

136 70 42 17.22 20 0.54 NV

133 70 60 23.29 248 9.16 NV

134 70 42 20.86 91 2.97 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

135 70 60 27.42 89 3.87 NV

109 68.5 42 17.58 454 12.59 NV

110 68.5 60 23.66 337 12.67 NV

112 68.5 42 21.21 64 2.12 NV

111 68.5 60 27.77 58 2.57 NV

181 17.9 33 5.73 831 7.75 NV

183 17.9 40 6.91 508 5.72 NV

182 17.9 33 6.54 896 9.50 NV

184 17.9 45 8.76 457 6.51 NV

177 17 33 5.76 714 6.50 NV

178 17 40 6.94 684 7.75 NV

179 17 33 6.57 540 5.75 NV

180 17 45 8.79 664 9.48 NV

169 17.2 33 5.75 611 5.73 NV

170 17.2 41 7.10 817 9.46 NV

171 17.2 33 6.57 731 7.78 NV

172 17.2 45 8.79 456 6.51 NV

146 21.9 33 5.58 802 7.56 NV

145 21.9 39 6.59 587 6.51 NV

148 21.9 33 6.40 684 7.32 NV

147 21.9 45 8.62 654 9.15 NV

186 36 35 7.86 125 1.58 NV

185 36 50 11.10 103 1.85 NV

188 36 35 9.74 283 4.40 NV

187 36 50 13.49 206 4.46 NV

176 34 35 7.97 523 6.70 NV

173 34 50 11.21 190 3.43 NV

175 34 35 9.84 780 12.27 NV

174 34 50 13.59 843 18.39 NV

167 36.2 35 7.85 353 4.45 NV

168 36.2 50 11.09 244 4.37 NV

166 36.2 35 9.73 120 1.86 NV

165 36.2 50 13.48 492 10.65 NV

163 34.7 35 7.93 124 1.58 NV

164 34.7 50 11.17 288 5.19 NV

161 34.7 35 9.81 740 11.59 NV

162 34.7 50 13.56 386 8.40 NV

158 68 42 17.70 28 0.77 NV

157 68 60 23.77 28 1.07 NV

159 68 42 21.32 11 0.38 NV

160 68 60 27.88 23 1.01 NV

156 69.5 42 17.34 123 3.37 NV

155 69.5 60 23.42 48 1.80 NV

153 69.5 42 20.98 94 3.09 NV

154 69.5 60 27.54 48 2.09 NV

189 65 42 18.30 117 3.37 NV

190 65 60 24.38 46 1.77 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

191 65 42 21.90 152 5.22 NV

192 65 60 28.46 75 3.36 NV

150 70 42 17.22 192 5.21 NV

149 70 60 23.29 91 3.36 NV

152 70 42 20.86 54 1.79 NV

151 70 60 27.42 52 2.26 NV

229 17.5 33 5.74 2515 23.54 NV

230 17.5 35 6.08 2831 28.06 NV

231 17.5 33 6.56 4618 49.07 VJ

232 17.5 45 8.78 3074 43.84 VJ

219 20 33 5.65 4661 42.91 SJ

218 20 40 6.83 4152 46.26 SJ

217 20 33 6.47 4938 51.76 SJ

220 20 45 8.69 3804 53.71 SJ

215 18 33 5.73 4358 40.65 VJ

213 18 41 7.07 3688 42.53 SJ

214 18 33 6.54 2092 22.17 NV

216 18 45 8.76 5225 74.39 SJ

194 18 33 5.73 1987 18.54 NV

193 18 44 7.56 1077 13.29 NV

196 18 33 6.54 1475 15.63 NV

195 18 45 8.76 935 13.31 NV

226 36.5 35 7.83 170 2.14 NV

225 36.5 50 11.07 1350 24.14 NV

227 36.5 35 9.71 2294 35.60 VJ

228 36.5 50 13.46 721 15.58 NV

224 37 35 7.80 424 5.32 NV

223 37 50 11.04 397 7.07 NV

222 37 35 9.68 395 6.11 NV

221 37 50 13.43 2130 45.94 VJ

204 37 35 7.80 823 10.32 NV

203 37 50 11.04 647 11.53 NV

202 37 35 9.68 75 1.16 NV

201 37 50 13.43 1413 30.48 VJ

200 37.2 35 7.79 764 9.57 NV

199 37.2 50 11.03 276 4.91 NV

198 37.2 35 9.67 26 0.40 NV

197 37.2 50 13.42 99 2.14 NV

239 70 42 17.22 22 0.60 NV

237 70 60 23.29 286 10.59 NV

240 70 42 20.86 42 1.39 NV

238 70 60 27.42 290 12.59 NV

210 70.5 42 17.09 17 0.47 NV

212 70.5 60 23.16 130 4.77 NV

211 70.5 42 20.73 19 0.63 NV

209 70.5 60 27.29 25 1.08 NV

235 71.5 42 16.81 5 0.14 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

236 71.5 60 22.88 35 1.29 NV

233 71.5 42 20.47 535 17.21 VJ

234 71.5 60 27.03 168 7.20 NV

206 72 42 16.66 453 11.90 NV

208 72 60 22.73 444 16.05 VJ

207 72 42 20.32 492 15.72 VJ

205 72 60 26.88 546 23.27 VJ

241 18.2 33 5.72 3638 33.89 VJ

242 18.2 37 6.40 3124 32.57 NV

243 18.2 33 6.53 2255 23.87 NV

244 18.2 45 8.75 1651 23.49 NV

277 19.5 33 5.67 3033 28.02 VJ

279 19.5 40 6.85 5133 57.34 SJ

278 19.5 33 6.49 4835 50.83 SJ

280 19.5 45 8.71 2639 37.34 VJ

260 20 33 5.65 5509 50.72 SJ

259 20 38 6.50 5663 59.99 SJ

258 20 33 6.47 4784 50.15 SJ

257 20 45 8.69 2636 37.22 VJ

284 20 33 5.65 5051 46.50 SJ

281 20 37 6.33 4792 49.44 SJ

283 20 33 6.47 3550 37.21 VJ

282 20 45 8.69 2521 35.59 VJ

245 37 35 7.80 2272 28.50 VJ

246 37 50 11.04 1795 32.00 VJ

247 37 35 9.68 844 13.06 NV

248 37 50 13.43 1287 27.76 NV

268 38 35 7.74 1357 16.89 NV

267 38 50 10.98 1689 29.96 NV

266 38 35 9.62 803 12.34 NV

265 38 50 13.38 2218 47.62 VJ

263 35 35 7.91 1639 20.86 NV

264 35 50 11.16 1843 33.20 NV

262 35 35 9.79 1133 17.73 NV

261 35 50 13.54 2267 49.28 NV

286 35 35 7.91 3020 38.44 VJ

285 35 50 11.16 2970 53.51 VJ

288 35 35 9.79 2228 34.86 VJ

287 35 50 13.54 1884 40.96 NV

251 72 42 16.66 262 6.89 NV

252 72 60 22.73 557 20.13 NV

250 72 42 20.32 34 1.09 NV

249 72 60 26.88 478 20.35 NV

269 71.9 42 16.69 625 16.46 VJ

272 71.9 60 22.76 437 15.80 NV

271 71.9 42 20.35 934 29.89 VJ

270 71.9 60 26.91 385 16.42 NV

256 69.8 42 17.27 417 11.35 VJ



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

253 69.8 60 23.34 150 5.56 NV

255 69.8 42 20.91 346 11.37 NV

254 69.8 60 27.47 28 1.20 NV

275 74 42 16.00 501 12.65 VJ

276 74 60 22.08 376 13.17 VJ

274 74 42 19.69 367 11.37 NV

273 74 60 26.25 474 19.73 VJ

314 18 33 5.73 3433 32.02 VJ

315 18 35 6.07 3784 37.40 VJ

313 18 33 6.54 1708 18.10 NV

316 18 45 8.76 43 0.61 NV

295 16.9 33 5.77 2912 27.35 NV

296 16.9 37 6.44 1555 16.33 NV

294 16.9 33 6.58 2644 28.19 NV

293 16.9 45 8.80 1327 18.97 NV

310 20 33 5.65 4378 40.31 VJ

311 20 41 6.99 3446 39.33 VJ

312 20 33 6.47 4557 47.77 VJ

309 20 45 8.69 1684 23.78 NV

292 18.5 33 5.71 3227 30.00 VJ

290 18.5 37 6.38 2580 26.86 VJ

291 18.5 33 6.52 1788 18.90 NV

289 18.5 45 8.74 1794 25.49 NV

324 36 35 7.86 510 6.45 NV

323 36 50 11.10 819 14.68 NV

321 36 35 9.74 561 8.72 NV

322 36 50 13.49 702 15.21 NV

304 37 35 7.80 1472 18.47 NV

303 37 50 11.04 2256 40.23 VJ

302 37 35 9.68 2966 45.89 VJ

301 37 50 13.43 2215 47.76 NV

320 35 35 7.91 187 2.38 NV

319 35 50 11.16 1058 19.07 NV

318 35 35 9.79 1376 21.52 NV

317 35 50 13.54 2268 49.31 NV

299 35 35 7.91 1421 18.08 NV

300 35 50 11.16 2802 50.48 VJ

297 35 35 9.79 1510 23.63 NV

298 35 50 13.54 789 17.15 NV

332 70 42 17.22 4 0.10 NV

329 70 60 23.29 616 22.80 VJ

330 70 42 20.86 214 7.01 NV

331 70 60 27.42 103 4.49 NV

333 67 42 17.91 588 16.63 VJ

336 67 60 23.99 157 5.97 NV

334 67 42 21.53 256 8.68 NV

335 67 60 28.09 110 4.87 NV

328 73 42 16.34 10 0.25 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

325 73 60 22.42 729 25.95 VJ

326 73 42 20.02 337 10.60 NV

327 73 60 26.58 151 6.38 NV

308 69 42 17.47 769 21.18 SJ

305 69 60 23.54 797 29.80 SJ

307 69 42 21.10 589 19.54 VJ

306 69 60 27.66 413 18.11 VJ

379 18.2 33 5.72 29 0.27 NV

377 18.2 40 6.90 2205 24.80 NV

380 18.2 33 6.53 1895 20.06 NV

378 18.2 45 8.75 610 8.67 NV

347 17.5 33 5.74 2631 24.62 NV

346 17.5 40 6.92 2586 29.20 NV

348 17.5 33 6.56 2217 23.56 NV

345 17.5 45 8.78 1467 20.92 NV

373 18.2 33 5.72 5668 52.80 SJ

376 18.2 35 6.06 3778 37.30 VJ

374 18.2 33 6.53 2224 23.54 VJ

375 18.2 45 8.75 2629 37.40 VJ

351 14.2 33 5.86 4063 38.75 VJ

350 14.2 40 7.03 1945 22.31 VJ

352 14.2 33 6.67 621 6.71 NV

349 14.2 45 8.89 2106 30.42 NV

364 34.1 35 7.96 753 9.64 NV

362 34.1 50 11.21 521 9.42 NV

363 34.1 35 9.84 1096 17.22 NV

361 34.1 50 13.59 1077 23.50 NV

384 34 35 7.97 615 7.89 NV

382 34 50 11.21 498 9.01 NV

383 34 35 9.84 1195 18.80 NV

381 34 50 13.59 883 19.27 NV

356 34.9 35 7.92 742 9.44 NV

355 34.9 50 11.16 543 9.79 NV

354 34.9 35 9.80 1596 24.99 NV

353 34.9 50 13.55 1431 31.11 NV

357 35.2 35 7.90 689 8.75 NV

360 35.2 50 11.15 523 9.42 NV

359 35.2 35 9.78 411 6.42 NV

358 35.2 50 13.53 2002 43.49 VJ

344 73 42 16.34 57 1.48 NV

343 73 60 22.42 154 5.48 NV

342 73 42 20.02 252 7.94 NV

341 73 60 26.58 301 12.69 NV

340 72.9 42 16.38 127 3.28 NV

339 72.9 60 22.45 155 5.52 NV

338 72.9 42 20.05 56 1.76 NV

337 72.9 60 26.61 149 6.29 NV

371 71.2 42 16.89 136 3.62 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

370 71.2 60 22.97 508 18.54 VJ

369 71.2 42 20.55 47 1.53 NV

372 71.2 60 27.11 261 11.23 NV

368 73.2 42 16.28 313 8.04 NV

367 73.2 60 22.35 347 12.32 NV

366 73.2 42 19.96 114 3.59 NV

365 73.2 60 26.52 623 26.18 VJ

403 17.9 33 5.73 3938 36.76 SJ

401 17.9 45 7.72 3514 44.33 SJ

402 17.9 33 6.54 4214 44.69 SJ

404 17.9 45 8.76 3795 54.05 SJ

400 17.5 33 5.74 4212 39.41 SJ

398 17.5 45 7.74 4039 51.04 SJ

397 17.5 33 6.56 4108 43.65 VJ

399 17.5 45 8.78 2559 36.51 VJ

390 15 33 5.83 4504 42.77 VJ

391 15 45 7.82 3387 43.28 VJ

392 15 33 6.64 1065 11.46 NV

389 15 45 8.86 1654 23.82 NV

385 16 33 5.80 4121 38.90 VJ

387 16 40 6.97 1529 17.39 NV

388 16 33 6.61 1631 17.47 NV

386 16 45 8.83 3692 52.97 VJ

425 37 35 7.80 712 8.94 NV

427 37 50 11.04 400 7.14 NV

426 37 35 9.68 796 12.32 NV

428 37 50 13.43 761 16.40 NV

429 35 35 7.91 42 0.54 NV

432 35 50 11.16 32 0.58 NV

431 35 35 9.79 29 0.45 NV

430 35 50 13.54 32 0.69 NV

422 35 35 7.91 710 9.03 NV

421 35 50 11.16 332 5.98 NV

424 35 35 9.79 652 10.20 NV

423 35 50 13.54 734 15.95 NV

420 35 35 7.91 663 8.44 NV

418 35 50 11.16 550 9.90 NV

417 35 35 9.79 1250 19.57 NV

419 35 50 13.54 889 19.33 NV

414 70 42 17.22 182 4.94 NV

416 70 60 23.29 333 12.33 NV

415 70 42 20.86 71 2.32 NV

413 70 60 27.42 180 7.80 NV

411 67 42 17.91 168 4.75 NV

412 67 60 23.99 347 13.21 NV

410 67 42 21.53 47 1.58 NV

409 67 60 28.09 253 11.26 NV

395 67.6 42 17.78 255 7.16 NV



(W/m2/K)

VCC

(kg/h/m2)

Observations on

boiling pattern

393 67.6 60 23.86 327 12.40 NV

394 67.6 42 21.41 129 4.34 NV

396 67.6 60 27.97 52 2.32 NV

408 69 42 17.47 224 6.16 NV

405 69 60 23.54 371 13.89 NV

407 69 42 21.10 110 3.66 NV

406 69 60 27.66 398 17.45 NV

Appendix D: Replicate128 Data Set - Experimental Design and Results 279

APPENDIX D: REPLICATE128 DATA

SET - EXPERIMENTAL DESIGN AND

RESULTS

D.1 Introductory Remarks

This appendix presents the results of the Replicates128 experiments conducted

with the evaporator rig. Four tubes were tested with a range of operating conditions.

Brix of 20 and 70 were selected to keep the experiment in manageable size. Table D.1

presents the experimental design. The HTC and VCC results of the Replicate128

experiments are shown in Table D.2. Table D.2 includes the visual observations for

each test.


Table D.1 Order of tests for the Replicate128 experiment

Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

5 2 44.45 20 20 400 149 33

7 2 44.45 20 20 400 149 45

6 2 44.45 20 20 400 126 33

8 2 44.45 20 20 400 126 45

25 2 44.45 20 30 600 149 33

27 2 44.45 20 30 600 149 45

26 2 44.45 20 30 600 126 33

28 2 44.45 20 30 600 126 45

9 2 44.45 20 40 800 149 33

10 2 44.45 20 40 800 149 45

11 2 44.45 20 40 800 126 33

12 2 44.45 20 40 800 126 45

1 2 44.45 20 50 1000 149 33

3 2 44.45 20 50 1000 149 45

2 2 44.45 20 50 1000 126 33

4 2 44.45 20 50 1000 126 45

21 2 44.45 70 30 600 29 42

22 2 44.45 70 30 600 29 60

23 2 44.45 70 30 600 22 42

24 2 44.45 70 30 600 22 60

30 2 44.45 70 45 900 29 42

29 2 44.45 70 45 900 29 60

32 2 44.45 70 45 900 22 42

31 2 44.45 70 45 900 22 60

14 2 44.45 70 55 1100 29 42

13 2 44.45 70 55 1100 29 60

15 2 44.45 70 55 1100 22 42

16 2 44.45 70 55 1100 22 60

18 2 44.45 70 70 1400 29 42

17 2 44.45 70 70 1400 29 60

20 2 44.45 70 70 1400 22 42

19 2 44.45 70 70 1400 22 60

69 3 44.45 20 20 400 149 33

70 3 44.45 20 20 400 149 45

72 3 44.45 20 20 400 126 33

71 3 44.45 20 20 400 126 45

89 3 44.45 20 30 600 149 33

91 3 44.45 20 30 600 149 45

90 3 44.45 20 30 600 126 33

92 3 44.45 20 30 600 126 45

65 3 44.45 20 40 800 149 33

67 3 44.45 20 40 800 149 45

66 3 44.45 20 40 800 126 33

68 3 44.45 20 40 800 126 45

95 3 44.45 20 50 1000 149 33

94 3 44.45 20 50 1000 149 45

282 Appendix D: Replicate128 Data Set - Experimental Design and Results

Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

96 3 44.45 20 50 1000 126 33

93 3 44.45 20 50 1000 126 45

81 3 44.45 70 30 600 29 42

83 3 44.45 70 30 600 29 60

82 3 44.45 70 30 600 22 42

84 3 44.45 70 30 600 22 60

74 3 44.45 70 45 900 29 42

73 3 44.45 70 45 900 29 60

75 3 44.45 70 45 900 22 42

76 3 44.45 70 45 900 22 60

86 3 44.45 70 55 1100 29 42

85 3 44.45 70 55 1100 29 60

87 3 44.45 70 55 1100 22 42

88 3 44.45 70 55 1100 22 60

77 3 44.45 70 70 1400 29 42

79 3 44.45 70 70 1400 29 60

78 3 44.45 70 70 1400 22 42

80 3 44.45 70 70 1400 22 60

37 2 38.1 20 20 600 149 33

38 2 38.1 20 20 600 149 45

40 2 38.1 20 20 600 126 33

39 2 38.1 20 20 600 126 45

57 2 38.1 20 30 900 149 33

59 2 38.1 20 30 900 149 45

58 2 38.1 20 30 900 126 33

60 2 38.1 20 30 900 126 45

33 2 38.1 20 40 1200 149 33

35 2 38.1 20 40 1200 149 45

34 2 38.1 20 40 1200 126 33

36 2 38.1 20 40 1200 126 45

63 2 38.1 20 50 1500 149 33

62 2 38.1 20 50 1500 149 45

64 2 38.1 20 50 1500 126 33

61 2 38.1 20 50 1500 126 45

49 2 38.1 70 30 900 29 42

51 2 38.1 70 30 900 29 60

50 2 38.1 70 30 900 22 42

52 2 38.1 70 30 900 22 60

42 2 38.1 70 45 1350 29 42

41 2 38.1 70 45 1350 29 60

43 2 38.1 70 45 1350 22 42

44 2 38.1 70 45 1350 22 60

54 2 38.1 70 55 1650 29 42

53 2 38.1 70 55 1650 29 60

55 2 38.1 70 55 1650 22 42

56 2 38.1 70 55 1650 22 60

45 2 38.1 70 70 2100 29 42

47 2 38.1 70 70 2100 29 60


Test TL

(m)

TD

(mm)

Brix JL (% tube

height)

JL (abs in

mm)

HS (kPa

abs)

ΔP

(kPa)

46 2 38.1 70 70 2100 22 42

48 2 38.1 70 70 2100 22 60

101 3 38.1 20 20 600 149 33

102 3 38.1 20 20 600 149 45

104 3 38.1 20 20 600 126 33

103 3 38.1 20 20 600 126 45

121 3 38.1 20 30 900 149 33

123 3 38.1 20 30 900 149 45

122 3 38.1 20 30 900 126 33

124 3 38.1 20 30 900 126 45

97 3 38.1 20 40 1200 149 33

99 3 38.1 20 40 1200 149 45

98 3 38.1 20 40 1200 126 33

100 3 38.1 20 40 1200 126 45

127 3 38.1 20 50 1500 149 33

126 3 38.1 20 50 1500 149 45

128 3 38.1 20 50 1500 126 33

125 3 38.1 20 50 1500 126 45

113 3 38.1 70 30 900 29 42

115 3 38.1 70 30 900 29 60

114 3 38.1 70 30 900 22 42

116 3 38.1 70 30 900 22 60

106 3 38.1 70 45 1350 29 42

105 3 38.1 70 45 1350 29 60

107 3 38.1 70 45 1350 22 42

108 3 38.1 70 45 1350 22 60

118 3 38.1 70 55 1650 29 42

117 3 38.1 70 55 1650 29 60

119 3 38.1 70 55 1650 22 42

120 3 38.1 70 55 1650 22 60

109 3 38.1 70 70 2100 29 42

111 3 38.1 70 70 2100 29 60

110 3 38.1 70 70 2100 22 42

112 3 38.1 70 70 2100 22 60


Table D.2 Results from the Replicate128 experiment


(W/m2/K)

VCC

(kg/h//m2)

5 17.9 33 5.73 3449 32.19

7 17.9 37 6.41 2963 30.94

6 17.9 33 6.54 2139 22.68

8 17.9 45 8.76 1567 22.32

25 21.7 33 5.59 2832 25.77

27 21.7 40 6.76 4782 52.76

26 21.7 33 6.40 4506 46.76

28 21.7 45 8.62 2451 34.35

9 20.0 33 5.65 4958 45.65

10 20.0 38 6.50 5097 53.99

11 20.0 33 6.47 4306 45.13

12 20.0 45 8.69 2372 33.50

1 16.3 33 5.79 3364 31.71

3 16.3 37 6.46 3539 37.29

2 16.3 33 6.60 3845 41.12

4 16.3 45 8.69 2655 37.48

21 70.0 42 16.66 257 6.75

22 70.0 60 22.73 546 19.73

23 70.0 42 20.86 33 1.07

24 70.0 60 27.42 459 19.94

30 67.0 42 17.91 548 15.47

29 67.0 60 23.99 390 14.85

32 67.0 42 20.35 878 28.10

31 67.0 60 26.91 362 15.43

14 67.6 42 17.78 372 10.45

13 67.6 60 23.86 7 0.28

15 67.6 42 21.41 311 10.46

16 67.6 60 27.97 25 1.11

18 69.0 42 17.47 436 12.02

17 69.0 60 23.54 335 12.51

20 69.0 42 21.10 326 10.81

19 69.0 60 27.66 821 35.98

69 18.9 33 5.69 1878 17.41

70 18.9 40 6.87 1139 12.77

72 18.9 33 6.51 1168 12.32

71 18.9 45 8.73 867 12.30

89 20.5 33 5.63 4227 38.78

91 20.5 45 7.63 3971 49.47

90 20.5 33 6.45 1961 20.50

92 20.5 45 8.67 4335 61.07

65 16.0 33 5.80 2707 25.56

67 16.0 45 7.79 1963 24.97

66 16.0 33 6.61 2128 22.79

68 16.0 45 8.83 1009 14.47

95 17.0 33 5.76 3203 30.06

94 17.0 45 7.76 3443 43.62

286 Appendix D: Replicate128 Data Set - Experimental Design and Results


(W/m2/K)

VCC

(kg/h//m2)

96 17.0 33 6.57 3529 37.60

93 17.0 45 8.79 3960 56.60

81 70.0 42 17.22 75 2.03

83 70.0 60 23.29 237 8.79

82 70.0 42 20.86 109 3.59

84 70.0 60 27.42 55 2.38

74 67.0 42 17.91 149 4.22

73 67.0 60 23.99 27 1.02

75 67.0 42 21.21 217 7.23

76 67.0 60 27.77 254 11.20

86 67.6 42 17.78 20 0.57

85 67.6 60 23.86 254 9.62

87 67.6 42 21.41 93 3.12

88 67.6 60 27.97 92 4.07

77 68.5 42 17.58 431 11.96

79 68.5 60 23.66 320 12.04

78 68.5 42 21.21 60 2.02

80 68.5 60 27.77 56 2.45

37 20.00 33 5.65 2633 24.24

38 20.00 35 5.99 2960 28.91

40 20.00 33 6.47 4822 50.54

39 20.00 45 8.69 3199 45.16

57 16.00 33 5.80 4772 45.06

59 16.00 40 6.97 4270 48.57

58 16.00 33 6.61 5075 54.35

60 16.00 45 8.83 3931 56.40

33 19.00 33 5.69 4298 39.84

35 19.00 41 7.03 3633 41.68

34 19.00 33 6.50 2061 21.72

36 19.00 45 8.72 5142 72.90

63 20.00 33 5.65 1913 17.61

62 20.00 44 7.49 1033 12.62

64 20.00 33 6.47 1417 14.85

61 20.00 45 8.69 895 12.64

49 72.00 42 17.22 23 0.62

51 72.00 60 23.29 429 15.88

50 72.00 42 20.32 65 2.09

52 72.00 60 26.88 443 18.89

42 69.70 42 17.29 20 0.56

41 69.70 60 23.37 154 5.73

43 69.70 42 20.73 23 0.76

44 69.70 60 27.29 30 1.29

54 68.00 42 17.70 5 0.14

53 68.00 60 23.77 36 1.35

55 68.00 42 21.32 539 18.07

56 68.00 60 27.88 171 7.56

45 70.00 42 17.22 482 13.09

47 70.00 60 23.29 477 17.65



(W/m2/K)

VCC

(kg/h//m2)

46 70.00 42 20.86 527 17.30

48 70.00 60 27.42 589 25.60

101 18.00 33 5.73 3617 33.73

102 18.00 40 6.90 3478 39.16

104 18.00 33 6.54 3846 40.76

103 18.00 45 8.76 3598 51.22

121 16.90 33 5.77 3186 29.91

123 16.90 40 6.94 3327 37.68

122 16.90 33 6.58 2754 29.36

124 16.90 45 8.80 2832 40.49

97 20.00 33 5.65 4010 36.92

99 20.00 41 6.99 3561 40.64

98 20.00 33 6.47 3284 34.42

100 20.00 45 8.69 3273 46.21

127 18.50 33 5.71 2705 25.15

126 18.50 36 6.22 2248 22.78

128 18.50 33 6.52 2235 23.62

125 18.50 45 8.74 3204 45.52

113 66.80 42 17.95 251 7.10

115 66.80 60 24.03 339 12.95

114 66.80 42 21.57 263 8.93

116 66.80 60 28.13 315 14.05

106 67.00 42 17.91 258 7.29

105 67.00 60 23.99 357 13.60

107 67.00 42 21.53 443 15.00

108 67.00 60 28.09 233 10.39

118 67.60 42 17.78 448 12.57

117 67.60 60 23.86 448 17.00

119 67.60 42 21.41 424 14.29

120 67.60 60 27.97 404 17.90

109 69.00 42 17.47 593 16.33

111 69.00 60 23.54 381 14.26

110 69.00 42 21.10 381 12.63

112 69.00 60 27.66 113 4.96

Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests 289

APPENDIX E: HTCmax AND VCCmax

RESULTS OF ORIGINAL432 AND

REPLICATE128 TESTS

E.1 Introductory Remarks

This appendix presents the HTCmax results of the Original432 and Replicates128

experiments. The selection of HTCmax results is detailed in section 5.7.2 on page 131.

Tests were undertaken at four juice levels and an optimum juice level was determined,

which corresponded to the maximum heat transfer coefficient. The HTCmax and

VCCmax results are presented along with the corresponding operating conditions during

the test. For the target operating conditions, refer to Table C.1 and D.1 using the test

number for Original432 and Replicate128 tests respectively.


Table E.1 HTCmax and VCCmax results from the Original432 experiment

Test TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

HTCmax

(W/m2/K)

VCCmax

(kg/h/m2)

8 4 44.45 17.8 30 1200 149 33 5.73 3542 33.08

30 4 44.45 17 40 1600 149 45 7.76 3725 47.19

3 4 44.45 15 50 2000 126 33 6.64 3134 33.73

29 4 44.45 17 40 1600 126 45 8.79 3806 54.39

9 4 44.45 34 35 1400 94 35 7.97 3530 45.24

27 4 44.45 34.7 60 2400 94 50 11.17 2989 53.93

47 4 44.45 36.2 45 1800 72 35 9.73 2628 40.85

46 4 44.45 36.2 45 1800 72 50 13.48 2651 57.35

23 4 44.45 65 55 2200 29 42 18.3 261 7.54

37 4 44.45 69.5 45 1800 29 60 23.42 412 15.32

20 4 44.45 66 70 2800 22 42 21.72 249 8.5

22 4 44.45 65 55 2200 22 60 28.46 441 19.9

74 3 38.1 20 40 1200 149 33 5.65 4221 38.86

73 3 38.1 20 40 1200 149 41 6.99 3749 42.78

77 3 38.1 17.9 20 600 126 33 6.54 4133 43.83

78 3 38.1 17.9 20 600 126 45 8.76 3867 55.08

70 3 38.1 38 35 1050 94 35 7.74 3998 49.77

82 3 38.1 38 45 1350 94 50 10.98 3231 57.3

66 3 38.1 38 60 1800 72 35 9.62 2161 33.24

67 3 38.1 38 60 1800 72 50 13.38 1806 38.78

53 3 38.1 69 70 2100 29 42 17.47 539 14.84

92 3 38.1 67.6 55 1650 29 60 23.86 427 16.19

57 3 38.1 67 45 1350 22 42 21.53 466 15.79

89 3 38.1 67.6 55 1650 22 60 27.97 385 17.05

102 3 44.45 20 30 900 149 33 5.65 4343 39.98

104 3 44.45 20 30 900 149 45 7.65 4084 51

97 3 44.45 18 50 1500 126 33 6.54 3620 38.37

103 3 44.45 20 30 900 126 45 8.69 4459 62.96

107 3 44.45 36.5 60 1800 94 35 7.83 3632 45.74

106 3 44.45 36.5 60 1800 94 50 11.07 3550 63.48

108 3 44.45 36.5 60 1800 72 35 9.71 2794 43.36

105 3 44.45 36.5 60 1800 72 50 13.46 2134 46.11

109 3 44.45 68.5 70 2100 29 42 17.58 454 12.59

110 3 44.45 68.5 70 2100 29 60 23.66 337 12.67

113 3 44.45 68.5 45 1350 22 42 21.21 197 6.57

114 3 44.45 68.5 45 1350 22 60 27.77 231 10.18

181 4 50.8 17.9 20 800 149 33 5.73 831 7.75

170 4 50.8 17.2 40 1600 149 41 7.1 817 9.46

182 4 50.8 17.9 20 800 126 33 6.54 896 9.5

180 4 50.8 17 30 1200 126 45 8.79 664 9.48

176 4 50.8 34 35 1400 94 35 7.97 523 6.7

164 4 50.8 34.7 60 2400 94 50 11.17 288 5.19

175 4 50.8 34 35 1400 72 35 9.84 780 12.27

174 4 50.8 34 35 1400 72 50 13.59 843 18.39

150 4 50.8 70 70 2800 29 42 17.22 192 5.21

149 4 50.8 70 70 2800 29 60 23.29 91 3.36

191 4 50.8 65 55 2200 22 42 21.9 152 5.22

192 4 50.8 65 55 2200 22 60 28.46 75 3.36

219 2 38.1 20 30 600 149 33 5.65 4661 42.91

218 2 38.1 20 30 600 149 40 6.83 4152 46.26

292 Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests

Test TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

HTCmax

(W/m2/K)

VCCmax

(kg/h/m2)

217 2 38.1 20 30 600 126 33 6.47 4938 51.76

216 2 38.1 18 40 800 126 45 8.76 5225 74.39

204 2 38.1 37 45 900 94 35 7.8 823 10.32

225 2 38.1 36.5 20 400 94 50 11.07 1350 24.14

227 2 38.1 36.5 20 400 72 35 9.71 2294 35.6

221 2 38.1 37 35 700 72 50 13.43 2130 45.94

206 2 38.1 72 70 1400 29 42 16.66 453 11.9

208 2 38.1 72 70 1400 29 60 22.73 444 16.05

233 2 38.1 71.5 55 1100 22 42 20.47 535 17.21

205 2 38.1 72 70 1400 22 60 26.88 546 23.27

260 2 44.45 20 40 800 149 33 5.65 5509 50.72

259 2 44.45 20 40 800 149 38 6.5 5663 59.99

278 2 44.45 19.5 30 600 126 33 6.49 4835 50.83

280 2 44.45 19.5 30 600 126 45 8.71 2639 37.34

286 2 44.45 35 60 1200 94 35 7.91 3020 38.44

285 2 44.45 35 60 1200 94 50 11.16 2970 53.51

288 2 44.45 35 60 1200 72 35 9.79 2228 34.86

261 2 44.45 35 45 900 72 50 13.54 2267 49.28

269 2 44.45 71.9 45 900 29 42 16.69 625 16.46

252 2 44.45 72 30 600 29 60 22.73 557 20.13

271 2 44.45 71.9 45 900 22 42 20.35 934 29.89

249 2 44.45 72 30 600 22 60 26.88 478 20.35

310 2 50.8 20 40 800 149 33 5.65 4378 40.31

315 2 50.8 18 20 400 149 35 6.07 3784 37.4

312 2 50.8 20 40 800 126 33 6.47 4557 47.77

289 2 50.8 18.5 50 1000 126 45 8.74 1794 25.49

304 2 50.8 37 35 700 94 35 7.8 1472 18.47

300 2 50.8 35 60 1200 94 50 11.16 2802 50.48

302 2 50.8 37 35 700 72 35 9.68 2966 45.89

317 2 50.8 35 45 900 72 50 13.54 2268 49.31

308 2 50.8 69 70 1400 29 42 17.47 769 21.18

305 2 50.8 69 70 1400 29 60 23.54 797 29.8

307 2 50.8 69 70 1400 22 42 21.1 589 19.54

306 2 50.8 69 70 1400 22 60 27.66 413 18.11

373 3 50.8 18.2 40 1200 149 33 5.72 5668 52.8

376 3 50.8 18.2 40 1200 149 35 6.06 3778 37.3

374 3 50.8 18.2 40 1200 126 33 6.53 2224 23.54

375 3 50.8 18.2 40 1200 126 45 8.75 2629 37.4

364 3 50.8 34.1 20 600 94 35 7.96 753 9.64

355 3 50.8 34.9 45 1350 94 50 11.16 543 9.79

354 3 50.8 34.9 45 1350 72 35 9.8 1596 24.99

358 3 50.8 35.2 60 1800 72 50 13.53 2002 43.49

368 3 50.8 73.2 70 2100 29 42 16.28 313 8.04

370 3 50.8 71.2 55 1650 29 60 22.97 508 18.54

342 3 50.8 73 30 900 22 42 20.02 252 7.94

365 3 50.8 73.2 70 2100 22 60 26.52 623 26.18

390 4 38.1 15 40 1600 149 33 5.83 4504 42.77

398 4 38.1 17.5 30 1200 149 45 7.74 4039 51.04

402 4 38.1 17.9 20 800 126 33 6.54 4214 44.69

404 4 38.1 17.9 20 800 126 45 8.76 3795 54.05

425 4 38.1 37 20 800 94 35 7.8 712 8.94

418 4 38.1 35 60 2400 94 50 11.16 550 9.9


Table E.2 HTCmax and VCCmax results from the Replicate128 experiment

Test TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

HTCmax

(W/m2/K)

VCCmax

(kg/h/m2)

9 2 44.45 20 40 800 149 33 5.65 4958 45.65

10 2 44.45 20 40 800 149 38 6.5 5097 53.99

26 2 44.45 21.7 30 600 126 33 6.4 4506 46.76

4 2 44.45 16.3 50 1000 126 45 8.69 2655 37.48

30 2 44.45 67 45 900 29 42 17.91 548 15.47

22 2 44.45 70 30 600 29 60 22.73 546 19.73

32 2 44.45 67 45 900 22 42 20.35 878 28.1

19 2 44.45 69 70 1400 22 60 27.66 821 35.98

89 3 44.45 20.5 30 600 149 33 5.63 4227 38.78

91 3 44.45 20.5 30 600 149 45 7.63 3971 49.47

96 3 44.45 17 50 1000 126 33 6.57 3529 37.6

92 3 44.45 20.5 30 600 126 45 8.67 4335 61.07

77 3 44.45 68.5 70 1400 29 42 17.58 431 11.96

79 3 44.45 68.5 70 1400 29 60 23.66 320 12.04

75 3 44.45 67 45 900 22 42 21.21 217 7.23

76 3 44.45 67 45 900 22 60 27.77 254 11.2

97 3 38.1 20 40 1200 149 33 5.65 4010 36.92

99 3 38.1 20 40 1200 149 41 6.99 3561 40.64

104 3 38.1 18 20 600 126 33 6.54 3846 40.76

103 3 38.1 18 20 600 126 45 8.76 3598 51.22

109 3 38.1 69 70 2100 29 42 17.47 593 16.33

117 3 38.1 67.6 55 1650 29 60 23.86 448 17

107 3 38.1 67 45 1350 22 42 21.53 443 15

120 3 38.1 67.6 55 1650 22 60 27.97 404 17.9

57 2 38.1 16 30 900 149 33 5.8 4772 45.06

59 2 38.1 16 30 900 149 40 6.97 4270 48.57

58 2 38.1 16 30 900 126 33 6.61 5075 54.35

36 2 38.1 19 40 1200 126 45 8.72 5142 72.9

45 2 38.1 70 70 2100 29 42 17.22 482 13.09

47 2 38.1 70 70 2100 29 60 23.29 477 17.65

55 2 38.1 68 55 1650 22 42 21.32 539 18.07

48 2 38.1 70 70 2100 22 60 27.42 589 25.6

Appendix F: Individual sections HTC Results of Original432 experiments 295

APPENDIX F: INDIVIDUAL SECTIONS

HTC RESULTS OF ORIGINAL432

EXPERIMENTS

F.1 Introductory Remarks

This appendix presents the HTC results of the individual sections from the

Original432 experiments. Section 1 is the top-most section of the tube and section 4

is the bottom-most section of the tube. The tube dimensions and operating conditions

of the HTC results are presented in Table C.1 and C.2 in Appendix C.


Table F Individual section HTC results for the Original432 experiment

Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

36 4512 2579 1950 2261

33 4618 2641 1700 2248

35 5010 3311 1619 1935

34 5496 4570 2009 1820

8 4484 4627 2784 2273

6 4949 3450 3355 1319

5 2378 2456 1658 511

7 4691 4557 3631 933

32 4679 3318 2040 1864

30 5415 4574 3298 1614

31 4824 4198 2006 1444

29 4953 5019 3948 1303

1 2769 1874 628 493

4 5002 4543 3115 1723

3 4415 4282 2741 1099

2 4451 4135 3107 693

13 787 1085 1161 561

16 391 1022 1666 2420

15 1147 2059 3044 2981

14 1444 2054 2567 2570

9 5034 4833 3281 973

12 623 1373 2689 3344

11 1172 2206 3243 3355

10 2181 2505 2508 2546

45 2669 3665 4504 2476

48 360 589 1353 2227

47 1908 2671 3060 2873

46 2005 2579 3106 2912

26 3429 3569 2389 1218

27 3698 4004 3117 1135

25 3485 3255 2384 917

28 2018 2294 2635 2330

42 10 108 323 139

44 72 279 372 284

43 14 133 304 133

41 4 235 306 203

39 0 219 348 175

37 535 497 360 255

38 19 73 257 121

40 26 265 306 202

23 142 426 316 160

24 406 278 299 250

21 29 106 107 42

22 479 535 471 279

19 206 203 124 63

298 Appendix F: Individual sections HTC Results of Original432 experiments

Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

18 382 491 425 244

20 249 333 309 104

17 460 527 427 224

80 4838 3995 3018 3695

79 4737 4132 2812 3269

77 4415 5042 3890 3185

78 4198 4244 3963 3065

93 3394 4966 2109 3087

96 3747 4829 2389 3118

95 3469 4123 2221 1853

94 3688 3792 2433 1999

74 4708 5327 3114 3736

73 4492 4677 2957 2869

76 4332 4067 2560 2869

75 4277 4197 3054 2252

51 3155 3413 2475 1423

52 3137 3284 1105 1181

49 3126 3169 1659 710

50 3444 3414 3856 1741

86 753 1080 2500 3747

85 1712 2845 3069 3315

88 257 225 257 446

87 498 661 940 1101

70 3386 4082 4485 4039

69 1097 2463 3672 4626

72 397 1101 1460 1619

71 412 894 1263 1455

81 2935 3827 4709 3580

82 2306 3064 3934 3620

84 1112 1559 1677 1780

83 861 936 1182 1023

68 213 980 1048 1120

65 1894 1951 2173 2146

66 1940 2033 2293 2378

67 1230 1571 2025 2399

62 62 50 508 414

64 80 76 571 672

63 184 110 359 432

61 302 61 311 626

59 63 326 370 327

58 204 78 482 738

57 721 275 453 416

60 123 53 268 539

91 503 466 417 320

92 319 238 470 682

90 506 419 300 392

89 294 156 550 538


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

53 970 466 404 315

54 262 321 434 369

56 988 176 67 154

55 86 100 155 70

121 1459 2587 514 3295

122 785 575 209 3203

124 388 516 1662 2326

123 288 384 1235 1729

102 5111 5036 4629 2594

104 4684 4487 4550 2614

101 2195 2360 2070 1438

103 4624 4544 5067 3602

118 900 2537 3959 4291

120 449 2406 1553 4012

117 761 1384 3661 3348

119 349 622 1158 2188

100 4637 4274 2735 1508

98 4379 4195 3722 1823

97 4036 4232 3691 2523

99 4431 4372 4581 2843

139 44 35 17 408

138 32 20 6 765

137 0 0 0 677

140 0 0 0 776

130 269 644 240 1038

129 42 301 302 705

132 81 207 501 1151

131 78 138 1254 1880

128 404 528 1122 1545

127 482 445 972 1203

125 50 455 912 1116

126 110 457 907 1321

107 3175 3569 4133 3652

106 3569 3547 3803 3281

108 1913 2355 3544 3365

105 2197 1956 2257 2126

142 0 0 57 228

141 0 0 422 482

143 0 0 101 316

144 0 0 34 175

115 0 92 340 121

116 0 28 54 17

113 0 258 350 180

114 199 220 261 246

136 0 0 0 79

133 41 78 484 388

134 0 0 78 284


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

135 0 1 19 337

109 685 564 303 263

110 431 365 303 249

112 63 112 48 31

111 67 83 47 37

181 428 970 461 1463

183 135 563 260 1074

182 233 782 415 2154

184 155 329 319 1026

177 242 513 499 1603

178 362 820 389 1237

179 148 614 283 1171

180 176 590 314 1627

169 166 690 318 1315

170 215 723 384 1993

171 383 867 412 1308

172 156 331 322 1035

146 312 707 673 1516

145 103 393 477 1374

148 317 502 498 1419

147 449 315 447 1344

186 10 128 206 155

185 25 42 72 274

188 288 257 131 454

187 192 304 206 121

176 233 498 262 1097

173 11 64 79 605

175 63 306 1407 1344

174 206 157 1209 1800

167 330 521 353 207

168 249 222 113 392

166 29 49 84 318

165 16 700 609 644

163 10 127 204 154

164 50 433 291 377

161 39 686 1050 1184

162 111 85 384 964

158 0 0 69 41

157 33 16 51 15

159 0 0 16 29

160 22 12 32 25

156 174 200 90 29

155 0 19 123 52

153 0 111 195 68

154 0 0 64 128

189 165 189 85 28

190 30 36 81 37


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

191 95 286 116 109

192 105 121 54 18

150 120 362 147 138

149 128 147 66 22

152 36 42 96 43

151 41 66 71 30

229 1016 1993 1573 5480

230 1259 2156 2975 4932

231 3836 5532 3828 5275

232 2958 2265 3149 3924

219 4602 5961 3051 5028

218 4652 5227 2479 4253

217 4447 6803 2997 5505

220 3221 3917 3396 4684

215 5403 4294 2525 5210

213 2484 3736 2359 6174

214 1959 2563 1664 2181

216 4990 5706 4485 5719

194 760 2205 1756 3229

193 713 726 665 2203

196 958 2216 1286 1440

195 526 778 1046 1388

226 32 121 210 316

225 765 1105 1553 1977

227 2798 2385 2202 1793

228 674 470 710 1029

224 294 346 498 558

223 567 239 249 531

222 266 369 535 408

221 1825 1578 2317 2801

204 667 513 1040 1072

203 593 388 699 907

202 67 57 42 133

201 1354 1206 1296 1798

200 510 740 961 846

199 84 233 488 298

198 22 13 25 41

197 105 58 44 189

239 0 0 5 83

237 59 220 66 800

240 0 0 0 170

238 23 16 224 896

210 0 0 0 69

212 0 105 221 193

211 0 0 0 77

209 0 0 32 68


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

235 0 0 0 21

236 32 36 43 31

233 321 611 626 580

234 124 119 337 93

206 357 461 532 462

208 172 158 950 498

207 528 517 394 528

205 535 138 608 904

241 2645 3621 4560 3726

242 2602 1078 4612 4204

243 2100 2098 2594 2227

244 1420 1250 1815 2121

277 5012 2506 2398 2214

279 5050 5813 5250 4420

278 4711 6014 4836 3779

280 1562 2254 2851 3888

260 5294 5909 5740 5093

259 5217 6179 6151 5105

258 4561 5098 5122 4355

257 885 2020 3271 4368

284 4738 5632 5384 4448

281 4571 5360 5024 4212

283 2140 3416 4875 3767

282 1910 2180 2400 3592

245 515 2618 3119 2834

246 465 899 2076 3739

247 916 597 1036 827

248 628 514 1384 2624

268 1368 1497 1278 1284

267 1220 1080 1374 3083

266 552 521 900 1237

265 3222 1757 1666 2226

263 1667 1643 1988 1260

264 1440 1369 1563 3001

262 723 920 1381 1508

261 3067 2159 1972 1870

286 2899 2811 2999 3372

285 3558 3039 2440 2844

288 2623 1781 1991 2517

287 2921 2010 1463 1143

251 348 280 242 177

252 602 619 547 462

250 61 42 16 17

249 543 512 457 399

269 440 725 692 643

272 217 369 590 571

271 1551 868 751 564


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

270 271 447 426 396

256 568 465 354 281

253 0 0 171 428

255 471 386 293 233

254 43 25 17 25

275 654 544 435 372

276 422 399 355 327

274 500 409 312 248

273 598 415 493 392

314 3391 3262 3681 3396

315 3706 3791 3747 3892

313 913 2324 898 2695

316 48 49 43 30

295 3131 2693 2746 3080

296 1431 1365 1538 1884

294 2793 2832 2175 2776

293 1284 1413 1171 1440

310 4246 4484 4497 4283

311 3026 3572 3564 3623

312 4252 4539 4676 4762

309 823 1309 1642 2962

292 3328 2645 2849 4084

290 2544 2364 2107 3306

291 1791 1635 1530 2197

289 1764 1726 1262 2425

324 371 491 544 635

323 774 708 773 1021

321 385 336 297 1224

322 462 562 547 1239

304 871 997 1192 2828

303 1380 1240 2399 4005

302 2419 2602 2841 4002

301 1368 1583 2231 3677

320 114 129 220 285

319 1328 953 862 1091

318 1269 1020 1378 1835

317 2190 2028 2231 2625

299 864 1255 1392 2172

300 2123 2466 2720 3897

297 1298 1286 1432 2024

298 353 499 744 1559

332 0 1 2 11

329 198 563 845 858

330 0 23 81 750

331 0 37 16 361

333 510 246 769 828

336 0 0 0 627


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

334 0 0 242 784

335 0 0 0 438

328 0 0 17 21

325 717 773 692 732

326 0 222 541 583

327 0 0 29 577

308 1729 785 193 366

305 824 805 776 782

307 891 568 479 418

306 692 62 341 558

379 23 22 35 36

377 1142 854 2824 4001

380 364 879 2418 3919

378 235 23 627 1553

347 1270 2198 3176 3879

346 2177 2076 2691 3401

348 1280 1438 2584 3564

345 654 868 1344 3000

373 5600 5900 5480 5693

376 3686 3594 4014 3818

374 1286 1436 2635 3537

375 3242 2833 2116 2326

351 4283 4041 3938 3989

350 994 1159 2117 3508

352 48 289 655 1491

349 1012 1255 2397 3762

364 315 666 879 1152

362 248 337 643 856

363 226 301 1240 2615

361 169 414 1055 2672

384 255 285 815 1106

382 221 417 638 715

383 74 586 1782 2339

381 134 434 1037 1928

356 237 634 940 1155

355 235 432 698 808

354 354 1085 2104 2843

353 2288 716 789 1929

357 316 587 840 1012

360 264 463 604 762

359 89 301 483 771

358 2189 2136 2073 1612

344 0 37 44 148

343 0 33 213 370

342 0 66 342 600

341 0 86 571 548

340 0 165 195 148


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

339 41 199 208 172

338 0 78 88 57

337 37 219 205 136

371 157 128 144 115

370 571 537 473 451

369 73 54 39 23

372 295 302 249 200

368 297 393 281 281

367 185 443 392 368

366 259 81 34 83

365 806 645 520 521

403 4147 3730 4360 3517

401 4177 3447 3965 2468

402 4248 3933 4515 4161

404 3816 3722 4317 3325

400 4376 4291 4518 3663

398 3674 3818 4373 4290

397 3701 4137 4689 3903

399 2027 2394 3112 2704

390 4312 5078 4605 4020

391 3380 3517 3865 2787

392 167 1552 1123 1416

389 762 1272 1237 3346

385 4308 4156 4734 3285

387 1416 1562 1705 1433

388 1510 1667 1819 1528

386 3795 3774 3865 3335

425 137 703 594 1415

427 167 289 424 721

426 264 295 725 1902

428 458 226 806 1554

429 64 54 39 12

432 12 21 37 57

431 15 22 37 41

430 27 27 37 36

422 399 867 587 986

421 148 155 391 633

424 157 77 520 1853

423 0 604 637 1694

420 285 557 764 1047

418 304 418 539 938

417 388 854 1399 2361

419 253 423 840 2042

414 52 176 266 234

416 252 286 425 370

415 70 56 94 64

413 152 204 208 154


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

411 9 184 261 219

412 286 340 399 362

410 0 56 76 54

409 210 271 315 216

395 142 238 283 357

393 376 208 331 394

394 86 124 132 175

396 47 46 47 70

408 67 240 322 265

405 258 358 466 403

407 59 130 143 108

406 329 470 455 338

Appendix G: Individual sections VCC Results of Original432 experiments 307

APPENDIX G: INDIVIDUAL SECTIONS

VCC RESULTS OF ORIGINAL432

EXPERIMENTS

G.1 Introductory Remarks

This appendix presents the VCC results of the individual sections of the heating

tube from the Original432 experiments. Section 1 is the top-most section of the tube

and section 4 is the bottom-most section of the tube. The tube dimensions and

operating conditions of the experiments are presented in Table C.1 and C.2 in

Appendix C.


Table G Individual section VCC results for the Original432 experiment

Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

36 42.11 24.07 18.20 21.11

33 52.03 29.75 19.16 25.33

35 53.13 35.11 17.17 20.52

34 78.27 65.08 28.61 25.92

8 41.87 43.21 26.00 21.23

6 62.47 43.55 42.34 16.65

5 25.24 26.05 17.59 5.42

7 66.84 64.92 51.73 13.29

32 43.91 31.14 19.15 17.49

30 68.59 57.94 41.77 20.44

31 51.40 44.72 21.38 15.38

29 70.79 71.74 56.42 18.62

1 26.29 17.79 5.96 4.68

4 57.17 51.92 35.60 19.69

3 47.52 46.09 29.50 11.83

2 64.10 59.54 44.75 9.98

13 9.94 13.71 14.68 7.09

16 7.00 18.31 29.86 43.37

15 17.85 32.03 47.36 46.38

14 31.27 44.48 55.59 55.65

9 64.51 61.94 42.05 12.46

12 11.27 24.85 48.68 60.54

11 18.43 34.70 51.02 52.77

10 47.60 54.67 54.73 55.55

45 33.68 46.25 56.83 31.24

48 6.44 10.54 24.22 39.87

47 29.66 41.51 47.56 44.66

46 43.37 55.79 67.21 63.01

26 43.73 45.52 30.48 15.53

27 66.72 72.25 56.25 20.48

25 54.62 51.01 37.36 14.38

28 43.93 49.92 57.34 50.71

42 0.27 3.01 9.03 3.89

44 2.71 10.53 14.05 10.71

43 0.47 4.47 10.20 4.46

41 0.19 10.39 13.50 8.98

39 0.00 5.99 9.53 4.80

37 19.91 18.50 13.38 9.49

38 0.61 2.42 8.49 3.99

40 1.14 11.55 13.37 8.83

23 4.10 12.29 9.13 4.62

24 15.72 10.76 11.56 9.68

21 0.99 3.67 3.68 1.43

22 21.62 24.15 21.22 12.59

19 5.88 5.80 3.55 1.79

310 Appendix G: Individual sections VCC Results of Original432 experiments

Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

18 14.67 18.87 16.35 9.36

20 8.52 11.37 10.57 3.55

17 20.61 23.63 19.15 10.02

80 45.15 37.29 28.16 34.49

79 53.37 46.55 31.68 36.83

77 46.81 53.47 41.25 33.77

78 59.78 60.45 56.44 43.64

93 30.88 45.19 19.19 28.09

96 41.34 53.27 26.35 34.40

95 36.00 42.79 23.05 19.23

94 51.69 53.14 34.10 28.02

74 43.34 49.05 28.67 34.39

73 51.26 53.38 33.75 32.75

76 45.41 42.64 26.83 30.07

75 60.39 59.26 43.12 31.80

51 29.73 32.16 23.33 13.41

52 32.18 33.69 11.33 12.12

49 33.42 33.88 17.74 7.59

50 49.36 48.93 55.26 24.95

86 9.40 13.47 31.19 46.75

85 30.41 50.54 54.53 58.89

88 3.95 3.47 3.96 6.87

87 10.71 14.21 20.20 23.68

70 42.15 50.81 55.83 50.28

69 19.46 43.68 65.13 82.05

72 6.11 16.93 22.46 24.91

71 8.86 19.20 27.11 31.25

81 36.53 47.64 58.62 44.56

82 40.89 54.34 69.77 64.21

84 17.10 23.97 25.79 27.37

83 18.48 20.10 25.37 21.96

68 2.65 12.20 13.04 13.94

65 33.60 34.60 38.54 38.07

66 29.84 31.26 35.27 36.58

67 26.41 33.73 43.48 51.51

62 1.75 1.40 14.38 11.74

64 3.06 2.92 21.78 25.66

63 6.23 3.74 12.18 14.66

61 13.47 2.71 13.86 27.89

59 1.79 9.22 10.44 9.25

58 7.78 2.99 18.35 28.13

57 24.41 9.31 15.35 14.10

60 5.46 2.36 11.94 23.98

91 14.11 13.07 11.70 8.99

92 12.11 9.01 17.80 25.83

90 17.04 14.10 10.11 13.19

89 13.05 6.90 24.39 23.86


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

53 26.73 12.84 11.13 8.67

54 9.81 12.01 16.23 13.82

56 32.78 5.83 2.21 5.11

55 3.77 4.37 6.81 3.09

121 13.62 24.15 4.80 30.76

122 8.84 6.48 2.35 36.09

124 4.12 5.47 17.63 24.67

123 4.11 5.46 17.59 24.62

102 47.06 46.37 42.62 23.88

104 58.49 56.04 56.82 32.64

101 23.01 24.73 21.70 15.08

103 65.29 64.15 71.55 50.86

118 8.29 23.36 36.45 39.51

120 5.61 30.05 19.40 50.10

117 7.98 14.51 38.38 35.09

119 4.92 8.79 16.35 30.89

100 43.25 39.86 25.51 14.07

98 55.22 52.90 46.92 22.99

97 42.78 44.85 39.11 26.74

99 63.07 62.24 65.22 40.47

139 0.56 0.44 0.21 5.15

138 0.57 0.35 0.10 13.72

137 0.00 0.00 0.00 10.54

140 0.00 0.00 0.00 16.82

130 3.34 7.98 2.97 12.88

129 0.74 5.33 5.34 12.46

132 1.24 3.17 7.68 17.64

131 1.68 2.96 26.86 40.28

128 5.05 6.60 14.02 19.31

127 8.58 7.91 17.28 21.39

125 0.77 7.02 14.07 17.21

126 2.36 9.83 19.52 28.41

107 39.97 44.94 52.05 45.98

106 63.81 63.42 68.01 58.67

108 29.68 36.54 54.99 52.22

105 47.47 42.26 48.77 45.95

142 0.00 0.00 1.55 6.19

141 0.00 0.00 15.63 17.85

143 0.00 0.00 3.31 10.37

144 0.00 0.00 1.48 7.59

115 0.00 2.56 9.43 3.36

116 0.00 1.05 2.03 0.63

113 0.00 8.60 11.69 6.01

114 8.74 9.67 11.47 10.84

136 0.00 0.00 0.00 2.16

133 1.52 2.87 17.89 14.36

134 0.00 0.00 2.55 9.32


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

135 0.00 0.04 0.81 14.64

109 19.02 15.66 8.40 7.29

110 16.21 13.72 11.39 9.36

112 2.11 3.74 1.60 1.05

111 2.94 3.65 2.07 1.64

181 4.00 9.05 4.30 13.66

183 1.52 6.35 2.92 12.10

182 2.47 8.29 4.41 22.84

184 2.21 4.68 4.55 14.61

177 2.20 4.67 4.54 14.59

178 4.00 9.05 4.30 13.65

179 1.53 6.38 2.94 12.15

180 2.46 8.27 4.40 22.80

169 1.53 6.35 2.93 12.11

170 2.46 8.25 4.39 22.74

171 4.01 9.09 4.31 13.71

172 2.21 4.68 4.55 14.61

146 2.94 6.66 6.34 14.29

145 1.15 4.36 5.29 15.23

148 3.39 5.37 5.33 15.17

147 6.44 4.51 6.41 19.25

186 0.13 1.62 2.61 1.96

185 0.45 0.75 1.29 4.90

188 4.49 4.01 2.04 7.07

187 4.17 6.59 4.46 2.61

176 2.98 6.39 3.36 14.06

173 0.19 1.15 1.43 10.96

175 0.98 4.81 22.13 21.14

174 4.50 3.42 26.38 39.28

167 4.16 6.58 4.46 2.61

168 4.46 3.98 2.03 7.02

166 0.45 0.76 1.30 4.94

165 0.34 15.15 13.18 13.92

163 0.13 1.62 2.61 1.96

164 0.90 7.81 5.25 6.80

161 0.60 10.75 16.46 18.55

162 2.42 1.86 8.36 20.97

158 0.00 0.00 1.93 1.15

157 1.23 0.59 1.91 0.55

159 0.00 0.00 0.52 0.98

160 0.97 0.52 1.43 1.10

156 4.77 5.46 2.46 0.80

155 0.00 0.70 4.58 1.93

153 0.00 3.67 6.44 2.25

154 0.00 0.00 2.79 5.57

189 4.77 5.46 2.46 0.80

190 1.17 1.38 3.13 1.42


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

191 3.28 9.84 4.01 3.76

192 4.76 5.45 2.45 0.80

150 3.27 9.82 4.00 3.75

149 4.75 5.44 2.45 0.80

152 1.18 1.38 3.15 1.43

151 1.79 2.86 3.06 1.30

229 9.51 18.65 14.71 51.27

230 12.48 21.38 29.50 48.89

231 40.76 58.79 40.68 56.05

232 42.20 32.30 44.91 55.97

219 42.37 54.89 28.09 46.30

218 51.82 58.23 27.61 47.38

217 46.62 71.31 31.41 57.71

220 45.48 55.30 47.95 66.13

215 50.40 40.05 23.55 48.60

213 28.65 43.08 27.20 71.20

214 20.77 27.16 17.63 23.11

216 71.03 81.24 63.85 81.42

194 7.09 20.56 16.38 30.12

193 8.80 8.96 8.20 27.19

196 10.16 23.48 13.63 15.27

195 7.49 11.08 14.89 19.76

226 0.40 1.53 2.65 3.98

225 13.67 19.76 27.77 35.35

227 43.42 37.01 34.16 27.83

228 14.56 10.16 15.33 22.24

224 3.69 4.34 6.25 7.00

223 10.12 4.26 4.44 9.48

222 4.11 5.71 8.28 6.32

221 39.36 34.04 49.96 60.40

204 8.36 6.44 13.05 13.44

203 10.58 6.92 12.46 16.18

202 1.03 0.89 0.65 2.05

201 29.20 26.00 27.95 38.77

200 6.39 9.27 12.03 10.60

199 1.49 4.14 8.69 5.31

198 0.35 0.20 0.39 0.64

197 2.26 1.26 0.96 4.07

239 0.00 0.00 0.15 2.25

237 2.19 8.14 2.43 29.59

240 0.00 0.00 0.00 5.57

238 1.00 0.71 9.73 38.93

210 0.00 0.00 0.00 1.86

212 0.00 3.85 8.15 7.09

211 0.00 0.00 0.00 2.53

209 0.00 0.00 1.37 2.94


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

235 0.00 0.00 0.00 0.55

236 1.16 1.30 1.57 1.12

233 10.35 19.67 20.14 18.66

234 5.30 5.09 14.43 4.00

206 9.39 12.11 13.98 12.14

208 6.21 5.71 34.29 17.97

207 16.89 16.53 12.59 16.88

205 22.80 5.89 25.89 38.51

241 24.64 33.73 42.48 34.71

242 27.13 11.24 48.09 43.83

243 22.24 22.21 27.47 23.58

244 20.19 17.78 25.82 30.18

277 46.30 23.15 22.16 20.46

279 56.42 64.94 58.65 49.38

278 49.53 63.22 50.84 39.72

280 22.11 31.90 40.34 55.01

260 48.74 54.41 52.85 46.89

259 55.27 65.46 65.16 54.08

258 47.81 53.44 53.69 45.65

257 12.50 28.52 46.19 61.67

284 43.63 51.86 49.57 40.96

281 47.16 55.31 51.84 43.46

283 22.44 35.80 51.10 39.48

282 26.97 30.78 33.89 50.71

245 6.47 32.85 39.13 35.55

246 8.29 16.03 37.02 66.68

247 14.17 9.24 16.03 12.80

248 13.54 11.09 29.84 56.58

268 17.03 18.63 15.91 15.99

267 21.63 19.16 24.36 54.68

266 8.49 8.02 13.84 19.03

265 69.19 37.72 35.77 47.79

263 21.22 20.91 25.30 16.03

264 25.94 24.66 28.16 54.06

262 11.31 14.40 21.61 23.59

261 66.67 46.93 42.87 40.65

286 36.90 35.78 38.17 42.92

285 64.11 54.75 43.96 51.23

288 41.04 27.87 31.15 39.39

287 63.50 43.69 31.80 24.85

251 9.16 7.37 6.36 4.66

252 21.76 22.34 19.74 16.68

250 1.95 1.35 0.50 0.56

249 23.13 21.82 19.48 16.98

269 11.60 19.09 18.23 16.93

272 7.86 13.35 21.33 20.65

271 49.66 27.80 24.04 18.06


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

270 11.57 19.04 18.18 16.88

256 15.46 12.66 9.63 7.66

253 0.00 0.00 6.35 15.87

255 15.49 12.68 9.65 7.68

254 1.89 1.07 0.76 1.10

275 16.52 13.73 10.97 9.39

276 14.80 13.98 12.45 11.46

274 15.49 12.68 9.65 7.68

273 24.89 17.24 20.49 16.30

314 31.63 30.42 34.34 31.68

315 36.63 37.47 37.04 38.47

313 9.68 24.63 9.52 28.56

316 0.68 0.70 0.61 0.43

295 29.40 25.29 25.79 28.92

296 15.03 14.34 16.15 19.79

294 29.78 30.19 23.19 29.59

293 18.35 20.20 16.74 20.59

310 39.10 41.29 41.40 39.43

311 34.54 40.76 40.67 41.34

312 44.57 47.57 49.02 49.92

309 11.61 18.48 23.19 41.82

292 30.94 24.59 26.49 37.98

290 26.48 24.61 21.93 34.41

291 18.93 17.28 16.17 23.22

289 25.07 24.52 17.92 34.46

324 4.69 6.20 6.88 8.03

323 13.88 12.69 13.87 18.30

321 5.99 5.23 4.63 19.04

322 10.00 12.16 11.85 26.82

304 10.93 12.50 14.95 35.48

303 24.60 22.12 42.78 71.43

302 37.43 40.26 43.95 61.91

301 29.50 34.14 48.11 79.29

320 1.45 1.65 2.80 3.63

319 23.92 17.16 15.54 19.65

318 19.86 15.96 21.57 28.72

317 47.60 44.08 48.49 57.07

299 10.99 15.97 17.72 27.64

300 38.26 44.43 49.01 70.21

297 20.31 20.12 22.41 31.67

298 7.67 10.86 16.18 33.90

332 0.00 0.03 0.06 0.31

329 7.34 20.84 31.27 31.76

330 0.00 0.76 2.67 24.60

331 0.00 1.61 0.69 15.68

333 14.41 6.97 21.73 23.40

336 0.00 0.00 0.00 23.88


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

334 0.00 0.00 8.20 26.54

335 0.00 0.00 0.00 19.50

328 0.00 0.00 0.43 0.55

325 25.53 27.53 24.65 26.09

326 0.00 7.00 17.04 18.37

327 0.00 0.00 1.23 24.28

308 47.65 21.64 5.33 10.09

305 30.81 30.12 29.00 29.26

307 29.56 18.84 15.88 13.89

306 30.32 2.73 14.95 24.45

379 0.22 0.21 0.33 0.34

377 12.84 9.60 31.77 45.01

380 3.86 9.30 25.60 41.49

378 3.35 0.33 8.92 22.09

347 11.88 20.57 29.71 36.30

346 24.58 23.44 30.38 38.39

348 13.61 15.28 27.46 37.88

345 9.33 12.38 19.18 42.80

373 52.17 54.96 51.05 53.03

376 36.40 35.48 39.63 37.70

374 13.62 15.20 27.90 37.45

375 46.11 40.30 30.10 33.09

351 40.86 38.55 37.56 38.05

350 11.40 13.30 24.29 40.25

352 0.52 3.12 7.08 16.11

349 14.62 18.13 34.61 54.32

364 4.04 8.53 11.25 14.75

362 4.48 6.10 11.63 15.48

363 3.55 4.73 19.50 41.11

361 3.68 9.03 23.02 58.29

384 3.26 3.66 10.44 14.18

382 4.01 7.55 11.54 12.94

383 1.16 9.22 28.02 36.79

381 2.93 9.47 22.62 42.07

356 3.01 8.07 11.98 14.72

355 4.24 7.79 12.59 14.56

354 5.53 16.98 32.95 44.50

353 49.76 15.57 17.16 41.96

357 4.02 7.46 10.68 12.86

360 4.75 8.34 10.86 13.71

359 1.39 4.71 7.55 12.06

358 47.54 46.39 45.02 35.02

344 0.00 0.96 1.14 3.82

343 0.00 1.17 7.60 13.16

342 0.00 2.08 10.76 18.90

341 0.00 3.64 24.05 23.09

340 0.00 4.27 5.05 3.81


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

339 1.45 7.09 7.40 6.13

338 0.00 2.46 2.77 1.79

337 1.54 9.25 8.63 5.74

371 4.18 3.40 3.84 3.06

370 20.84 19.59 17.25 16.47

369 2.36 1.76 1.25 0.75

372 12.67 12.95 10.70 8.58

368 7.63 10.10 7.21 7.21

367 6.58 15.73 13.93 13.05

366 8.13 2.54 1.08 2.62

365 33.88 27.10 21.84 21.88

403 38.70 34.81 40.69 32.83

401 52.70 43.48 50.01 31.14

402 45.05 41.70 47.88 44.13

404 54.35 53.01 61.48 47.35

400 40.94 40.15 42.27 34.28

398 46.43 48.25 55.27 54.22

397 39.33 43.96 49.83 41.48

399 28.91 34.15 44.39 38.57

390 40.95 48.22 43.73 38.17

391 43.19 44.94 49.39 35.61

392 1.80 16.71 12.09 15.24

389 10.97 18.32 17.81 48.18

385 40.68 39.23 44.69 31.01

387 16.10 17.77 19.39 16.30

388 16.17 17.85 19.48 16.37

386 54.45 54.15 55.45 47.84

425 1.72 8.82 7.45 17.75

427 2.98 5.15 7.56 12.86

426 4.08 4.56 11.21 29.44

428 9.87 4.87 17.37 33.50

429 0.81 0.68 0.50 0.15

432 0.22 0.38 0.67 1.03

431 0.23 0.35 0.58 0.64

430 0.58 0.59 0.81 0.78

422 5.07 11.03 7.47 12.55

421 2.66 2.79 7.05 11.41

424 2.45 1.21 8.13 29.00

423 0.00 13.13 13.84 36.83

420 3.63 7.08 9.73 13.33

418 5.47 7.53 9.70 16.90

417 6.06 13.36 21.89 36.95

419 5.49 9.20 18.25 44.39

414 1.40 4.77 7.22 6.37

416 9.32 10.59 15.73 13.70

415 2.28 1.82 3.08 2.11

413 6.59 8.85 9.06 6.71


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

411 0.25 5.20 7.37 6.19

412 10.91 12.97 15.20 13.78

410 0.00 1.88 2.58 1.84

409 9.35 12.06 14.03 9.61

395 4.00 6.69 7.93 10.02

393 14.24 7.89 12.54 14.92

394 2.88 4.16 4.45 5.89

396 2.08 2.02 2.06 3.10

408 1.86 6.61 8.86 7.31

405 9.64 13.39 17.43 15.08

407 1.96 4.33 4.76 3.59

406 14.43 20.58 19.96 14.82

Appendix H: Individual sections HTC Results of Replicate128 experiments 319

APPENDIX H: INDIVIDUAL SECTIONS

HTC RESULTS OF REPLICATE128

EXPERIMENTS

H.1 Introductory Remarks

This appendix presents the HTC results of the individual sections of the heating

tube from the Replicate128 experiments. Section 1 is the top-most section of the tube


operating conditions of the experiments are presented in Table D.1 and D.2 in

Appendix D.


Table H Individual section HTC results for the Replicate128 experiment

Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

5 2508 3433 4324 3533

7 2467 1022 4374 3987

6 1992 1990 2461 2113

8 1347 1186 1722 2013

25 4681 2340 2240 2068

27 4705 5415 4891 4117

26 4390 5604 4506 3521

28 1451 2094 2648 3611

9 4765 5318 5166 4583

10 4695 5561 5536 4594

11 4105 4588 4610 3920

12 797 1818 2944 3931

1 2485 2322 3422 5228

3 2666 3039 3311 5141

2 2099 3490 5082 4710

4 1548 1746 2496 4828

21 342 275 237 174

22 590 606 536 453

23 58 40 15 17

24 522 492 439 383

30 386 635 606 563

29 194 329 526 509

32 1458 816 706 530

31 255 420 401 372

14 507 415 316 251

13 0 0 13 16

15 423 346 264 210

16 39 22 16 23

18 569 473 378 324

17 376 355 316 291

20 443 363 276 220

19 1027 663 804 789

69 1395 2474 491 3151

70 749 549 199 3059

72 371 493 1588 2222

71 275 366 1178 1649

89 4975 4902 4505 2524

91 4555 4364 4424 2542

90 2136 2295 2014 1399

92 4495 4417 4926 3501

65 834 2350 3668 3975

67 419 2244 1448 3741

66 708 1287 3404 3113

68 326 582 1082 2045

95 4516 4162 2663 1469

94 4272 4093 3630 1779

322 Appendix H: Individual sections HTC Results of Replicate128 experiments

Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

96 3935 4125 3598 2460

93 4325 4268 4472 2775

81 0 0 60 239

83 0 0 443 506

82 0 0 106 332

84 0 0 36 183

74 0 100 367 131

73 0 30 59 18

75 0 283 385 198

76 218 242 287 271

86 0 0 0 81

85 42 80 496 398

87 0 0 80 291

88 0 1 19 347

77 651 536 288 250

79 410 347 288 236

78 60 107 45 30

80 63 79 45 35

37 1064 2086 1646 5736

38 1317 2255 3111 5157

40 4006 5777 3998 5508

39 3078 2356 3276 4083

57 4713 6104 3124 5149

59 4784 5375 2549 4373

58 4571 6992 3080 5658

60 3328 4047 3509 4840

33 5329 4235 2490 5139

35 2447 3680 2323 6082

34 1931 2525 1639 2149

36 4910 5615 4414 5628

63 732 2122 1690 3108

62 684 696 638 2114

64 920 2128 1235 1384

61 504 746 1002 1330

49 0 0 8 83

51 89 330 99 1200

50 0 0 0 261

52 35 25 343 1371

42 0 0 0 82

41 0 125 263 229

43 0 0 0 93

44 0 0 38 82

54 0 0 0 21

53 32 36 44 31

55 324 616 630 584

56 126 121 343 95

45 380 490 566 492

47 185 170 1019 534


Test Section 1 HTC

(W/m2/K)

Section 2 HTC

(W/m2/K)

Section 3 HTC

(W/m2/K)

Section 4 HTC

(W/m2/K)

46 566 554 422 566

48 577 149 655 975

101 4502 3718 2808 3439

102 4408 3845 2617 3042

104 4108 4692 3619 2963

103 3906 3949 3687 2851

121 3190 4668 1983 2902

123 3541 4563 2257 2947

122 3276 3894 2098 1750

124 3507 3605 2313 1901

97 4472 5061 2958 3549

99 4267 4444 2809 2726

98 4115 3864 2432 2725

100 4063 3987 2901 2139

127 3262 3528 2559 1472

126 3240 3392 1141 1220

128 3225 3270 1712 733

125 3544 3513 3968 1791

113 60 48 492 402

115 78 74 554 652

114 178 107 348 419

116 293 59 302 607

106 60 310 351 311

105 194 75 457 701

107 685 261 430 396

108 117 50 255 512

118 528 489 438 336

117 335 250 493 716

119 531 440 315 411

120 309 164 578 565

109 1067 513 444 346

111 289 353 477 406

110 1087 193 73 169

112 95 110 171 77

Appendix I: Individual sections VCC Results of Replicate128 experiments 325

APPENDIX I: INDIVIDUAL SECTIONS

VCC RESULTS OF REPLICATE128

EXPERIMENTS

I.1 Introductory Remarks

This appendix presents the VCC results of the individual sections of the heating

tube from the Replicate128 experiments. Section 1 is the top-most section of the tube


operating conditions of the experiments are presented in Table D.1 and D.2 in

Appendix D.


Table I Individual section VCC results from the 2 × 2 factorial experiment

Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

5 23.40 32.05 40.36 32.97

7 25.77 10.67 45.68 41.64

6 21.12 21.10 26.09 22.40

8 19.18 16.89 24.53 28.67

25 42.60 21.29 20.38 18.82

27 51.90 59.74 53.96 45.43

26 45.56 58.16 46.77 36.55

28 20.34 29.35 37.11 50.61

9 43.87 48.97 47.57 42.20

10 49.74 58.91 58.64 48.67

11 43.03 48.09 48.32 41.09

12 11.25 25.67 41.57 55.50

1 23.42 21.88 32.25 49.27

3 28.09 32.02 34.88 54.16

2 22.44 37.32 54.34 50.37

4 21.86 24.65 35.24 68.17

21 8.98 7.22 6.23 4.56

22 21.32 21.90 19.34 16.35

23 1.91 1.33 0.49 0.55

24 22.67 21.38 19.09 16.64

30 10.90 17.95 17.14 15.91

29 7.39 12.55 20.05 19.41

32 46.68 26.13 22.60 16.98

31 10.87 17.90 17.09 15.87

14 14.23 11.64 8.86 7.05

13 0.00 0.00 0.50 0.60

15 14.25 11.67 8.88 7.06

16 1.73 0.98 0.70 1.01

18 15.69 13.04 10.42 8.92

17 14.06 13.28 11.83 10.89

20 14.72 12.05 9.17 7.29

19 45.02 29.07 35.24 34.60

69 12.94 22.94 4.56 29.22

70 8.40 6.16 2.23 34.29

72 3.91 5.20 16.74 23.44

71 3.90 5.19 16.71 23.39

89 45.65 44.98 41.34 23.16

91 56.74 54.36 55.11 31.66

90 22.32 23.99 21.05 14.62

92 63.33 62.23 69.40 49.33

65 7.87 22.19 34.63 37.53

67 5.33 28.55 18.43 47.59

66 7.58 13.78 36.46 33.34

68 4.68 8.35 15.53 29.34

95 42.39 39.06 25.00 13.79

94 54.12 51.84 45.99 22.53

328 Appendix I: Individual sections VCC Results of Replicate128 experiments

Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

96 41.93 43.95 38.33 26.21

93 61.81 61.00 63.91 39.66

81 0.00 0.00 1.62 6.50

83 0.00 0.00 16.41 18.74

82 0.00 0.00 3.47 10.88

84 0.00 0.00 1.56 7.97

74 0.00 2.82 10.38 3.69

73 0.00 1.16 2.24 0.70

75 0.00 9.46 12.85 6.61

76 9.61 10.64 12.61 11.92

86 0.00 0.00 0.00 2.26

85 1.60 3.02 18.79 15.08

87 0.00 0.00 2.68 9.79

88 0.00 0.05 0.85 15.37

77 18.07 14.87 7.98 6.93

79 15.40 13.04 10.82 8.89

78 2.00 3.56 1.52 0.99

80 2.79 3.47 1.97 1.56

37 9.79 19.20 15.15 52.81

38 12.86 22.02 30.38 50.36

40 41.99 60.55 41.90 57.74

39 43.46 33.27 46.26 57.65

57 44.49 57.63 29.49 48.61

59 54.41 61.14 28.99 49.74

58 48.95 74.88 32.98 60.59

60 47.75 58.06 50.35 69.44

33 49.39 39.25 23.08 47.63

35 28.07 42.22 26.66 69.78

34 20.35 26.62 17.28 22.65

36 69.61 79.61 62.58 79.79

63 6.74 19.54 15.56 28.61

62 8.36 8.51 7.79 25.83

64 9.65 22.31 12.94 14.50

61 7.12 10.53 14.14 18.78

49 0.00 0.00 0.22 2.25

51 3.28 12.21 3.65 44.39

50 0.00 0.00 0.00 8.35

52 1.50 1.07 14.59 58.39

42 0.00 0.00 0.00 2.23

41 0.00 4.62 9.77 8.51

43 0.00 0.00 0.00 3.03

44 0.00 0.00 1.64 3.52

54 0.00 0.00 0.00 0.57

53 1.21 1.37 1.65 1.18

55 10.87 20.66 21.14 19.60

56 5.56 5.34 15.16 4.20

45 10.33 13.32 15.38 13.35

47 6.84 6.28 37.72 19.77


Test Section 1 VCC

(kg/m2/h)

Section 2 VCC

(kg/m2/h)

Section 3 VCC

(kg/m2/h)

Section 4 VCC

(kg/m2/h)

46 18.58 18.19 13.85 18.57

48 25.08 6.48 28.48 42.36

101 41.99 34.68 26.19 32.07

102 49.63 43.29 29.46 34.25

104 43.54 49.73 38.36 31.41

103 55.60 56.21 52.49 40.59

121 29.96 43.83 18.62 27.25

123 40.10 51.67 25.56 33.37

122 34.92 41.51 22.36 18.66

124 50.14 51.55 33.08 27.18

97 41.18 46.60 27.24 32.67

99 48.69 50.71 32.06 31.11

98 43.14 40.50 25.49 28.57

100 57.37 56.29 40.97 30.21

127 30.33 32.81 23.79 13.68

126 32.83 34.37 11.56 12.36

128 34.09 34.56 18.09 7.74

125 50.34 49.91 56.37 25.45

113 1.70 1.36 13.95 11.39

115 2.97 2.83 21.13 24.89

114 6.04 3.63 11.81 14.22

116 13.06 2.62 13.45 27.06

106 1.70 8.76 9.92 8.78

105 7.39 2.84 17.43 26.73

107 23.19 8.85 14.58 13.40

108 5.19 2.24 11.34 22.78

118 14.82 13.72 12.28 9.44

117 12.71 9.46 18.69 27.12

119 17.89 14.81 10.62 13.85

120 13.70 7.25 25.61 25.06

109 29.41 14.13 12.24 9.54

111 10.79 13.21 17.85 15.20

110 36.06 6.42 2.43 5.62

112 4.14 4.81 7.49 3.40

Appendix J: Replicate128 ANOVA 331

APPENDIX J: REPLICATE128 ANOVA

J.1 Introductory Remarks

This appendix presents analysis of variance for Replicate128 dataset. Six-order

interactions were identified to be significant. The replicate tests were undertaken to

investigate the tube length and tube diameter interaction, which was found to be

significant. The repeatability of the results might have caused the higher order

interactions to be significant. Hence the interactions with small effects could have been

enhanced with the replicate dataset.


Table J.1 Analysis of variance of HTC from Replicates128 tests

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 1 2972755 59.4 0.004

TD 1 8878 0.18 –

TL:TD 1 90300 1.8 –

Rep. block 1 67392 1.34 –

Residuals 3 50000

B 1 540897084 13211.7 0.000

JL 3 3837648 93.7 0.000

TL:B 1 2523627 61.6 0.000

TL:JL 3 1719539 42 0.000

TD:B 1 168255 421 –

TD:JL 3 7370316 180 0.000

B:JL 3 4562838 111.4 0.000

TL:TD:B 1 1662573 40.6 0.000

TL:TD:JL 3 1837374 44.9 0.000

TL:B:JL 3 3047831 74.4 0.000

TD:B:JL 3 7768684 189.7 0.000

TL:TD:B:JL 3 3107923 75.9 0.000

Residuals 28 40941

HS 1 2991066 42.3 0.000

ΔP 1 1222742 17.3 0.000

TL:HS 1 21903 0.3 –

TL:ΔP 1 170075 2.4 –

TD:HS 1 2996850 42.3 0.000

TD:ΔP 1 368220 5.2 0.02

B:HS 1 2701716 38.2 0.000

B:ΔP 1 1130956 16 0.000

JL:HS 3 238895 3.3 0.02

JL:ΔP 3 1133 0.01 –

HS:ΔP 1 310652 4.4 0.04

TL:TD:HS 1 962319 13.6 0.000

TL:TD:ΔP 1 44783 0.6 –

TL:B:HS 1 353375 4.9 0.027

TL:B:ΔP 1 235904 3.3 –

TL:JL:HS 3 331440 4.68 0.004

TL:JL:ΔP 3 370581 5.24 0.002

TL:HS:ΔP 1 928468 13.1 0.000

TD:B:HS 1 2294969 32.4 0.000

334 Appendix J: Replicate128 ANOVA

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:HS 3 483572 6.8 0.000

TD:JL:ΔP 3 534105 7.5 0.000

TD:HS:ΔP 1 1331837 18.8 0.000

B:JL:HS 3 812727 11.5 0.000

B:JL:ΔP 3 271251 3.8 0.012

B:HS:ΔP 1 107684 1.5 –

JL:HS:ΔP 3 559847 7.9 0.000

TL:TD:B:HS 1 660345 9.3 0.003

TL:TD:B:ΔP 1 30926 0.4 –

TL:TD:JL:HS 3 305339 4.3 0.006

TL:TD:JL:ΔP 3 219707 3.1 0.03

TL:TD:HS:ΔP 1 882603 12.5 0.000

TL:B:JL:HS 3 726525 10.2 0.000

TL:B:JL:ΔP 3 722577 10.2 0.000

TL:B:HS:ΔP 1 1131436 16 0.000

TL:JL:HS:ΔP 3 467698 6.6 0.000

TD:B:JL:HS 3 287100 4.1 0.009

TD:B:JL:ΔP 3 779639 11.02 0.000

TD:B:HS:ΔP 1 1927592 27.2 0.000

TD:JL:HS:ΔP 3 836470 11.8 0.000

B:JL:HS:ΔP 3 425708 6 0.001

TL:TD:B:JL:HS 3 148790 2.1 –

TL:TD:B:JL:ΔP 3 289268 4.1 0.01

TL:TD:B:HS:ΔP 1 1134543 16 0.000

TL:TD:JL:HS:ΔP 3 617297 8.7 0.000

TL:B:JL:HS:ΔP 3 450794 6.4 0.006

TD:B:JL:HS:ΔP 3 928153 13.1 0.000

TL:TD:B:JL:HS:ΔP 3 543758 7.7 0.000

Residuals 96 70725


Table J.2 Analysis of variance of HTCmax from Replicate128 tests

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 1 2972755 59.4 0.004

TD 1 8878 0.18 –

TL:TD 1 90300 1.8 –

Rep. block 1 67392 1.34 –

Residuals 3 50000

B 1 234649442 2938.5 0.000

TL:B 1 726293 9.1 0.04

TD:B 1 8081 0.1 –

TL:TD:B 1 846369 10.6 0.03

Residuals 4 79852

HS 1 486583 32.2 0.000

ΔP 1 768900 50.9 0.000

TL:HS 1 44403 2.9 –

TL:ΔP 1 253808 16.8 0.000

TD:HS 1 1633123 108.1 0.000

TD:ΔP 1 56357 3.73 –

B:HS 1 420344 27.8 0.000

B:ΔP 1 248413 16.44 0.000

HS:ΔP 1 28301 1.8 –

TL:TD:HS 1 987705 65.4 0.000

TL:TD:ΔP 1 588238 38.9 0.000

TL:B:HS 1 358152 23.7 0.000

TL:B:ΔP 1 121264 8.03 0.01

TL:HS:ΔP 1 416645 27.6 0.000

TD:B:HS 1 1449987 95.9 0.000

TD:B:ΔP 1 1010 0.07 –

TD:HS:ΔP 1 421039 27.8 0.000

B:HS:ΔP 1 33539 2.22 0.000

TL:TD:B:HS 1 1097005 72.6 0.000

TL:TD:B:ΔP 1 165025 10.9 0.003

TL:TD:HS:ΔP 1 730890 48.4 0.000

TL:B:HS:ΔP 1 220068 14.6 0.001

TD:B:HS:ΔP 1 314605 20.8 0.000

TL:TD:B:HS:ΔP 1 506313 33.5 0.000

Residuals 24 15109

Appendix K: Comparison of individual sections HTC for Tests with Brix-70 337

APPENDIX K: COMPARISON OF

INDIVIDUAL SECTIONS HTC FOR

TESTS WITH BRIX-70

K.1 Introductory Remarks

This appendix presents the uniform boiling pattern results from the Original432

and Replicate128 experiments in Table L.1 and Table L.2 respectively. This boiling

pattern shows that the HTC of the four individual sections was within 15% of the

overall HTC.


Table K.1 Individual section HTC comparison with M2 tube with Brix-70

results

Test Original432 Replicate128 Test

Section 1 Section 2 Section 3 Section 4 Section 1 Section 2 Section 3 Section 4

251 1 0 0 -1 1 0 0 -1 21

252 -1 1 0 0 0 0 0 -1 22

250 1 0 -1 -1 1 1 -1 -1 23

249 1 0 0 -1 0 0 0 -1 24

269 0 0 0 -1 -1 1 0 0 30

272 -1 -1 1 1 -1 -1 1 1 29

271 -1 -1 0 1 1 0 -1 -1 32

270 0 0 0 0 -1 1 0 0 31

256 1 1 -1 -1 1 0 -1 -1 14

253 1 0 -1 -1 -1 -1 1 1 13

255 1 0 -1 -1 1 0 -1 -1 15

254 1 0 0 -1 1 0 -1 0 16

275 0 0 0 -1 1 0 0 -1 18

276 -1 1 0 0 0 0 0 0 17

274 1 0 -1 0 1 0 -1 -1 20

273 1 0 0 -1 1 -1 0 0 19

Category Comparison of results (%)

Individual section HTC in same zone 58

Individual section HTC one zone apart 34


340 Appendix K: Comparison of individual sections HTC for Tests with Brix-70

Table K.2 Individual section HTC comparison with S2 tube with Brix-70 results



237 -1 -1 -1 1 -1 -1 -1 1 49

240 -1 -1 -1 1 -1 -1 -1 1 51

238 -1 -1 -1 1 -1 -1 -1 1 50

210 -1 0 1 0 -1 -1 -1 1 52

212 -1 -1 -1 1 -1 -1 -1 1 42

211 -1 -1 1 1 -1 -1 1 1 41

209 0 0 1 0 -1 -1 -1 1 43

235 -1 -1 1 0 -1 -1 1 1 44

236 -1 -1 -1 1 -1 -1 -1 1 54

233 -1 -1 -1 1 0 0 1 0 53

234 -1 0 1 0 -1 0 1 0 55

206 0 0 -1 0 -1 -1 1 -1 56

208 -1 -1 -1 1 -1 0 1 0 45

207 -1 -1 1 1 -1 -1 1 0 47

205 -1 -1 1 -1 0 0 -1 0 46

239 0 -1 0 1 0 -1 0 1 48






Table K.3 Individual section HTC comparison with M3 tube with Brix-70

results



142 -1 -1 -1 1 -1 -1 -1 1 81

141 -1 -1 1 0 -1 -1 1 1 83

143 -1 -1 -1 1 -1 -1 0 1 82

144 1 1 -1 -1 -1 -1 -1 1 84

115 -1 -1 1 1 -1 -1 1 0 74

116 -1 0 1 -1 -1 0 1 -1 73

113 -1 -1 1 1 -1 1 1 0 75

114 1 0 0 -1 0 0 0 0 76

136 -1 -1 0 1 -1 -1 -1 1 86

133 -1 1 1 0 -1 -1 1 1 85

134 -1 -1 0 1 -1 -1 0 1 87

135 0 1 -1 -1 -1 -1 -1 1 88

109 -1 -1 -1 1 1 1 -1 -1 77

110 0 0 0 0 1 0 0 -1 79

112 -1 -1 -1 1 0 1 -1 -1 78

111 1 1 -1 -1 0 1 -1 -1 80





342 Appendix K: Comparison of individual sections HTC for Tests with Brix-70

Table K.4 Individual section HTC comparison with S3 tube with Brix-70 results



86 -1 -1 1 1 -1 -1 1 1 113

85 -1 1 1 1 -1 -1 1 1 115

88 1 0 0 -1 -1 -1 1 1 114

87 1 0 -1 -1 0 -1 0 1 116

70 -1 -1 1 1 -1 1 1 1 106

69 -1 -1 1 1 -1 -1 1 1 105

72 -1 -1 0 1 1 -1 0 0 107

71 -1 0 1 0 -1 -1 0 1 108

81 -1 -1 1 1 1 0 0 -1 118

82 1 -1 0 0 -1 -1 0 1 117

84 1 0 -1 0 1 0 -1 0 119

83 1 -1 -1 -1 -1 -1 1 1 120

68 0 -1 0 1 1 0 -1 -1 109

65 -1 -1 0 1 -1 0 1 0 111

66 -1 -1 1 1 1 -1 -1 -1 110

67 -1 0 1 -1 -1 0 1 -1 112





Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets 343

APPENDIX L: UNIFORM BOILING

PATTERN RESULTS – ORIGINAL432 AND

REPLICATE128 DATASETS

L.1 Introductory Remarks

This appendix presents the uniform boiling pattern results from the Original432 and

Replicate128 experiments in Table M.1 and Table M.2 respectively. This boiling pattern shows

that the HTC of the top section (section 1) was lower than 15% of the overall HTC.


Table L.1 Results from Original432 tests demonstrating uniform boiling pattern

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 44.45 34 35 1400 72 50 13.59 2181 2505 2508 2546 2435

4 44.45 34.7 60 2400 72 50 13.56 2018 2294 2635 2330 2319

3 38.1 38 60 1800 94 50 10.98 1894 1951 2173 2146 2041

3 38.1 38 60 1800 72 35 9.62 1940 2033 2293 2378 2161

3 44.45 36.5 60 1800 94 35 7.83 3175 3569 4133 3652 3632

3 44.45 36.5 60 1800 94 50 11.07 3569 3547 3803 3281 3550

3 44.45 36.5 60 1800 72 50 13.46 2197 1956 2257 2126 2134

3 44.45 68.5 45 1350 22 60 27.77 199 220 261 246 231

2 38.1 18 40 800 126 45 8.76 4990 5706 4485 5719 5225

2 44.45 19.5 30 600 149 40 6.85 5050 5813 5250 4420 5133

2 44.45 20 40 800 149 33 5.65 5294 5909 5740 5093 5509

2 44.45 20 40 800 149 38 6.5 5217 6179 6151 5105 5663

2 44.45 20 40 800 126 33 6.47 4561 5098 5122 4355 4784

2 44.45 20 50 1000 149 33 5.65 4738 5632 5384 4448 5051

2 44.45 20 50 1000 149 37 6.33 4571 5360 5024 4212 4792

2 44.45 38 35 700 94 35 7.74 1368 1497 1278 1284 1357

2 44.45 35 60 1200 94 35 7.91 2899 2811 2999 3372 3020

2 44.45 74 70 1400 29 60 22.08 422 399 355 327 376

2 50.8 18 20 400 149 33 5.73 3391 3262 3681 3396 3433

2 50.8 18 20 400 149 35 6.07 3706 3791 3747 3892 3784

2 50.8 16.9 30 600 149 33 5.77 3131 2693 2746 3080 2912

2 50.8 16.9 30 600 126 45 8.8 1284 1413 1171 1440 1327

2 50.8 20 40 800 149 33 5.65 4246 4484 4497 4283 4378

2 50.8 20 40 800 149 41 6.99 3026 3572 3564 3623 3446

346 Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 44.45 34 35 1400 72 50 13.59 2181 2505 2508 2546 2435

4 44.45 34.7 60 2400 72 50 13.56 2018 2294 2635 2330 2319

3 38.1 38 60 1800 94 50 10.98 1894 1951 2173 2146 2041

3 38.1 38 60 1800 72 35 9.62 1940 2033 2293 2378 2161

3 44.45 36.5 60 1800 94 35 7.83 3175 3569 4133 3652 3632

3 44.45 36.5 60 1800 94 50 11.07 3569 3547 3803 3281 3550

3 44.45 36.5 60 1800 72 50 13.46 2197 1956 2257 2126 2134

3 44.45 68.5 45 1350 22 60 27.77 199 220 261 246 231

2 38.1 18 40 800 126 45 8.76 4990 5706 4485 5719 5225

2 44.45 19.5 30 600 149 40 6.85 5050 5813 5250 4420 5133

2 44.45 20 40 800 149 33 5.65 5294 5909 5740 5093 5509

2 44.45 20 40 800 149 38 6.5 5217 6179 6151 5105 5663

2 44.45 20 40 800 126 33 6.47 4561 5098 5122 4355 4784

2 44.45 20 50 1000 149 33 5.65 4738 5632 5384 4448 5051

2 44.45 20 50 1000 149 37 6.33 4571 5360 5024 4212 4792

2 44.45 38 35 700 94 35 7.74 1368 1497 1278 1284 1357

2 44.45 35 60 1200 94 35 7.91 2899 2811 2999 3372 3020

2 44.45 74 70 1400 29 60 22.08 422 399 355 327 376


Table L.2 Results from Replicate128 tests demonstrating uniform boiling pattern

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 21.7 30 600 149 40 6.76 4705 5415 4891 4117 4782

2 44.45 20 40 800 149 33 5.65 4765 5318 5166 4583 4958

2 44.45 20 40 800 149 38 6.5 4695 5561 5536 4594 5097

2 44.45 20 40 800 126 33 6.47 4105 4588 4610 3920 4306

2 44.45 69 70 1400 29 60 23.54 376 355 316 291 335

3 44.45 67 45 900 22 60 27.77 218 242 287 271 255

2 38.1 19 40 1200 126 45 8.72 4910 5615 4414 5628 5142

Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 349

APPENDIX M: RESULTS SHOWING

LOW HTC AT TOP SECTION –

ORIGINAL432 AND REPLICATE128

DATASETS

M.1 Introductory remarks

This appendix presents the non-uniform boiling pattern showing low HTC at top

section results from the Original432 and Replicate128 experiments in Table M.1 and

Table M.2 respectively. This boiling pattern shows that the HTC of the top section

(section 1) was lower than 15% of the overall HTC.


Table M.1 Results from Original432 tests demonstrating low HTC at the top section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 44.45 36 20 800 94 50 11.1 391 1022 1666 2420 1374

4 44.45 36 20 800 72 35 9.74 1147 2059 3044 2981 2308

4 44.45 36 20 800 72 50 13.49 1444 2054 2567 2570 2159

4 44.45 34 35 1400 94 50 11.21 623 1373 2689 3344 2007

4 44.45 34 35 1400 72 35 9.84 1172 2206 3243 3355 2494

4 44.45 36.2 45 1800 94 35 7.85 2669 3665 4504 2476 3328

4 44.45 36.2 45 1800 94 50 11.09 360 589 1353 2227 1132

4 44.45 36.2 45 1800 72 35 9.73 1908 2671 3060 2873 2628

4 44.45 36.2 45 1800 72 50 13.48 2005 2579 3106 2912 2651

4 44.45 68 30 1200 29 42 17.7 10 108 323 139 145

4 44.45 68 30 1200 29 60 23.77 72 279 372 284 252

4 44.45 68 30 1200 22 42 21.32 14 133 304 133 146

4 44.45 68 30 1200 22 60 27.88 4 235 306 203 187

4 44.45 69.5 45 1800 29 42 17.34 0 219 348 175 186

4 44.45 69.5 45 1800 22 42 20.98 19 73 257 121 118

4 44.45 69.5 45 1800 22 60 27.54 26 265 306 202 200

4 44.45 65 55 2200 29 42 18.3 142 426 316 160 261

4 44.45 65 55 2200 22 42 21.9 29 106 107 42 71

3 38.1 37.7 20 600 94 35 7.76 753 1080 2500 3747 2020

3 38.1 37.7 20 600 94 50 11 1712 2845 3069 3315 2735

3 38.1 37.7 20 600 72 50 13.39 498 661 940 1101 800

3 38.1 38 35 1050 94 35 7.74 3386 4082 4485 4039 3998

3 38.1 38 35 1050 94 50 10.98 1097 2463 3672 4626 2964

3 38.1 38 35 1050 72 35 9.62 397 1101 1460 1619 1144

3 38.1 38 35 1050 72 50 13.38 412 894 1263 1455 1006

3 38.1 38 45 1350 94 35 7.74 2935 3827 4709 3580 3763

3 38.1 38 45 1350 94 50 10.98 2306 3064 3934 3620 3231

352 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 38.1 38 45 1350 72 35 9.62 1112 1559 1677 1780 1532

3 38.1 38 60 1800 94 35 7.74 213 980 1048 1120 840

3 38.1 38 60 1800 72 50 13.38 1230 1571 2025 2399 1806

3 38.1 66.8 30 900 29 42 17.95 62 50 508 414 258

3 38.1 66.8 30 900 29 60 24.03 80 76 571 672 350

3 38.1 66.8 30 900 22 42 21.57 184 110 359 432 271

3 38.1 67 45 1350 29 42 17.91 63 326 370 327 272

3 38.1 67 45 1350 29 60 23.99 204 78 482 738 376

3 38.1 67 45 1350 22 60 28.09 123 53 268 539 246

3 38.1 67.6 55 1650 29 60 23.86 319 238 470 682 427

3 38.1 67.6 55 1650 22 60 27.97 294 156 550 538 385

3 38.1 69 70 2100 29 60 23.54 262 321 434 369 347

3 38.1 69 70 2100 22 60 27.66 86 100 155 70 103

3 44.45 17.9 20 600 149 33 5.73 1459 2587 514 3295 1964

3 44.45 17.9 20 600 149 40 6.91 785 575 209 3203 1193

3 44.45 17.9 20 600 126 33 6.54 388 516 1662 2326 1223

3 44.45 17.9 20 600 126 45 8.76 288 384 1235 1729 909

3 44.45 20 40 1200 149 33 5.65 900 2537 3959 4291 2922

3 44.45 20 40 1200 149 45 7.65 449 2406 1553 4012 2105

3 44.45 20 40 1200 126 33 6.47 761 1384 3661 3348 2288

3 44.45 20 40 1200 126 45 8.69 349 622 1158 2188 1079

3 44.45 35.9 20 600 94 35 7.86 44 35 17 408 126

3 44.45 35.9 20 600 94 50 11.11 32 20 6 765 206

3 44.45 35.9 20 600 72 35 9.74 0 0 0 677 169

3 44.45 35.9 20 600 72 50 13.49 0 0 0 776 194

3 44.45 38.5 35 1050 94 35 7.71 269 644 240 1038 548

3 44.45 38.5 35 1050 94 50 10.95 42 301 302 705 337

3 44.45 38.5 35 1050 72 35 9.59 81 207 501 1151 485

3 44.45 38.5 35 1050 72 50 13.35 78 138 1254 1880 838


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 44.45 37.5 45 1350 94 35 7.77 404 528 1122 1545 900

3 44.45 37.5 45 1350 94 50 11.01 482 445 972 1203 775

3 44.45 37.5 45 1350 72 35 9.65 50 455 912 1116 633

3 44.45 37.5 45 1350 72 50 13.4 110 457 907 1321 698

3 44.45 36.5 60 1800 72 35 9.71 1913 2355 3544 3365 2794

3 44.45 70 30 900 29 42 17.22 0 0 57 228 71

3 44.45 70 30 900 29 60 23.29 0 0 422 482 226

3 44.45 70 30 900 22 42 20.86 0 0 101 316 104

3 44.45 70 30 900 22 60 27.42 0 0 34 175 52

3 44.45 68.5 45 1350 29 42 17.58 0 92 340 121 138

3 44.45 68.5 45 1350 29 60 23.66 0 28 54 17 25

3 44.45 68.5 45 1350 22 42 21.21 0 258 350 180 197

3 44.45 70 55 1650 29 42 17.22 0 0 0 79 20

3 44.45 70 55 1650 29 60 23.29 41 78 484 388 248

3 44.45 70 55 1650 22 42 20.86 0 0 78 284 91

3 44.45 70 55 1650 22 60 27.42 0 1 19 337 89

4 50.8 17.9 20 800 149 33 5.73 428 970 461 1463 831

4 50.8 17.9 20 800 149 40 6.91 135 563 260 1074 508

4 50.8 17.9 20 800 126 33 6.54 233 782 415 2154 896

4 50.8 17.9 20 800 126 45 8.76 155 329 319 1026 457

4 50.8 17 30 1200 149 33 5.76 242 513 499 1603 714

4 50.8 17 30 1200 149 40 6.94 362 820 389 1237 684

4 50.8 17 30 1200 126 33 6.57 148 614 283 1171 540

4 50.8 17 30 1200 126 45 8.79 176 590 314 1627 664

4 50.8 17.2 40 1600 149 33 5.75 166 690 318 1315 611

4 50.8 17.2 40 1600 149 41 7.1 215 723 384 1993 817

4 50.8 17.2 40 1600 126 33 6.57 383 867 412 1308 731

4 50.8 17.2 40 1600 126 45 8.79 156 331 322 1035 456

4 50.8 21.9 50 2000 149 33 5.58 312 707 673 1516 802


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 50.8 21.9 50 2000 149 39 6.59 103 393 477 1374 587

4 50.8 21.9 50 2000 126 33 6.4 317 502 498 1419 684

4 50.8 21.9 50 2000 126 45 8.62 449 315 447 1344 654

4 50.8 36 20 800 94 35 7.86 10 128 206 155 125

4 50.8 36 20 800 94 50 11.1 25 42 72 274 103

4 50.8 34 35 1400 94 35 7.97 233 498 262 1097 523

4 50.8 34 35 1400 94 50 11.21 11 64 79 605 190

4 50.8 34 35 1400 72 35 9.84 63 306 1407 1344 780

4 50.8 34 35 1400 72 50 13.59 206 157 1209 1800 843

4 50.8 36.2 45 1800 72 35 9.73 29 49 84 318 120

4 50.8 36.2 45 1800 72 50 13.48 16 700 609 644 492

4 50.8 34.7 60 2400 94 35 7.93 10 127 204 154 124

4 50.8 34.7 60 2400 94 50 11.17 50 433 291 377 288

4 50.8 34.7 60 2400 72 35 9.81 39 686 1050 1184 740

4 50.8 34.7 60 2400 72 50 13.56 111 85 384 964 386

4 50.8 68 30 1200 29 42 17.7 0 0 69 41 28

4 50.8 68 30 1200 22 42 21.32 0 0 16 29 11

4 50.8 69.5 45 1800 29 60 23.42 0 19 123 52 48

4 50.8 69.5 45 1800 22 42 20.98 0 111 195 68 94

4 50.8 69.5 45 1800 22 60 27.54 0 0 64 128 48

4 50.8 65 55 2200 29 60 24.38 30 36 81 37 46

4 50.8 65 55 2200 22 42 21.9 95 286 116 109 152

4 50.8 70 70 2800 29 42 17.22 120 362 147 138 192

4 50.8 70 70 2800 22 42 20.86 36 42 96 43 54

4 50.8 70 70 2800 22 60 27.42 41 66 71 30 52

2 38.1 17.5 20 400 149 33 5.74 1016 1993 1573 5480 2515

2 38.1 17.5 20 400 149 35 6.08 1259 2156 2975 4932 2831

2 38.1 17.5 20 400 126 33 6.56 3836 5532 3828 5275 4618

2 38.1 20 30 600 126 45 8.69 3221 3917 3396 4684 3804


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 38.1 18 40 800 149 41 7.07 2484 3736 2359 6174 3688

2 38.1 18 50 1000 149 33 5.73 760 2205 1756 3229 1987

2 38.1 18 50 1000 149 44 7.56 713 726 665 2203 1077

2 38.1 18 50 1000 126 33 6.54 958 2216 1286 1440 1475

2 38.1 18 50 1000 126 45 8.76 526 778 1046 1388 935

2 38.1 36.5 20 400 94 35 7.83 32 121 210 316 170

2 38.1 36.5 20 400 94 50 11.07 765 1105 1553 1977 1350

2 38.1 37 35 700 94 35 7.8 294 346 498 558 424

2 38.1 37 35 700 72 35 9.68 266 369 535 408 395

2 38.1 37 45 900 94 35 7.8 667 513 1040 1072 823

2 38.1 37.2 60 1200 94 35 7.79 510 740 961 846 764

2 38.1 37.2 60 1200 94 50 11.03 84 233 488 298 276

2 38.1 37.2 60 1200 72 35 9.67 22 13 25 41 26

2 38.1 70 30 600 29 42 17.22 0 0 5 83 22

2 38.1 70 30 600 29 60 23.29 59 220 66 800 286

2 38.1 70 30 600 22 42 20.86 0 0 0 170 42

2 38.1 70 30 600 22 60 27.42 23 16 224 896 290

2 38.1 70.5 45 900 29 42 17.09 0 0 0 69 17

2 38.1 70.5 45 900 29 60 23.16 0 105 221 193 130

2 38.1 70.5 45 900 22 42 20.73 0 0 0 77 19

2 38.1 70.5 45 900 22 60 27.29 0 0 32 68 25

2 38.1 71.5 55 1100 29 42 16.81 0 0 0 21 5

2 38.1 71.5 55 1100 22 42 20.47 321 611 626 580 535

2 38.1 71.5 55 1100 22 60 27.03 124 119 337 93 168

2 38.1 72 70 1400 29 42 16.66 357 461 532 462 453

2 38.1 72 70 1400 29 60 22.73 172 158 950 498 444

2 44.45 18.2 20 400 149 33 5.72 2645 3621 4560 3726 3638

2 44.45 18.2 20 400 149 37 6.4 2602 1078 4612 4204 3124

2 44.45 19.5 30 600 126 45 8.71 1562 2254 2851 3888 2639


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 20 40 800 126 45 8.69 885 2020 3271 4368 2636

2 44.45 20 50 1000 126 33 6.47 2140 3416 4875 3767 3550

2 44.45 20 50 1000 126 45 8.69 1910 2180 2400 3592 2521

2 44.45 37 20 400 94 35 7.8 515 2618 3119 2834 2272

2 44.45 37 20 400 94 50 11.04 465 899 2076 3739 1795

2 44.45 37 20 400 72 50 13.43 628 514 1384 2624 1287

2 44.45 38 35 700 94 50 10.98 1220 1080 1374 3083 1689

2 44.45 38 35 700 72 35 9.62 552 521 900 1237 803

2 44.45 35 45 900 94 50 11.16 1440 1369 1563 3001 1843

2 44.45 35 45 900 72 35 9.79 723 920 1381 1508 1133

2 44.45 71.9 45 900 29 42 16.69 440 725 692 643 625

2 44.45 71.9 45 900 29 60 22.76 217 369 590 571 437

2 44.45 71.9 45 900 22 60 26.91 271 447 426 396 385

2 44.45 69.8 55 1100 29 60 23.34 0 0 171 428 150

2 50.8 18 20 400 126 33 6.54 913 2324 898 2695 1708

2 50.8 20 40 800 126 45 8.69 823 1309 1642 2962 1684

2 50.8 36 20 400 94 35 7.86 371 491 544 635 510

2 50.8 36 20 400 72 35 9.74 385 336 297 1224 561

2 50.8 36 20 400 72 50 13.49 462 562 547 1239 702

2 50.8 37 35 700 94 35 7.8 871 997 1192 2828 1472

2 50.8 37 35 700 94 50 11.04 1380 1240 2399 4005 2256

2 50.8 37 35 700 72 35 9.68 2419 2602 2841 4002 2966

2 50.8 37 35 700 72 50 13.43 1368 1583 2231 3677 2215

2 50.8 35 45 900 94 35 7.91 114 129 220 285 187

2 50.8 35 60 1200 94 35 7.91 864 1255 1392 2172 1421

2 50.8 35 60 1200 94 50 11.16 2123 2466 2720 3897 2802

2 50.8 35 60 1200 72 50 13.54 353 499 744 1559 789

2 50.8 70 30 600 29 42 17.22 0 1 2 11 4

2 50.8 70 30 600 29 60 23.29 198 563 845 858 616


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 50.8 70 30 600 22 42 20.86 0 23 81 750 214

2 50.8 70 30 600 22 60 27.42 0 37 16 361 103

2 50.8 67 45 900 29 60 23.99 0 0 0 627 157

2 50.8 67 45 900 22 42 21.53 0 0 242 784 256

2 50.8 67 45 900 22 60 28.09 0 0 0 438 110

2 50.8 73 55 1100 29 42 16.34 0 0 17 21 10

2 50.8 73 55 1100 22 42 20.02 0 222 541 583 337

2 50.8 73 55 1100 22 60 26.58 0 0 29 577 151

3 50.8 18.2 20 600 149 33 5.72 23 22 35 36 29

3 50.8 18.2 20 600 149 40 6.9 1142 854 2824 4001 2205

3 50.8 18.2 20 600 126 33 6.53 364 879 2418 3919 1895

3 50.8 18.2 20 600 126 45 8.75 235 23 627 1553 610

3 50.8 17.5 30 900 149 33 5.74 1270 2198 3176 3879 2631

3 50.8 17.5 30 900 149 40 6.92 2177 2076 2691 3401 2586

3 50.8 17.5 30 900 126 33 6.56 1280 1438 2584 3564 2217

3 50.8 17.5 30 900 126 45 8.78 654 868 1344 3000 1467

3 50.8 18.2 40 1200 126 33 6.53 1286 1436 2635 3537 2224

3 50.8 14.2 50 1500 149 40 7.03 994 1159 2117 3508 1945

3 50.8 14.2 50 1500 126 33 6.67 48 289 655 1491 621

3 50.8 14.2 50 1500 126 45 8.89 1012 1255 2397 3762 2106

3 50.8 34.1 20 600 94 35 7.96 315 666 879 1152 753

3 50.8 34.1 20 600 94 50 11.21 248 337 643 856 521

3 50.8 34.1 20 600 72 35 9.84 226 301 1240 2615 1096

3 50.8 34.1 20 600 72 50 13.59 169 414 1055 2672 1077

3 50.8 34 35 1050 94 35 7.97 255 285 815 1106 615

3 50.8 34 35 1050 94 50 11.21 221 417 638 715 498

3 50.8 34 35 1050 72 35 9.84 74 586 1782 2339 1195

3 50.8 34 35 1050 72 50 13.59 134 434 1037 1928 883

3 50.8 34.9 45 1350 94 35 7.92 237 634 940 1155 742


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 50.8 34.9 45 1350 94 50 11.16 235 432 698 808 543

3 50.8 34.9 45 1350 72 35 9.8 354 1085 2104 2843 1596

3 50.8 35.2 60 1800 94 35 7.9 316 587 840 1012 689

3 50.8 35.2 60 1800 94 50 11.15 264 463 604 762 523

3 50.8 35.2 60 1800 72 35 9.78 89 301 483 771 411

3 50.8 73 30 900 29 42 16.34 0 37 44 148 57

3 50.8 73 30 900 29 60 22.42 0 33 213 370 154

3 50.8 73 30 900 22 42 20.02 0 66 342 600 252

3 50.8 73 30 900 22 60 26.58 0 86 571 548 301

3 50.8 72.9 45 1350 29 42 16.38 0 165 195 148 127

3 50.8 72.9 45 1350 29 60 22.45 41 199 208 172 155

3 50.8 72.9 45 1350 22 42 20.05 0 78 88 57 56

3 50.8 72.9 45 1350 22 60 26.61 37 219 205 136 149

3 50.8 73.2 70 2100 29 60 22.35 185 443 392 368 347

4 38.1 17.5 30 1200 126 45 8.78 2027 2394 3112 2704 2559

4 38.1 15 40 1600 126 33 6.64 167 1552 1123 1416 1065

4 38.1 15 40 1600 126 45 8.86 762 1272 1237 3346 1654

4 38.1 37 20 800 94 35 7.8 137 703 594 1415 712

4 38.1 37 20 800 94 50 11.04 167 289 424 721 400

4 38.1 37 20 800 72 35 9.68 264 295 725 1902 796

4 38.1 37 20 800 72 50 13.43 458 226 806 1554 761

4 38.1 35 35 1400 94 50 11.16 12 21 37 57 32

4 38.1 35 35 1400 72 35 9.79 15 22 37 41 29

4 38.1 35 35 1400 72 50 13.54 27 27 37 36 32

4 38.1 35 45 1800 94 35 7.91 399 867 587 986 710

4 38.1 35 45 1800 94 50 11.16 148 155 391 633 332

4 38.1 35 45 1800 72 35 9.79 157 77 520 1853 652

4 38.1 35 45 1800 72 50 13.54 0 604 637 1694 734

4 38.1 35 60 2400 94 35 7.91 285 557 764 1047 663


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 38.1 35 60 2400 94 50 11.16 304 418 539 938 550

4 38.1 35 60 2400 72 35 9.79 388 854 1399 2361 1250

4 38.1 35 60 2400 72 50 13.54 253 423 840 2042 889

4 38.1 70 30 1200 29 42 17.22 52 176 266 234 182

4 38.1 70 30 1200 29 60 23.29 252 286 425 370 333

4 38.1 70 30 1200 22 60 27.42 152 204 208 154 180

4 38.1 67 45 1800 29 42 17.91 9 184 261 219 168

4 38.1 67 45 1800 29 60 23.99 286 340 399 362 347

4 38.1 67 45 1800 22 42 21.53 0 56 76 54 47

4 38.1 67 45 1800 22 60 28.09 210 271 315 216 253

4 38.1 67.6 55 2200 29 42 17.78 142 238 283 357 255

4 38.1 67.6 55 2200 22 42 21.41 86 124 132 175 129

4 38.1 69 70 2800 29 42 17.47 67 240 322 265 224

4 38.1 69 70 2800 29 60 23.54 258 358 466 403 371

4 38.1 69 70 2800 22 42 21.1 59 130 143 108 110

4 38.1 69 70 2800 22 60 27.66 329 470 455 338 398


Table M.2 Results from Replicate128 tests demonstrating low HTC at the top section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 17.9 20 400 149 33 5.73 2508 3433 4324 3533 3450

2 44.45 17.9 20 400 149 37 6.41 2467 1022 4374 3987 2963

2 44.45 21.7 30 600 126 45 8.62 1451 2094 2648 3611 2451

2 44.45 20 40 800 126 45 8.69 797 1818 2944 3931 2373

2 44.45 16.3 50 1000 149 33 5.79 2485 2322 3422 5228 3364

2 44.45 16.3 50 1000 149 37 6.46 2666 3039 3311 5141 3539

2 44.45 16.3 50 1000 126 33 6.6 2099 3490 5082 4710 3845

2 44.45 16.3 50 1000 126 45 8.69 1548 1746 2496 4828 2655

2 44.45 67 45 900 29 42 17.91 386 635 606 563 548

2 44.45 67 45 900 29 60 23.99 194 329 526 509 390

2 44.45 67 45 900 22 60 26.91 255 420 401 372 362

2 44.45 67.6 55 1100 29 60 23.86 0 0 13 16 7

3 44.45 18.9 20 400 149 33 5.69 1395 2474 491 3151 1878

3 44.45 18.9 20 400 149 40 6.87 749 549 199 3059 1139

3 44.45 18.9 20 400 126 33 6.51 371 493 1588 2222 1169

3 44.45 18.9 20 400 126 45 8.73 275 366 1178 1649 867

3 44.45 16 40 800 149 33 5.8 834 2350 3668 3975 2707

3 44.45 16 40 800 149 45 7.79 419 2244 1448 3741 1963

3 44.45 16 40 800 126 33 6.61 708 1287 3404 3113 2128

3 44.45 16 40 800 126 45 8.83 326 582 1082 2045 1009

3 44.45 70 30 600 29 42 17.22 0 0 60 239 75

3 44.45 70 30 600 29 60 23.29 0 0 443 506 237

3 44.45 70 30 600 22 42 20.86 0 0 106 332 110

3 44.45 70 30 600 22 60 27.42 0 0 36 183 55

3 44.45 67 45 900 29 42 17.91 0 100 367 131 150

3 44.45 67 45 900 29 60 23.99 0 30 59 18 27

3 44.45 67 45 900 22 42 21.21 0 283 385 198 217


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 44.45 67.6 55 1100 29 42 17.78 0 0 0 81 20

3 44.45 67.6 55 1100 29 60 23.86 42 80 496 398 254

3 44.45 67.6 55 1100 22 42 21.41 0 0 80 291 93

3 44.45 67.6 55 1100 22 60 27.97 0 1 19 347 92

2 38.1 20 20 600 149 33 5.65 1064 2086 1646 5736 2633

2 38.1 20 20 600 149 35 5.99 1317 2255 3111 5157 2960

2 38.1 20 20 600 126 33 6.47 4006 5777 3998 5508 4822

2 38.1 16 30 900 126 45 8.83 3328 4047 3509 4840 3931

2 38.1 19 40 1200 149 41 7.03 2447 3680 2323 6082 3633

2 38.1 20 50 1500 149 33 5.65 732 2122 1690 3108 1913

2 38.1 20 50 1500 149 44 7.49 684 696 638 2114 1033

2 38.1 20 50 1500 126 33 6.47 920 2128 1235 1384 1417

2 38.1 20 50 1500 126 45 8.69 504 746 1002 1330 896

2 38.1 72 30 900 29 42 17.22 0 0 8 83 23

2 38.1 72 30 900 29 60 23.29 89 330 99 1200 430

2 38.1 72 30 900 22 42 20.32 0 0 0 261 65

2 38.1 72 30 900 22 60 26.88 35 25 343 1371 444

2 38.1 69.7 45 1350 29 42 17.29 0 0 0 82 21

2 38.1 69.7 45 1350 29 60 23.37 0 125 263 229 154

2 38.1 69.7 45 1350 22 42 20.73 0 0 0 93 23

2 38.1 69.7 45 1350 22 60 27.29 0 0 38 82 30

2 38.1 68 55 1650 29 42 17.7 0 0 0 21 5

2 38.1 68 55 1650 22 42 21.32 324 616 630 584 539

2 38.1 68 55 1650 22 60 27.88 126 121 343 95 171

2 38.1 70 70 2100 29 42 17.22 380 490 566 492 482

2 38.1 70 70 2100 29 60 23.29 185 170 1019 534 477

3 38.1 66.8 30 900 29 42 17.95 60 48 492 402 251

3 38.1 66.8 30 900 29 60 24.03 78 74 554 652 340

3 38.1 66.8 30 900 22 42 21.57 178 107 348 419 263


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 38.1 67 45 1350 29 42 17.91 60 310 351 311 258

3 38.1 67 45 1350 29 60 23.99 194 75 457 701 357

3 38.1 67 45 1350 22 60 28.09 117 50 255 512 234

3 38.1 67.6 55 1650 29 60 23.86 335 250 493 716 449

3 38.1 67.6 55 1650 22 60 27.97 309 164 578 565 404

3 38.1 69 70 2100 29 60 23.54 289 353 477 406 381

3 38.1 69 70 2100 22 60 27.66 95 110 171 77 113

Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets 365

APPENDIX N: RESULTS SHOWING

LOW HTC AT BOTTOM SECTION –

ORIGINAL432 AND REPLICATE128

DATASETS

N.1 Introductory Remarks

This appendix presents the non-uniform boiling pattern showing low HTC at

bottom section results from the Original432 and Replicate128 experiments in Table

N.1 and Table N.2 respectively. This boiling pattern shows that the HTC of the bottom

section (section 4) was lower than 15% of the overall HTC.


Table N.1 Results from Original432 tests demonstrating low HTC at the bottom section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 44.45 17.9 20 800 149 33 5.73 4512 2579 1950 2261 2826

4 44.45 17.9 20 800 149 40 6.91 4618 2641 1700 2248 2802

4 44.45 17.9 20 800 126 33 6.54 5010 3311 1619 1935 2969

4 44.45 17.9 20 800 126 45 8.76 5496 4570 2009 1820 3474

4 44.45 17.8 30 1200 149 33 5.73 4484 4627 2784 2273 3542

4 44.45 17.8 30 1200 149 45 7.73 4949 3450 3355 1319 3269

4 44.45 17.8 30 1200 126 33 6.55 2378 2456 1658 511 1751

4 44.45 17.8 30 1200 126 45 8.77 4691 4557 3631 933 3453

4 44.45 17 40 1600 149 33 5.76 4679 3318 2040 1864 2975

4 44.45 17 40 1600 149 45 7.76 5415 4574 3298 1614 3725

4 44.45 17 40 1600 126 33 6.57 4824 4198 2006 1444 3118

4 44.45 17 40 1600 126 45 8.79 4953 5019 3948 1303 3806

4 44.45 15 50 2000 149 33 5.83 2769 1874 628 493 1441

4 44.45 15 50 2000 149 40 7.01 5002 4543 3115 1723 3596

4 44.45 15 50 2000 126 33 6.64 4415 4282 2741 1099 3134

4 44.45 15 50 2000 126 45 8.86 4451 4135 3107 693 3097

4 44.45 36 20 800 94 35 7.86 787 1085 1161 561 898

4 44.45 34 35 1400 94 35 7.97 5034 4833 3281 973 3530

4 44.45 36.2 45 1800 94 35 7.85 2669 3665 4504 2476 3328

4 44.45 34.7 60 2400 94 35 7.93 3429 3569 2389 1218 2651

4 44.45 34.7 60 2400 94 50 11.17 3698 4004 3117 1135 2989

4 44.45 34.7 60 2400 72 35 9.81 3485 3255 2384 917 2510

4 44.45 69.5 45 1800 29 60 23.42 535 497 360 255 412

4 44.45 65 55 2200 29 42 18.3 142 426 316 160 261

4 44.45 65 55 2200 29 60 24.38 406 278 299 250 308

4 44.45 65 55 2200 22 42 21.9 29 106 107 42 71

4 44.45 65 55 2200 22 60 28.46 479 535 471 279 441

368 Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

4 44.45 66 70 2800 29 42 18.11 206 203 124 63 149

4 44.45 66 70 2800 29 60 24.19 382 491 425 244 386

4 44.45 66 70 2800 22 42 21.72 249 333 309 104 249

4 44.45 66 70 2800 22 60 28.28 460 527 427 224 409

3 38.1 17.9 20 600 126 33 6.54 4415 5042 3890 3185 4133

3 38.1 17.9 20 600 126 45 8.76 4198 4244 3963 3065 3867

3 38.1 21.7 30 900 126 33 6.4 3469 4123 2221 1853 2917

3 38.1 21.7 30 900 126 45 8.62 3688 3792 2433 1999 2978

3 38.1 20 40 1200 149 41 6.99 4492 4677 2957 2869 3749

3 38.1 20 40 1200 126 33 6.47 4332 4067 2560 2869 3457

3 38.1 20 40 1200 126 45 8.69 4277 4197 3054 2252 3445

3 38.1 16.3 50 1500 149 33 5.79 3155 3413 2475 1423 2616

3 38.1 16.3 50 1500 149 36 6.29 3137 3284 1105 1181 2177

3 38.1 16.3 50 1500 126 33 6.6 3126 3169 1659 710 2166

3 38.1 16.3 50 1500 126 45 8.82 3444 3414 3856 1741 3114

3 38.1 67.6 55 1650 29 42 17.78 503 466 417 320 427

3 38.1 69 70 2100 29 42 17.47 970 466 404 315 539

3 38.1 69 70 2100 22 42 21.1 988 176 67 154 346

3 38.1 69 70 2100 22 60 27.66 86 100 155 70 103

3 44.45 20 30 900 149 33 5.65 5111 5036 4629 2594 4343

3 44.45 20 30 900 149 45 7.65 4684 4487 4550 2614 4084

3 44.45 20 30 900 126 33 6.47 2195 2360 2070 1438 2016

3 44.45 20 30 900 126 45 8.69 4624 4544 5067 3602 4459

3 44.45 18 50 1500 149 33 5.73 4637 4274 2735 1508 3288

3 44.45 18 50 1500 149 45 7.72 4379 4195 3722 1823 3530

3 44.45 18 50 1500 126 33 6.54 4036 4232 3691 2523 3620

3 44.45 18 50 1500 126 45 8.76 4431 4372 4581 2843 4057

3 44.45 68.5 45 1350 29 60 23.66 0 28 54 17 25

3 44.45 68.5 70 2100 29 42 17.58 685 564 303 263 454


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 44.45 68.5 70 2100 29 60 23.66 431 365 303 249 337

3 44.45 68.5 70 2100 22 42 21.21 63 112 48 31 64

3 44.45 68.5 70 2100 22 60 27.77 67 83 47 37 58

4 50.8 36 20 800 72 50 13.49 192 304 206 121 206

4 50.8 36.2 45 1800 94 35 7.85 330 521 353 207 353

4 50.8 68 30 1200 29 60 23.77 33 16 51 15 28

4 50.8 69.5 45 1800 29 42 17.34 174 200 90 29 123

4 50.8 69.5 45 1800 22 42 20.98 0 111 195 68 94

4 50.8 65 55 2200 29 42 18.3 165 189 85 28 117

4 50.8 65 55 2200 29 60 24.38 30 36 81 37 46

4 50.8 65 55 2200 22 42 21.9 95 286 116 109 152

4 50.8 65 55 2200 22 60 28.46 105 121 54 18 75

4 50.8 70 70 2800 29 42 17.22 120 362 147 138 192

4 50.8 70 70 2800 29 60 23.29 128 147 66 22 91

4 50.8 70 70 2800 22 42 20.86 36 42 96 43 54

4 50.8 70 70 2800 22 60 27.42 41 66 71 30 52

2 38.1 36.5 20 400 72 35 9.71 2798 2385 2202 1793 2294

2 38.1 71.5 55 1100 22 60 27.03 124 119 337 93 168

2 44.45 19.5 30 600 149 33 5.67 5012 2506 2398 2214 3033

2 44.45 19.5 30 600 126 33 6.49 4711 6014 4836 3779 4835

2 44.45 35 45 900 94 35 7.91 1667 1643 1988 1260 1639

2 44.45 35 45 900 72 50 13.54 3067 2159 1972 1870 2267

2 44.45 35 60 1200 72 50 13.54 2921 2010 1463 1143 1884

2 44.45 72 30 600 29 42 16.66 348 280 242 177 262

2 44.45 72 30 600 29 60 22.73 602 619 547 462 557

2 44.45 72 30 600 22 42 20.32 61 42 16 17 34

2 44.45 72 30 600 22 60 26.88 543 512 457 399 478

2 44.45 71.9 45 900 22 42 20.35 1551 868 751 564 934

2 44.45 69.8 55 1100 29 42 17.27 568 465 354 281 417


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 69.8 55 1100 22 42 20.91 471 386 293 233 346

2 44.45 74 70 1400 29 42 16 654 544 435 372 501

2 44.45 74 70 1400 22 42 19.69 500 409 312 248 367

2 44.45 74 70 1400 22 60 26.25 598 415 493 392 474

2 50.8 18 20 400 126 45 8.76 48 49 43 30 43

2 50.8 69 70 1400 29 42 17.47 1729 785 193 366 769

2 50.8 69 70 1400 22 42 21.1 891 568 479 418 589

3 50.8 35.2 60 1800 72 50 13.53 2189 2136 2073 1612 2002

3 50.8 71.2 55 1650 29 42 16.89 157 128 144 115 136

3 50.8 71.2 55 1650 22 42 20.55 73 54 39 23 47

3 50.8 71.2 55 1650 22 60 27.11 295 302 249 200 261

3 50.8 73.2 70 2100 22 42 19.96 259 81 34 83 114

3 50.8 73.2 70 2100 22 60 26.52 806 645 520 521 623

4 38.1 17.9 20 800 149 45 7.72 4177 3447 3965 2468 3514

4 38.1 15 40 1600 149 45 7.82 3380 3517 3865 2787 3387

4 38.1 16 50 2000 149 33 5.8 4308 4156 4734 3285 4121

4 38.1 35 35 1400 94 35 7.91 64 54 39 12 42

4 38.1 69 70 2800 22 60 27.66 329 470 455 338 398


Table N.2 Results from Replicate128 tests demonstrating low HTC at the bottom section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 21.7 30 600 149 33 5.59 4681 2340 2240 2068 2832

2 44.45 21.7 30 600 126 33 6.4 4390 5604 4506 3521 4505

2 44.45 70 30 600 29 42 16.66 342 275 237 174 257

2 44.45 70 30 600 29 60 22.73 590 606 536 453 546

2 44.45 70 30 600 22 42 20.86 58 40 15 17 33

2 44.45 70 30 600 22 60 27.42 522 492 439 383 459

2 44.45 67 45 900 22 42 20.35 1458 816 706 530 878

2 44.45 67.6 55 1100 29 42 17.78 507 415 316 251 372

2 44.45 67.6 55 1100 22 42 21.41 423 346 264 210 311

2 44.45 69 70 1400 29 42 17.47 569 473 378 324 436

2 44.45 69 70 1400 22 42 21.1 443 363 276 220 326

3 44.45 20.5 30 600 149 33 5.63 4975 4902 4505 2524 4227

3 44.45 20.5 30 600 149 45 7.63 4555 4364 4424 2542 3971

3 44.45 20.5 30 600 126 33 6.45 2136 2295 2014 1399 1961

3 44.45 20.5 30 600 126 45 8.67 4495 4417 4926 3501 4335

3 44.45 17 50 1000 149 33 5.76 4516 4162 2663 1469 3203

3 44.45 17 50 1000 149 45 7.76 4272 4093 3630 1779 3444

3 44.45 17 50 1000 126 33 6.57 3935 4125 3598 2460 3530

3 44.45 17 50 1000 126 45 8.79 4325 4268 4472 2775 3960

3 44.45 67 45 900 29 60 23.99 0 30 59 18 27

3 44.45 68.5 70 1400 29 42 17.58 651 536 288 250 431

3 44.45 68.5 70 1400 29 60 23.66 410 347 288 236 320

3 44.45 68.5 70 1400 22 42 21.21 60 107 45 30 61

3 44.45 68.5 70 1400 22 60 27.77 63 79 45 35 56

2 38.1 68 55 1650 22 60 27.88 126 121 343 95 171

3 38.1 18 20 600 126 33 6.54 4108 4692 3619 2963 3846

3 38.1 18 20 600 126 45 8.76 3906 3949 3687 2851 3598


TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 38.1 16.9 30 900 126 33 6.58 3276 3894 2098 1750 2755

3 38.1 16.9 30 900 126 45 8.8 3507 3605 2313 1901 2832

3 38.1 20 40 1200 149 41 6.99 4267 4444 2809 2726 3562

3 38.1 20 40 1200 126 33 6.47 4115 3864 2432 2725 3284

3 38.1 20 40 1200 126 45 8.69 4063 3987 2901 2139 3273

3 38.1 18.5 50 1500 149 33 5.71 3262 3528 2559 1472 2705

3 38.1 18.5 50 1500 149 36 6.22 3240 3392 1141 1220 2248

3 38.1 18.5 50 1500 126 33 6.52 3225 3270 1712 733 2235

3 38.1 18.5 50 1500 126 45 8.74 3544 3513 3968 1791 3204

3 38.1 67.6 55 1650 29 42 17.78 528 489 438 336 448

3 38.1 69 70 2100 29 42 17.47 1067 513 444 346 593

3 38.1 69 70 2100 22 42 21.1 1087 193 73 169 381

3 38.1 69 70 2100 22 60 27.66 95 110 171 77 113

Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets

373

APPENDIX O: RESULTS SHOWING

LOW HTC AT INTERMEDIATE

SECTIONS – ORIGINAL432 AND

REPLICATE128 DATASETS

O.1 Introductory Remarks

This appendix presents the non-uniform boiling pattern showing low HTC at

intermediate section (section 2 and/or 3) results from the Original432 and

Replicate128 experiments in Table O.1 and Table O.2 respectively. This boiling

pattern shows that the HTC of the intermediate sections (section 2 and/or 3) were lower

than 15% of the overall HTC while the HTC of the top and bottom sections being

within or higher than 15% of the overall HTC.

Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets 375

Table O.1 Results from Original432 tests demonstrating low HTC at an intermediate section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

3 38.1 17.9 20 600 149 33 5.73 4838 3995 3018 3695 3886

3 38.1 17.9 20 600 149 40 6.91 4737 4132 2812 3269 3737

3 38.1 21.7 30 900 149 33 5.59 3394 4966 2109 3087 3389

3 38.1 21.7 30 900 149 40 6.76 3747 4829 2389 3118 3521

3 38.1 20 40 1200 149 33 5.65 4708 5327 3114 3736 4221

3 38.1 67 45 1350 22 42 21.53 721 275 453 416 466

3 38.1 67.6 55 1650 22 42 21.41 506 419 300 392 404

3 38.1 69 70 2100 22 42 21.1 988 176 67 154 346

4 50.8 68 30 1200 22 60 27.88 22 12 32 25 23

2 38.1 20 30 600 149 33 5.65 4602 5961 3051 5028 4661

2 38.1 20 30 600 149 40 6.83 4652 5227 2479 4253 4152

2 38.1 20 30 600 126 33 6.47 4447 6803 2997 5505 4938

2 38.1 18 40 800 126 33 6.54 1959 2563 1664 2181 2092

2 38.1 72 70 1400 22 42 20.32 528 517 394 528 492

2 44.45 19.5 30 600 149 33 5.67 5012 2506 2398 2214 3033

2 44.45 37 20 400 72 35 9.68 916 597 1036 827 844

2 44.45 38 35 700 72 50 13.38 3222 1757 1666 2226 2218

2 44.45 35 60 1200 94 50 11.16 3558 3039 2440 2844 2970

2 44.45 35 60 1200 72 35 9.79 2623 1781 1991 2517 2228

2 44.45 69.8 55 1100 22 60 27.47 43 25 17 25 28

2 50.8 16.9 30 600 126 33 6.58 2793 2832 2175 2776 2644

2 50.8 35 45 900 94 50 11.16 1328 953 862 1091 1058

3 50.8 18.2 40 1200 126 45 8.75 3242 2833 2116 2326 2629

3 50.8 73.2 70 2100 22 42 19.96 259 81 34 83 114

4 38.1 70 30 1200 22 42 20.86 70 56 94 64 71

376 Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets

Table O.2 Results from Replicate128 tests demonstrating low HTC at an intermediate section

TL

(m)

TD

(mm)

Brix JL (%

tube

height)

JL

(mm)

HS

(kPa

abs)

ΔP

(kPa)

ΔT

(°C)

Section 1

(W/m2/K)

Section 2

(W/m2/K)

Section 3

(W/m2/K)

Section 4

(W/m2/K)

Overall

(W/m2/K)

2 44.45 17.9 20 400 126 45 8.76 1347 1186 1722 2013 1567

2 44.45 69 70 1400 22 60 27.66 1027 663 804 789 821

2 38.1 20 20 600 126 45 8.69 3078 2356 3276 4083 3198

2 38.1 16 30 900 149 33 5.8 4713 6104 3124 5149 4773

2 38.1 16 30 900 149 40 6.97 4784 5375 2549 4373 4270

2 38.1 16 30 900 126 33 6.61 4571 6992 3080 5658 5075

2 38.1 19 40 1200 149 33 5.69 5329 4235 2490 5139 4298

2 38.1 19 40 1200 126 33 6.5 1931 2525 1639 2149 2061

2 38.1 70 70 2100 22 42 20.86 566 554 422 566 527

2 38.1 70 70 2100 22 60 27.42 577 149 655 975 589

3 38.1 18 20 600 149 33 5.73 4502 3718 2808 3439 3617

3 38.1 18 20 600 149 40 6.9 4408 3845 2617 3042 3478

3 38.1 16.9 30 900 149 33 5.77 3190 4668 1983 2902 3186

3 38.1 16.9 30 900 149 40 6.94 3541 4563 2257 2947 3327

3 38.1 20 40 1200 149 33 5.65 4472 5061 2958 3549 4010

3 38.1 67 45 1350 22 42 21.53 685 261 430 396 443

Appendix P: Analysis of Variance 377

APPENDIX P: ANALYSIS OF VARIANCE

P.1 Introductory Remarks

This appendix presents the analysis of variance for individual section HTCmax

from the Original432 dataset. The significant interactions are analysed in section 6.5.2.


Table P.1 Analysis of variance of HTC of section 1 from Original432 tests with

3rd order interactions

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 2604453 0.14 –

TD 2 37594189 2.01 –


B 2 240942219 141.94 0.000

JL 3 4517936 2.66 –

TL:B 4 195755 0.12 –

TL:JL 6 2091768 1.23 –

TD:B 4 16901863 9.96 0.000

TD:JL 6 5808118 3.42 0.014

B:JL 6 2390898 1.41 –

TL:TD:B 8 4899175 2.89 0.021

TL:TD:JL 12 1800409 1.06 –

TL:B:JL 12 1438937 0.85 –

TD:B:JL 12 2239058 1.32 –


HS 1 7420366 15.06 0.000

ΔP 1 414099 0.84 –

TL:HS 2 268549 0.55 –

TL:ΔP 2 437831 0.89 –

TD:HS 2 329020 0.67 –

TD:ΔP 2 36412 0.07 –

B:HS 2 5883033 11.94 0.000

B:ΔP 2 919474 1.87 –

JL:HS 3 588920 1.20 –

JL:ΔP 3 104759 0.21 –

HS:ΔP 1 848451 1.72 –

TL:TD:HS 4 1411947 2.87 0.026

TL:TD:ΔP 4 259696 0.53 –

TL:B:HS 4 1035779 2.10 –

TL:B:ΔP 4 2060539 4.18 0.003

TL:JL:HS 6 442951 0.90 –

TL:JL:ΔP 6 22534 0.05 –

TL:HS:ΔP 2 828208 1.68 –

TD:B:HS 4 727702 1.48 –

TD:B:ΔP 4 394429 0.80 –

TD:JL:HS 6 852412 1.73 –

380 Appendix P: Analysis of Variance

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:ΔP 6 126252 0.26 –

TD:HS:ΔP 2 21839 0.04 –

B:JL:HS 6 447021 0.91 –

B:JL:ΔP 6 252769 0.51 –

B:HS:ΔP 2 279976 0.57 –

JL:HS:ΔP 3 640105 1.30 –

TL:TD:B:HS 8 1637427 3.32 0.002

TL:TD:B:ΔP 8 792984 1.61 –

TL:TD:JL:HS 12 479053 0.97 –

TL:TD:JL:ΔP 12 189417 0.38 –

TL:TD:HS:ΔP 4 644665 1.31 –

TL:B:JL:HS 12 228510 0.46 –

TL:B:JL:ΔP 12 619137 1.26 –

TL:B:HS:ΔP 4 445405 0.90 –

TL:JL:HS:ΔP 6 134491 0.27 –

TD:B:JL:HS 12 396152 0.80 –

TD:B:JL:ΔP 12 183922 0.37 –

TD:B:HS:ΔP 4 887954 1.80 –

TD:JL:HS:ΔP 6 757523 1.54 –

B:JL:HS:ΔP 6 1071255 2.17 –





Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 2944228 0.21 –

TD 2 36326252 2.63 –


B 2 270365235 225.35 0.000

JL 3 6011506 5.01 0.008

TL:B 4 1753123 1.46 –

TL:JL 6 1313665 1.09 –

TD:B 4 17277802 14.40 0.000

TD:JL 6 5212019 4.34 0.004

B:JL 6 3592189 2.99 0.025

TL:TD:B 8 3224738 2.69 0.029

TL:TD:JL 12 1204478 1.00 –

TL:B:JL 12 934821 0.78 –

TD:B:JL 12 2091457 1.74 –


HS 1 8233992 15.52 0.000

ΔP 1 2993187 5.64 0.019

TL:HS 2 1570721 2.96 –

TL:ΔP 2 551977 1.04 –

TD:HS 2 106519 0.20 –

TD:ΔP 2 72817 0.14 –

B:HS 2 2434233 4.59 0.012

B:ΔP 2 1794202 3.38 0.037

JL:HS 3 582780 1.10 –

JL:ΔP 3 117523 0.22 –

HS:ΔP 1 128171 0.24 –

TL:TD:HS 4 1875343 3.53 0.009

TL:TD:ΔP 4 109680 0.21 –

TL:B:HS 4 613484 1.16 –

TL:B:ΔP 4 1772718 3.34 0.013

TL:JL:HS 6 813745 1.53 –

TL:JL:ΔP 6 217394 0.41 –

TL:HS:ΔP 2 1945960 3.67 0.029

TD:B:HS 4 1099621 2.07 –

TD:B:ΔP 4 664627 1.25 –

TD:JL:HS 6 625522 1.18 –


Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:ΔP 6 165139 0.31 –

TD:HS:ΔP 2 129015 0.24 –

B:JL:HS 6 831381 1.57 –

B:JL:ΔP 6 142575 0.27 –

B:HS:ΔP 2 288089 0.54 –

JL:HS:ΔP 3 377618 0.71 –

TL:TD:B:HS 8 1316409 2.48 0.016

TL:TD:B:ΔP 8 488272 0.92 –

TL:TD:JL:HS 12 410278 0.77 –

TL:TD:JL:ΔP 12 360950 0.68 –

TL:TD:HS:ΔP 4 453564 0.85 –

TL:B:JL:HS 12 232740 0.44 –

TL:B:JL:ΔP 12 258963 0.49 –

TL:B:HS:ΔP 4 1198271 2.26 –

TL:JL:HS:ΔP 6 226203 0.43 –

TD:B:JL:HS 12 338076 0.64 –

TD:B:JL:ΔP 12 282008 0.53 –

TD:B:HS:ΔP 4 457428 0.86 –

TD:JL:HS:ΔP 6 1023934 1.93 –

B:JL:HS:ΔP 6 739208 1.39 –





Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 5238741 0.48 –

TD 2 24368868 2.24 –


B 2 195834632 192.40 0.000

JL 3 2487131 2.44 –

TL:B 4 2583420 2.54 –

TL:JL 6 1001641 0.98 –

TD:B 4 7354507 7.23 0.001

TD:JL 6 3183947 3.13 0.021

B:JL 6 1451101 1.43 –

TL:TD:B 8 8666000 8.51 0.000

TL:TD:JL 12 1184585 1.16 –

TL:B:JL 12 929436 0.91 –

TD:B:JL 12 2103079 2.07 –


HS 1 3671847 8.41 0.004

ΔP 1 90232 0.21 –

TL:HS 2 951134 2.18 –

TL:ΔP 2 50905 0.12 –

TD:HS 2 1884 0.00 –

TD:ΔP 2 241653 0.55 –

B:HS 2 1262975 2.89 –

B:ΔP 2 319674 0.73 –

JL:HS 3 308350 0.71 –

JL:ΔP 3 231172 0.53 –

HS:ΔP 1 6518 0.01 –

TL:TD:HS 4 2271100 5.20 0.001

TL:TD:ΔP 4 521496 1.19 –

TL:B:HS 4 1021409 2.34 –

TL:B:ΔP 4 770458 1.76 –

TL:JL:HS 6 1217942 2.79 0.014

TL:JL:ΔP 6 382103 0.87 –

TL:HS:ΔP 2 783002 1.79 –

TD:B:HS 4 2449519 5.61 0.000

TD:B:ΔP 4 653670 1.50 –

TD:JL:HS 6 467145 1.07 –


Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:ΔP 6 426961 0.98 –

TD:HS:ΔP 2 777742 1.78 –

B:JL:HS 6 383282 0.88 –

B:JL:ΔP 6 117219 0.27 –

B:HS:ΔP 2 70671 0.16 –

JL:HS:ΔP 3 530396 1.21 –

TL:TD:B:HS 8 1829232 4.19 0.000

TL:TD:B:ΔP 8 611433 1.40 –

TL:TD:JL:HS 12 494240 1.13 –

TL:TD:JL:ΔP 12 213654 0.49 –

TL:TD:HS:ΔP 4 136662 0.31 –

TL:B:JL:HS 12 489947 1.12 –

TL:B:JL:ΔP 12 392197 0.90 –

TL:B:HS:ΔP 4 494315 1.13 –

TL:JL:HS:ΔP 6 244354 0.56 –

TD:B:JL:HS 12 428737 0.98 –

TD:B:JL:ΔP 12 343756 0.79 –

TD:B:HS:ΔP 4 775777 1.78 –

TD:JL:HS:ΔP 6 515891 1.18 –

B:JL:HS:ΔP 6 679222 1.55 –





Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 23005300 6.46 –

TD 2 3029998 0.85 –

Residuals 4 3561657

B 2 228926494 164.08 0.000

JL 3 1646634 1.18 –

TL:B 4 7395276 5.30 0.003

TL:JL 6 262645 0.19 –

TD:B 4 4404220 3.16 0.032

TD:JL 6 2101835 1.51 –

B:JL 6 2508045 1.80 –

TL:TD:B 8 6782373 4.86 0.001

TL:TD:JL 12 1025176 0.73 –

TL:B:JL 12 801337 0.57 –

TD:B:JL 12 1595094 1.14 –


HS 1 2759219 7.99 0.006

ΔP 1 404000 1.17 –

TL:HS 2 1910367 5.53 0.005

TL:ΔP 2 286007 0.83 –

TD:HS 2 920855 2.67 –

TD:ΔP 2 587660 1.70 –

B:HS 2 4181468 12.10 0.000

B:ΔP 2 1133612 3.28 0.041

JL:HS 3 159447 0.46 –

JL:ΔP 3 54178 0.16 –

HS:ΔP 1 256235 0.74 –

TL:TD:HS 4 1333719 3.86 0.006

TL:TD:ΔP 4 233408 0.68 –

TL:B:HS 4 890520 2.58 0.041

TL:B:ΔP 4 615935 1.78 –

TL:JL:HS 6 979781 2.84 0.013

TL:JL:ΔP 6 544900 1.58 –

TL:HS:ΔP 2 222621 0.64 –

TD:B:HS 4 880790 2.55 0.043

TD:B:ΔP 4 250105 0.72 –

TD:JL:HS 6 557469 1.61 –


Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TD:JL:ΔP 6 481403 1.39 –

TD:HS:ΔP 2 1003789 2.91 –

B:JL:HS 6 308585 0.89 –

B:JL:ΔP 6 318169 0.92 –

B:HS:ΔP 2 99847 0.29 –

JL:HS:ΔP 3 934017 2.70 0.049

TL:TD:B:HS 8 1405498 4.07 0.000

TL:TD:B:ΔP 8 268047 0.78 –

TL:TD:JL:HS 12 580347 1.68 –

TL:TD:JL:ΔP 12 283201 0.82 –

TL:TD:HS:ΔP 4 347121 1.00 –

TL:B:JL:HS 12 451839 1.31 –

TL:B:JL:ΔP 12 380459 1.10 –

TL:B:HS:ΔP 4 96748 0.28 –

TL:JL:HS:ΔP 6 117894 0.34 –

TD:B:JL:HS 12 438159 1.27 –

TD:B:JL:ΔP 12 394936 1.14 –

TD:B:HS:ΔP 4 426997 1.24 –

TD:JL:HS:ΔP 6 338920 0.98 –

B:JL:HS:ΔP 6 596374 1.73 –



Table P.5 Analysis of variance of HTCmax of section 1 from Original432 tests

with 3rd order interactions

Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 7397941 1.88 –

TD 2 17219568 4.37 –

Residuals 4 3943846 –

B 2 100189005 59.65 0.000

TL:B 4 697330 0.42 –

TD:B 4 6970377 4.15 0.041

Residuals 8 1679629

HS 1 2892285 6.95 0.012

ΔP 1 328451 0.79 –

TL:HS 2 622307 1.50 –

TL:ΔP 2 394636 0.95 –

TD:HS 2 1529004 3.67 0.035

TD:ΔP 2 110523 0.27 –

B:HS 2 1139347 2.74 –

B:ΔP 2 294905 0.71 –

HS:ΔP 1 46050 0.11 –

TL:TD:HS 4 303932 0.73 –

TL:TD:ΔP 4 490645 1.18 –

TL:B:HS 4 1067305 2.57 –

TL:B:ΔP 4 414015 1.00 –

TL:HS:ΔP 2 1709616 4.11 0.025

TD:B:HS 4 1367720 3.29 0.021

TD:B:ΔP 4 309287 0.74 –

TD:HS:ΔP 2 265289 0.64 –

B:HS:ΔP 2 5395 0.01 –

Residuals 36 416058



Source

Degrees of

freedom

Mean

square

Variance

ratio

Significance

level

TL 2 6324521 2.16 –

TD 2 17020978 5.80 –


B 2 125156668 81.04 0.000

TL:B 4 2316491 1.50 –

TD:B 4 7177250 4.65 0.031

Residuals 8 1544436

HS 1 4037071 9.81 0.003

ΔP 1 2158471 5.24 0.028

TL:HS 2 524878 1.27 –

TL:ΔP 2 370180 0.90 –

TD:HS 2 939946 2.28 –

TD:ΔP 2 160539 0.39 –

B:HS 2 779351 1.89 –

B:ΔP 2 1112463 2.70 –

HS:ΔP 1 22473 0.05 –

TL:TD:HS 4 594776 1.44 –

TL:TD:ΔP 4 116680 0.28 –

TL:B:HS 4 510687 1.24 –

TL:B:ΔP 4 694956 1.69 –

TL:HS:ΔP 2 2295074 5.57 0.008

TD:B:HS 4 1341997 3.26 0.022

TD:B:ΔP 4 122488 0.30 –

TD:HS:ΔP 2 38065 0.09 –

B:HS:ΔP 2 15643 0.04 –

Residuals 36 411687



Source

Degrees

of freedom

Mean

square

Variance

ratio

Significance

level

TL 2 6579628 3.01 –

TD 2 10700357 4.89 –


B 2 85051627 25.85 0.000

TL:B 4 1398117 0.42 –

TD:B 4 2635829 0.80 –

Residuals 8 3290632

HS 1 485522 1.28 –

ΔP 1 317775 0.84 –

TL:HS 2 679622 1.79 –

TL:ΔP 2 130499 0.34 –

TD:HS 2 713698 1.88 –

TD:ΔP 2 265858 0.70 –

B:HS 2 629141 1.66 –

B:ΔP 2 267951 0.71 –

HS:ΔP 1 116040 0.31 –

TL:TD:HS 4 572017 1.51 –

TL:TD:ΔP 4 273890 0.72 –

TL:B:HS 4 414545 1.09 –

TL:B:ΔP 4 429535 1.13 –

TL:HS:ΔP 2 559623 1.48 –

TD:B:HS 4 1998697 5.28 0.002

TD:B:ΔP 4 769559 2.03 –

TD:HS:ΔP 2 248426 0.66 –

B:HS:ΔP 2 92440 0.24 –

Residuals 36 378714



Source

Degrees of

freedom

Mean square Variance

ratio

Significance

level

TL 2 11810395 14.26 0.015

TD 2 1706308 2.06 –


B 2 84167518 40.25 0.000

TL:B 4 2582220 1.23 –

TD:B 4 1848260 0.88 –

Residuals 8 2091126

HS 1 19115 0.06 –

ΔP 1 897736 2.69 –

TL:HS 2 682222 2.05 –

TL:ΔP 2 144119 0.43 –

TD:HS 2 154443 0.46 –

TD:ΔP 2 419801 1.26 –

B:HS 2 1002893 3.01 –

B:ΔP 2 546795 1.64 –

HS:ΔP 1 48607 0.15 –

TL:TD:HS 4 800473 2.40 –

TL:TD:ΔP 4 215572 0.65 –

TL:B:HS 4 714230 2.14 –

TL:B:ΔP 4 153447 0.46 –

TL:HS:ΔP 2 135278 0.41 –

TD:B:HS 4 401190 1.20 –

TD:B:ΔP 4 417037 1.25 –

TD:HS:ΔP 2 355596 1.07 –

B:HS:ΔP 2 70135 0.21 –

Residuals 36 333262

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