An improved model for a once-through counter-cross-flow ... · Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1983 An improved model for a once-through

Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1983

An improved model for a once-through

counter-cross-flow waste heat recovery unit.

Wesco, Steven L.

Monterey, California. Naval Postgraduate School

http://hdl.handle.net/10945/19842

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THESISAN IMPROVED MODEL FOR A ONCE-THROUGP

CROSS- FLOW WASTE HEAT RECOVERY[ COUNTER-UNIT

by

Steven L. Wesco

September 19 83

Th<Bsis Adv isor: ?. F. Pucci

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An Improved Model for a Once-ThroughCounter-Cross-Flow Waste HeatRecovery Unit

5. TYPE OF REPORT a PERIOO COVERED

Master's Thesis;September 1983

S. PERFORMING ORG. REPORT NUMBER

7. AUTHOR^ 8. CONTRACT OR GRANT NUMSERfi;

Steven L. Wesco

S. PERFORMING ORGANIZATION NAME ANO ADDRESS

Naval Postgraduate SchoolMonterev, California 93943

10. PROGRAM ELEMENT, PROJECT, TASKAREA a WORK UNIT NUMBERS

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IS. SUPPLEMENTARY NOTES

19. KEY WOROS fContinue on •••fit aido If nacaaaarr ana1 Idontffy by block numbar)

Counter-Cross-Flow Heat ExchangerWaste Heat Recovery Unit (WHRU)RACER System

20. ABSTRACT fConttnua on rovatoo aid*) l( nacaatary mid tdontlty by block numbar)

An improved model for a once-through counter-cross-flowwaste heat recovery unit with a segmented fin-tube arrangementwas developed. The model was coded in FORTRAN IV computerlanguage fcr use on an IBM-30 33 computer system, and was testedfor various conditions of uniform and non-uniform gas flowdistributions. Additional parameters varied were heat exchangersize, steam outlet pressure, steam outlet temperature and gas flow

DO | j°m*7S 1473 EDITION OF I MOV 4S IS OBSOLETE UNCLASSIFIEDS.'N 0102- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Snia-a<-

#20 - ABSTRACT - (CONTINUED)

rate. The effect of each variation on WHRU performancewas evaluated and the interrelationship discussed. Resultsindicate the ideal design is a high steam temperature,low operating pressure, flow distribution controlledheat exchanger.

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Approved for public release; distribution unlimited

An Improved Model for a Once-Through Counter-Cross-Flow Waste Heat Recovery Unit

by

Steven L. jtfesco

Lieutenant Commander, United States NavyB.S. in Applied Science, Miami University, 19 73

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOL

September 1983

ABSTRACT

An improved model for a once-through counter-cross-flow

waste heat recovery unit with a segmented fin-tube arrange-

ment was developed. The model was coded in FORTRAN IV

computer language for use on an IBM- 30 33 computer system,

and was tested for various conditions of uniform and non-

uniform gas glow distributions. Additional parameters

varied were heat exchanger size, steam outlet pressure,

steam outlet temperature and gas flow rate. The effect of

each variation on WHRU performance was evaluated and the

interrelationship discussed. Results indicate the ideal

design is a high steam temperature, low operating pressure,

flow distribution controlled heat exchanger.

TABLE OF CONTENTS

I. INTRODUCTION 15

A. BACKGROUND 15

B. OBJECTIVES 17

II. MODEL DESCRIPTION 19

A. OVERVIEW 19

B. INITIAL CALCULATIONS 24

C. GEOMETRY 26

D. SUPERHEATER NODAL ANALYSIS 29

E. BOILING NODAL ANALYSIS 37

F. HEATING NODAL ANALYSIS 44

G. HEAT EXCHANGER SOLUTION PROCEDURE 4 6

III. DISCUSSION OF RESULTS 49

A. INITIAL TESTING 49

B. EFFECT OF NON-UNIFORM DISTRIBUTIONS 52

C. EFFECT OF HEAT EXCHANGER SIZE 5 5

D. EFFECT OF STEAM OUTLET TEMPERATURE 5 7

E. EFFECT OF HEAT EXCHANGER PRESSURE 5 8

F. EFFECT OF GAS FLOW RATE ON HEATEXCHANGER PERFORMANCE 60

G. EFFECT OF NON-UNIFORM MASS DISTRIBUTIONON EXHAUST GAS TEMPERATURE 6 2

IV. CONCLUSIONS 64

V. RECOMMENDATIONS FOR FURTHER RESEARCH 66

A. WHRU MODEL IMPROVEMENT AND EXPANSION 66

1. Fluid-Side Pressure Drop 67

2. Additional Geometries 67

3. Fouling 57

4. Alternate Working Fluids 67

5. Non-Uniform Temperature Distributions 68

APPENDIX A 121

LIST OF REFERENCES 194

INITIAL DISTRIBUTION LIST 195

LIST OF TABLES

I, Normalized Flow Distribution 69

II-A. Gas Flow Distributions (m = 121.8 lbm/s) 70y

II-B. Gas Flow Distributions (m =99.1 lbm/s) 70g

II-C. Gas Flow Distributions (m =77.4 lbm/s) 71g

II-D. Gas Flow Distributions (m = 66.7 lbm/s) 71

III. Isentropic Power for Various Gas FlowDistributions, Gas Flow Rates and SteamOutlet Temperatures 72

IV. Fluid Mass Flow Rate for Various Gas FlowRates, Gas Flow Distributions and SteamOutlet Temperatures 73

V. Power and Fluid Flow Rate for VariousSize Heat Exchangers 74

VI. Power and Fluid Flow Rate for VariousSteam Operating Pressures 75

LIST OF FIGURES

1. Waste Heat Recovery Unit Layout 76

2. Heat Exchanger Nodal Arrangement 77

3. Typical Nodal Gas and Fluid Flow 78

4. Nodal Gas and Fluid Flow for End of PassCondition 79

5. Tube Fin Configuration 80

6. Waste Heat Recovery Unit Tube Layout 80

1 ' hTPf

//h£

vs* Quality 81

8-A. Uniform Flow Distribution 82

8-B. Flow Distribution #1 83

8-C. Flow Distribution #2 84

8-D. Flow Distribution #3 85

8-E. Flow Distribution #4 86

8-F. Flow Distribution #5 87

8-G. Flow Distribution #6 88

8-H. Flow Distribution #7 89

8-1. Flow Distribution #8 90

9-A. Power vs. Gas Flow Rate (Distr.'s U, 1, 2) 91

9-B. Power vs. Gas Flow Rate (Distr.'s U, 3, 4) 92

9-C. Power vs. Gas Flow Rate (Distr.'s U, 5, 6) 93

9-D. Power vs. Gas Flow Rate (Distr.'s U, 7, 8) 94

9-E. Power vs. Gas Flow Rate (Composite) 95

10-A. Fluid Flow Rate vs. Gas Flow Rate(Distr.'s U, 1, 2) 96

10-B. Fluid Flow Rate vs. Gas Flow Rate(Distr.'s U, 3, 4) 97

10-C. Fluid Flow Rate vs. Gas Flow Rate(Distr.'s U, 5, 6) 98

10-D. Fluid Flow Rate vs. Gas Flow Rate(Distr.'s U, 7, 8) 99

10-E. Fluid Flow Rate vs. Gas Flow Rate (Composite) — 100

11-A. Power vs. No. of Heat Exchanger Passes(m = 121.8 lbm/s) 101

11-B. Power vs. No. of Heat Exchanger Passes(m =99.1 lbm/s) 102

y

11-C. Power vs. No. of Heat Exchanger Passes(m =77.4 lbm/s) 103

11-D. Power vs. No. of Heat Exchanger Passes(m =66.7 lbm/s) 104

g

11-E. Fluid Flow Rate vs. No. of Heat ExchangerPasses (m = 121.8 lbm/s) 105

y

11-F. Fluid Flow Rate vs. No. of Heat ExchangerPasses (m =99.1 lbm/s) 106

y

ll-G. Fluid Flow Rate vs. No. of Heat ExchangerPasses Cm = 77.4 lbm/s) 107

g

11-H. Fluid Flow Rate vs. No. of Heat ExchangerPasses (m =66.7 lbm/s) 108

g

12-A. Power vs. Steam Outlet Temperature 109

12-B. Fluid Mass Flow Rate vs. Steam OutletTemperature 110

13-A. Power vs. Heat Exchanger Operating Pressure 111

13-B. Fluid Mass Flow Rate vs. Heat ExchangerOperating Pressure 112

14-A. Fluid Temperature vs. Tube Length(m = 121.8 lbm/s) 113

g

14-B. Fluid Temperature vs. Tube Length(m =99.1 lbm/s) 114

g

14-C. Fluid Temperature vs. Tube Length(m =77.4 lbm/s) 115

y

14-D. Fluid Temperature vs. Tube Length(m =66.7 lbm/s) 116

g

14-E. Fluid Temperature vs. Tube Length (Distr. 1,m = 121.8 lbm/s) H 7

y

14-F. Fluid Temperature vs. Tube Length (Distr. 's U,

1; m = 121.8 lbm/s) 118g

15-A. Gas Temperature Distribution (Uniform,m = 121.8 lbm/s) 119y

15-B. Gas Temperature Distribution (Distr. 1,

m = 121.8 lbm/s) 12°g

10

NOMENCLATURE

English Letter Symbols

A - Area (ft2

)

2A, - Frontal Area Blocked by Tubes and Fins (ft )

2A, - Bare Tube Area (ft )

2A- - Heat Exchanger Frontal Area (ft )

2A,. - Fin Area (ft )fin

2A« - Cross Sectional Area for Fluid Flow (ft )

2A. - Inside Heat Transfer Area Per Node (ft )

IP2

A . - Minimum Cross Sectional Area for Gas Flow (ft )mm2

A - Outside Heat Transfer Area Per Node (ft )op2

A , . - Total Heat Exchanger Inside Area (ft )

2A. - Total Heat Exchanger Outside Area (ft )

C - Constant

C - Maximum Heat Capacity (BTU/hr-F)max e jl

C . - Minimum Heat Capacity (3TU/hr-F)mm c *

Cf

- Heat Capacity of Water/Steam (BTU/hr-F)

C - Heat Capacity of Gas (BTU/hr-F)g

Cf

- Specific Heat of Water/Steam (BTU/lbm-F)

C - Specific Heat of Gas (BTU/lbm-F)pg v

df

- Fin Outside Diameter (ft)

d_, - Diameter of Fin Base (ft)

d. - Inside Tube Diameter (ft)

d - Outside Tube Diameter (ft)o

11

d - Fin Root Diameter (ft)r

2G - Flow Rate Per Unit Area (lbm/hr-ft )

h - Fluid Enthalpy (BTU/lbm)

h - Fluid-Side Heat Transfer Coefficient (BTU/hr-ft -F)

2h - Gas-Side Heat Transfer Coefficient (BTU/hr-ft -F)y

hf

- Enthalpy Increment for Boiling (BTU/lbm)

h„ - Fluid-Side Heat Transfer Coefficient for TotallyLiquid Flow (BTU/hr-ft -F)

h_pf- Heat Exchanger Inside Heat Transfer Coefficient in

the Two-Phase Region (BTU/hr-ft 2 -F)

j- Heat Transfer Colburn j-factor

K - Thermal Conductivity of Gas (BTU/hr-ft-F)y

K - Thermal Conductivity of Steam/Water (BTU/hr-ft-F)

K - Thermal Conductivity of Heat Exchanger Tubew Wall (BTU/hr-ft-F)

i - Fin Height (ft)

i - Length of Cut from Fin Tip (ft)

L - Tube Length Per Node (ft)

m - Number of Heat Exchanger Passes

mf

- Steam/Water Mass Flow Rate (lbm/hr)

m - Gas Mass Flow Rate (lbm/hr)y

n - Number of Heat Exchanger Gas Paths

NTU - Number of Transfer Units

N-. - Number of Fins Per Inch

N - Number of Segments in One Fins =

N .- Number of Tubes Per Row

P - Heat Exchanger Operating Pressure (psia)

Q - Heat Transfer Rate (BTU/hr)

12

q" - Heat Flux (BTU/hr-f

t

2)

2R ,

- Thermal Resistance (hr-ft -F/BTU)

2R - Heat Exchanger Outside Resistance (hr-ft -F/BTU)

S - Tube Spacing Normal to Gas Flow (ft)

S - Tube Spacing Parallel to Gas Flow (ft)P

T - Fluid Temperature (F)

T - Gas Temperature (F)y

T,-^ - Fluid Bulk Temperature (F)ID

T - Gas Bulk Temperature (F)

T r - Gas-Side Film Temperature (F)gf

T - Average Outside Wall Temperature (F)

2U - Overall Heat Transfer Coefficient (BTU/hr-ft -F)oi

w - Fin Segment Width (ft)

x - Steam Quality

x - Average Steam Quality Per Node

Dimensionless Groups

Nu - Nusselt Number

Pr - Prandtl Number

Re - Reynolds Number

St - Stanton Number

Greek Letter Symbols

£ - Effectiveness

p. - Viscosity of Fluid (lbm/ft-hr)

y - Viscosity of Vapor (lbm/ft-hr)

n f- Fin Efficiency

13

p - Density (lbm/ft)

p - Density of Saturated Water (lbm/ft)

p - Density of Saturated Vapor (lbm/ft)

14

I. INTRODUCTION

A. BACKGROUND

Since the introduction of the DD-963 class ships into

the fleet, the U.S. Navy has become firmly committed to gas

turbine propulsion plants. Currently, besides the DD-963

class, there are four additional ship classes which are, or

will be, gas turbine powered. These are the Patrol Hydro-

foil Missile (PHM's), the Oliver Hazard Perry FFG-7 class,

the Ticonderoga CG-47 class and the soon to be built DDG-51

class

.

This commitment to gas turbine propulsion has stimulated

great interest in the concept of converting the waste heat

from the gas turbine engines into useful shaft power. In

December 19 79 the Naval Sea Systems Command awarded contracts

for development of a conceptual design of a new generation

of waste heat recovery systems. The goal of the design was

to provide a system which would realize a 25 percent minimum

improvement in ship propulsion fuel consumption and increase

the ship's operating range by 1000 nautical miles. The out-

growth of the effort has been the RAnkine Cycle Energy Recovery

(RACER) system. As conceived, the RACER system will be an

unfired waste heat recovery system designed to convert waste

heat from the exhaust of the main propulsion gas turbine

engines into useful shaft horsepower. Such a system has

15

I

commonly been called a COGAS or combined Gas And Steam system.

The hot exhaust gases of the main propulsion turbine are

passed through a Waste Heat Recovery Unit (WHRU) , where steam

of the desired temperature and pressure is generated. The

steam is used to drive a steam turbine which operates in

parallel with the propulsion gas turbine through a common

reduction gear.

Numerous papers have been written concerning the RACER

system. Halkola, Cambell and Jung [Ref. 1] discussed the

conceptual design for the system. Mattson [Ref. 2] presented

a plan for designing reliability and maintainability into

the RACER system and Combs [Ref. 3] developed a computer model

of a COGAS system which designs a waste heat recovery unit

and allows comparison of system performance by variation of

system parameters.

References 1, 2 and 3 all agree that the desired goal of

fuel conservation must not come as a result of increased

maintenance, manpower, or main propulsion system down-time.

The design philosophy dictates that the system have high

reliability, be inherently safe, have low maintenance require-

ments and be essentially automatic in operation.

Reference 1 states that the waste heat recovery unit

paces the design of the system. The majority of effort by

Combs [Ref. 3] was to create a WHRU design model which would

simulate the performance characteristics of a physical boiler.

Since great expense is involved in the design, fabrication

16

and operation of prototype systems, it is of primary impor-

tance to achieve a realistic mathematical simulation first.

To this end, Combs devised a model which designs a WHRU

when given feedwater inlet temperature, steam outlet tempera-

ture, operating pressure, inlet and outlet gas conditions

and gas flow rate.

In this study, the initial model of Combs was considered

and an improved computer model of the waste heat recovery

unit was developed. A once-through counter-cross-flow heat

exchanger was selected because of the advantages of lower

initial cost, faster response, compactness and low operating

cost. The improvement in the model is that the heat exchanger

is discretized into individual "nodes" much in the manner

done by Shu and Kuo [Ref. 4]. This procedure treats smaller

physical pieces of the overall heat exchanger as individual

small heat exchangers to attain a better understanding of

the temperature distributions within the WHRU. The improved

model allows an analysis of the effect of non-uniform velocity

distributions on the performance of the WHRU, and ultimately,

the RACER system.

B. OBJECTIVES

There were five main objectives for this thesis.

1. Devise an improved computer model for the once- through

WHRU. This model was to predict the performance of various

size WHRU's given feedwater inlet temperature, steam outlet

17

temperature, WHRU operating pressure, inlet gas mass flow

distribution and inlet gas temperature distribution.

2. Enable the designer to establish a design WHRU size

based on the performance of the model with various input

conditions.

3. Evaluate the design WHRU utilizing various uniform

and non-uniform inlet gas distributions for both on-design

and off-design conditions.

4. Re-evaluate the WHRU utilizing the same uniform and

non-uniform gas distributions into the WHRU, but with

different steam outlet temperatures.

5. Provide a framework for future studies involving a

development of a three dimensional model of a WHRU and a

detailed, complete COGAS system cycle analysis and optimization

18

4

II. MODEL DESCRIPTION

A. OVERVIEW

The waste heat recovery unit chosen was a once-through

counter-cross-flow heat exchanger. A computer program was

written to model this type heat exchanger for analysis of

the effect of uniform and non-uniform inlet gas mass distri-

butions. Variation of other parameters, other than the gas

distribution, provides a thorough understanding of the oper-

ation of the heat exchanger in a multitude of conditions.

The model was written for incorporation into a RACER system

analysis, but it is not limited to that application.

Figure 1 shows a three dimensional representation of a

typical layout of a marine gas turbine waste heat recovery

unit. The unit is headered on the fluid inlet and exit and

designed to be installed in the gas turbine exhaust gas

duct. The exhaust gas entering the bottom of the WHRU pro-

vides the energy for transfer to the fluid-side of the system,

The fluid (feedwater) enters at the upper header of the WHRU

and flows alternately back and forth through the unit until

exiting as steam at the lower header. The U-bends shown in

Figure 1 at the ends of the tube passes allow each tube to

enter and exit the heat exchanger as a continuous path for

fluid flow. As a tube makes one horizontal traverse across

the WHRU it is referred to as a pass. Therefore, the number

19

ydl

of times a tube passes through the gas flow defines the

vertical size of the heat exchanger as a 15, 20, 25, etc.,

pass heat exchanger.

A gas flow distribution is depicted as entering the WHRU

in Figure 1. The gas flow is shown oriented along the tube

pass as a non-uniform distribution. Additionally, the gas

flow may be non-uniform in the direction into the heat

exchanger, i.e., along the axis of the headers as shown in

Figure 1. This two dimensional gas flow distribution may be

non-uniform in both mass and temperature. The nature of the

heat exchanger, by virtue of the cross flow of the fluid,

decrees that, even if the mass and temperature distributions

entering the heat exchanger were uniform in both directions,

these distributions can become distorted and non-uniform as

the gas passes through the heat exchanger in the third

dimension. This distortion can be caused by the variation

of the heat transfer characteristics along the tube. The

problem of analysis becomes more complicated if cross mixing

of the gas is considered.

The model of Combs [Ref. 3 J treated the gas distribution

as a uniform and constant value in one direction. Combs

assumed the mass and temperature of the gas along the axis

of the tube was everywhere the same for a complete pass.

The model yielded results which were close to the results

attained by other studies and gave a reasonable estimate of

the overall heat transfer characteristics of the heat

20

exchanger. The model, however, could not predict the effect

of non-uniformity of the gas distribution on the performance

of the WHRU. This study discretizes the dimension along the

axis of the tube pass and enables the designer to evaluate

the effects of variations in mass flow rate and temperature.

It is assumed, however, that the distributions along the

axis of the headers are all the same as the outer distribu-

tion. The concept of discretization and "nodal" arrangement

is shown in Figure 2 . The representation shows a matrix

arrangement where the number of rows corresponds to the

number of passes in the heat exchanger, and the number of

columns corresponds to the number of gas paths in the

discretization. The number of passes is a user defined input

to the model but the number of gas paths is fixed in the

model at ten.

Use of the model requires that the user provide the

following conditions. First, the number of passes that a

particular water/steam tube is to make through the heat

exchanger must be specified. This parameter will physically

size the heat exchanger in the vertical direction. The mass

flow rate of the gas turbine exhaust gas, (m ) , for each ofy

ten exhaust gas paths through the heat exchanger must be

entered. For a uniform distribution, this is simply the

total exhaust gas mass flow divided by ten. A simplifying

assumption of the model is that there is no cross mixing of

flow as the gas passes through the heat exchanger; therefore,

21

the mass entering a particular gas path is constant through

the heat exchanger.

Next, the temperature of the gas entering each gas path

is entered. For this study the temperature distribution of

the gas was considered uniform for all runs; however, the

model is not constrained to uniform temperature distributions

The gas was assumed to be at atmospheric pressure

entering the heat exchanger and gas side pressure drops were

not considered in the calculations.

The user next enters the feedwater inlet temperature,

the steam outlet temperature and the fluid-side operating

pressure. These parameters are used in the initial calcula-

tions to determine a first "guess" mass flow rate on the

fluid-side of the heat exchanger. The minimum allowed

exhaust gas temperature is entered. This value is a user

desired constraint and is specified as the minimum acceptable

temperature the user can accept to prohibit hot side corro-

sion. The model is not constrained to maintain the exhaust

gas temperature above the user specified temperature.

The number of feet in length, per node, is entered.

This parameter is based on the physical size of the heat

exchanger being analyzed in the horizontal direction. For

all runs in this study, an assumed tube row length of ten

feet divided by ten gas paths yielded a tube length per node

of one foot. There is no constraint on the length parameter,

within reasonable limits.

22

The heat exchanger model was written as a two dimensional

analysis, i.e., all parameters in the third dimension were

assumed uniform. The next parameter entered is the number

of tubes per row, which is used to size the heat exchanger

in the third dimension. Figure 1 shows a three dimensional

representation of the heat exchanger design. Each particular

tube enters at the top of the heat exchanger and passes

alternately back and forth below itself until exiting the

heat exchanger at the bottom. The tubes in each subsequent

plane, behind the first, enter and exit in the same manner,

but alternate slightly up and down to give a staggered tube

arrangement. The nodes are numbered in standard matrix format

with the upper left being node (1,1), and counting across

row one as (1,2), (1,3), etc., to (1,10); then node (2,1)

is directly below node (1,1) , and so on, to the bottom of

the matrix. Figure 2 shows the nodal arrangement of the

heat exchanger. The fluid may enter from either side of

the heat exchanger. If the heat exchanger has an even number

of passes, the fluid will enter on the same side as the

steam exit, and on the opposite side for an odd number of

passes. Each tube is continuous from entry to exit.

The final user entry is the geometric scaling factor

which is used in the geometry portion of the model to scale

all the physical dimensions of the tube, with the exception

of the length, up or down.

23

Two additional simplifications were assumed in the model.

First, the fluid side pressure drop was not considered.

Lastly, even though the tube passes were discretized to

determine the temperature distributions, the tube length

within a node still has a significant length for a tempera-

ture gradient. For analysis, the gas temperature at any

node was assumed to be uniform across the length of the node

at both the entry and exit.

B. INITIAL CALCULATIONS

The WHRU is essentially analyzed in three sections;

superheating, boiling and heating. Given an inlet gas distri-

bution, water/steam inlet and outlet temperatures, and an

operating pressure, there is a unique fluid-side mass flow

rate which will satisfy all boundary conditions. The model

attempts, through iteration, to determine the resultant

fluid-side mass flow rate. The analysis is also greatly

affected by the number of passes (i.e., the physical size)

of the heat exchanger. There are clearly combinations of

parameters for which no solution is possible, or the solu-

tion is trivial in that the mass flow rate of the fluid is

so small as to be meaningless.

For calculations, variable assignment is as follows:

(1) m (m,n) = gas flow rate through gas path n at tube^ pass m;

(2) T (m,n) = gas temperature into node (m,n). Theg gas temperature out of node (m,n) will

be the gas temperature into node (m-l,n);

24

(3) T-(m,n) = fluid temperature into node (m,n) . Thefluid temperature out node (m,n) willequal the fluid temperature into node(m,n+l) if the fluid is flowing to theright (see Fig. 3) , or the fluidtemperature out of node (m,n) will equalthe fluid inlet temperature of node(m,n-l) if the fluid is flowing to theleft.At the end of a fluid pass the fluidout of a node will equal the fluidtemperature into the node directly below,i.e., T (m,n) = T

f(m+l,n);

(4) itu = fluid-side mass flow rate

Figures 3 and 4 are representations of typical nodes

depicting the above explanation of fluid and gas flow.

After all entries are made the program initializes by

summing the individual m (NR,n) elements to find m , ,3g 9 total'

then the T (NR.n) elements are averaged. The T (NR.n) ele-g

3 g '

ments are averaged by multiplying each element by the corres-

ponding fraction of the total gas mass that is passing through

each gas path. These "weighted" temperatures are summed and

the result is divided by the number of gas paths. The result

is then the average temperature of the gas into the heat

exchanger. An average gas temperature is determined using

the user specified minimum gas temperature out and the aver-

age gas temperature into the heat exchanger. Then:

Q = m . C (T - Tg total pg g avg in g avg out

where C is evaluated at the heat exchanger gas bulkpg

temperature. Now, a first "guess" fluid mass flow rate is

calculated from an energy balance

25

f h ,. ,

- h_ .

f out f in

where h- . and h- are the fluid inlet and outletf in f out

enthalpies at the user specified feedwater inlet temperature

and steam outlet temperature.

C . GEOMETRY

The geometry portion of the model is nearly identical to

that used by Combs [Ref. 3]. A fin-tube with helically

curved extended surfaces on circular tubes is assumed for

this model. The fins are segmented and the tubes are

configured in banks of one row each with the rows staggered.

The base tube surface is taken from Weirman, Taborek and

Marner [Ref. 5]. The description of the finned tubes is as

follows

:

d. = tube inside diameter = 1.86 in.l

d = tube outside diameter = 2.00 in.o

d = fin root diameter = 2.0 in.r

Nf

= fins per inch = 5.94

i = fin height = 1.015 in.

I = length of cut from fin tip = 0.82 in.

df

= fin outside diameter = 4.03 in.

t = fin thickness = 0.048 in.

w = fin segment width = 0.17 in.

N = number of segments in 360 degrees = 38

26

The finned tube configuration is shown in Figure 5. The

tube length, L, and the number of tubes per row, N. . , are

the user specified entries. The tube layout is shown in

Figure 6. The center to center tube spacing in the trans-

verse direction is 4.50 inches. The equilateral, staggered

tube arrangement used in this model leads to a spacing

normal to the gas flow, s , of 4.50 inches and a spacing

parallel to the gas flow, s , of 3.90 inches, as shown in

Figure 6. The heat exchanger height is established by the

number of WHRU passes (rows) and the tube spacing parallel

to the gas flow, s .

P

In order to establish the minimum gas flow cross-sectional

area the total "blocked" frontal area, A. , of the heat

exchanger must be calculated from

b t/r o f t/r f

and the minimum gas flow area is

A . = A- - A,min f Td

where Af

is the total frontal area of the heat exchanger

exposed to gas flow. The total inside area available for

heat transfer per pass is

A. = 7T d. L N. .

lp i t/r

27

The gas-side surface area available per pass for heat

transfer is the sum of the fin surface area and the bare

tube surface area per pass. The fin surface area per tube

is calculated from

A.. = N_L[N (2 £ w + 2 t. % + w t.) + J(dlL - d2 H

fin fs cs fc sf 2 fb o

where d-, = d- - 21 . The bare tube area per tube isrb f c c

bt o off

Therefor 2, the total outside area per pass available for

heat transfer is

A = N. , (A.. + A, . )op t/p fin Dt

The cross sectional area for fluid flow is calculated from

ff 4 l t/p

With the mass flow rates, terminal temperatures and heat

exchanger geometry established, the remainder of the model

may be solved by nodal analysis for the unique fluid mass

flow rate and the location of the beginning of the boiling

and superheating regimes.

28

D. SUPERHEATER NODAL ANALYSIS

In the heat exchanger there is only one node where two

conditions are initially known, and that is at the node

where the steam is exiting. At this node, both the gas inlet

mass flow rate and temperature and the fluid outlet tempera-

ture have been specified by the user. Using the initial

values of the fluid mass flow rate from the estimated overall

energy balance and the desired superheater steam outlet

temperature, the heat exchanger is analyzed in the reverse

direction through the superheater, through the boiler and

through the heater to arrive at the feedwater inlet. For

the given geometry and flow conditions, the model will calcu-

late the water inlet temperature consistent with the assumed

estimated mass flow rate. If the temperature arrived at by

analysis as the inlet to the first node does not match the

user specified feedwater inlet temperature, then the fluid-

side mass flow rate is adjusted up or down and the entire

process is begun again.

To begin, at the final node the gas inlet temperature

and mass flow rate are known. Also, the fluid outlet tempera-

ture and a first "guess" fluid mass flow rate are known.

It is then assumed that the bulk (average) fluid and gas

temperatures for the node are equal to these known tempera-

tures. All fluid and gas properties for a node are evaluated

at the bulk temperatures.

The gas-side Reynolds number for the node is calculated

using the bulk temperature. With the Reynolds number, a

29

j-factor is obtained from a polynomial fit to the data for

tube layout number 5 in Ref . 5 (Fig. 6) . By definition,

the j-factor is related to the heat transfer coefficient,

V by

= StPr^

By introducing

St =Nu

Re Pr '

the previous expression can be written as

Nu 2/3 Nu3 Re Pr

Pr_ 1/3 '

g g Re Prg 9

and

1/3Nu = i Re Pr '

g g

where

Nu =h d_3. °Kg

and K = the thermal conductivity of the gas. Therefore, ag

relationship may be written for the heat transfer coefficient

as follows:

30

h = j _2_ Re Pr1/3g d g g

In the superheat region, the water-side heat transfer

coefficient is calculated by using the Dittus-Boelter

correlation

h.. = 0.023 -t— Re,. Pr£f d. f f1

where all properties are obtained at the bulk temperature of

the steam in the node. Using the tube wall resistance

together with h and h , the overall heat transfer coeffi-

cient for the node can be written as

1U . (m.n) — - s j-g 7-3 it

-

01 , A. in {d /d ) A. ,

_L + _iE 9. i_ + _i£ ±h^ 2tt K N., L A n.hf w t/p op t g

where

:

A..

nt- l - (i-n

f)

-K—op

The fin efficiency, n f, is calculated from the expression

tanh MLnf ML

where

M = /h P/KAg

31

and, if the fin is approximated by a set of rectangular

strips extending from the tube wall,

d- - dL = f

n S

Now, the cross-sectional area, A, of a rectangular strip

may be written as

A = w t_s f

and the perimeter is

P = 2 (w + t-J .

s r

So, using known geometric parameters and the thermal conduc-

tivity of the fin metal, the parameter ML may be expressed

as

where

ML = C /hg

df " doM/2(w s

+tf

)

C = (-±-« -)w t,. Ks f

Now,

tanh C/h~ A _

.

n. = [1 - (1 SL-) -^]t C/h op

g

32

The pass effectiveness is calculated using the effective-

ness-NTU method. The correlation for the effectiveness for

a single pass, cross flow heat exchanger with both fluids

unmixed is taken from Incropera and DeWitt [Ref. 6]

z =1- exp[(i (NTU)0,22

{exp[-C (NTU) ° *78

] -1} ]

P cr

r

where

C .

= minr C

max

U^. (m,n) A.

NTU = _oi ip

mm

C is the lesser of C r and C wheremm f g

f pf f

and

C = C m (m,n)g pg g

and C is the greater of the two. All fluid and gasmax 3 3

properties are again evaluated at the bulk temperature.

Two equations must be satisfied to find the solution to

a node. These are the rate equation

Q = £ C . (T . - T_ . )min g in f in

33

and the energy equation

f pf f out f in

In the two equations the only unknown is Tf

. . Equating

the two and solving for T,. . yields^ f m J

e C . T . - m, C _ T.T _ min g in f pf f putf in e C . - m_ C ^mm f pf

Now, Q for the node is

Q = m, C .(TV .- T-. . )f pf f out f in

and

rn _ rp «gout gin ^

g pg

Next, new bulk temperatures for the node are calculated as

T , -. (T . + T . ) /2g bulk gin g out

and

f bulk f out f in '

An average outside tube wall temperature is calculated from

34

U . A .

T = T -01 —(T - T )

wo g bulk h Auv gB fB ;

3 g to

where A. ./A are total inside/outside areas for the node

and T B/Tf_ are the new node bulk temperatures . The expres-

sion for T is derived from the following formulation forwo 3

heat transfer in the node

T „ - T^„ T _ - TgB fB _ gB wo

Q =

^thlxoI

R- R-

which reduces to

RT = T — (T - T )

wo gBJRfch

l gB fB ;

where

Ro r\. h A,

't g to

and

l Hth U . A.

01 ti

The gas-side film temperature is

T _ + TgB wo

gf 2

35

This gas-side film temperature is now introduced at the

beginning of the calculations for the node as the new gas

bulk temperature.

The assumed bulk temperatures, at the beginning of the

calculations, were obviously too high since the gas inlet

and fluid outlet temperatures were used. This assumption,

however, allowed a solution for the node to be found. The

model stores the result of this first pass and returns to

the beginning utilizing the new bulk temperatures to calcu-

late a new solution to the node. At the end of the second

pass through, the result of the calculation for T isr r g out

compared to the result obtained the first time. If Tr g out

has changed, then the new result is stored and the process

is repeated. When T no longer changes, the process has

converged to a good solution for the node.

A check is made to determine if the fluid inlet tempera-

ture is less than or equal to the saturation temperature for

the pressure specified. If the temperature is higher than

the saturation temperature, the model proceeds to the next

node of the superheater and repeats the entire process.

If the fluid temperature equals the saturation temperature,

superheating has theoretically begun at the interface between

this and the final node of the boiling portion of the model.

If this condition exists, the model proceeds to the boiling

nodal analysis.

36

As mentioned previously, the model works through the

heat exchanger in the direction opposite to fluid flow.

When it is determined that the fluid temperature into a node

is below the saturation temperature, the node is "split" to

determine the physical location in the node where super-

heating begins.

To split the node the m quantity into the node and the

physical length, L, are halved. The geometry is recomputed

as if the node were only half as large. The solution

process is reinitiated and, when a solution is achieved, the

saturation temperature check is redone. If the temperature

into the node is still below the saturation temperature, mg

and the length are halved again and the process is repeated.

This procedure is continued until the temperature into the

node is found to equal the saturation temperature or be

above it. If the temperature is above the saturation temp-

erature, then the m and L parameters are changed to a value

halfway between the current and previous values, and the

process is continued until the temperature into the partial

node exactly equals the saturation temperature. The values

for Q, T , T r . and U are stored to be used later tog out ' fin 01

develop weighted averages with the boiling portion parameters

The remainder of the node is solved in the boiling

portion of the model.

E. BOILING NODAL ANALYSIS

Nodes in the boiling section are solved by the same

iterative scheme developed in the superheating section. The

37

correlations utilized to determine the solution are differ-

ent since flow in the boiling regime will involve two phases

on the fluid-side. In two phase flow the inside heat trans-

fer coefficient will change with quality, x, and the heat

flux, q" . The correlation selected for this model is the

same as that used by Combs [Ref. 3] which was recommended

by Tong [Ref. 7] for both nucleate boiling and forced convec-

tion. The analysis presented by Combs is presented here.

The equation for the two-phase flow heat transfer coeffi-

cient was given by Schrock and Grossman in Tong [Ref. 7] as

^ = B [gSC_ + A(-^) n

] .

h„ G h £ x,I fg tt

3The constants are given by Wright [Ref. 7] : B = 6.70 x 10 ,

-4A = 3.5 x 10 , and n = 0.66. The heat transfer coefficient,

assuming a totally liquid flow is

K„ d. G(l-x) 0.8 C \iQ

0.1h

9= 0.023 Ji[-±—

][-ES—i]

and the Martinelli parameter is

0.9 P 0.5 ]i 0.1

x 1-x p y ntt v I

The limits of the data for this correlation are:

quality: 0.05— 0.57

heat flux: 6 . x 104 — 1 . 45 x 10

6 BTU/hr-ft 2,

38

In this model, heat flux in the boiling section will be at

4 2levels considerably below 6 x 10 BTU/hr-ft and the full

range of quality must be considered. Therefore, in order to

predict the performance of the Schrock and Grossman correla-

tion at lower heat flux and quality above 0.57, a plot was

made (Fig. 7), of the ratio h _/h_ vs. quality where h is1 C A. Li la

the heat transfer coefficient from the Dittus-Boelter corre-

lation for water at saturated liquid conditions. The corre-

lation of Dengler and Addoms , as given in Tong [Ref. 7],

indicates that low heat flux and high water-vapor mixture

velocity favor the forced convection mechanism. After a

review of the information available in Tong, it is not

entirely clear whether the forced convection or the nucleate

boiling mechanism is dominant for the relatively low flow

velocities and low heat flux of this model. In any case,

the Schrock and Grossman correlation applied at low heat

flux represents a type of compromise between the entirely

forced convection assumptions of Dengler and Addoms and the

"mixed" assumption of Schrock and Grossman.

A simplification assumed in the model is that the

quality in the node is the average quality for the entire

length of the node. Also, to expedite the numerical proce-

dure, it is assumed that the node effectiveness is 0.25,

initially. The effectiveness rarely attains a value higher

than this for this type heat exchanger, so the assumption is

valid. The value of the effectiveness is adjusted to the

"true" value in the iterative process. In a process involving

39

a change of phase the fluid is isothermal. In actuality,

there is a slight temperature change through the boiling

regime but for purposes of analysis this change is neglected.

For this reason the fluid bulk temperature in any node in

the boiling portion is equal to the fluid saturation tempera-

ture. Therefore, to determine the amount of energy absorbed

by the fluid in a node, the change in fluid enthalpy between

the inlet and outlet is calculated.

In the first node in the boiler, which is the node imme-

diately before the superheater or a partial node if the node

was split, the gas bulk temperature is again set equal to

the gas inlet temperature. The gas-side heat transfer coeffi-

cient is calculated using the same procedure as delineated

in the superheater nodal analysis. Next, a Q for the node

is calculated from

Q = e m C (T . - T- . )

9 pg 9 in f in

where the effectiveness, z, is initially assumed to be 0.25

and T- . is equal to the fluid saturation temperature. A

fluid inlet enthalpy is derived from

h £ - h_ • . - (Q/m^)f in f satv w f

where h^ = enthalpy of the fluid at saturated vaporf satv ifl

The fluid bulk enthalpy is

40

h._ = (h_ . + h, . )/2 .fB f in f satv '

The average quality for the node is calculated from

- fB f satlavg h_ - h c . ,

f satv f satl

where h , is the enthalpy of the fluid at a saturatedz sat J.

liquid condition. The Martinelli parameter is determined

from

x 0.9 p 0.5 y 0.1

x. , 1-x p y„tt avg v I

where pp/p are the liquid/vapor densities at the saturation

temperature and p /y are the liquid/vapor viscosities at

the saturation temperature. Now the heat transfer coefficient

for totally liquid flow is calculated

K d.G(l-x ) 0. 8 C „ y 0.1. A AO _ x, r l avg ,

rpic I,

h£

°- 023 a- l—^-^-]

'-^r-

From this the heat transfer coefficient is calculated for

two-phase flow

hTPf = Vb{ gF7-+ A(^7

,ni1

fg tt

where h_ = h,. - h,. . , and the constants A, B and nfg f satv f satl

have the aforementioned values and G is the mass flow rate

41

per unit area. Finally, the node overall heat transfer

coefficient is calculated from

Uoi ', A~. £n(d /d. ) A~

'

h_,_ -. 2tt K N. , L A h n.TPf w t/p op g t

Whenever two phase flow is involved, the heat capacity of

the fluid is assumed infinite. For this reason, within

the boiling regime, C . will always equal the heat capacity

of the hot side, so,

C . = m Cmin g pg

and the Number of Transfer Units, NTU, is

U . A.NTU = °^ *P

min

The node effectiveness is

e = 1 - exp(-NTU) .

Now, a revised Q for the node is calculated from

Q = e C . (T - T- . ) .mm gin f in

From this Q a revised gas outlet temperature is calculated

42

T = T (Q/C . ) .

g out g in w min

With this gas temperature out, a new film temperature is

calculated in the same manner as for the superheating section.

The gas outlet temperature is stored and the film temp-

erature is used to repeat the process for the node. At the

end of the second time through, the gas outlet temperature

derived is compared with the result from the first. If

equality exists, a solution for the node has been found and

the model proceeds to the next node. If inequality exists,

the result of the current iteration is stored for comparison

with the results of the following iteration.

When a final solution is attained, the enthalpy of the

fluid at the inlet to the node is checked against the

enthalpy of saturated water at the heat exchanger pressure.

If the inlet enthalpy is greater than or equal to the enthalpy

of saturated water, the model proceeds to the next node and

begins the solution process again. If the inlet enthalpy

is less than the enthalpy of saturated water then the model

proceeds to a node splitting routine similar to that used

when transitting from the superheating regime to the boiling

regime.

The node splitting is again accomplished by halving the

mass flow rate on the gas-side and halving the physical

length, L, of the node. The remaining geometric parameters

are recomputed and the solution process is reinitiated. The

43

mass and length adjustment procedure is continued until the

inlet enthalpy is equal to the enthalpy of saturated water.

When this is achieved, the values of T . . U and Q areg out' 01 v

stored to be recombined as weighted averages with the heating

portion of the node to give the overall nodal values.

The remainder of the node is solved in the heating portion

of the model

.

F. HEATING NODAL ANALYSIS

The procedure for analyzing a node in the heating portion

of the model is identical to that used in the superheating

portion. Each node is analyzed in an iterative process, and

it makes no difference if the first node was a split node.

The first node in the heating section will have a gas inlet

temperature equal to the gas outlet temperature of the node

directly below. The fluid outlet temperature will equal the

fluid saturation temperature for the specified pressure.

An outline of the calculations is as follows:

1. Calculate the gas-side heat transfer coefficient

using the node gas inlet temperature as the gas bulk

temperature.

2. Calculate the fluid-side heat transfer coefficient

initially using the fluid saturation temperature as

the fluid bulk temperature.

3. Calculate the overall heat transfer coefficient using

the effectiveness-NTU method.

44

4. Determine the node fluid inlet temperature from

£ C . T . - iiu C .- T-T = mm g in f pf f outf in e C - itu C j.mm f pf

5. Calculate a first "guess" for Q for the node from

f pf f out f in'

6. Calculate the node gas outlet temperature from

T . = T . (Q/m C ) .

g out g in g pg

7. Calculate T , ,, = (T + T . ) /2g bulk g in g out

8. Calculate a node average film temperature from

T . = (T _, + T )/2gf gB wo

9. Store the result of the first pass through the model

and iterate until procedure converges to solution,

utilizing gas outlet temperature for comparison at

each pass.

All properties of the gas and fluid are evaluated at the

respective bulk temperatures for the node. The process is

repeated node by node until the node at the fluid inlet to

the heat exchanger is completed. The final node is either

45

node (1,1) for an odd number of passes, or node (1,10) for

an even number of passes in the heat exchanger.

G. HEAT EXCHANGER SOLUTION PROCEDURE

When the procedure of the heating section has arrived at

a solution for the final node of the heat exchanger, the

fluid inlet temperature for the node is compared to the user

specified feedwater inlet temperature. If equality exists,

the model proceeds to an output routine where the matrices

of water/steam temperatures, exhaust gas temperatures,

overall heat transfer coefficients and individual heat

transfer per node are printed. Additionally, the fluid-side

mass flow rate, minimum pinch point temperature difference,

total Q for the heat exchanger and isentropic steam turbine

power are calculated and printed.

The pinch point temperature difference is defined in

this model as the minimum difference in the heat exchanger

between the gas inlet temperature and the fluid inlet temp-

erature to any node. Consideration of the effect of a pinch

point below approximately 25 deg. F is cause for concern

only if the low pinch point is coupled with a low gas temp-

erature. This combination is non-prohibitive to hot side

corrosion. If the final node fluid inlet temperature is not

equal to the user specified feedwater inlet temperature, then

the fluid mass flow rate that was "guessed" at the beginning

is adjusted and the entire model is run again. If the solution

46

temperature is too high the "guessed" fluid mass flow rate

is lowered. With less mass going through the heat exchanger

the flow velocity is decreased. A lower flow velocity through

the heat exchanger enables more energy from the gas-side to

be transferred to the fluid-side. A larger Q will increase

the temperature differential between the fluid inlet and

outlet which will yield a lower solution fluid inlet temp-

erature the second time through the model. The process is

opposite, i.e., mass is added, if the fluid inlet temperature

to the first node is found to be too low.

The model will continue to adjust the mass after each

iteration in smaller amounts until an exact match is made to

the user specified feedwater inlet temperature. When equality

is achieved, the model proceeds to the output routine where

the above mentioned parameters are printed.

Included, as Appendix A, are sample outputs of the model

for the uniform distribution, distribution 1 and distribu-

tion 5 for all four of the selected gas mass flow rates.

The run numbers at the top of the first page of each output

were utilized for accounting purposes. The uniform distri-

bution was used for runs 1, 10, 19 and 28; distribution 1 was

used for runs 2, 11, 20 and 29; and distribution 5 was used

for runs 6, 15, 24 and 33. The first page of the output shows

the inter-active questions asked by the model and the user

responses. The following pages show the matrices developed

by the model in the solution process. Comparison of the

47

matrices for the uniform and non-uniform distributions

demonstrates the serious impact of the non-uniformity on the

performance. The non-uniform distribution profiles can be

seen as projected profiles on the results of each of the

matrices. The final page of the output is a listing of

additional parameters which are calculated by the model includ-

ing the fluid mass flow rate, Q based on the individual

matrices, location of the beginning of boiling and super-

heating within the WHRU and the isentropic horsepower.

48

III. DISCUSSION OF RESULTS

A. INITIAL TESTING

The foregoing model was coded in FORTRAN IV and applied

in a computer simulation on an IBM-3033 computer.

To properly test the model and develop an understanding

of the operation of the WHRU several runs were made utilizing

a uniform gas distribution with a total mass flow rate and

temperature corresponding to a gas turbine horsepower rating

for approximately a 20 kt. speed. The conditions presupposed

usage of a General Electric LM2500 Gas Turbine Engine, and

gas mass and temperature data was taken from [Ref. 8]. Initially,

the model was run with attention to pinch point temperatures.

The number of passes was varied to find the largest heat ex-

changer which could be used and still maintain a pinch point

in excess of 25 degrees fahrenheit. Under conditions of non-

uniform flow distributions the model definition of pinch point

is misleading since small gas mass flow rates through a

particular gas path may yield a nearly zero pinch point when

the overall performance of the heat exchanger is not affected.

Inspection of the model output for the non-uniform distribu-

tions will demonstrate this result. The preliminary runs

allowed selection of a 23 pass heat exchanger with a 29.4 deg

.

F pinch point. Therefore, the 23 pass heat exchanger became

the "design." The performance data tabulated for the LM2500

engine [Ref. 8] was utilized to select four gas mass flow

49

rates and inlet temperatures which correspond closely to

data points on a cubic power curve. The four combinations

of mass and temperature chosen were:

m = 121.8 lbm/s, T = 844° F, SHP = 17500, NPT = 3000 rpm

m = 99.1 lbm/s, T = 755° F, SHP = 10000, NPT = 2400 rpmg g in c

m = 77.4 lbm/s, T . = 702° F, SKP = 5000, NPT = 1800 rpmg g in c

m =66.7 lbm/s, T . = 694° F, SHP = 3000, NPT = 1200 rpmg gin ' ' r

Each of these was run in the model as uniform and various

non-uniform distributions.

To develop the non-uniform distributions, a normalized

flow distribution table was constructed and is presented as

Table I. This table shows the fraction of the total mass

flow rate which is passing through each individual gas path

for each of nine different flow distributions. The flow

distributions were arbitrarily derived in an attempt to

develop a spectrum of distributions that may enter the heat

exchanger. A graphical display of each of the flow distribu-

tions is shown in Figures 8A-8I. The total mass flow rate

used was multiplied by each entry in the normalized flow

distribution table to arrive at the mass flow rate through

each of the ten gas paths for any of the nine distributions.

This procedure allowed a comparison of the effects of non-

uniform distributions on the performance of the heat ex-

changer. All nine distributions were run for each of the

50

four chosen mass and temperature combinations. The actual

mass flow distributions used are shown in Tables II-A--II-D.

The combination of nine distributions and four different

total gas flow rates yielded 36 runs. For the runs, the

remaining parameters were:

a) feedwater inlet temperature = 20 deg . F

b) desired steam temperature = 650 deg. F

c) steam operating pressure = 400 psia

d) minimum allowed gas outlet temperature = 300 deg. F

e) node length = 1.0 ft.

f) number of tubes per row = 32

g) geometric scaling factor = 1.0

The model calculates the isentropic horsepower that would

be developed by an ideal steam turbine. This power can also

be viewed as the maximum power available from the developed

superheated steam exhausting to a fixed condenser pressure.

The method of calculation is to determine the enthalpy of the

steam at the outlet pressure and temperature and then sub-

tract the enthalpy of the steam after isentropic expansion

to a condenser pressure of 2 psia. The difference in enthalpy

was multiplied by the fluid mass flow rate, with the appro-

priate conversions, to arrive at a horsepower value. The

horsepower calculated for each run is tabulated in Table III.

The table lists the results of each run of the model for all

36 runs for each of 5 different steam outlet temperatures.

Table IV is a similar table showing the solution values of

51

the fluid mass flow rates derived in each run. The two

tables demonstrate the variation of fluid mass flow rate and

power which is attained by varying the desired steam outlet

temperature; and the effect of the non-uniform distributions

on performance.

B. EFFECT OF NON-UNIFORM DISTRIBUTIONS

The data from column 1 of Table III was plotted and is

shown in Figures 9A-9E as power vs. gas flow rate. Figure

9A shows the comparison of the uniform distribution with

distributions 1 and 2. Figure 9B shows the comparison of

the uniform distribution with distributions 3 and 4, etc.

From the graphs it can be seen that the distribution inflicting

the most serious impact on the heat exchanger performance is

distribution 1 (see Figure 8-B) . Distribution 1 is highly

center concentrated and utilizes the area available for heat

transfer the least efficiently. For comparison, distribution

3 is a nearly uniform distribution and it inflicts a relatively

minor impact on the performance. Distributions 2 and 4 are

ranked next in order of impact. These are also distributions

where the mass is centrally concentrated, but to a lesser

degree than distribution 1. Distributions 5 and 6 are mirror

images of one another and also have a zero mass flow rate

through two of the gas paths. A zero mass flow rate indicates

that the flow through that particular pass has no velocity.

In a real situation there will be a transient heat transfer

52

from the still mass of gas surrounding the tubes by natural

convection until the gas temperature reaches the tube wall

or fluid temperature. In any case, the amount of heat

transferred in such a node is negligible compared to the

nodes experiencing a gas flow rate. For the model, a zero

gas flow rate in a node will be treated as having zero heat

transfer, i.e., a "dead node," therefore, the Q for the node

was set to zero, the fluid inlet temperature and fluid outlet

temperature were set equal and the gas outlet temperature

was set equal to the gas inlet temperature. In reality, the

gas temperature in a "dead node" will attain the temperature

of the fluid in the node but for pinch point calculation pur-

poses the original gas inlet temperature was maintained.

Also, since the model assumes no cross-mixing of the gas

between gas paths as the distribution passes through the

heat exchanger, this assumption ignores the potential tendency

of the gas mass distribution to become uniform during passage.

Distributions 5 and 6 are skewed to the left and right,

respectively. The combination of the null gas flow paths and

the skewedness of these distributions caused the second most

detrimental effect on the heat exchanger. It should be noted,

however, that whether the distribution was skewed to the right

or left side had relatively no effect; that is, the results

for distribution 5 are nearly identical to those for distri-

bution 6. The same result was true for distributions 7 and

8, which are also mirror images of each other with left and

53

right skewedness. The effect of distributions 7 and 8 were

very nearly the same as those for distribution 4. Figure 9E

is a composite which demonstrates the effect of all the dis-

tributions. The ranking as to effect yields:

1. the uniform distribution gives the best performance

2. distr. 3, nearly uniform

3. distr. 4, least center concentrated, nearly same as

distr. ' s 7 and 8

4. distr. 2, intermediately center concentrated

5. distr.' s 5 and 6, skewed with null flow paths

6. distr. 1, highly center concentrated

The ranking can be viewed as a measure of the efficiency

of the distribution in utilizing the area available in the

heat exchanger for heat transfer. As the amount of distor-

tion of the flow increases, the quantity of energy trans-

ferred decreases.

Figures 10A-10E are graphical representations of the

solution fluid mass flow rates vs. the gas mass flow rates

for each of the distributions; exactly as was done to develop

Figures 9A-9E. As was to be expected, the results for Figures

10A-10E are identical to those for power vs. gas flow rate,

since power is directly proportional to the fluid mass flow

rate.

After these preliminary results, it was decided to con-

duct the remaining runs utilizing only the uniform distribu-

tions and the worst of the non-uniform distributions; i.e.,

54

distribution 1. It was assumed that results for the remain-

ing distributions would fall between the values of these two

C. EFFECT OF HEAT EXCHANGER SIZE

Next, an analysis was done to determine the effect on

output power and fluid mass flow rate by varying the number

of heat exchanger passes. Using the four chosen gas mass

flow rates, runs were conducted for heat exchangers of 20,

21, 23 and 25 passes. All runs were for 650 deg . F outlet

steam at 400 psia operating pressure. Therefore, the runs

for the 23 pass heat exchanger were the "design" runs and

the runs for 20, 21 and 25 passes were the "off-design" runs

provided for comparison. The results of these runs are

tabulated in Table V and graphically presented in Figures

11A-11H as power and fluid mass flow rate, respectively, vs.

the number of heat exchanger passes. Again, because of the

relationship between power and fluid mass flow rate, the

graphical results are similar in contour. The results show

that as the size of the heat exchanger is increased, so will

the power out. To provide the increased power the mass flow

rate of the fluid must increase since for the different

sized heat exchangers the inlet and outlet enthalpies of the

fluid is not changing. The limit to the increase in size is

the available energy in the gas. Increasing the heat ex-

changer size to the point where sufficient energy is trans-

ferred from the gas to the fluid to attain the minimum

55

acceptable exhaust gas temperature is the maximum size

possible.

The curves display an interesting result concerning the

differences between the uniform distribution and the non-

uniform distribution. As the size of the heat exchanger

increases, the two curves are converging with the difference

in power (or fluid mass flow rate) being less for the larger

heat exchanger than for the smaller. From the data of Table

V, it can be seen that, for the 121.8 lbm/s gas flow rate,

the power from distribution 1 is 89% of the power attained

from the uniform distribution for a 20 pass heat exchanger.

This increases to approximately 91% for the 25 pass heat

exchanger. The more rapid increase in power for the non-

uniform distribution is caused by the mass concentration in

the center gas paths. For a particular size heat exchanger,

the paths with a small gas mass flow will attain the temper-

ature of the fluid, usually in the boiling region. From that

point on, these paths contribute little, or not at all, to

the total heat transfer. The high concentration of mass

in the center paths, however, contribute greatly to the total

heat transfer because of the high velocity of the flow and

the high heat transfer coefficients. These paths of high

concentration will contribute until the gas exits the heat

exchanger. By adding more passes to the heat exchanger

it is as if the "dead areas" in the low mass flow paths were

placed in the path of the high mass flows. The effect is a

56

significant increase in the heat transfer. The high heat

transfer coefficients, mass velocity and temperature differ-

entials all contribute to a greater percentage increase per

pass than is achieved by the uniform distribution. As addi-

tional passes are added, the performance of the non-uniform

distribution improves, but it will never attain the level of

the uniform distribution. For two heat exchangers of equal

size, the uniform distribution gives the most efficient use

of the available area for heat transfer.

D. EFFECT OF STEAiM OUTLET TEMPERATURE

Each distribution, uniform and distributions 1-8, was

run at each of the four gas flow rates for five specified

steam outlet temperatures. The power and fluid mass flow

calculated by the model are presented in Tables III and IV.

The results are also presented graphically in Figures 12-A

and 12-B for the uniform distribution and distribution 1

at each of the four gas flow rates.

Both the tabular and graphical data shows a nearly uni-

form increase in fluid mass flow rate with the linear de-

crease in steam outlet temperature. The tabular data for

power demonstrates a non-linear result, showing initially a

decrease in power with a decrease in steam outlet temperature,

and then increasing to attain a power higher than that for

a 650 deg. F steam outlet temperature.

The non-linearity of the power is caused by the non-

linearity of the steam enthalpy as the steam outlet temperature

57

decreases. The combination of the change in enthalpy and

the change in the fluid mass flow rate results in a mislead-

ing impression of attaining a higher power at a lower steam

temperature. The total power does increase but the specific

power decreases. The increase in fluid mass flow between a

650 deg . F steam outlet temperature and a 550 deg. F steam

outlet temperature is approximately 7%. The increase in

power at the lower steam outlet temperature is less than 0.2%

The penalty to utilize a lower steam temperature and main-

tain an equivalent power output is a water/steam system which

must be able to circulate 7% more fluid in the same time

period. This result may have serious impact in the design

when condenser size, circulating pump size, valves, piping

and the steam turbine are taken into consideration. The

steam turbine must also be considered with respect to the

lower steam temperature having a lower quality through the

latter stages of the expansion. The effects of overly "wet"

steam can be disastrous to many turbines. The end result

is that the sacrifice in power at the higher steam tempera-

ture is justified by the decrease in fluid flow required

and higher end point quality.

E. EFFECT OF HEAT EXCHANGER PRESSURE

The uniform distribution and distribution 1 were run for

each of the four gas flow rates with three different speci-

fied heat exchanger operating pressures. The pressures were

the "design" pressure of 400 psia and then 500 psia and 600

58

psia. The tabulated results of these runs are presented in

Table VI, and graphically presented in Figures 13-A and 13-B

for power and fluid mass flow rate, respectively, vs. heat

exchanger pressure. Again, because of the direct correla-

tion between fluid mass flow rate and power, the contours of

the graphical results are similar.

The curves show a decrease in power and fluid mass flow

rate as heat exchanger pressure is increased. As the pres-

sure is increased by 50% above the design level, there is a

4% drop in the system fluid mass flow rate and a 7.5% loss

in power. Clearly, the benefits derived from the decrease

in system fluid mass flow rate does not justify the sacri-

fice in system power. With respect to the analysis of the

previous section, a compromise must be reached to achieve

the maximum power from the system within the confines of a

maximum acceptable fluid mass flow rate.

The graphical results also show the effect of the non-

uniform distribution for each of the four gas flow rates.

As the gas flow rate decreases, the penalty for non-uniformity

has a lesser effect. The percentage loss for the four flow

rates are approximately 9, 8, 7 and 6 percent, respectively,

from highest flow rate to lowest. The loss is approaching

zero as the flow rate approaches zero. The loss in power is

directly related to the decrease in fluid mass flow rate

determined in the solution; and the decrease in fluid flow

rate is a result of the ineffectiveness of the non-uniformity

on the operation of the heat exchanger.

59

F. EFFECT OF GA.S FLOW RATE ON HEAT EXCHANGER PERFORMANCE

The data from the matrix of water/steam temperatures for

the four gas flow rates as uniform distributions was plotted

as a function of tube length. The curves are shown in

Figures 14-A— 14-D. Figure 14-E is a plot of the water/

steam temperatures as a function of tube length for distri-

bution 1 with a gas mass flow rate of 121.8 lbm/s . Figure

14-F is a superposition of Figure 14-E on Figure 14-A.

Analysis of Figures 14-A through 14-D shows the effect

of the decrease in gas flow rate on the rate of heat trans-

fer as the fluid passes through the heat exchanger. The

higher the gas flow, the steeper is the slope of the curve

in the superheat region. A steeper slope is indicative of

a shorter tube length required to attain the desired super-

heat temperature. The effect, as the gas flow rate is

decreased, is that more of the heat exchanger is dedicated

to superheating. The length of the tube required to raise

the water from a saturated liquid to a saturated vapor

condition is nearly the same for all gas flow rates with

only a "left shift" on the plots caused by the superheat

conditions. The slope of the curves in the heating region

is the opposite of that of the superheat. As the gas flow

rate decreases the slope of the curve in the heating region

increases

.

Since, for all conditions, the feedwater inlet tempera-

ture and steam outlet temperature are the same, all tubes

60

are continuous and of the same length, the difference in the

curves is attributable to the rate of heat transfer and the

total amount of energy transferred. The rate equation is

Q = £ C . (T . - T. . )mm g in f in

and this must equal the energy balance equation

Q = m C (T - T .)g pg g in g out

= m,, C . (T_ - T, . )

f pf f out f in

The change in gas mass flow rate will obviously decrease the

total amount of energy transferred since less gas in means

less energy into the heat exchanger. If the curves were

plotted in a third dimension with Q, the smallest Q would

occur with the smallest gas flow rate. The forced equality

with the rate equation means that, as the gas flow rate

decreases, the rate of heat transfer must decrease. The

figures show the total effect on the profile operation of

the heat exchanger is of little consequence. The similarity

of the curves is an indication of the "physical operation"

of the heat exchanger under varying conditions. For the test

runs, a decrease in gas flow rate was coupled with a decrease

in gas inlet temperature. The two parameters changing and

the similarity of the curves emphasizes the physical constancy

of the design.

61

Figure 14-E is the plot for distribution 1. The "ripple"

effect in the heating and superheating regions is a result

of the non-uniformity of the gas mass distribution, but the

superposition shown in Figure 14-F demonstrates the oblivious-

ness of the physical properties of the heat exchanger to a

variation of input.

G. EFFECT OF NON-UNIFORM MASS DISTRIBUTION ON EXHAUST GASTEMPERATURE

For all runs of the model the temperature distribution

of the exhaust gas entering the heat exchanger was assumed

uniform. To determine the effects of a non-uniform gas mass

distribution on the exhaust gas temperature profile, a plot

was made of the gas temperatures across several of the heat

exchanger passes. The matrix of exhaust gas temperatures

was used and data was plotted for both a uniform distribu-

tion and distribution 1. The gas mass flow rate was 121.8

lbm/s. Figures 15-A and 15-B show the results.

Figure 15-A demonstrates that with a uniform mass and

temperature distribution at the inlet to the heat exchanger,

the distribution is virtually undistorted by passage through

the WHRU. This result must be considered ideal with respect

to the assumption of no cross-mixing of the gas during passage

There is a smooth transition of energy from inlet to outlet

which accounts for the best performance of the heat exchanger

under this condition. The effect of the non-uniformity is

clearly seen in Figure 15-B. The temperature distribution is

62

rapidly distorted to become almost a replica of the gas flow

distribution. This is a result of the disparity of heat

transferred and heat transfer rates from node to node in

the WHRU. A slight smoothing effect is seen in the boiling

portion, but distortion is again accentuated in the heating

section. In a real situation there will be some non-

uniformity of temperature as it enters the heat exchanger.

The analysis shows that the condition will be worsened to

the degree of the mass non-uniformity with the subsequent

loss of performance in the WHRU.

The distortion of the exhaust gas temperature distribu-

tion forces consideration of pinch point. When the tempera-

ture differential between the exhaust gas and the tube

becomes less than approximately 25 deg. F coupled with a gas

temperature less than approximately 300 deg. F, the WHRU may

experience localized hot-side corrosion due to sulphur products

in the exhaust gas. It should be noted that this condition

will exist only near the top of the heat exchanger near the

exhaust gas exit. If the degree of flow distortion is

severe and maintained for a long period, the effects can be

disastrous

.

63

IV. CONCLUSIONS

The waste heat recovery unit is a practical method of

recouping thermal energy from gas turbine engine exhaust

gases for fuel economy improvement. In the design and

installation of a RACER system several factors must be taken

into consideration.

1. Mass Flow Distribution. The performance of a waste

heat recovery unit is adversely affected by a non-uniform gas

mass distribution; and the degradation is directly propor-

tional to the degree of non-uniformity. To ensure acceptable

results, the system should have flow distribution control

devices installed between the gas turbine and the WHRU.

2. Operating Pressure. The operating pressure of the

system affects the power output inversely. A higher pressure

system requires less fluid to deliver the same power but the

percent reduction in fluid required does not justify the

percent loss in power. Since the system is not a main pro-

pulsion system requiring a large volume of fluid, the model

suggests using a low pressure system.

3. Steam Outlet Temperature. Reducing the outlet temp-

erature required forces an increase in fluid mass flow rate

to maintain the same power out. High temperature steam, how-

ever, has a greater wear effect on system components such as

valves, seals and piping. The model suggests a steam tempera-

ture as high as practical should be used, within material

constraints

.

64

4. Heat Exchanger Size. Power and fluid mass flow rate

are directly related to heat exchanger size. The size of

the WHRU should be as large as the available space and

weight constraints allow, or as large as necessary to pro-

duce the power required. Consideration must be given to the

system as a whole since, as the heat exchanger becomes larger,

so does the piping, valves, pumps and condenser necessary to

operate.

5. Speed. Power developed is a function of the energy

available in the exhaust gas flow. At higher gas turbine

speeds more horsepower is available from the WHRU to assist

the main propulsion system. Utilizing the latest NAVSEA

speed profile, the heat exchanger should be sized in accordance

with the ship speed most commonly used.

All data suggests a WHRU as large as physically possi-

ble, operated at a low steam pressure, high steam temperature,

and with flow distribution control devices installed provides

the best performance.

65

V. RECOMMENDATIONS FOR FURTHER RESEARCH

A. WHRU MODEL IMPROVEMENT AND EXPANSION

The control imposed on the WHRU model in this study was

adjustment of the steam flow rate to maintain a user speci-

fied steam outlet temperature. This forces the steam system

to respond to a variation of gas inlet conditions by "throt-

tling" the feedwater system to maintain the required steam

temperature.

This is only one of several types of control systems

which may be used in a RACER system installation. Two

possible alternative systems are: one which maintains a

constant steam flow rate while allowing the steam tempera-

ture to fluctuate, and one in which pressure is allowed to

"float" with steam demand. In this second type system, the

flow resistance of the system is used, and as the fluid mass

flow rate decreases (steam demand decreases) , the pressure

required decreases. Knowing the inter-relationship will

yield a "floating" Tf

as well. Investigation into the

performance of a WHRU with these types of control could lead

to an improved output. The investigation of all types of

control should consider the effects on the entire system

because, the type of control may dictate the type steam

turbine which must be used.

To expand the understanding of the effects of non-uniform

gas distributions on the WHRU performance, the current

66

model could be enlarged to allow a variation of the input in

an additional dimension. A two dimensional non-uniform input

will yield a three dimensional picture of the temperature

distributions as the gas passes through the heat exchanger.

An analysis of this type would help design the flow distri-

bution control devices to eliminate severe trouble spots

contributing to hot side corrosion and to maximize the WHRU

performance.

In addition to the expansion to a three dimensional

analysis, the current model could be improved by including

the following items.

1. Fluid-Side Pressure Drop

The water/steam-side pressure drop may be a signifi-

cant percentage of the system operating pressure. Calculation

of the pressure drop and its effect on system performance

should be included.

2

.

Additional Geometries

Additional fin-tube configurations should be con-

sidered for possible improvement of the heat transfer charac-

teristics and the weight and space requirements of the WHRU.

3. Fouling

Consideration of inside and outside heat transfer

surface fouling should be given when investigating possible

fin-tube configurations.

4

.

Alternate Working Fluids

Working fluids, other than water, should be investi-

gated for possible enhanced thermodynamic characteristics at

67

a minimum cost in system maintainability, while maintaining

safety to operating personnel.

5 . Non-Uniform Temperature Distributions

The current model could be utilized to determine the

effects of non-uniform temperature distributions. The gas

is at a uniform temperature as it exits the gas turbine, but

it probably is not uniform at the inlet to the WHRU. Inves-

tigation into the effects of non-uniformity of both gas mass

and temperature should be accomplished.

The model should be incorporated into a complete

RACER system analysis, including models of the steam turbine,

condenser and circulating pump. Variations of gas distribu-

tion input can then be analyzed to determine total system

effect. Understanding the total system effect and the inter-

relationship of the variables could then be used to optimize

the system.

68

w

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69

TABLE II-A

GAS FLOW DISTRIBUTIONS (m = 121.8 LBM/S)

gas mass Plow rate b. 121.8 lsm/s

cas ie.mpe»«ru|)( at heat 'exchange* inlet s 8a* deg. f

CASE S7S CREP8 » * MP * 1*500 nPT s 3000

OIST.

NO.

u

1

2

3

A

S

6

7

9

t 2

GAS

3

PATH

A 5 6 7 8 <» 10

1 2. 1 B 12.18 12.19 12.18 12.18 12.18 12. 19 1 12.(8 1 2. ie_12.18

2.07 S.97 8.2B I3-5* 30.9* 30.94 13.64 i6.26 s.97 2.07

3.78 S.36 1 0. «7 16.20 25 .09 25.09 16.20 | 1 0.A7 5.36 3. 78

9.'* I 0.96 12.18 13.40 14.62 14.62 13.40 | 12. 18 to.96 9.74

3.05 7.92 12. 79 17.05 20.10 20. 10 1 7.05 j12.79 7.02 3. 05

12.18 27.28 23.29 19.35 ' 15.96 I I .69 7.80 | 3.65 .00 0. 00

d.oo 0.00 3.65 7 .80 1 1 1 .69 15.96 19.95 | 23.29 27.2ft 12.18

1 5.471

23. 63 14.12 15. 1|10.47 8.39 8. 1 I

j8.3» 7.75 S.2*

5.24 7.75 8.0* 8. 1 1 !8.8<» 10.47

.

1 S. 1 j 19.12 23. 6J 15.47

TABLE II-B

GAS FLOW DISTRIBUTIONS (m =99.1 LBM/S)

GAS >«ASS FlOW RATE = 99.1 LflM/S

GAS T£MBES»ruBE AT M£ A T EXCHANGE? I

H

k £T r 755 DEi. P

CASE Sbl (AEF 8' SMP = 10000 NPT = 2*00

OIST.

NO.

u

1

2

3

A

5

6

7

8

1 2

GAS

3

PATH

A 5 6 7 8 9 10

9-91 9.9! 9.91 9.91 9.91 9.91 9.91 9.91 9.91 9.91

1 .68 4.85 6.74 11.10 25.17 25. 1 7 11.10 6.74 4.85 I . b8

3.08 4.36 8. 52 13.18 20.4 I 20.41 13.18 9.52 4.36 3. 08

7.92 8.92 9.91 10.90 1 1 .90 1 1 .90 10 . 90 9.91 9.92 7.92

2.48 6.44 1 0. «t 13.37 16.35 16. 35 13.87 1 0. » 1 6.44 2. Afl

9.91 22.20 19.03 16.15 12.99 9. SI 6.35 2.97 0.00 0. 00

0.00 0.00 2.97 6.35 9.51 l 2.99]

16. 15 I 9.03 22.20 9.91

1 2.59 19.23 1 5.56 12.29 8.S2 7.23j

6.60 6.54 6.31 4. 26

4.2b 6.31 6.5a 6. SO 7.23 8.52J

1 2.29 I 5.56 19.23 1 2.S9

70

TABLE II-C

GAS FLOW DISTRIBUTIONS (m =77.4 LBM/S)

CAS MASS FLO» PATE = 77. A LBM/S

GAS TEMPERATURE AT MEAT EXCHANGER INLET = 702 DE G . F

CASE SS3 (»Sf8 ) SHP 5000 NPT s 1800

OIST.

NO.

u

1

2

3

A

5

6

7

3

I 2

GAS

3

PATH

A 5^ 6 7 8 9 10

7.7* 7. 7* 7. 7A 7.7* 7 .7* 7. 74 7. 74 7.74 7. 7» 7. 74

1 .31 3.80 5.26 8.67 19.66 1 9.66 8.67 5.26 3.80 I .31

2.41 3. At 6. 65 1 0.29 1 S. 94 15.9* 10.29 6.65 3.41 2.*I

6. 1 9 6.97 7. 74 8. SI 9.29 9.29 8.51 7.7* 6. 9? 6. 19

1 .9' S.03 8. 13 10.33 12.77 12.77 10.83 8. 1 3 S.03 I .94

7.74 |7.3a 1 4.86 12.61 10.15 7.43 4.96 ! 2.32 0.00 .00

O.OO .00 2. 32 A. 96 7.43 10.15 12.61 4.86 17.3% 7. 74

9-83 1 S.02 12. 15 9.60 6.6S 5. 65 5. 15 1 5. 1 I 4.93 3.33

3. 33 «• .93 5. 11 5.15 5.65 6.6S 9.60j12.15 IS. 02 9.83

TABLE II-D

GAS FLOW DISTRIBUTIONS (m =66.7 LBM/S)g

GAS MASS FU3W RATE = 67.7 LBM/S

GAS TEMPERATURE AT m£a T EXCHANGER INLET = 694 DEG. F

CASE 5A5 ( REF 8 ) SHP r 3OO0 MPT s 1200

OIST .

NO.

J

1

2

3

4

5

6

7

a

i 2

GAS

3

PATH

A 5 e> 7 8 9 10

6.77 6.77 6.77 6.77 6. 77 6.77 6 .77 6.77 6.77 6.77

1 .1 5 3.32 4.60 7.58 17.20 1 7. ?0 7. SB 4.60 3.32 1.15

2.11 2.98 5.82 9.00 13.94 13.9* 9. 00 S.82 2.98 2. 1 1

5.41 6. 10 6. 77 7.44 8.13 8. 1 3 7.4* 6.77 6. 10 S.4I

1 . 70 4.40 7. 1 1 9.4 7 11.17 11.17 9.47 7.11 *.*0 I . 70

6. 7 7 15.17 1 3. 00 11.03 3.aa 6. SO 4 .3* 2.33 O.OO 0. 00

0.00 0.00 2.03 4 .34 6.50 6.88 I 1 .03 13.00 1 5. 17 6. 77

8.60 13.14 10.63 8.40 5.82 4. 94 *. 50 4.47 4.31 2.91

2.91 4.31 4.47 4.50 4.9. S.82 s. *a 1 0.63 13.1* a. to

71

TABLE III

ISENTROPIC POWER FOR VARIOUS GAS FLOW DISTRIBUTIONS,GAS FLOW RATES AND STEAM OUTLET TEMPERATURES

RUN

NO.

DISTR.

NO. 65

STEAM TEMPERATURE

625 600 575 550

GAS

MASS

121.8

LBM/S

1 U 6944 6943 6933 6946 6956

2 1 6286 6315 6295 6317 63 4 8

3 2 6550 657 6550 6580 6598

4 3 692 4 6925 6910 6927 6939

5 « 6692 670 8 6691 6713 6 73

6 K 6397 641 9 6415 6420 6434 |

7 6 639 6382 6407 6431 64o4j

8 7 675 4 6742

6733

6722

6744~6727

6763

6750j

9 8 6715 6762|

GAS

MASS

99.1

LBM/S

10 U 4 43 4 4489 4488 4500 4510

11 1 4123 4123 4153 4155 4133 I

12 2 4276 4277 4292 4296 4323

13 3 44/5 447 7 4479 4489 4C.0 1 l

14 4 4256 4359 4368 4375 4396

15 5 4161 4187 4203 4222. 4227

16 6 4165 419h 4187 4220 4 24 5|

17 7 4365 439 5 4337 4392 4399

18 8 4379 4373 4379 4408 4417i

GAS

MASS

77.4

LBM/S

19 U 2943 2957 2957 2967 2974 1

20 1 2756 2779 2 7 79 2801 2609|

21 2 2 840 2357 2353 2872 2632!

22 -3

2 94 3 2953 2953 2962 2 970

23 4 2S8 2 2S97 2898 2910 2919

24 5 2770 2793 2812 2333 2837

25 6 2773 2795 2811 2821 2 64 2

26 7 2 891 2901 2914 2 13 2921

27 8 2 89 2906 2901 2913 2933

GAS

MASS

67.7

LBM/S

28 U 2 515 2522 2522 2530 2536

29 1 236 5 2389 23 93 2411 2417

30 2 2 43 4 2451 2451 2462 2471

31 3 2 512 2519 2519 2527 2533

32 4 2 46 5 2479 2 480 2490 2498

33 5 2 37 7 240 5 2418 2435 2437

34 6 2339 2406 2416 2425 2442

35 7 2476 2481 2492 2496 2499

36 8 2469 2487 2 4 82 2496 2507—

72

TABLE IV

FLUID MASS FLOW RATE FOR VARIOUS GAS FLOW RATES, GAS FLOWDISTRIBUTIONS AND STEAM OUTLET TEMPERATURES

RUN

NO.

D1STR.

NO. 650

STEAM TEMPERATURE

625 600 575 550

GAS

MASS

121.8

LBM/S

1 u 12.33 12.54 12.75 12.97 13.20

2 1 11.17 11.41 11.53 1 1 . 79 12.04

3 2 11.63 11.87 12.05 12 .28 12 .52

4 3 12.30 12.51 12.71 12.93 13.17

5 4 11.89 12.12 12.31 12.53 12.77

6 5 LI. 36 11.59 11 .30 11 .99 12.21

7 6 11 .3 5 11.53 11 .73 12.01 12.27

8 7 12.00 12.13 12.36 12.56 12 .31

9 8 11.93 12. 16 12.40 12.63 12.33

GAS

MASS

99.1

LBM/S

10 U 7.96 8.11 3.25 8 .40 8.56

11 1 7.32 7.46 7.64 7.76 7.94

12 2 7.60 7.72 7.39 3.02 8.20

13 3 7.95 8.09 8 .24 9 .38 3 .54

14 4 7.74 7.87 3.03 3. 17 3.34

15 5 7.39 7.56 7.74 7.33 3.0 2'

16 6 7.40 7.58 7.70 7.33 8.05 1

17 7 7.75 7.94 8.07 3.20 8.35|

18 3 7.78 7.90 8.05 3.23 8.33|

GAS

MASS

77.4

LBM/S

19 U 5.24 5.3n 5.44 5.54 5.64J

20 1 4.90 5.02 5.11 5.23 5.33

21 2 5.04 5.16 5.2b 5.36 5.47

22 3 5.2 3 5.33 5.^3 5. 53 5.64

23 4 5.12 5.23 5 .33 5 .43 5.54

24 s 4.92 5.05 5. 17 5. 29 5.38

25 6 4 .93 5.05 5.17 5.27 5.39

26 7 5.14 5.24 5.36 5.45 5.54

27 8 5.13 . 5.25 5.34 5.45 5.56

GAS

MASS

67.7

LBM/S

28 U 4 .47 4.5o 4.64 4.72 4.81

29 1 4.20 4.32 4.^0 4. 50 4.59

30 2 4.32 4.43 4.51 4.60 4.69

31 3 4.46 4.55 4.63 4.72 4.81

32 4 4.38 4.43 4.56 4.65 4.74

33 5 4.22 4.34 4.h5 4.55 4.62

34 6 4.24 4.35 4.n4 4.53 4.63

35 7 4.40 4.48 4.53 4.66 4.74

36 a 4.3 9 4.49 4.56 4.66 *.76

73

TABLE V. POWER AND FLUID FLOW RATE

FOR VARIOUS SIZE HEAT EXCHANGERS

DISTR. NUMBER OF HEAT EXCHANGER PASSES UNITS

20 21 23 25

U 6746 6820 694 4 704 3 HP

GAS I 6010 6110 62 8 6 6433 HP

MASS

121.8 U 11.99 12.11 12.31 12.51 LBM/S

LBM/S I 10.67 10.85 11.17 11.43 LBM/S

u 4 3 70 4414 448 4 4538 H?

GAS 1 3964 4020 4123 4211 HP

MASS

99.1 u 7.76 7.84 7.96 8.06 LBM/S

LBM/S 1 7.04 7.14 7.32 7.48 LBM/S

u 2884 2 90 8 2948 2978 HP

GAS 1 2654 2693 2756 2309 HP

M4SS

77.4 u 5.12 5.17 5.24 5.29 LBM/5

LBM/S I 4.71 4.78 4.90 4.99 LBM/S

u 2h66 2485 251 5 2537 HP

GAS 1 2281 2312 2365 2408 HP

MASS

66.7 u 4.38 4.4 1 4.47 4.51 LBM/S

LBM/S 1 4.05 4.1 1 4.20 4.28 LBM/S

74

TABLE VI. POWER AND FLUID FLOW RATE FOR VARIOUS

STEAH OPERATING PRESSURES

DISTR. OPERATING PRESSURE

400 500 600

UNITS

GAS

MASS

121.8

LBM/S

U

1

U

1

6944

6286

12.33

11. 17

6672

6041

12.06

10.92

6423

5821

11.82

10.71

HP

HP

LBM/S

LBM/S

GAS

MASS

99.1

LBM/S

u

1

u

1

4484

4123

7 .96

7.32

4245

3 904

7.67

7.05

4027

3697

7.41

6.80

HP

HP

LBM/S

LBM/S

GAS

MASS

77.4

LBM/S

u

1

u

1

2948

2756

5.24

4.90

2749

2 571

4.97

4.65

256 9

2398

4.73

4.41

HP

HP

LBM/S

LBM/S

GAS

MASS

66.7

LBM/S

u

1

u

1

2515

2365

4.47

4.20

2339

220S

4.23

3 .99

2179

2055

4.01

3.79

HP

H?

LBM/S

LBM/S

75

LAYOUT OF MARINE GAS TURBINE WASTE-HEAT STEAM GENERATOR: ONCE-THROUGH,COUNTER-CROSS FLOW HEAT EXCHANGER

WATER IN

WAH_«MANIFOLD

CjAS

Figure 1. Waste Heat Recovery Unit Layout

76

NR = Number of Heat Exchanger Passes

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APPENDIX A

Sample runs of the computer output are provided for a

comparison of the effects of the non-uniform gas mass

distributions on the temperatures within the heat exchanger

and the effect on overall performance.

Runs 1, 2 and 6 utilized a total gas flow rate of

121.8 lbm/s with the uniform distribution, distribution 1 and

distribution 5, respectively. Runs 10, 11 and 15 utilized

the same distributions but with a total gas flow rate of

99.1 lbm/s. Runs 19, 20 and 24; and runs 28, 29 and 3 3

also utilized the same distributions but with mass flow

rates of 77.4 lbm/s and 66.7 lbm/s, respectively.

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LIST OF REFERENCES

1. Halkola, J.T., Cambell, A.H. and Jung, D. , "RacerConceptual Design," ASME Paper No. 83-GT-50.

2. Mattson, W.S., "Designing Reliability and Maintainabilityinto the Racer System," Naval Engineers Journal , v. 95,no. 3, May 19 83.

3

.

Combs , R . M . , Waste Heat Recovery Unit Design for GasTurbine Propulsion Systems , Master's Thesis, NavalPostgraduate School, September 1979.

4. Shu, H.T. and Kuo, S.C., "Flow Distribution ControlCharacteristics in Marine Gas Turbine Waste-Heat SteamGenerators," United Technologies Research Center, AnnualTechnical Report, No. R82-955750-4 , July 1982.

5. Weirman, C. , Taborak, J., and Marner, W.J., Comparisonof Inline and Staggered Banks of Tubes with SegmentedFins , paper presented at the Fifteenth National HeatTransfer Conference AIChE-ASME, San Francisco, California,1975.

6. Incropera, F.P. and DeWitt, D.P., Fundamentals of HeatTransfer , John Wiley and Sons, Inc., 19 81.

7. Tong, L.C., Boiling Heat Transfer and Two-Phase Flow ,

John Wiley and Sons, Inc., 1965.

8. General Electric Company, Performance Data for theGeneral Electric LM2500 Gas Turbine Engine , MID-TD-2500-8, Revised November 1978.

194

INITIAL DISTRIBUTION LISTNo. Copies

1. Defense Technical Information Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 014 2 2

Naval Postgraduate SchoolMonterey, California 939 43

3. Department Chairman, Code 69 1

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 9 39 43

4. Professor Paul F. Pucci, Code 69Pc 5

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 9 3943

5. LCDR S.L. Wesco 3

c/o Mike Smith1383 Barnhart RoadTroy, Ohio 45373

6. LCDR J.S. Pine 1

Executive OfficerU.S.S. Oldendorf DD-9 72F.P.O. San Francisco, California 96674

7. Donald Tempesco 2

Code SEA 5 6X3Naval Sea Systems CommandWashington, D.C. 20362

8. Dr. Keith Ellingsworth 1

Office of Naval Research800 Quincy St.Arlington, VA 22 217

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