Thermal Design and Optimization of Heat Recovery … Thermal Design and Optimization of Heat Recovery Steam Generators and Waste Heat Boilers Ali Rezaie Navaie Berlin 2017 Technische

Dissertation

Thermal Design and Optimization of Heat Recovery Steam Generators and

Waste Heat Boilers

Ali Rezaie Navaie

Berlin 2017

Technische Universität Berlin Institut für Energietechnik

Thermal Design and Optimization of Heat Recovery Steam Generators and

Waste Heat Boilers

vorgelegt von

M. Sc.

Ali Rezaie Navaie

geb. in Sary, Iran

von der Fakultät III – Prozesswissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

- Dr. –Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzende: Prof. Dr. Tetyana Morozyuk

Gutachter: Prof. Dr. -Ing. George Tsatsaronis

Gutachter: Prof. Dr.-Ing. Udo Hellwig

Tag der wissenschaftlichen Aussprache: 12.04.2017

Berlin 2017

To my lovely wife, Delara

my darling son, Kian

and

my beloved parents, Mahmood and Monir

Acknowledgements This work was carried out during my stay as a doctoral student at the Institute for Energy Engineering of the Technische Universität Berlin. At facing the finishing time of my dissertation, I have to express my appreciation to all people who helped, supported and accompanied me to complete this work. First of all, I have to express my sincere appreciation and gratitude to Professor George Tsatsaronis who gave me a chance to be under his supervision in my research work. Always, he had an open door and was passionate, creative, generous, and helpful. I have to appreciate him for his excellent support and patience during the past years. I am thankful to Professor Tetyana Morozyuk for her willingness to chair my defense. I place on record, my special thanks to the Professor Udo Hellwig, for his supports and kind attentions to me to carry out my favorite research project that is the design and technology of the boilers. This work was not possible without his support. He has given me a lot of favors and helped me with all he could whenever I needed. I appreciate Mr. Alexis Hellwig who helped me during the time that I stayed in Berlin. I use this opportunity to say my thanks to the colleagues, Michael Beyer, Mario Nowitzki, Stefan Kohn, Marcel Kamin, Nicolai Sachno and the others for the fruitful technical discussions. I am also grateful Mr. Max Hellwig for having reviewed the writing and grammar of my thesis. I would then thank my beloved brother, Amir Rezaie and my dear old friend,

Shahrokh Zehtabian for their constructive help and guide.

This work was not possible without the support and accompanying of my lovely

wife, Delara. Your sacrifices and encouragement have been the most important

and powerful motivator to my work. I would like to express my honest and

eternal gratitude towards you for your understanding, help and patience during

the past years. I never forget your encouragement and strong back at all levels.

The last but not the least, I would dedicate my special thanks to my solid

backing, my parents, Mahmood and Monir who I couldn’t be where I am

without them. I can hardly find meaningful words to appreciate my parents.

They gave me everything they ever could and supported me in every phase of

my life. I will never forget their great encouragement and strong back at all

levels.

Abstract

Heat recovery steam generators (HRSG) are important and critical equipment of

combined cycle power plants (CCPP) that connect the gas turbine system to the

steam cycle. The thermal design and the optimization of an HRSG are important

for achieving safe operation, higher efficiency and reduced product cost in a

combined cycle power plant. This work deals with the comprehensive

optimization of the thermal design and cost of an HRSG using a genetic

algorithm (GA). Based on actual and existing HRSG in most combined cycle

power plants, a water tube HRSG including two superheaters, one evaporator

and one economizer is considered in the optimization. A comprehensive

program was developed in Visual Basic for this purpose.

The optimization variables include the fin tube arrangement (transverse pitch,

longitudinal pitch, number of rows in flue gas direction, number of tubes on the

circumference of a header, in line or staggered tube arrangement), fin tube

specification (tube diameter, fin height, fin thickness, fin type (solid or serrated),

fin per meter, segment width of serrated fin) and also approach point, water

and steam velocity. On the other hand, the pressure at the exit of the gas

turbine, fin tube metal temperature, amount of desuperheater spray water

flow, steam pressure drop, guarantee of minimum HRSG thermal efficiency, gap

between fin tubes and overall dimension of HRSG (Length, width, height) have

been considered as the main constraints in the optimization.

The developed method selects and provides the best geometric parameter and

arrangement of finned tubes based on minimum capital cost and relevant

defined constraints. However, any other objective function such as minimum

flue gas pressure drop, minimum heat transfer surface area, maximum rate of

heat transfer, etc. could be defined as objective functions in the program and

optimized easily.

In order to test this method, the results of the optimized design have been

compared to an existing HRSG of a combined cycle power plant. All design

parameters and the HRSG arrangement could be easily determined based on

any optimization strategy and constraints. Moreover, the existing work could be

easily expanded to consider triple pressure HRSG.

Zusammenfassung

Abhitzekessel (AHK) sind wichtige und entscheidende Geräte in

Kombikraftwerken, die das Gasturbinensystem mit dem Dampfkreislauf

verbinden. Die wärmetechnische Berechnung und Optimierung eines AHK sind

wichtig für den sicheren Betrieb, höhere Wirkungsgrade und niedrigere

Produktkosten in einem Kombikraftwerk. Diese Arbeit behandelt die

Optimierung der wärmetechnischen Berechnung und Kosten eines AHK mit Hilfe

eines genetischen Algorithmus. Auf Grundlage von tatsächlichen, bestehenden

AHK in den meisten Kombikraftwerken, wird bei der Optimierung ein

Wasserrohr-AHK einschließlich zweier Überhitzer, eines Verdampfers und eines

Economisers angenommen. Für diesen Zweck wurde in Visual Basic ein

umfassendes Programm entwickelt.

Die Optimierungsvariabeln schließen die Rippenrohranordnung (Querteilung,

Längsteilung, Anzahl der Reihen in Rauchgasrichtung, Anzahl der um die

Sammler herum angebrachten Rohre, fluchtende oder versetzte Anordnung),

Rippenrohrgeometrie (Rohrdurchmesser, Rippenhöhe, Rippendicke, Rippenart

[vollrippe oder segmentierte Rippe], Rippen pro Meter, Segmentbreite der

segmentierte Rippen) und auch Approach Point, Wasser- und

Dampfgeschwindigkeit. Auf der anderen Seite wurden der Druck beim Austritt

aus der Gasturbine, Temperatur des Metalls der Rippenrohre,

Spritzwasserdurchflussmenge des Einspritzkühlers, Dampfdruckabfall,

Gewährleistung eines Minimums an thermischem Wirkungsgrad des AHK, Lücke

zwischen Rippenrohren und Gesamtmaße des AHK (Länge, Breite, Höhe) als

Hauptbegrenzungen der Optimierung berücksichtigt.

Das entwickelte Verfahren wählt und bietet die besten geometrischen

Parameter und die beste Anordnung von Rippenrohren auf Grundlage von

minimalen Kapitalkosten und entsprechenden festgelegten Nebenbedingungen.

Allerdings könnte jedwede andere Zielfunktion wie Mindestdruckabfall des

Rauchgases, Mindestoberfläche der Wärmeübertragung, höchste

Wärmeübergangszahl usw. in dem Programm als Zielfunktion festgelegt und

leicht optimiert werden. Um dieses Verfahren zu testen, wurden die Ergebnisse

des optimierten Entwurfs mit einem bestehenden AHK eines Kombikraftwerks

verglichen. Alle Entwurfsparameter und die AHK-Anordnung können leicht auf

Grundlage irgendwelcher Optimierungsstrategien und -nebenbedingungen

bestimmt werden. Darüber hinaus könnte die bestehende Arbeit leicht

erweitert werden, um Dreidruck-AHK zu berücksichtigen.

Contents

i

Contents 1. Introduction 1

1.1. Brief description of combined cycle and cogeneration plants . . . . . . . . 4

1.2. Heat recovery steam generator (HRSG) . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3. Individual design of an HRSG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4. State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2. Thermoeconomics and cost balance of HRSGs 12

2.1. Economic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2. Thermoeconomics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3. Cost balance of HRSGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3. Thermal design of HRSG sections 17

3.1. Thermal design demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2. HRSG temperature profile, pinch point and approach point . . . . . . . . . 18

3.3. Necessity of using finned tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4. Thermal design simulation of the HRSG sections . . . . . . . . . . . . . . . . . . 23

3.4.1. Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4.2. Water, steam and flue gas properties . . . . . . . . . . . . . . . . . . . . . . 24

3.4.3. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4.4. Overall heat transfer coefficient of HRSG sections . . . . . . . . . . . . 25

3.4.4.1. Average inside heat transfer coefficient . . . . . . . . . . . . . . 26

3.4.4.2. Average outside heat transfer coefficient . . . . . . . . . . . . . 26

Contents

ii

3.4.5. Pressure drop across fin tube bundle . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.6. Pressure drop in the tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4. Constraints in the thermal design of HRSGs 37

4.1. General description of the constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2. Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.1. Allowable draft loss of the flue gas . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.2. Pinch point, Approach point and economizer steaming . . . . . . . . 39

4.2.3. Overall dimensions of heat recovery steam generator . . . . . . . . 40

4.2.4. Steam and water pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2.5. Constraints of the finning (fin tube manufacturing) . . . . . . . . . . . 42

4.2.6. Fin tube and operating data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.7. Maximum spray water flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5. Optimization and genetic algorithm 44

5.1. Introduction to optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2. Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3. Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.4. Optimization constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.5. Operating conditions and hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.6. Optimization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.6.1. Calculus methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.6.2. Search methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.6.3. Other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Contents

iii

5.7. Genetic algorithm used in the optimization of thermal design and

heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.8. Optimizing thermal systems with genetic algorithms . . . . . . . . . . . . . . 56

5.8.1. Optimization of systems, converting and transferring energy . . . 57

5.8.1.1. Heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.8.1.2. Power generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.8.1.3. Heat exchanger networks (HENs), design integration and

chemical plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.8.1.4. Heating, ventilation, air conditioning and refrigeration

(HVAC&R) systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.8.2. Other applications of genetic algorithms . . . . . . . . . . . . . . . . . . . . 60

5.9. Description of genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.9.1. Introducing the parameters of a genetic algorithm . . . . . . . . . . . 62

5.9.2. General Description of the genetic algorithm method . . . . . . . . . 62

6. Optimization program 65

6.1. Modules of the program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1.1. Thermal simulation of superheater no. 2 . . . . . . . . . . . . . . . . . . . 66

6.1.2. Thermal simulation of superheater no. 1 . . . . . . . . . . . . . . . . . . . 66

6.1.3. Thermal simulation of the evaporator . . . . . . . . . . . . . . . . . . . . . . 67

6.1.4. Thermal simulation of the economizer . . . . . . . . . . . . . . . . . . . . . 68

6.1.5. Water and steam property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.1.6. Flue gas properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.1.7. Genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.2. Definition of the optimization variables . . . . . . . . . . . . . . . . . . . . . . . . . 71

Contents

iv

6.2.1. Approach point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.2.2. Tube diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.3. Fin type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.4. Fins per meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.5. Fin height and fin thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2.6. Steam and water velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2.7. Number of tubes on the circumference of a header . . . . . . . . . . 74

6.3. Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

7. Results and comparison 79

7.1. Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.1.1. Flue gas data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.1.2. Steam and water data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.2. HRSG optimization, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.2.1. Variation ranges of the optimization variables, case 1 . . . . . . . . . 81

7.2.2. Constraints and their range of variation, case 1 . . . . . . . . . . . . . . 84

7.2.3. Optimization results and comparison, case 1 . . . . . . . . . . . . . . . . 85

7.2.3.1. Optimization variables and thermal design results of the

HRSG sections, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.2.3.2. General data and cost (objective function) comparison of

the optimized and existing HRSGs, case 1 . . . . . . . . . . . . . . . . . 95

7.2.3.3. Comparison of the heat transfer surface in the existing and

optimized HRSGs, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.3. HRSG optimization, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Contents

v

7.3.1. Variation ranges of the optimization variables, case 2 . . . . . . . . . 99

7.3.2. Constraints and their range of variation, case 2 . . . . . . . . . . . . . 101

7.3.3. Optimization results and comparison, case 2 . . . . . . . . . . . . . . . 102

7.3.3.1. Optimization variables and thermal design results of the

HRSG sections, case2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.3.3.2. General data and cost (objective function) comparison of

the optimized and existing HRSG, case 2 . . . . . . . . . . . . . . . . 111


optimized HRSG, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

8. Conclusion 115

Glossary 119

References 120

Nomenclature

vi

Nomenclature dimensionless pressure drop acceleration term

m² bare tube outside surface area

m² fin surface area

m² total inside surface area

m² total outside surface area

m² prime outside surface area

m²/m finned tube projected cross sectional area per unit length of tube

m² cross sectional flow area of the ducts

m² net free area in a tube row

J/kg.K heat capacity at constant pressure

m outside diameter of fin

m tube inside diameter

m tube outside diameter

dimensionless fin efficiency

dimensionless fanning friction factor

dimensionless friction factor

dimensionless friction coefficient

kg/s.m² mass velocity

Nomenclature

vii

m fin height

W/m²·K average inside heat transfer coefficient

W/m²·K average outside heat transfer coefficient

W/m²·K average outside radiation heat transfer coefficient

W/m²·K average outside convection heat transfer coefficient

W/m²·K fluid thermal conductivity

dimensionless resistance coefficient for one 90° bend

dimensionless total resistance coefficient

dimensionless entrance resistance coefficient

dimensionless exit resistance coefficient

dimensionless total resistance coefficient

W/m²·K average fin thermal conductivity

W/m²·K average tube wall thermal conductivity

m roughness of tube wall

°C logarithmic mean temperature difference

m mean radiating length

m finned length of the tubes

m straight length of the tube

Kg/s flue gas mass flow rate

Kg/s water mass flow rate

https://en.wikipedia.org/wiki/Logarithmic_mean_temperature_difference

Nomenclature

viii

dimensionless number of tube rows in the direction of flow

dimensionless number of tubes per row

dimensionless number of 90° elbow

1/m number of fins per unit length of tubes

bar pressure

bar total partial pressure of and

dimensionless prandtl number

W total heat transfer rate

mm bending radius

W/m²·K inside fouling resistance

W/m²·K outside fouling resistance

dimensionless reynolds number

m fin spacing

°C water or steam inlet temperature of each section

°C water or steam outlet temperature of each section

°C flue gas inlet temperature of each section

°C average outside fluid temperature

°C average fin temperature

°C flue gas outlet temperature of each section

m fin thickness

Nomenclature

ix

m tube wall thickness

m longitudinal pitch

m transverse pitch

m/s velocity

U W/m²·K overall heat transfer coefficient

m segment width of serrated fin

kg/m³ fluid density

kg/m³ flue gas inlet density

kg/m³ flue gas outlet density

kg/m³ average flue gas density at bulk temperature

mbar pressure drop across fin tube bundle

Pa pressure drop in the tube

Pa.s viscosity

dimensionless contraction factor

Btu/hr ft2 F radiation factor

Abbreviations

x

Abbreviations CCPP combined cycle power plant

ECO economizer

EVA evaporator

GA genetic algorithm

GT gas turbine

HRSG heat recovery steam generator

SH1 superheater no. 1

SH2 superheater no. 2

ST steam turbine

List of figures

xi

List of figures Figure 1.1 schematic diagram of a combined cycle power plant . . . . . . . . . 4

Figure 1.2 heat recovery steam generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 1.3 heat recovery steam generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 1.4 cross sectional view of a heat recovery steam generator . . . . . . 8

Figure 1.5 top view of a heat recovery steam generator . . . . . . . . . . . . . . . 9

Figure 2.1 schematic diagram of a combined cycle plant . . . . . . . . . . . . . . 14

Figure 3.1 temperature profile in the HRSG . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 3.2 tube with serrated fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 3.3 tube with solid fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 3.4 general Arrangement of HRSG . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 3.5 fin tube specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 3.6 fin tube arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 3.7 correction factor of the mean radiating length . . . . . . . . . . . . . 30

Figure 3.8 flue gas radiation factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 3.9 moody’s friction factor diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 4.1 typical temperature profile of an HRSG . . . . . . . . . . . . . . . . . . . 40

Figure 5.1 Heat transfer related articles using GAs reported in a review . 56

Figure 5.2 flow chart of a Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . 64

List of figures

xii

Figure 6.1 regions and equations of IAPWS-IF97 . . . . . . . . . . . . . . . . . . . . 70

Figure 6.2 single row and multiple row harp . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 6.3 thermal design and optimization program, Main page . . . . . . 76

Figure 6.4 thermal design and optimization program, optimization

variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Figure 6.5 thermal design and optimization program, Thermal design

data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Figure 7.1 heat transfer surface of the HRSG and its sections, case 1 . . . . 98

Figure 7.2 heat transfer surface of the HRSG and its sections, case 2 . . . 114

List of tables

xiii

List of tables Table 3.1

friction coefficient ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Table 3.2

resistance coefficient for a 90° bend ( ) . . . . . . . . . . . . . . . . . 36

Table 7.1

flue gas data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Table 7.2

water and steam data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Table 7.3

design variables and variation range for superheater no. 2 and superheater no. 1, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Table 7.4

design variables and variation range for the evaporator and economizer, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Table 7.5

constraints and their variation range, case 1 . . . . . . . . . . . . . . . 84

Table 7.6

variables of existing and optimized superheaters no. 2, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Table 7.7

thermal design results of the existing and optimized superheater no. 2, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Table 7.8

variables of existing and optimized superheater no. 1, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Table 7.9

thermal design results of the existing and optimized superheater no. 1, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90

Table 7.10

variables of the existing and optimized evaporators, case 1 . . 91

Table 7.11

thermal design results of the existing and optimized evaporators, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Table 7.12

variables of the existing and optimized economizers, case 1 . . 94

Table 7.13

thermal design result of the existing and optimized economizers, case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Table 7.14

comparison of the existing and optimized HRSGs, case 1 . . . . 96

Table 7.15

design variables and variation range for superheater no. 2 and superheater no. 1, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

List of tables

xiv

Table 7.16

design variables and variation range for evaporator and economizer, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Table 7.17

constraints and their variation range, case 2 . . . . . . . . . . . . . . 102

Table 7.18

variables of the existing and optimized superheaters no. 2, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Table 7.19

thermal design results of the existing and optimized superheaters no. 2, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Table 7.20

variables of existing and optimized superheater no. 1, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Table 7.21

thermal design results of the existing and optimized superheaters no. 1, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Table 7.22

variables of the existing and optimized evaporators, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Table 7.23

thermal design results of the existing and optimized evaporators, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Table 7.24

variables of existing and optimized economizer, Case 2 . . . . 110

Table 7.25

thermal design results of the existing and optimized economizers, case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Table 7.26

comparison of the existing and optimized HRSGs, case 2 . . . 112

Chapter 1 Introduction

1

CHAPTER 1

1. Introduction

Nowadays, extending the energy supply, design optimization and increasing the

efficiency are the main goals and targets of the industries and their future plans.

Due to the increase of human population, a continuously increasing amount of

electricity needs to be generated. There are various technologies for power

generation in the world, such as wind energy, water energy, steam turbines (ST)

and gas turbines (GT). In this regard, steam is used as the main source of energy

for processes, heating, chemical reactions, power generation, etc. in most

industries. On the other hand, the costs of the fuels are increasing continuously

in the entire world. Consequently development of new methods for electricity

and power generation, increasing efficiency and also cost optimization of power

plants are attractive subjects for engineers.


2

Some part of the world’s power is generated in thermal power plants by using

fired boilers and steam turbines.

But, combined cycle power plants (CCPPs) are more efficient in power

generation. CCPPs have currently the highest efficiency for power production.

The thermal efficiency of a CCPP can exceed 60% depending on the ambient

conditions and the design of its components. Gas turbines and steam turbines

are two main components of a CCPP. In a CCPP, the exhaust gas from the gas

turbine is used in a heat recovery steam generator (HRSG) to produce steam.

Then, the produced steam is used in steam turbines for electricity production.

The gas turbine and the steam turbine produce approximately 65% and 35%

respectively of the total produced power in a CCPP. In a combined cycle,

Brayton and Rankine Cycles are linked by the HRSG, which is a very important

component and shall follow both the requirements of steam turbine and the

constraints of the gas turbine. Therefore, the HRSG has to be designed carefully

to fulfil the requirements of the steam cycle, without affecting the operation of

the gas turbine which is supposed to maximize the transferred heat, provide

expected and guaranteed thermal efficiency, and minimize the costs to improve

the overall performance of the CCPP. Any change in design of the HRSG directly

affects the CCPP efficiency, produced net power, production cost and some

other variables of the overall system. As an advantage of the current market,

several gas turbine systems are available with different operating parameters,

such as back pressure and exhaust gas temperature. The latter is very important

in HRSG design (in general, the exhaust gas temperature can range from 700 to

950K). For each selected gas turbine, a compatible design of the steam cycle

(combination of HRSG and steam turbine) is required. The thermal efficiency of

the steam cycle is strongly dependent on the HRSG thermal design.

Similar to thermal power plants, combined cycle power plants produce

thousands of megawatts of power. In combined cycle power plants, steam

pressure and temperature of the heat recovery steam generators have been

increased to produce more electricity. Multi-pressure HRSGs are designed and

developed to increase energy recovery. By using a modern HRSG, steam is

produced with similar parameters as in the steam boilers that are used in

thermal power plants. Also, any probable emissions of NOx, SOx and CO could


3

be reduced in the process of heat recovery. Apart from improving the gas

turbine technology in the recent decades, developing the HRSG was one of the

main targets of power plant engineering, in order to increase the efficiency and

reduce the cost. Engineers have spent plenty of time and carried out much

research and many optimization projects to increase the efficiency from a level

of 35% of the Rankine cycle to the 60% level in combined cycle plants.

Considering the wide range of the exhaust gas temperature and relevant

specifications, heat recovery steam generators play a very important role in the

CCPPs.

Apart from the gas turbine exhaust gas, waste gases are available in many

processes and could be recovered. Sometimes, these available waste gases are

used to heat other fluids. But, steam production is the main application of a

waste gas. In this regard, heat recovery steam generators are used in chemical

plants, refineries and cogeneration plants to produce the steam for both power

generation and plant internal consumption. Therefore, the terms waste heat

boiler and heat recovery boiler are considered synonyms.

The thermal efficiency of the steam cycle strongly depends on the HRSG’s

thermal design. For each selected gas turbine, a compatible design of a steam

cycle with a combination of HRSG and a steam turbine is required. These facts

demonstrate that the HRSG is one of the most critical equipment in a combined

plant and must be carefully designed. It should be considered when designing

an HRSG, the total cost would be very high, if the main target were to maximize

the thermal efficiency. Therefore, economic considerations play a very

important role in the design of HRSGs.


4

Fig. 1.1: Schematic diagram of a combined cycle power plant [11]

1.1. Brief description of combined cycle and cogeneration plants

Gas turbines are used in both combined cycle and cogeneration plants as an

important component. A gas turbine not only produces power, but also

supplies the thermal energy for the heat recovery boiler to produce steam.

Fig. 1.1 shows the general arrangement of an unfired HRSG. Nowadays, big

combined cycle plants are designed to produce hundreds of megawatts.

Refineries, chemical plants and many process plants use HRSGs to supply steam

in cogeneration plants.

Considering the improvement of gas turbines, developing HRSGs and also the

thermodynamic combination of the Brayton and Rankine cycles (including gas

turbine, HRSG and steam turbine) provides the most efficient electricity

generating system that is available now.

Focusing on the thermodynamic aspect, a combination of Brayton and Rankine

cycles leads us to thermal efficiencies above the 45% level that was the

maximum limit of the efficiency previously reached in large thermal power

plants. Both oil and natural gas could be fired in gas turbines. Similar to thermal

power plants, it could be expected that fuel supply is uncomplicated in a

combined cycle power plant.


5

To sum up, combined cycle plants have a number of advantages that are

summarized below:

- Combined cycle plants have short start-up times.

- Combined cycle plants can be built in shorter time than a large coal-fired

power plant.

- Combined cycle plants have higher efficiencies. They may exceed 60%.

- Emissions of NOx and CO are very low.

- Due to higher efficiencies and the small ratio of a Rankine cycle power to

total power output, cooling water requirements are lower. Cooling water

is not required for the Brayton cycle.

- Nowadays, large-capacity combined cycle plants are feasible.

Several gas turbine systems are available on the market. Hence, design

development and adaption of the HRSG design to a gas turbine is still an

attractive subject for research and development.

1.2. Heat recovery steam generator (HRSG)

A heat recovery steam generator is an inevitable part of a combined cycle and a

cogeneration plant.

Also, these steam generators are used in refineries, chemical plants and process

systems as waste heat boilers. Generally, these boilers have a similar function.

But, the main difference is based on whether the boiler is used for heat

recovery and steam production or for the process purposes such as cooling

waste gas or heating the process streams. Fig. 1.2 and 1.3 show the general

view of an HRSG including the inlet duct, heating surfaces, drum, stack, etc.


6

Fig. 1.2: Heat recovery steam generator [12]


7

Fig. 1.3: Heat recovery steam generator [13]


8

In combined cycle plants, natural gas is the main fuel burned. Therefore, clean

flue gas is expected. In general, water tube boilers with extended surfaces are

used for heat recovery and steam production. The range of inlet gas

temperatures of HRSGs varies from 700 to 950 K and flue gas pressure typically

is a little higher than atmosphere pressure. Both flue gas temperature and

pressure are the main and most important constraints that have to be

considered in the design of an HRSG. Fig. 1.4 shows the cross sectional view of a

double pressure HRSG with supplementary firing. Fig. 1.5 illustrates the top view

of an HRSG. It shows that steam enters the drum via riser tubes and riser

manifolds.

Fig. 1.4: Cross sectional view of a heat recovery steam generator [14]


9

Fig. 1.5: Top view of a heat recovery steam generator [15]


10

1.3. Individual design of an HRSG

On the recent market, there are several gas turbine systems that are

standardized. But, HRSG are expected to be designed individually for each CCPP.

The reasons include the following:

- The fuels are varied. Therefore, requirements of the relevant flue gas

should be considered in the HRSG design.

- Cycle optimization differs in the CCPP.

- Ambient conditions change and affect the GT output.

In CCPPs, HRSGs are always designed individually. However, various parts of an

HRSG are standardized for easy construction. But, HRSG design and optimization

is still an important item in CCPPs.

1.4. State of the art

Many authors have optimized CCPPs and defined optimal operation parameters

for HRSGs [1-6]. Franco and Russo [3] proposed a method based on hierarchical

strategy for optimization of HRSG operating parameters and efficiency

increasing of CCPP. Valdés et al. [5] carried out a thermoeconomic optimization

by considering the HRSG’s thermodynamic parameters as variables. Also, Valdés

et al. [6] conducted a thermoeconomic optimization of a CCPP using genetic

algorithms by considering the HRSG’s thermodynamic parameters as

optimization variables. Valdés et al. [7] performed an optimization of a CCPP

focusing on the operating parameters of the HRSG. Franco and Giannini [8]

developed a method for HRSG optimization focusing on decreasing draft loss

and increasing compactness based on a hierarchical strategy.

Manassaldi et al. [9] proposed a method to optimize the HRSG design based on

maximization of the net power, ratio between net power and material weight,

and net heat transfer. Durán et al. [10] proposed a method for developing the

design of an HRSG, which has three sections (economizer, evaporator and one

superheater) by obtaining a small heat transfer area and low pressure losses.


11

The cost optimization of an HRSG is always an important and more difficult topic

than the above-mentioned studies. The work reported here, considers cost

optimization and provides a comprehensive thermal design of an HRSG. A

genetic algorithm (GA) is used as the optimization tool. Because of the required

high steam temperature at the inlet to the steam turbine and the desired

control of this steam temperature, steam should be superheated in two

superheaters and spray water should be injected between them to control the

outlet steam temperature. In this work, four sections (two superheaters,

evaporator, and economizer) are considered for the HRSG design similarly to

the actual and existing HRSGs in power plants.

The contributions of this work can be summarized as follows:

- A comprehensive program using visual basic was developed for the

thermal design and cost optimization of an HRSG.

- A genetic algorithm was applied to the optimization module.

- The best values of pinch point and approach point were determined after

optimizing the HRSG.

- The best values of parameters and an optimal HRSG arrangement were

determined after minimizing the cost of HRSG.

- All geometric parameters in each HRSG section, including tube diameter,

tube arrangement (staggered or in-line), transverse pitch, longitudinal

pitch, number of tube rows, number of tubes on the circumference of

header, fin height, fin thickness, fin density, fin type (solid or serrated),

segment width, steam velocity and approach point were selected as

variables of optimization.

- Flue gas draft loss, steam and water pressure drops, tube wall

temperatures, fin metal temperatures, pinch point, approach point,

allowable gap between fins and the overall dimensions of the HRSG have

been set as the main constraints.

Chapter 2 Thermoeconomics and cost balance of HRSGs

12

CHAPTER 2

2. Thermoeconomics and cost balance

of HRSGs

Thermoeconomics and the cost balance of HRSGs are presented in this chapter.

2.1. Economic analysis In thermal design projects, major costs (including capital investment, fuel cost,

cost of final product, etc.) shall be estimated properly [16]. In this regard,

various predictions, assumptions, and constrains such as technical

requirements, economic aspects and engineering techniques that are related to

the system must be considered by designers. Usually, the cost of the final

product is the main and most important factor that affects the thermal design

of a system or system component. The cost of each item is defined as the

amount of money that has to be paid to purchase or produce it. Considering


13

the competition on the market, minimizing the product cost is the target of the

overall analysis.

The market price of any product is affected by various factors such as

production costs, supply, demand, regulations and competition.

During the thermal design of a system or component, designers need to

consider the market price to optimize the design.

The total costs of a system or component is split into fixed costs and variable

costs.

Fixed costs mean those costs that are not related to the production rate. For

instance, insurance, depreciation and maintenance belong to the fixed costs.

On the other hand, variable costs mean those costs that are related to the

volume of output. Cost of material, fuel and electric power belong to the

variable costs. Accurate cost estimation would be the main issue and key factor

of a successful design to compete on the market. As a main rule in economic

considerations, cost estimation should be considered in all steps of the system

design.

After finalizing the design of the whole combined cycle plant (or cogeneration

plant), all thermodynamic parameters of the components are obtained. In a

CCPP, steam is the product of an HRSG. This work focuses on the cost

estimation and optimization of the HRSG product.

2.2. Thermoeconomics

Thermoeconomics is a branch of engineering that uses both exergy analysis and

economic principles to provide a cost-effective system [16]. The end user needs

to know the real cost of the product for a desired investment and competition

on the market. Thermoeconomic analysis can be considered for the entire

system or a single component. The output of thermoeconomics will be the

calculation of product cost, understanding the cost formation process and

optimizing the variables that belong to the component.

Principally, cost accounting of a system is conducted as follows:


14

- determining the actual product cost

- defining a reasonable and rational basis for pricing

- defining means of allocation and control of expenditures

- defining the information on which operating decisions may be based and

evaluated

In an economic analysis, a cost balance is defined by:

(1)

A cost balance shows that the cost rate associated with the product is equal

to the sum of fuel cost rate , the cost rate associated with capital investment

and the cost rate associated with operating and maintenance .

Fig.2.1: Schematic diagram of a combined cycle plant

2.3. Cost balance of HRSGs Product cost accounting is part of the economic evaluations conducted for a

system. This work focuses on the economic optimization of the HRSG. Fig. 2.1


15

shows the schematic diagram of a CCPP. The HRSG is separately optimized for

cost. For an HRSG operating at steady state, the exhaust flue gas of the gas

turbine and the feed water are the two entering material streams, while the

exhaust flue gas of the HRSG and the steam are the exiting material streams.

Exergy costing was applied to the HRSG. The cost rate associated with each

exergy stream is given by:

, (2)

where is the cost rate, is the average cost per unit of exergy, is the rate

of exergy transfer, is the mass flow rate and is the specific exergy of the

stream . Equation (3) shows the cost balance applied to the HRSG. The sum of

the cost rates related to the exiting streams is equal to the sum of the cost rates

related to the entering streams plus the contribution of the capital investment

as well as operating and maintenance costs, denoted by and

respectively.

(3)

(4)

For the required auxiliary relation, equation (5) was chosen appropriately

(5)

Therefore, the average cost per unit of exergy for the product stream is:

(6)

The exergy of the stream entering the HRSG is provided by the combustion

chamber. By charging all investment and maintenance costs associated with the


16

gas turbine system and the costs of all exergy destructions within this system to

the net power generated by the same system, we obtain

(7)

Thus

(8)

In a specific application, the parameter , the average cost of fuel (e.g. natural

gas) is given. Also, after selecting a gas turbine system from the ones available

on the market, and are also given. The value of the parameter (and

) is usually provided by the company placing the order for an HRSG. The fuel

of the HRSG is supplied by the gas turbine and the product of the HRSG is fixed.

In addition, the cost of operation and maintenance is more or less fixed. These

facts lead us to focus on the minimization of the capital investment of the HRSG

as a target of the cost optimization.

Chapter 3 Thermal design of HRSG sections

17

CHAPTER 3

3. Thermal design of HRSG sections

For the desired cost optimization of the HRSG, the thermal design needs to be

carried out as accurately as possible. The thermal design simulation and the

heat transfer calculation of the HRSG are explained in this section.

3.1. Thermal design demand

HRSGs are used to absorb the maximum thermal energy and produce an

expected amount of steam for maximum recovery. HRSG design is a very exact

work which cannot be revised or corrected by additional considerations. In case

of any probable error, heating surfaces cannot be added to reach the expected

efficiency or defined output of steam generation. Hence, any fault should be

avoided in the design of the HRSGs. These facts lead us to focus on the accurate

thermal design of the HRSGs.

Some reasons that explain the importance of the HRSG design are given below:


18

- In case of any fault in the HRSG’s thermal design, a lot of heating surfaces

needs to be added to reduce the flue gas temperature and this is not

feasible.

- Inserting additional heating surfaces in the designed space is difficult.

- GT back pressure is given by GT manufacturer and needs to be limited to

never affect GT performance. Any additional heating surface or changing

the heating surface arrangements may increase the flue gas pressure

drop and affect the performance of the whole system.

- In general, the cost of the HRSG which is a very important component of

the CCPP is very high. Unreasonable design will unnecessarily increase

the cost of HRSG.

Apart from the above mentioned points, there are several reasons for the

importance of HRSGs thermal design when comparing the designs of HRSGs and

fired boilers. Some of these reasons are listed below:

- In unfired HRSGs, there is no luminous radiant heat transfer. But,

nonluminous radiation needs to be considered between the tubes.

- In HRSGs, it is necessary to use finned tubes for better heat transfer.

Consequently, the pressure drop would be higher in the HRSGs rather

than the fired boilers. Hence, there are many restrictions for the HRSG

design.

- Apart from the tube diameter and tube arrangement, different

parameters such as fin type, fin spacing, fin thickness and fin height

should be considered in the thermal design of HRSGs.

- Apart from tube material, fin material and fin temperature need to be

checked carefully.

3.2. HRSG temperature profile, pinch point and approach point

The starting point in the thermal design of an HRSG is the evaluation of its

steam generation and temperature profiles of the gas and steam. Due to the

low inlet gas temperature (700 - 950 K in an unfired HRSG) and the large ratio of


19

gas to steam flow, the thermal design of an HRSG would be different than that

of fired boilers. In this regard, the flue gas exit temperature is an important

factor for the HRSG. Due to the low temperature of the gas entering the HRSG,

less steam will be generated than in conventional steam generators with the

same gas flow. Therefore, the economizer duty in the HRSG will also be low. To

generate as much steam as possible, the HRSG should be designed to absorb

the maximum heat from flue gas.

In thermal design of the CCPP, the requirements of the HRSG are provided by

the plant designers. Steam generation capacity, operating parameters and

expected efficiency of the HRSG are usually provided by the company placing

the order for an HRSG. All of these parameters ned to be guaranteed by the

HRSG designers.

Fig. 3.1 shows the temperature profile of the HRSG. Comparing the HRSG

sections (superheaters, evaporator and economizer), the superheater

temperature profile can be obtained easily. The steam flow and the steam inlet

and outlet temperatures are specified. Therefore, the heat capacity of the

superheater, and consequently the inlet and outlet temperature of the flue gas

can be calculated easily.

Downstream the superheaters, the next stages of gas cooling are in the

evaporator and the economizer. Focusing on the temperature profiles of the

evaporator and economizer, the definition of two important variables that are

known as “pinch point” and “approach point” is very important. The pinch point

is the difference between the gas temperature leaving the evaporator and the

saturated steam temperature. The approach point is the difference between the

saturated steam temperature and the temperature of the water leaving

economizer. Selection of these two variables extremely affects the evaporator

and economizer size and also their specifications. Both pinch point and

approach point could be considered the most important parameters in the

thermal design of an HRSG. For a specified thermal performance, a bigger pinch

point leads to a smaller evaporator and a bigger economizer. On the other hand,

selecting a larger approach point leads to a bigger evaporator and smaller

economizer. In this regard, selecting the optimal values for pinch and approach

point is one of the most important objectives that needs to be considered by


20

designers. After selecting pinch point and approach point, the HRSG can be

designed and the surface areas of the HRSG sections are determined.

Fig. 3.1: Temperature profile in the HRSG

3.3. Necessity of using finned tubes

When comparing fired boilers to heat recovery steam generators, it becomes

obvious that an HRSG absorbs heat from the flue gas with medium temperature.

Consequently, a large amount of heating surface is required for steam

generation and steam superheating. It is not possible to design an HRSG with

plain tubes. Nowadays, finned tubes with closely spaced fins are the best

solution for the thermal design of HRSGs. Using finned tubes and considering a


21

counter flow arrangement are suitable features for the thermal design of the

HRSGs.

Figs. 3.2 and 3.3 show two types of finned tubes (with serrated and solid fins)

that are used in HRSGs. Comparing the serrated and solid fins, serrated fins

provide more heating surface and also a higher heat transfer coefficient (at the

same size). But they are suitable for clean gas that doesn’t contain particles.

Particles extremely reduce the heat transfer in tubes with serrated fins. Also,

the pressure drop of the gas is higher with serrated fins. Considering the higher

performance of serrated fins, most of the HRSGs are built with serrated fins.

But, the fin tip temperature and also the pressure drop need to be controlled

exactly. Solid fins are used for various gases. Fin cooling works better with solid

fins and the gas pressure drop is lower, too.


22

Fig. 3.2: Tube with serrated fins [17]

Fig. 3.3: Tube with solid fins [17]


23

3.4. Thermal design simulation of the HRSG sections

In order to simulate the performance of an HRSG, the LMTD method

(logarithmic mean temperature difference) has been used to calculate the heat

transfer in each section (superheaters, evaporator, and economizer). Both

convective and radiation heat transfers are considered in the thermal design of

each section. The geometric parameters of the finned tubes including outside

tube diameter, tube arrangement (staggered or inline), number of tube rows,

number of tubes on the circumference of a header, fin density, fin height, fin

thickness, fin type (solid or serrated fin), segment width, as well as steam

velocity inside the superheater tubes and the approach point are the variables

of optimization. The gas pass width and gas pass length needs to be the same

for all components. Therefore, the effectiveness-NTU method and an iteration

loop are considered for achieving the same length for all components.

Fig. 3.4: General arrangement of HRSG

https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwiZ68e1_6jSAhWFJSwKHadiCHkQFggaMAA&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLogarithmic_mean_temperature_difference&usg=AFQjCNE7XyUG9QEqdFNAYH1TJ-VYGAb6Yw&bvm=bv.148073327,d.bGg


24

3.4.1. Input data

The following input data are provided for the heat transfer calculations:

- Flue gas conditions including the mass flow rate, chemical composition, inlet

pressure and inlet temperature; the expected outlet temperature or

minimum required thermal efficiency of the HRSG is obtained from the

thermodynamic optimization of the CCPP and is used as the main

requirement and guaranteed variable of HRSG.

- The inlet water conditions are provided as input data including the mass flow

rate, inlet pressure and inlet temperature.

- The steam outlet conditions including the mass flow rate, temperature and

pressure are also provided.

3.4.2. Water, steam and flue gas properties

- Correlations and data taken from publications by the international

association for the properties of water and steam (IAPWS) [18] have been

used to calculate the water and steam properties. An individual module is

provided in the program to calculate water and steam properties like density,

specific heat, conductivity, viscosity, and enthalpy.

- Correlations taken from “The properties of gases and liquids” *19] have been

used to calculate flue gas properties. An individual module within the

program is provided to calculate flue gas properties like specific heat,

conductivity, and viscosity.

- An individual module within the program is provided to calculate the

enthalpy of flue gas based on ASME PTC4 [20].

3.4.3. Assumptions

Some assumptions for simulating an HRSG are given below

- Heat loss to environment is negligible.


25

- Finned tube specifications are considered based on the production

capabilities (such as length and diameter of finned tube).

- Metal properties are taken from ASME Sec. II [21].

- ASME Sec. I is used for tube wall strength calculations [22].

- Considering the erection requirements, width and length of all sections will

be the same.

- The maximum spray water flow will be 5% of the HRSG steam capacity.

3.4.4. Overall heat transfer coefficient of HRSG sections

The LMTD method has been has been taken into consideration for the heat

transfer calculation and the thermal design simulation based on following

equation:

(9)

with

⁄ (10)

In order to minimize the capital cost, the heat transfer calculations shall be

conducted as accurately as possible. The overall heat transfer coefficient of each

section is defined by the following equation [23]:

⁄ (11)

Considering the necessity of equal length and width of all four sections, the

required number of tube rows in flue gas direction would be non-integer and

need to be rounded accordingly. In this case, the effectiveness-NTU method is

used for rounding the number of tube rows. Details on the effectiveness-NTU

method and relevant calculations are given by Rohsenow [24] and Holman [25].


26

Considering the use of finned tubes in all sections of the HRSG, the calculation

of the overall heat transfer coefficient would be more complicated than that for

bare tubes. Fin efficiency plays an especially important role in the overall heat

transfer coefficient. There are various methods for calculating the outside heat

transfer coefficient of finned tubes. Both convection and radiation heat transfer

coefficients are considered in the calculation of flue gas heat transfer

coefficient. Annaratone [23] proposed a methodology for the calculation of the

finned tube heat transfer coefficient. Also, Manassaldi et al. [9] have used the

same method to calculate the overall heat transfer coefficient. Calculation of

the inside and outside heat transfer coefficients are presented in sections

3.4.4.1 and 3.4.4.2.

3.4.4.1. Average inside heat transfer coefficient

The average inside heat transfer coefficient is defined by the following equation

[24]:

(12)

The Reynolds number is obtained by the following equation

(13)

3.4.4.2. Average outside heat transfer coefficient

Both convection and radiation heat transfer coefficients are considered in the

calculation of the average outside heat transfer coefficient [23].

(14)

Figures 3.5 and 3.6 illustrate the geometry and arrangement of serrated and

solid finned tubes.


27

Fig. 3.5: Fin tube specification [26]

Fig. 3.6: Fin tube arrangement [26]

The average outside convection heat transfer coefficient is calculated by the

following equation [23], [26]:

(15)

For serrated fins, the coefficients are obtained from equation (16).


28

(16)

The coefficient has been calculated for inline and staggered arrangement by

equations (17) and (18) respectively.

(17)

(18)

Moreover, equations (19) and (20) are used to obtain coefficient for inline

and staggered arrangement respectively.

(19)

( ) (20)

For solid fins, coefficient is obtained from equation (21)

(21)

Equations (22) and (23) present the correlations to obtain coefficient for

inline and staggered arrangements respectively.

(22)

(23)

Also, equations (24) and (25) are considered to obtain coefficient for inline

and staggered arrangements respectively.


29

(24)

( ) (25)

In this regard, the Reynolds number is calculated with equations (26), (27) and

(28).

(26)

(27)

(28)

As per equation (11), fin efficiency is calculated to obtain the overall heat

transfer coefficient. The efficiency of serrated fins is calculated with equations

(29) – (34).

(29)

(30)

(31)

(32)

(33)

(34)

For solid fins, fin efficiency is obtained from equations (35)-(37)

(35)

(36)


30

(37)

The average outside radiation heat transfer coefficient [26] is calculated with

equation (38)

(38)

The mean radiating length ( ) is obtained from equation (39). Fig. 3.7

illustrates the correction factor of the mean radiating length ( )

(39)

Fig. 3.7: Correction factor of the mean radiating length [26]


31

Also, Fig. 3.8 shows the outside radiation factor ( ). and are obtained

from equations (29) and (30). Both temperatures should be calculated in

Fahrenheit.

Fig. 3.8: Flue gas radiation factor [26]

3.4.5. Pressure drop across fin tube bundle

The flue gas pressure drop is a main constraint of the HRSG thermal design [9].

A relatively high allowable flue gas pressure drop leads to a lower heat transfer

area and lower costs. Equation (39) was used for the calculation of the flue gas

pressure drop across a fin tube bundle [26].

(39)


32

For serrated fins, the factors and were obtained from equations (40) and

(41):

(40)

(41)

Coefficient was calculated for inline and staggered arrangement with


⁄

⁄

(42)

⁄

⁄

(43)

Also, equations (44) and (45) were used to obtain the coefficient for inline

and staggered arrangement respectively.

⁄ (44)

⁄

⁄

(45)

For solid fins, factors and was obtained from equations (46) and (47):

(46)

(47)


33

Coefficient was calculated for inline and staggered arrangement with


⁄

⁄

(48)

⁄

⁄

(49)

Equations (50) and (51) were used to obtain the coefficient for inline and

staggered arrangement respectively.

⁄ (50)

⁄

⁄

(51)

For both serrated and solid fins, factor was obtained from equations (52) and

(53)

(52)

(53)

3.4.6. Pressure drop in the tubes The pressure drop in the tubes [27] is obtained from equation (54)


34

(54)

The Colebrook equation is often used to calculate the friction factor in turbulent

flow [16].

√

⁄

√ (55)

Also, the friction factor has been developed by Moody [28]. Fig. 3.9 illustrates

Moody’s friction factor diagram

Fig. 3.9: Moody’s friction factor diagram [24]

Ref. [24] presents Moody’s friction factor correlation as equation (56)

(56)


35

Total resistance coefficient is obtained from equation (57)

(57)

where

Equation (58) is used to calculate the bends resistance coefficient

(58)

Friction coefficient ( ) and resistance coefficient for a 90° bend ( ) are

illustrated in tables 3.1 and 3.2 respectively

Table 3.1 Friction coefficient ( )

Tube diameter (mm)

Tube diameter

(mm)

15 0.027 65, 80 0.018

20 0.025 100 0.017

25 0.023 125 0.016

32 0.022 150 0.015

40 0.021 200, 250 0.013

50 0.019 300,400 0.012


36

Table 3.2 Resistance coefficient for a 90° bend ( )

⁄

⁄

1 8

1.5 10

2 12

3 14

4 16

6 20

Chapter 4 Constraints in the thermal design of HRSGs

37

CHAPTER 4

4. Constraints in the thermal design of

HRSGs

There are several important constraints in the thermal design of HRSGs. All

constraints limit the design of an HRSG. The main constraints to the thermal

design and optimization of HRSGs are explained in this chapter.

4.1. General description of the constraints

In combined cycle power plants, the flue gas exiting the gas turbine passes

through a heat recovery steam generator. To describe this briefly, there are two

separate steps of power generation in combined cycle power plants. Firstly, a

gas turbine generates power. Then, the exhaust gas of the gas turbine passes

through the heat recovery steam generator to generate steam for the steam


38

turbine. The steam turbine is the second stage of power generation in combined

cycle power plants. Therefore, the heat recovery steam generator connects the

gas and steam turbines and needs to follow all requirements of both.

The heat recovery steam generator is located behind a gas turbine. Therefore, it

must never create unacceptably high resistance to the gas cycle. In general, a

heat recovery steam generator must never affect the performance of the gas

turbine. On the other hand, a steam turbine is located behind the heat recovery

steam generator. Therefore, the requirements of the steam cycle must also be

fulfilled by the heat recovery steam generator. Satisfying the requirements of

both the gas and steam cycles is very important. In this chapter, general

constraints and thermal design limitations of such a heat recovery steam

generator are described.

4.2. Constraints

In the thermal design of heat recovery steam generators, there are many

important constrains that have to be considered together. The main constraints

of the HRSG thermal design and optimization are described in the following.

4.2.1. Allowable draft loss of the flue gas

The draft loss of the heat recovery steam generator is the main and most

important constraint that needs to be satisfied properly. The performance of

the gas turbine significantly depends on the back pressure. Each gas turbine

manufacturer specifies the maximum allowable back pressure behind gas

turbine. Therefore, optimization shall be carried out in the allowable range of

the flue gas pressure drop. It means that the sum of all pressure drops of flue

gas behind the gas turbine (including the pressure drop in all ducts, dampers,

the heat recovery steam generator and stack) must be less than the allowable

back pressure of the gas turbine. In this regard, the pressure drop in the heat

recovery steam generator that includes the fin tubes is very important and

needs to be calculated properly.


39

To decrease the pressure drop, the compactness of an HRSG needs to be

decreased. Therefore, the cost of the HRSG will increase. Typically, the pressure

of the flue gas leaving a gas turbine is a few mbar above atmospheric pressure

and the allowable back pressure is around 35 mbar. Therefore, finding an

optimum design that meets the back pressure requirements and minimizes the

cost is one of the main targets in the design of a heat recovery steam generator.

4.2.2. Pinch point, approach point and economizer steaming

Fig. 4.1 shows the typical temperature profile of a heat recovery steam

generator. The difference between the flue gas outlet temperature in the

evaporator and the saturated steam temperature is defined as the pinch. Also,

the difference between the economizer water outlet temperature and the

saturated steam temperature is defined as the approach. These two

temperature differences play a very important role in the thermal design of heat

recovery steam generators. Selecting the best and reasonable pinch and

approach points is one of the main constraints and limitations for designers.

The pinch point can affect the capacity of steam production. By decreasing the

pinch point, steam production can be increased. But the heat transfer surface

will increase as well and, therefore, the cost of the heat recovery steam

generator will increase too. Focusing on the approach, this value affects heat

absorption in the economizer. In the thermal design of an economizer, steam

generation must be prevented in it. An appropriate approach point needs to be

considered by designers to prevent steaming in the economizer. On the other

hand, this value limits the heating surface of economizers. If we consider a

specified amount of steam generation in a heat recovery steam generator, the

sum of the pinch and approach points will be constant.

If the pinch point decreases, the approach point needs to be increased

accordingly. This means a bigger evaporator and a smaller economizer need to

be provided. Considering the concept of the heat transfer in the evaporator and

a constant value of saturated steam temperature, the cost of the evaporator

can be increased significantly.


40

If the pinch point increases, the approach point needs to be decreased

accordingly. This means a smaller evaporator and a bigger economizer need to

be provided. But, with a larger heat transfer surface of the economizer,

steaming might occur in the economizer. To reduce the cost, designers prefer to

decrease the approach point and increase the pinch point. But steaming in the

economizer must be prevented and the flue gas pressure drop needs to be

checked. Considering the concept of heat transfer in evaporator and

economizer, heat recovery in an economizer is cheaper than heat absorption in

an evaporator. Optimizing both pinch point and approach point is a very

important design consideration.

Fig. 4.1: Typical temperature profile of an HRSG [29]

4.2.3. Overall dimensions of the heat recovery steam generator

The overall dimension of the heat recovery steam generator is an important

constraint that has to be considered in the thermal design of an HRSG. This

constraint affects the optimization. In this regard, the length of the fin tubes (or

height of the HRSG) is very important. Firstly, finning capability (the maximum

possible length of the tubes that can be finned) shall be considered.

Moreover, pre-requirements of the natural water circulation need to be

considered in optimization. The static head of the water depends on the height


41

of the steam drum. Therefore, a minimum acceptable height of the HRSG needs

to be considered to meet the requirements of water circulation. Consequently,

the minimum height of the heat recovery steam generator or the length of fin

tubes is considered as an important constraint to satisfy natural water

circulation. Also, maximum acceptable height of the HRSG is considered as a

constraint of the optimization.

Apart from the height of the HRSG, the width of the HRSG needs to be

considered as an additional dimensional constraint. In general, the ratio of the

height and width of the HRSG is very important. There are various

recommendations for the ratio of height and width of heat recovery steam

generators. This ratio prevents any unusual configuration of the heat recovery

steam generator. Therefore, a maximum and a minimum width of the HRSG are

considered as further constraints to achieve dimensions acceptable in an HRSG.

4.2.4. Steam and water pressure drop

The pressure drop of the steam is an important constraint to the thermal design

and optimization of the superheaters. The total steam pressure drop in both

superheaters needs to be limited during optimization. According to the design

judgment and relevant recommendations, the total steam pressure drop in the

superheaters needs to be less than ten percent of the drum pressure. The

allowable steam pressure drop limits the selection of tube diameter and also

the possibilities for tube arrangement in the relevant headers. By increasing the

steam pressure drop, the working pressure will be increased too. However, a

higher drum pressure affects the strength calculation of the HRSG and the

thickness of the drum and pressure parts will consequently increase.

Similar to the superheaters, the economizer water pressure drop needs to be

limited in thermal design and optimization. A high water pressure drop may

increase the water inlet pressure and also the design pressure of the

economizer.

In this work, the “number of tubes on the circumference of a header” has been

considered as a variable of optimization to satisfy the constraints of steam and

water pressure drop.


42

4.2.5. Constraints of the finning (fin tube manufacturing)

In the design of a heat recovery steam generator, finning capabilities (fin tube

manufacturing) shall be considered as an important item. By the modern high

frequency fin tube machines, finning of tubes from 1” to 8” is possible.

However, the maximum tube diameter used in HRSGs is 2.5”. Apart from tube

specifications, fin specifications affect the fin tube performance extremely. In

this regard, fin height, fin thickness and fin density would be in the ranges of 9 -

38 mm, 0.8 - 2.6 mm and 1 - 8 fins per inch, respectively. Two types of fins, solid

or serrated, are used in the thermal design of an HRSG. Depending on the fin

tube metal temperature, both carbon steel and alloy steel could be used for fin

tubes.

4.2.6. Fin tube limitations

The hot flue gas passes through fin tubes in a heat recovery steam generator.

Therefore, the metal temperatures of fin and tube are very important. As a

critical point, the fin tip is the hottest point of the fin tube and the fin tip

temperature is important in thermal design and optimization. The fin tip

temperature needs to be checked during optimization to prevent the fin from

burning. Fin material is selected based on the fin tip temperature. The allowable

working temperatures of the alloy steels are higher than the allowable working

temperature of carbon steel. But alloy steels are more expensive than carbon

steels.

A higher fin density or lower tube pitch could increase the rate of heat transfer.

But the metal temperature of both fin and tube will increase too.

All fin specifications and data including fin height, fin thickness, fin density and

fin type will affect the heat transfer, pressure drop of the flue gas and fin tube

temperature. Therefore, all parameters are considered optimization variables.

Comparing solid and serrated fins, serrated fins provide higher heat transfer

coefficient and pressure drop at the same specifications. But there are some

limitations to using serrated fins for a flue gas with high fouling resistance.

Considering the existing clean flue gas, usually provided through combustion of


43

natural gas, designers prefer serrated fins in heat recovery steam generators.

But, the pressure drop and fin tube metal temperature need to be checked.

Even with clean flue gas, the fouling factor needs to be considered in thermal

design and heat transfer calculation. In this regard, an appropriate minimum

gap between the edges of two fins of the finned tubes close to each other needs

to be considered too.

4.2.7. Maximum spray water flow

A desuperheater injects water between two superheaters to control the steam

outlet temperature. When injecting a large amount of water, the overall

efficiency decreases and a bigger desuperheater needs to be selected.

Therefore, the cost will increase. Also, the turn down ratio of the desuperheater

is very important. For an appropriate optimization, maximum spray water flow

is limited to 5% of the total steam flow.

Chapter 5 Optimization and genetic algorithm

44

CHAPTER 5

5. Optimization and genetic algorithm

In this work, both thermal design and optimization of HRSGs are studied. A

general description on optimization, methods of optimization, the genetic

algorithm and also the background of using the genetic algorithms are explained

in this chapter.

5.1. Introduction to optimization

Basically, optimization is not a new concept. Normally, we try to optimize by

looking to obtain the largest possible amount of goods or output per unit of

expenditure. This is what drives us in our daily lives. It would be preferable to

get the maximum output or product with the least amount of work. The price of

various consumer goods like televisions, automobiles, also advertisements,

engineering work and even education per dollar spent, is often offered to


45

provide a measure of related cost-effectiveness. Thus, a buyer of a big power

plant will use the available information for the best choice for their money.

The necessity of optimization is similarly very important in the design of thermal

systems. Nowadays, optimization has become crucial in engineering works and

the design of a thermal system. In modern systems, it is not enough to achieve

only a workable or feasible thermal system that provides the desired tasks,

meets requirements and follows the given constraints. At least, it is expected

that several workable designs be generated and the finally selected design

would be the one that appropriately minimizes or maximizes the requirements.

In general, many competing factors affect the performance and cost of a

system. If we consider that the governing parameters, which specify a system,

are varied, then the optimum design can often be achieved in quantities such as

capital cost, cost per unit of product, power per unit fuel input, efficiency,

energy consumption per unit output, and other features of the system. But,

various characteristics of the system may be of particular interest and the most

important ones may be considered in optimization.

For example, weight is important in airplane design, acceleration in

automobiles, energy consumption in cooling systems, flow rate in a system

pumping water and heat loss in insulation. Therefore, these parameters can be

chosen for minimization or maximization. In thermal systems, minimizing cost

and maximizing efficiency are usually the goals of the optimization.

Acceptable designs will be obtained from the allowable ranges of the design

variables by meeting the expected requirements and staying within the

constraints.

In general, different designs of a system could be achieved for the same

requirements and no unique solution results as a final design.

On the other hand, a designer tries to find the best solution by optimizing in

order to minimize or maximize a feature or quantity of particular interest to the

application. Local optima can be found at different points in the area of

acceptable designs. But, only one global optimum design that specifies the

minimum or maximum of the whole domain is needed.

In optimization, an optimum solution of the application is found and the final

design of the system will be obtained on the basis of this solution.


46

The design variables are generally used to then select more usual sizes,

dimensions, and standard items that are available from a supplier or

manufacturer. For instance, a tube diameter of 30.15 mm is optimal but not

acceptable. Instead, a standard tube diameter such as 31.8 or 38.1 mm is

selected as optimum value.

Also, a safety margin is included to allow for the inaccuracies and uncertainties

in the calculation, simulation and design as well as the probable fluctuations of

the operating conditions and any unforeseen conditions. The optimum solution

has to be in line with the limitations of the fabrication or material. Basically, the

final optimized system will be obtained by involving all the items mentioned. Generally, a system’s hardware affects its optimization extremely. For instance,

arrangement, geometry, dimensions, materials and components are very

important in the optimization of a thermal system. The hardware refers to the

fixed sections of the system, i.e. those components that determine the overall

specifications of the system and cannot easily be varied. On the other hand, the

performance of a system depends on the operating conditions, such as

temperature, pressure, mass flow rate, heat input, etc.

Any cost of the system will affect the final cost of the product, i.e. the cost of

the component. Cost optimization of system components depends on the

component design and needs to be carried out carefully. In this case, the design

parameters of the heat transfer equipment may be considered as objects of

optimization.

In general, these parameters can vary within the system. But, the variations are

within the ranges that are determined by the hardware. Output and incurred

cost of the system could be optimized by defining the best and most acceptable

operating conditions and design parameters of the component.

5.2. Basic concepts

Basic concepts need to be followed to formulate the optimization of a thermal

system. The optimal design needs to meet the defined requirements and stay

within the constraints. Only then will it be considered as a best possible

candidate that is acceptable or workable. The search for an optimal design is


47

carried out in the area of acceptable designs. For instance, if several acceptable

designs of a heat recovery steam generator for a combined cycle power plant

are obtained by applying the design procedures, the best design among them

can be selected on the basis of specified criteria such as cost of the steam

production per unit of heat transfer area or unit exergy of the stream.

Basically, the conceptual design is fixed and a particular one is defined on the

basis of previous experience, environmental impact, available materials, etc.

Therefore, optimization is carried out for a specific conceptual design. Different

conceptual designs could be considered at the first stages of the design process.

However, if no acceptable design is obtained from a specific conceptual design,

the design optimization may be done with another and different conceptual

design.

5.3. Objective function

Any optimization requires specification of a quantity or function that has to be

minimized or maximized. This function is defined as the objective function for

optimization. The objective function shows the aspect or feature that is of

special interest in a given circumstance. Different costs including capital, initial,

maintenance and product costs are the most commonly used quantities that

have to be optimized. Many aspects could be employed in optimization. But, it

depends on the application of the thermal system.

Following characteristics are frequently optimized in thermal systems as an

objective function:

rate of energy consumption

costs incurred

efficiency

product cost

overall profit

heat transfer rate

system performance, output delivered

environmental effects


48

safety

weight, volume

Energy consumption is the most important objective function for thermal

systems and characterizes the efficiency of the system. Usually, it is considered

as energy consumption per unit of the product. Also, it is given in terms of the

energy rating of the system and specifies the power consumption for system

operation under given conditions.

Costs and profits are always important items in system design and optimization.

Economic optimization is one of the usual objectives that are considered in the

optimization of the thermal systems. In this regard, designers try to minimize

the costs or maximize the profits.

The output of the system is also of particular interest in many thermal systems.

However, if the designer wishes to maximize the output such as power

delivered by a power plant, then the associated cost will be increased and

should be an important consideration. Therefore, in many optimizations, the

objective function is defined as output per unit cost. Similarly, other

performance requirements are considered in terms of the unit costs too.

In some cases, the size of thermal systems may be optimized in order to

minimize the required amount of space. Also, efficiency, heat transfer rate,

system performance, safety, weight and several other such aspects are

important in various applications and may also be considered for optimization.

5.4. Optimization constraints

The constraints in a design problem or design optimization problem are related

to the limitations on the ranges of the variables, and to the basic conservation

principles that have to be satisfied.

In thermal systems, restrictions and limitations of the variables may arise due to

material properties, available space, equipment specification, process

specification, limitation, etc.


49

These constraints may restrict the dimensions of the system, the maximum

temperature in which components can operate safely, the allowable flow

pressure drop, mass flow rate, and so on.

For instance, a maximum allowable value of the temperature must be indicated

for the fin tip temperature of the finned tubes to prevent fin damage. Also,

sometimes the minimum acceptable values of the variable or physical

parameters restrict the design. Therefore, both minimum and maximum values

of the design variables need to be indicated. It is clear that the constraints will

limit the domain that is acceptable for design or optimum design of a system.

For instance, in heat treatment of a pressure vessel or HRSG, the minimum

temperature and time which are required for heat treatment will be defined by

relevant standard. On the other hand, the maximum allowable temperature

before the material might be damaged needs to be specified too.

In water tube boilers with natural circulation, a limitation on the height of the

boiler shall be considered to provide the required positive water-side pressure.

In the design of a thermal system, some constraints arise due to the

conservation laws, particularly the mass, momentum and energy conservation

laws. Under steady-state operative conditions, the inlet mass flow into the

system must be equal to the outlet mass flow. This restriction leads designers to

an equation that needs to be satisfied by the relevant design variables.

Therefore, restriction of the variable values may be employed in the

optimization.

Same as with the mass conservation law, energy balance considerations are

very important in the design of thermal systems and might limit the range of

heat flux, allowable temperatures, dimensions of the system, etc.

Usually, various constraints need to be taken into consideration during

modelling and simulation of the system, since the governing equations are

achieved based on the conservation principles. Thus, the optimized objective

function has already taken these constraints into account. In such cases, the

boundaries of the design domain need to be considered as additional

limitations.


50

5.5. Operating conditions and hardware

Optimization can be applied to a system to improve the design based on the

optimization of relevant hardware.

Mostly, optimization will focus on the system design so that the corresponding

hardware, such as dimensions, materials, components, etc. is optimized to

achieve the best and optimum design with respect to the defined objective

function.

But it is clear that performance and characteristics of the system are also

related to the operating conditions. Therefore, the conditions under which the

system performance will be optimized should be defined.

For instance, if the designer wants to maximize the efficiency of a steam boiler,

the boiler operating conditions (such as operating pressure and temperature)

need to be specified (i.e., 100 bar and 450°C respectively), at which this

condition the optimization will be met.

The operating conditions depend on each application and system. Generally, the

variation range of these conditions is fixed by the hardware. Therefore, if a

thermal heater is selected for the design of a furnace, the heat input and

temperature ranges are fixed by the specifications and requirements of the

heater.

In thermal systems, the operating conditions are commonly specified as

following variables:

heat input rate

temperature

pressure

mass flow rate

volume flow rate

velocity

chemical composition


51

Thus, applied temperature and pressure, as well as chemical composition and

the rate of the heat input, may be varied over the allowable ranges for a system,

such as a steam boiler.

The volume or mass flow rate is chosen for a system like a heat recovery steam

generator.

In defining the selected inlet conditions for a chemical reactor, the chemical

composition is very important, for instance in a food extruder where the

moisture content is an important variable.

All mentioned variables specifying the operating conditions of a thermal system

may be fixed at different values within the ranges determined by the system

design and therefore affect the system’s thermal output.

In the optimization of a thermal system, determining the optimum operating

conditions and respectively the corresponding system performance is very

important. In many cases, optimization of the output or performance of the

thermal system is a last target.

5.6. Optimization methods

There are various methods to solve the mathematical optimization problems of

a thermal system. Each method has some limitations and also advantages over

the others. Generally, the selection of the optimization method depends on the

nature of the equations that represent the objective function and also the

constraints of the problem.

It also depends on whether the mathematical modelling is developed in terms

of explicit functions or the objective function (and also constraint’s variation) is

determined by numerical solutions.

Considering the complicated nature of thermal systems and also of relevant

designs, usually numerical solutions of the governing equations are employed

for thermal design and optimization.

However in some cases, detailed numerical results are provided through

modelling a system and are curve-fitted to achieve analytical or algebraic

equations to show the specifications of the system. Then, optimization of the

system design may be undertaken on the basis of these relatively analytical or


52

algebraic equations. The frequently used methods for optimization are

described in the following:

5.6.1. Calculus methods

In calculus methods, optimum determination is based on derivatives of the

objective function and constraints. In these methods, derivatives are used to

show the location of a minimum or a maximum.

In order to form the derivative, the equations or the expressions that formulate

the optimization problem need to be continuous. Therefore, these are

differentiable over the domain of design.

One of the important methods that use calculus for optimization is the method

of Lagrange multipliers. Basically, this method converts the preceding problem

of finding the minimum or maximum into the solution of a system of algebraic

equations, thus providing a way of finding the optimum.

Considering the complexities that commonly arise in the design of thermal

systems, the use of calculus methods for the optimization of thermal systems is

limited.

5.6.2. Search Methods

As the name suggests, these methods select the best solution from a number of

workable and acceptable designs. If just certain fixed values can be chosen as

design variables, the acceptable design may be obtained through different

combinations of these variables. If the variables can be continuously varied

based on their allowable ranges, a finite number of acceptable designs can be

found by this way. In such cases, a series of acceptable designs is found and the

optimum design can be selected from them.

The simplest approach is to calculate the objective function at uniformly spaced

locations of the domain and the optimum value will be selected. This simple

approach, known as exhaustive search, is not appropriate and is an inefficient

method for optimizing complex thermal systems. Therefore, it is not used for

practical optimization of thermal systems. However, sometimes the basic


53

concept of selecting the best design from a set of acceptable designs is used as

an important method especially if a detailed optimization of the system is not

undertaken. In this case, sometimes a non-systematic search for the optimum

design is carried out based on previous knowledge of the system. This method is

known as heuristic search.

In many practical thermal systems, the design variables are not continuous

functions but finite values may be assumed for the design variables over their

acceptable ranges. This matter is related to the limited number of materials and

components available and acceptable for the design of a thermal system. For

instance, finite numbers of components such as pumps, fans, compressors, heat

exchangers are generally available from the manufacturers at defined

specifications. However, in some cases, additional intermediate specifications

can be obtained custom made which are cheaper and more convenient.

Similarly, a finite number of different materials such as diameter and thickness

of the pipes and tubes may be considered for the equipment.

To obtain an acceptable optimum design, modelling, simulation, and evaluation

of the design are required.

To determine the effect of the various design variables on the objective

function, results from the simulation procedures are required and a systematic

searching strategy is necessary. Simulation runs need to be done to get closer to

the optimum design. In this case, any random or unsystematic searches with

many simulation runs carried out over the design domain are very inefficient

and impractical.

Search methods are used for a wide range of optimization problems, from very

simple problems including unconstrained single-variable optimization to very

complicated systems with many constraints and variables. It is clear that search

methods provide desired approaches to find the optimum design of thermal

systems and also to improve existing thermal systems.

In the work at hand, a genetic algorithm is applied as optimization method

which is explained in this chapter.


54

5.6.3. Other methods

Considering the strong need for system and process optimization in the recent

years, various optimization methods have been developed [30]. Many of these

methods are developed particularly for certain applications and may not be

suitable for the optimization of thermal systems.

In this regard, shape, trajectory, and structural optimization methods involve

specialized techniques for the optimization. A finite element method is

frequently linked with the relevant optimization strategy.

Also, a method called monotonicity analysis has been developed for design

optimization which monotonically increases or decreases the objective

functions and constraints. This method focuses on the constraints and the

effects that these have on the optimization.

In the recent decades, various other methods and relevant approaches have

been developed for the optimization of thermal systems and relevant processes

as well.

Among them artificial neural networks (ANNs), fuzzy logic, and genetic

algorithms (GAs) deserve to be mentioned. These methods are based on

artificial intelligence methods that are being developed in the optimization

works continuously.

A brief explanation of genetic algorithms is provided in this section and is

expanded in the next sections. In the field of artificial intelligence, genetic

algorithms are search methods that are based on evolutionary algorithms. The

procedure is similar to evolutionary biology and involves inheritance, selection,

crossover and mutation. The optimization begins with an initial population of

solutions, called individuals, and progresses through generations and fitness

that have been defined by an objective function. All individuals are evaluated

based on the fitness function. Then multiple individuals are selected from the

initial generation based on the degree of fitness and are modified to produce

the next population by using the genetic algorithm operators (crossover and

mutation). This new population is then used in the next generation and the

optimization is continued to the desired optimum point. Regarding other

https://en.wikipedia.org/wiki/Artificial_intelligence


55

methods such as ANN and fuzzy logic, more explanations are available in the

references [30] and [31].

5.7. Genetic algorithms used in the optimization of thermal design

and heat transfer

The use of genetic algorithms is increasing rapidly in the optimization of thermal

systems [32]. In thermal design and optimization at hand, a genetic algorithm

was selected as optimization method. In this section, a quick review of genetic

algorithms and their applications in thermal systems are presented.

The words ‘‘genetic algorithm” was introduced by Bagley [33] and the first

application of a genetic algorithm was published in 1967. Genetic Algorithms

were developed as an optimization method in the 1970s and some work was

done in the field of evolutionary computation. The first main work and use of a

genetic algorithm was done by Holland [34] and De Jong [35] in 1975. Later,

Grefenstette [36], Baker [37] and Goldberg [38] contributed significant

improvements of genetic algorithms in the 1980s. Goldberg published a book on

the application of genetic algorithms. In [39], additional history of genetic

algorithm methods is provided. However, using and applying a genetic

algorithm as an optimization method in the area of thermal design and heat

transfer is more recent. It is probably due to the difficulty and long

computational time of most numerical problems in the field of thermal systems

and the heat transfer community.

In the GA optimization procedure, several simulations typically need to be

performed. But the computational time for the simulation of a design applying

CFD analysis may be too long.

Anyhow, use of genetic algorithms in heat transfer started in the mid-1990s,

and is used more and more regularly nowadays. Researchers of heat transfer

can expect to see a significant increase in the application of genetic algorithms

to many complex problems of thermal design and heat transfer optimization.

Also, with the increasing availability of high performance computers, genetic

algorithms can be used more easily in the optimization of thermal systems.

Gosselin [32] has reviewed the works related to heat transfer, numerical


56

modelling and optimization as well as energy systems in major journals. The

time distribution of the relevant publications is shown in Fig. 5.1.

Gosselin presented the summary of the most important features for the

publications of thermal design problems. Also, it has found that the complexity

of the system modelling varies greatly in the range from simple analytical

equations to advanced CFD.

5.8. Optimizing thermal systems with genetic algorithms

Design and optimization of thermal systems is the first group of heat transfer

problems that have been addressed in literature for applying a genetic

algorithm [32].

Fig. 5.1: Heat transfer related articles using GAs reported in a review [32]

For instance, heat exchangers, heat and fluid flow networks, fin, porous media,

heat sinks, etc.


57

5.8.1. Optimization of systems, converting and transferring energy

Applications of genetic algorithms in optimizing systems for conversion and

transfer of energy, and in particular, thermal energy have been reviewed by

Gosselin [32] too.

He has found that the number of possible designs was typically quite large, and

genetic algorithms were helpful for optimization. In summary, genetic

algorithms have been applied for the design and optimization of heat

exchangers, heat exchanger networks, chemical plants, power plants, heat

transfer problems, as well as of heating, ventilation, air conditioning and

refrigeration systems. The use of genetic algorithms for some thermal systems

and pieces of equipment is described below.

5.8.1.1. Heat exchangers

Heat exchanger design should be adapted well to the entire system. Otherwise

they could not be operated properly and relevant costs would be high. Genetic

algorithms are suitable current optimizing methods for relevant designs.

Usually, correlations and analytical modelling including empirical relations are

used to design heat exchangers and evaluate their performance.

Various objective functions such as minimum cost, maximum heat transfer and

minimum pressure drop have been considered for the optimization with genetic

algorithms based on the best selection of tube diameter, tube pitch, number of

passes, tube arrangement, etc.

For instance, a shell-and-tube heat exchanger designed with a GA by Selbas et

al. [40]: Cost of the heat exchanger was minimized and the variables were tube

diameter, tube pitch, number of passes, shell outer diameter and baffle cut.

Also the capital and operation cost of the shell and-tube heat exchangers has

been minimized with a GA by Wildi-Tremblay and Gosselin [41]. The design

variables were tube pitch, tube arrangement, number of tube passes, baffle

spacing at the center, baffle spacing at inlet and outlet, baffle cut, tube-to-baffle


58

diametrical clearance, outer diameter of the tube bundle, shell diameter and

outer tube diameter.

In [42], the cost of shell-and-tube heat exchanger has been minimized with a

GA. Three design variables (shell diameter, tube diameter, baffle spacing) were

considered. [43] presented a GA to minimize the annual cost (exergetic and

capital costs) of a shell-and-tube heat exchanger. In [44], a plate fin heat

exchanger designed with a GA based on two objectives: the weight and the

operation cost. The NTU per unit of pressure drop of an intercooler and a

regenerator was maximized by a GA in [45].

5.8.1.2. Power generation

Genetic algorithms have been applied to the optimization of power generation

to minimize the cost, maximize performance, etc. Particularly, complex power

plants including various components and energy sources have been designed

and optimized by genetic algorithms. The main objectives of the relevant works

are usually increasing the thermal efficiency and power output and also

minimizing the relevant cost. For instance, Sirikum and Techanitisawad [46]

minimized the overall cost of a power plant expansion applying a genetic

algorithm.

In [47], the values of cooling, heating and power generation have been

maximized by using a GA based on economy, thermal efficiency and emissions.

The gas engine series and number, the gas turbine series and number, the gas

turbine side cold water mass flow share, the hot water supply temperature, the

gas turbine side hot water mass flow share, the pinch floor cooling device and

the cold water supply temperature were the optimization variables.

Gas turbine power plants with single, dual and triple pressure (with and without

reheating) have been optimized using a GA in [48]. Pressures and temperatures

of the cycles were varied by the GAs. Minimizing the energy generation cost and

maximizing the cash flow were two objectives.

In [49], a GA has been applied to maximize the internal efficiency of a steam

turbine. Angle and velocity of flow on different parts of the turbine were the


59

variables. A GA was used to minimize the operation cost of multi-device energy

supplier in [50].

In [51], processes of multi-production plants were optimized with a GA.

Minimizing the energy cost was the objective. Also, a cogeneration plant

optimization was performed with a GA in [52]. In [53], the total electrical power

generated in a cogeneration system was maximized with a GA.

5.8.1.3. Heat exchanger networks (HENs), design integration and

chemical plants

In addition to the thermal design of the heat exchangers as described in section

5.8.1.1, genetic algorithms have been used in design and optimization of HENs

and chemical plants [32]. Usually, the main objectives of the HENs problems are

to minimize the cost or to maximize the energy recovery of the design.

For example, Pettersson and Soderman [54] optimized a heat recovery system

that minimizes the total cost. The total cost was a function of the number of

heat exchangers, heat exchanger areas and the costs of cold and hot utilities.

The design variables were the fluid matches and also the area of the heat

exchangers.

In the design of retrofit large HENs, GAs were used to separate a large system

into smaller subsystems [55]. [56] minimized the cost of structural change for a

fixed hot/cold fluid network topology, and then the cost of exchangers

optimizes with a GA. [57] used GAs for the optimization of HENs. It was

performed to minimize capital cost and energy cost.

In [58], the morphology of a HEN including five heat exchanger layers was

optimized by applying a GA. The HEN with set performance was optimized to

minimize the required utilities. In [59], total exergetic and capital costs

(considering the heat transfer surface) of a HEN have been minimized with a GA.

Both temperature difference and position of the heat exchangers were the

design variables.


60

5.8.1.4. Heating, ventilation, air conditioning and refrigeration

(HVAC&R) systems

Designing heating, ventilation, air conditioning and refrigeration (HVAC&R)

systems and minimizing energy consumption, minimizing cost and maximizing

comfort are the main issues to address with GAs in HVAC&R systems [32].

For instance, [60, 61] minimized the total power required for an HVAC system

by applying a GA. Various design variables were considered such as number of

operating chillers, number of operating chilled water pumps, number of

operating cooling coils, number of conditioned rooms, number of operating

condenser water pumps, number of operating cooling tower fans, temperature

of chilled water supply, temperature of condenser water supply, etc. The

optimal design resulted in 800 kWh saved per day. In [62], the power

consumption in an HVAC system was minimized with a GA.

Energy consumption and predicted percentage of dissatisfaction (comfort zone)

were minimized simultaneously by a GA in [63]. Static duct pressure set point,

chiller water temperature, supply air temperature set point and required reheat

were the parameters determined with a GA. In Ref. [64], the power

consumption of a HVAC system was minimized. In [65], the energy consumption

of an air conditioning system was optimized.

5.8.2. Other applications of genetic algorithms

Various other design and optimization problems have been solved with genetic

algorithms [32].

Various conduction heat transfer problems have been solved by GAs. For

instance, the design of fins with GA was presented in references [66]-[73]. Also,

several design problems based on the heat conduction equation have been

solved with GAs in references [74]-[78]. In references [79]-[91], the designing of

thermofluid systems with GAs has been presented too. Ref. [92] presents the

design of a radiative enclosure with a GA. The difference between desired and

estimated heat flux profile over the designed surface was minimized.


61

Also, several inverse heat transfer problems have been solved with GAs.

Radiation, conduction and convection inverse heat transfer were the topic of

references [93]-[111].

5.9. Description of genetic algorithms

The basic principle of a genetic algorithm was first provided by John Holland

[40]. GAs began to be used in heat transfer determination approximately in the

mid-1990s, timidly at first but more and more regularly nowadays [32]. Genetic

algorithms are based on natural selection as it is known from biological

evolution. Stronger individuals could probably be the winners in a competing

environment. Genetic algorithms use a similar analogy of natural evolution too.

They work under the supposition that a probable solution of a problem is an

individual and can be represented by specified parameters. These parameters

are considered genes of a chromosome. As an advantage, a genetic algorithm

does not require analytical equations of the system. It analyses the system

behaviour based on the fitness value of each individual. Generally, the fitness

value correlates with the objective function of the problem and shows the

degree of “suitability” of each chromosome.

Some advantages of genetic algorithms are given here [112]:

• A genetic algorithm uses the value of the fitness function and doesn’t

require derivative information.

• A genetic algorithm searches within a wide range of samples for cost.

• A genetic algorithm deals with a large quantity of variables.

• Variables with extremely complex cost functions could be optimized by a

genetic algorithm.

• A genetic algorithm obtains a list of optimum variables, not only a single

solution.

• A genetic algorithm can encode the variables, therefore the optimization

could be done with the encoded variables.


62

• A genetic algorithm could work with any numerically generated data,

experimental data, or analytical functions.

5.9.1. Introducing the parameters of a genetic algorithm

A genetic algorithm is based on evolutionary processes, mathematics, and

computer terms. Main components of the genetic algorithm are defined and

explained in the following:

Gene: variables of optimization

Chromosome: an array of genes that is passed on the cost function

Individual: a possible result, a single member of a population that consists of a

chromosome and its cost function

Population: a group of individuals

Generation: one iteration of the genetic algorithm

Objective function: evaluation function of the solutions or the function to be

optimized

GA operators: including selection, crossover and mutation

Selection: the process of choosing parents for reproduction (usually based on

fitness)

Crossover: an operator that forms a new chromosome from two parent

chromosomes by combining part of the information from each

Mutation: a reproduction operator that randomly alters the values of genes in a

parent chromosome

Reproduction: generation with the GA operators or the creation of offspring

Additional terms are defined in the glossary section.

5.9.2. General Description of the genetic algorithm method

A genetic algorithm is one of the evolutionary algorithms that is used in

optimization and is based on the principle of Darwinian selection. In general, the

work of a genetic algorithm can be described in the following steps:


63

- A population of the individuals is randomly generated. The individuals are

obtained by the randomly generated genes.

- All individuals are evaluated by means of the fitness function and are sorted

based on the fitness value.

- GA operators (selection, crossover and mutation) are applied for

reproduction and generation of the next generation. Firstly, most appropriate

individuals (with higher fitness values) are selected as parents of the next

generation. Then, crossover and mutation operators are applied to generate

new generations. The population size of each generation is the same.

- As in the second step, the new generation is evaluated by means of the

fitness function. A new generation is formed by fitter parents. Therefore,

each new generation is expected to be fitter than the previous one.

- The above process is repeated until reaching the ending criteria, such as a

specified number of generations.

A detailed description and explanation of genetic algorithms can be found in

many references such as Goldberg [38] and Bentley [113].

A flowchart of a genetic algorithm is presented in fig.5.2. This flowchart shows a

general overview of a genetic algorithm.


64

Fig. 5.2: Flow chart of a Genetic Algorithm [112]

Chapter 6 Optimization program

65

CHAPTER 6

6. Optimization program

Similarly to most design and engineering projects, providing an accurate and

adequate program is necessary for the thermal design and optimization of

thermal systems. In this work, a comprehensive program has been developed

for the thermal design and optimization of heat recovery steam generators.

Visual basic was used to program it. In many process plants, there is a large

amount of a gas or waste gas that is cooled in a waste heat boiler. The

developed program is suitable for the thermal design and optimization of these

waste heat boilers, too. A general description of the program is provided below.

6.1. Modules of the program

In order to design and optimize an HRSG, the performance of the HRSG needs to

be simulated and the heat transfer will then be calculated accurately. Selecting

the optimization variables is very important in thermal simulation and


66

optimization. All variables that affect the objective function need to be selected

appropriately.

The steam temperature is an important operating condition that has to be

guaranteed by designer. Because of the desired control of the outlet steam

temperature, the steam should be superheated in two superheaters and spray

water should be injected between them to control the outlet steam

temperature. Therefore, four sections (two superheaters, evaporator, and

economizer) are chosen for the HRSG design (similar to actual and existing

HRSGs in power plants). The modules of the program are described below.

6.1.1. Thermal simulation of superheater no. 2

Superheater no. 2 is the first section of the HRSG. High-temperature flue gas

enters this section. Both radiative and convective heat transfer are significant in

this section and need to be calculated accurately. Temperatures of the fin tips,

fin surface and tube walls are the main constraints of this section. Therefore,

accurate calculation of the heat transfer is very important. Especially, the term

of the radiative heat transfer is significant and needs to be calculated accurately

to prevent overheating of the fin tube.

Generally, fin tubes are used in HRSGs for better heat absorption. The steam

pressure drop is the other important constraint that has to be considered in

superheater no. 2.

This module provides complete thermal design, heat transfer calculation,

geometry, arrangement, steam pressure drop, flue gas pressure drop and metal

temperature of both fin and tube. Finally, the cost of superheater no. 2 is

calculated as the main goal and requirement of the optimization.

6.1.2. Thermal simulation of superheater no. 1

Superheater no.1 is the second section of the HRSG. Similarly to

superheater no. 2, high-temperature flue gas enters this section. Therefore,


67

both radiative and convective heat transfer are significant and need to be

calculated accurately.

As explained in previous chapters, the gas pass width and gas pass length of all

sections shall be equal. Fitting superheater no. 1 in the same width and length

of superheater no. 2 is an important constraint of this section.

Moreover, the temperatures of the fin tips, fin surface and tube walls are the

next constraints of superheater no. 1. Similar to superheater no. 2, the radiative

heat transfer is significant and is calculated accurately to prevent overheating of

the fin tubes. Both flue gas and steam pressure drops are the next constraints of

this section.


geometry, arrangement, steam pressure drop, flue gas pressure drop, spray

water flow rate and metal temperature of both fins and tubes. The cost of

superheater no. 1 is finally calculated as the main goal and requirement of the

optimization.

6.1.3. Thermal simulation of the evaporator

The evaporator is the third section of the HRSG and medium-temperature flue

gas enters this section.

Generally, the convective heat transfer is significant, and the radiative heat

transfer is not negligible.

The pinch point is the main constraint of this section. It not only affects the

operation of the HRSG, but may also increase its cost significantly. Therefore,

the pinch point has to be optimized accurately. Fitting the evaporator in the

same width and length as superheater no. 1 is the next constraint of this

section. Moreover, the flue gas pressure drop and the temperatures of the fin

tips, fin surface and tube walls need to be satisfied as another important

constraint.


geometry, arrangement, pinch point, flue gas pressure drop, metal temperature

of both fins and tubes, as well as the investment cost of the evaporator.


68

6.1.4. Thermal simulation of the economizer

The economizer is the last section of the HRSG and low-temperature flue gas

enters this section. Heat transfer is accomplished by convection. Generally, the

radiative heat transfer is negligible and designers don’t consider it in

economizers.

The approach point is the main and most important constraint of this section.

The approach point not only affects the operation of the HRSG, but may also

increase its cost significantly. Therefore, the approach point has to be optimized

accurately. The pressure drop of the water is the next constraint of this section.

The pressure drop of the water affects the design pressure and the cost of the

economizer. Similar to the other sections, the economizer needs to have the

same width and length too.

Because of the low-temperature flue gas that enters the economizer, a large

heat transfer surface area is required here. Therefore, the flue gas pressure

drop would be high. The flue gas pressure drop is another important constraint

that has to be calculated accurately. Also, the temperatures of the fin tips, fin

surface and tube walls need to be satisfied as additional constraints of this

section. This module provides complete thermal design, heat transfer

calculation, geometry, arrangement, approach point, flue gas pressure drop,

metal temperature of both fins and tubes and the investment cost of the

economizer.

6.1.5. Water and steam properties

Water and steam flow inside the tubes of the HRSG sections (superheaters,

evaporator and economizer). All properties of both water and steam are

required for the accurate thermal design and heat transfer calculation.

Especially thermal conductivity, specific heat, viscosity, density and enthalpy of

water and steam are required for the heat transfer calculations and the relevant

iterations. Considering many iterations in the calculation of all sections,

accurate values of the properties are necessary for the convergence of the

calculations.


69

Data, information and correlations of the “The International Association for the

Properties of Water and Steam” (IAPWS-If97) [18] were implemented to

calculate the water and steam properties.

For different regions, a set of equations can be found in the IAPWS industrial

formulation. The range of pressure and temperature that are covered by each

set of equations are given here [18]:

273.15 K ≤ T ≤ 1073.15 K , p ≤ 100 MPa

1073.15 K ≤ T ≤ 2273.15 K , p ≤ 50 MPa

Various regions into which the entire range of validity of IAPWS-IF97 is divided

into are shown in fig. 6.1. Except for the boundary between regions 2 and 3, the

regions’ boundaries can be taken from fig. 6.1 and a separate equation defines

this boundary. Both regions 1 and 2 are individually covered by a fundamental

equation for the specific Gibbs free energy g(p,T). A fundamental equation for

the specific Helmholtz free energy f(ρ,T) covers region 3, where ρ is the density,

and the saturation curve by a saturation-pressure equation .

The basic equations represent the corresponding values from the "IAPWS

Formulation for the Thermodynamic Properties of Ordinary Water Substance for

General and Scientific Use" [114] for the main properties specific volume ,

specific enthalpy , specific isobaric heat capacity , and saturation pressure

. More details and complete explanations of the used functions are available

in IAPWS-If97 [18].

In general, all properties of water and steam are calculated in the module for

water and steam properties.


70

Fig. 6.1: Regions and equations of IAPWS-IF97 [18]

6.1.6. Flue gas properties

Accurate physical properties of the flue gas are required for the design and

analysis of thermal systems. In a heat recovery steam generator, the heat

transfer coefficient of the flue gas (fluid outside the fin tubes) affects the overall

heat transfer coefficient significantly. Any errors in the properties of the fluid

can result in a significant error in thermal design calculations and especially in

relevant iterations. Therefore, accurate physical properties have been applied in

the thermal design and heat transfer calculations of the HRSG. Relevant

properties are needed for the heat transfer parameters and its dimensionless

groups that occur in the equations of conduction, convection, and radiation (i.e.

Nusselt number, Prandtl number and Reynolds number). Especially thermal

conductivity, specific heat, viscosity, density and enthalpy of the flue gas need

to be calculated accurately in the heat transfer calculation.

The flue gas consists of the combustion products that exit the gas turbine and

the combustion product includes , , , , etc. In the module of the


71

flue gas properties, the physical properties of all these gases are calculated

separately and then the physical property of the flue gas is obtained by

considering the mixture.

Considering the large number of iterations in each module of the program,

accurate values of the properties are required for the convergence of the

calculations. Data, information and correlations of the “The properties of gases

and liquids” [19] were implemented to calculate the flue gas properties. In

general, all required properties of the flue gas are calculated in the module of

the flue gas properties.

6.1.7. Genetic algorithm

A genetic algorithm was used to optimize the thermal design and cost of the

heat recovery steam generator. A genetic algorithm module was developed for

the optimization. All genes, chromosomes, costs, fitness, selection, crossover,

mutation, etc. are defined and calculated in this module.

6.2. Definition of the optimization variables

A single-pressure heat recovery steam generator including four sections (two

superheaters, evaporator and economizer) was considered for optimization. It is

also possible to develop a program for a multi-pressure heat recovery steam

generator. In general, specification of the heating surface of all sections, fluid

velocity and approach point are defined as optimization variables (genes) that

are described below:

6.2.1. Approach point

The approach point is the most important variable affecting the optimization of

a heat recovery steam generator. Selecting the best value of approach point and

pinch point are the most important parameters that have to be defined by the

engineers. Selecting and optimizing the approach point needs to be done

carefully to minimize the cost, prevent steaming and control the pinch point.


72

6.2.2. Tube diameter

In thermal design and heat transfer calculations of the heat recovery steam

generator, the tube diameter affects the inside heat transfer coefficient, inside

pressure drop, outside heat transfer coefficient, outside pressure drop and also

the cost of each section. Therefore, the tube diameter needs to be considered

as an optimization variable.

Actually, optimization of the heat recovery steam generator needs to be carried

out for reasonable value and range of the variables. Considering the tubes

available on the market, standard tube diameters were assumed for all sections

and optimization was carried out using the standard values of tube diameter. It

might be possible to obtain better optimization results and lower cost with a

non-standard tube diameter (i.e. 35.9 mm). But this tube diameter is not

available and cannot be selected for a heat recovery steam generator.

6.2.3. Fin type

Both serrated fins and solid fins were explained in section 3. Comparing serrated

fins to solid fins (with the same fin specification), the heat transfer coefficient of

the serrated fins is higher than that of the solid fins. Therefore, a higher heat

transfer rate and lower costs are expected. But then the pressure drop of the

flue gas is higher too. Moreover, the fin tip temperature in the serrated fin is

higher. Therefore, the fin type is selected as another optimization variable.

6.2.4. Fins per meter

Basically, designers select extended heat transfer surfaces in heat recovery

steam generators to increase the heat transfer surface. The number of fins per

meter is an important factor that affects the heat transfer coefficient, the

overall heat transfer surface and the flue gas pressure drop. Also, this variable

should be selected based on the composition of the flue gas. In general, there

are no solid particles in the combustion product of natural gas. Thus, a higher


73

value of fins per meter is allowed. But for a fuel including sulphur and ash, the

number of fins per meter has to be limited. Moreover, manufacturer capabilities

limit the choices in fins per meter. By increasing the number of fins per meter,

the heat transfer rate and heat transfer surface increase. But also the flue gas

pressure drop increases accordingly. In the optimization of this heat recovery

steam generator, this parameter shall be selected exactly.

6.2.5. Fin height and fin thickness

For the design and optimization of the fins, both fin tip temperature and fin

surface temperature need to be checked carefully. Otherwise, fins will be

burned and the harps will be damaged. Fin height and fin thickness are two

important variables that affect the fin tip temperature and fin surface

temperature. Both fin height and fin thickness are important in the calculation

of the heat transfer coefficient, heat transfer surface and pressure drop of flue

gas. Therefore, fin height and fin thickness are considered as optimization

variables.

6.2.6. Steam and water velocities

Steam velocity affects both heat transfer and steam pressure drop. Based on

the judgment and recommendation of boiler designers, the allowable range for

steam velocity has been specified in table 7.3.

Water velocity also affects the heat transfer and water pressure drop in the

economizer. Based on the judgment and recommendation of boiler designers,

the allowable ranges for the steam and water velocities have been specified in

tables 7.3 and 7.4 respectively.

Generally, it is recommended that the water velocity should be around 1 m/s.

But to prevent steaming in the economizer, the water velocity needs to be

higher than 0.6 m/s.


74

6.2.7. Number of tubes on the circumference of a header

Actually, a heat recovery steam generator consists of several harps that

configure its sections. Fig. 6.2 shows the cross sections of different kinds of

harps. The number of tubes on the circumference of a header is very important

in the configuration of harps. This variable is important to manufacture the harp

and affects the tube arrangement of each section and also the relevant cost.

6.3. Objective function

In the optimization of the thermal design and cost of a heat recovery steam

generator, all sections (two superheaters, evaporator and economizer) are

designed and optimized together. In this regard, many constraints need to be

satisfied. The cost functions of the separate sections are totally different from

one another. This fact is part of the concept of heat transfer and individual

constraints to each section. Moreover, some general constraints limit the

optimization significantly. For instance, the total pressure drop of all the

components needs to be in the allowable range of gas turbine back pressure.

Therefore, all components need to be optimized at the same time. The sum of

single row harp multiple row harp

Fig. 6.2: Single row and multiple row harp [12]


75

the cost functions of the four sections has been considered as the objective

function.

The objective function (investment cost of heat recovery steam generator)

needs to be optimized properly by satisfying various constraints such as flue gas,

allowable pressure drop, steam pressure drop, water pressure drop, spray

water value, pinch point, allowable temperature of fin tube material and overall

allowable dimensions of the heat recovery steam generator.

According to an ASME - Sec. II [21], metal temperature limits the selection of

material for the fins and tubes. Especially considering the high metal

temperature in superheaters, an alloy steel is selected. Higher material cost is

expected for an alloy steel alloy. Due to the average metal temperature in

evaporator and economizer, carbon steel material is selected for evaporator

and economizer.

Usually manufacturers calculate the cost of heat recovery steam generators

based on the weight of the components. In this work, cost of the heat recovery

steam generator was calculated based on the total weight of the heat transfer

surfaces in each section. The cost of carbon steel material and alloy steel

material was assumed to be 7 USD/kg and 10 USD/kg, respectively.

The complete and comprehensive design of the heat recovery steam generator

allows engineers to consider any other cost formula and method to evaluate the

cost. Some screenshots of the developed program are shown in figures 6.3, 6.4

and 6.5.


76

Fig. 6.3: Thermal design and optimization program, main page


77

Fig. 6.4: Thermal design and optimization program, optimization variables


78

Fig. 6.5: Thermal design and optimization program, thermal design data

Chapter 7 Results and comparison

79

CHAPTER 7

7. Results and comparison

The proposed method was applied to the optimization of an HRSG that is

operated in a combined cycle power plant. The plant began its operation some

years ago and the design data, heat transfer area and operating parameters of

the HRSG are known.

Based on the discussion of the cost balance of the heat recovery steam

generator in chapter 2, the objective is to minimize the cost of the HRSG. In this

regard, both thermal design and cost of the heat recovery steam generator have

been considered to obtain the best parameters and variables of the

optimization.

As explained in chapter 4, all constraints that are related to the design,

manufacturing and operation of the heat recovery steam generator have been


80

considered in the optimization. The existing HRSG has been optimized for two

cases in 7.3 and 7.4. Different variation ranges of variables and constraints have

been considered in case 1 and case 2. Then the results were compared with the

data of the existing heat recovery steam generator.

Alloy steel was used in both superheaters of the existing boiler. For better

comparison, alloy steel was selected for both superheaters in the optimization

too. But carbon steel is sufficient for evaporator and economizer.

7.1. Input data

A high-pressure section of a heat recovery steam generator with a capacity of

241.4 t/h, a working pressure of 97.5 bar and a steam temperature of 523°C is

considered for optimization. The relevant HRSG consists of four sections: two

superheaters, an evaporator and an economizer.

7.1.1. Flue gas data

The data of the exhaust gas of the gas turbine are the main input data for

thermal design and optimization. Table 7.1 shows the flue gas data including

mass flow rate, inlet temperature, expected minimum outlet temperature, gas

composition and fouling resistance.

Table 7.1 Flue gas data

Mass flow rate, kg/s 409.56

Inlet temperature, °C 631.15

Minimum outlet temperature, °C 245.9

Composition, volume % : 3.49, : 8.15, : 75, : 13.36

Fouling resistance, m²·K/W 0.00052


81

7.1.2. Steam and water data

Table 7.2 shows the input data associated with steam and water including

steam production capacity of the heat recovery steam generator, working

pressure, superheater outlet temperature, inlet water temperature, fouling

factor and spray water flow.

Table 7.2 Water and steam data

Steam mass flow rate, kg/s 67.07

Steam pressure, Bar 97.5

Outlet steam temperature, °C 523

Inlet water temperature, °C 182.4

Fouling resistance, m²·K/W 0.000081

Spray water mass flow rate, kg/s 0.433

7.2. HRSG optimization, case 1

In the first case of optimization, the variation range of variables and constraints

is considered close to the parameters of the existing boiler. Design variables,

constraints, design parameters and thermal design of the existing and optimized

HRSGs are explained and compared below.

7.2.1. Variation ranges of the optimization variables, case 1

Table 7.3 and 7.4 show the optimization variables (genes) and relevant

acceptable range of variations for the all sections of case 1.


82

Table 7.3 Design variables and variation range for superheater no. 2 and superheater no. 1, case 1

Superheater no. 2 Superheater no. 1

Variable From To From To

Tube diameter, mm 31.8, 33.7, 38.1 - 31.8, 33.7, 38.1 -

Tube arrangement in line,

staggered -

in line, staggered

-

Fin height, mm 8 13 12 18

Fin thickness, mm 0.8,0.9,1,1.1,1.2 - 0.8,0.9,1,1.1,1.2 -

Fins per meter 100 140 180 260

Fin type solid, serrated - solid, serrated -

Transvers pitch, mm 55 120 55 120

Longitudinal pitch, mm 55 120 55 120

Steam velocity, m/s 10 25 7 20

Number of tube rows 1 4 1 4

Segment width, mm 4, 4.5 - 4, 4.5 -

number of tubes on the circumference of a

header 2, 3 2, 3


83

Table 7.4 Design variables and variation range for the evaporator and economizer, case 1

Evaporator Economizer


Tube diameter, mm 38.1, 44.5 - 31.8, 33.7, 38.1 -


staggered -

in line, staggered

-


Fin thickness, mm 0.8,0.9,1,1.1,1.2 - 0.8,0.9,1,1.1,1.2 -





Water velocity, m/s - - 0.6 1.5



number of tubes on the circumference of a header

1, 2, 3 2, 3


84

7.2.2. Constraints and their range of variation, case 1

The most important constraints to the HRSG optimization and operation were

explained in chapter 4. Satisfying the mentioned constraints is very important in

the optimization and affects its result. Table 7.5 shows the main constraints of

optimization and their range of variations. In case 1, for a better comparison of

the optimized HRSG to the existing HRSG, the variation ranges of the constraints

were defined close and similar to the parameters of the existing HRSG. For

instance, the minimum and maximum allowable lengths of fin tubes were

considered close to the length of the existing HRSG. Optimization constraints of

the case 1 are shown in table 7.5.

Table 7.5 Constraints and their variation range, case 1

Constraint From To

Allowable flue gas draft loss, mbar - 13

Tube length, mm 14,000 20,000

Width of HRSG, mm 3,000 9,000

Carbon steel fin tip temperature, °C - 449

Alloy steel fin tip temperature , °C 450 650

Economizer water pressure drop, bar - 5

Pinch point, °C 8 22

Approach point, °C 12 27

Steam pressure drop, bar - 3

Maximum spray water flow as percentage of total steam flow, %

- 5


85

7.2.3. Optimization results and comparison, case 1

The results of the HRSG optimization (case 1) are presented here. Firstly, the

optimization variables and thermal design result of each section are presented

in 7.2.3.1. Relevant optimized variables are compared to the parameters of the

existing heat recovery steam generator. The general data, cost (objective

function) of the optimized heat recovery steam generator are compared with

the data of the existing heat recovery steam generator in 7.2.3.2. Finally, the

heat transfer surfaces of the optimized HRSG (case 1) and existing HRSG are

compared in 7.2.3.3.

7.2.3.1. Optimization variables and thermal design results of the HRSG

sections, case 1

In the first case of optimization, the variables and thermal design result from

the HRSG sections (superheater no. 2, superheater no. 1, evaporator and

economizer) and are presented hereafter. Then, the optimized variables and the

thermal design result of each optimized section are compared to the

parameters of the existing HRSG. Tables 7.6 and 7.7 present the optimization

variables (genes) and thermal design results of the optimized and existing

superheater no. 2. Compared to existing superheater no. 2, fins per meter, fin

thickness and longitudinal pitch ( ) of optimized superheater no. 2 were

decreased, but fin height and transverse pitch ( ) were increased. Also,

serrated fin was selected in the optimization. In general, the costs of both

existing and optimized superheater no. 2 are approximately the same.

Superheater no. 2 is the first section of the heat recovery steam generator and

the hot flue gas passes through this section. Practically, fin tip and tube wall

temperatures are the most important constraints to superheater no. 2.

Considering the optimization results, all variables have been selected properly

to fulfil the requirements of the fin tube metal temperature. The fin tip and

tube wall temperatures are within the allowable ranges.


86

Table 7.6 Variables of existing and optimized superheaters no. 2, case 1

Unit Existing

superheater no. 2 Optimized

superheater no. 2

Tube arrangement staggered staggered

Tube diameter, mm 38.1 38.1

Transverse pitch, mm 96 99.1

Longitudinal pitch, mm 90 79.4

Fin type - solid serrated

Fin height, mm 10 13

Fin thickness, mm 1.2 0.9

Fins per meter - 120 104

Segment width, mm 4 4

Number of rows, - 3 3

Steam velocity, m/s 15 16.2


- 3 3


87

Table 7.7 Thermal design results of the existing and optimized superheater no. 2, case 1

Unit Existing

superheater no. 2

Optimized superheater

no. 2

Length of fin tube mm 15,700 15,916.2

Gas pass length mm 15,736 15,964.2

Gas pass width mm 7,536 7,086

Tubes per row - 78 71

Overall heat transfer coefficient,

W/m²·K 61.8 56.9

Flue gas pressure drop, mbar 0.79 0.88

Heat transfer surface, m² 1,805.4 1939

Steam pressure drop bar 1.39 1.68

The optimization variables (genes) and thermal design results of the optimized

and existing superheaters no. 1 are shown in Table 7.8 and 7.9. Due to the

improved bundle arrangement and fin geometry of optimized

superheater no. 1, the overall heat transfer coefficient of the optimized

superheater no. 1 was increased by 25.5% compared to the overall heat transfer

coefficient of existing superheater no. 1. Therefore, the required heat transfer

surface has been decreased.

The number of rows in optimized superheater no. 1 is the main variable that

decreased significantly. As explained before, the same length and width are

considered for all sections. Therefore, finding the best transverse pitch and

rounding the number of rows is very important in superheater no. 1.

Considering the optimization variables, the transverse pitch of the optimized

HRSG is smaller than the transverse pitch of the existing HRSG. Therefore, the

number of tubes per row was increased in optimized superheater no. 1 and

consequently the number of rows was decreased too. Existing superheater no. 1


88

consists of three rows, while there are two rows in optimized superheater no. 1.

The total tube quantity of optimized superheater no. 1 is lower than the total

tube quantity of existing superheater no. 1. Moreover, fins per meter, fin

thickness and fin height of optimized superheater no. 1 are decreased in

comparison to existing superheater no. 1. Considering the lower heat transfer

surface, lower total tube quantity and also lower weight of the fins, the total

weight of optimized superheater no. 1 has been decreased to reduce the cost of

superheater no. 1 and obtain better fitness in this section. Similar to

superheater no. 2, the fin tip and tube wall temperatures are within the

allowable ranges.


89

Table 7.8 Variables of existing and optimized superheater no. 1, case 1

Unit Existing


superheater no. 1





Fin type - serrated serrated

Fin height, mm 15 13.2

Fin thickness, mm 1.2 1




Steam velocity, m/s 9.6 9.9

Number of tubes on the circumference of a

header - 3 2


90

Table 7.9 Thermal design result of the existing and optimized superheater no. 1, case 1

Unit Existing

superheater no.1


no. 1

Length of fin tubes mm 15,700 15,916.2





W/m²·K 40.4 50.7


Heat transfer surface, m² 4,843.2 3,629.4


Tables 7.10 and 7.11 present the optimization variables (genes) and thermal

design results of the optimized and existing evaporators. Due to the necessity to

have the same length and width in all sections, transverse pitch must be

optimized properly and the number of rows should be rounded in the optimized

evaporator.

Considering the optimization variables, fins per meter and fin height are

decreased compared to the existing evaporator to reduce its weight and obtain

better fitness in this section. Compared to the variables of the existing

evaporator, the ratios ( ) and ( ) were decreased in the optimized

evaporator. Consequently, the factors and were increased in equations

(18) and (20) respectively. Therefore, the outside heat transfer coefficient has

been increased in equation (15). Due to the high value of the inside heat

transfer coefficient of the evaporator, the overall heat transfer coefficient of the

evaporator mostly depends on the outside heat transfer coefficient. Considering

the mentioned points, the overall heat transfer coefficient has been increased in


91

the optimized evaporator. By increasing the overall heat transfer coefficient of

the evaporator, the required heat transfer surface of this section was

decreased. Therefore, the cost of the evaporator has been decreased.

Table 7.10 Variables of the existing and optimized evaporators, case 1

Unit Existing

evaporator Optimized evaporator



Transverse pitch, mm 96 105






Segment width, mm 4 4.5


Water/steam velocity, m/s - -


- 3 3


92

Table 7.11 Thermal design results of the existing and optimized evaporators, case 1

Unit Existing







W/m²·K 49.2 54




and existing economizers are presented in Tables 7.12 and 7.13.

As in the evaporator and superheater no. 1, the length and width of the

economizer needs to be equal to the other sections. Therefore, finding the best

transverse pitch and rounding the number of the rows is very important for the

economizer too.

Considering the results of the economizer optimization, the optimized tube

diameter is smaller than that of the existing economizer. Based on the ASME

code [22], the thickness of the tube wall was decreased due to the smaller tube

diameter of the optimized economizer and therefore the cost of the economizer

was decreased too.

Compared to the existing economizer, fins per meter, fin thickness and fin

height of the optimized economizer were decreased. Compared to the existing

economizer, the ratios ( ) and ( ) were decreased in the optimized

economizer. Therefore, the factors and were increased in equations (18)

and (20) and the outside heat transfer coefficient of the economizer was


93

increased in equation (15). In general, the inside heat transfer coefficient of the

economizer is much higher than the economizer’s outside heat transfer

coefficient. Considering equation (11), the overall heat transfer coefficient of

the economizer mostly depends on the outside heat transfer coefficient.

Consequently, the overall heat transfer coefficient of the economizer has been

increased in the optimized economizer. The overall heat transfer coefficient of

the optimized economizer was increased by 27.3% compared to the existing

economizer. Increasing the overall heat transfer coefficient of economizer

affects the required heat transfer surface and consequently the cost of this

section was decreased. Therefore the weight and cost of the economizer were

decreased and a better fitness was obtained in this section.


94

Table 7.12 Variables of the existing and optimized economizers, case 1

Unit

Existing economizer

Optimized economizer











Water velocity, m/s 0.67 1.09

Number of tubes on the circumference of a header

- 2 2

Approach point °C 21 16.17


95

Table 7.13 Thermal design result of the existing and optimized economizers, case 1

Unit Existing

economizer Optimized

economizer






W/m²·K 39.2 49.9




7.2.3.2. General data and cost (objective function) comparison of the

optimized and existing HRSGs, case 1

The general data and cost (objective function) of the existing and the optimized

HRSGs are compared in table 7.14.

In optimization case 1, the variation ranges of the constraints have been defined

close to the parameters of the existing HRSG. Therefore, the overall dimension

of the optimized and the existing HRSG are approximately the same. The length

of the optimized fin tube is only 1.3% more than the length of the existing fin

tube. Also, the gas pass length and gas pass width of the optimized and existing

HRSGs are close together.


96

Table 7.14 Comparison of the existing and optimized HRSGs, case 1

Unit Existing HRSG

Optimized HRSG




Flue gas outlet temperature °C 245.9 244.9


Pinch point °C 9.1 13.82



Economizer water pressure drop bar 4.8 1.18


Total weight t 281 216

Capital cost (Objective function) USD 2,113,428 1,598,428

To achieve the guaranteed capacity, pressure and temperature of the high

pressure steam, the flue gas outlet temperature of the optimized HRSG should

be at least equal to the flue gas outlet temperature of the existing HRSG.

Considering the data of the Table 7.14, the flue gas outlet temperature of the

optimized HRSG (244.9°C) is lower than the flue gas outlet temperature of the

existing HRSG (245.9°C). Therefore, the guaranteed steam capacity will be met

in the optimized HRSG.

The pinch and approach points and their effects on optimization have been

explained in 4.2.2. Apart from the optimization of the heating surface and

reducing the cost of the HRSG sections, finding the optimum values of the pinch


97

point and approach point is the main goal of work at hand. Due to the water

phase change in the evaporator, the temperature of water and steam in the

evaporator is constant. For constant steam generation and a fixed thermal

efficiency, the total heating capacities of the evaporator and economizer have

to be constant. Therefore, the sum of the pinch point and approach point has to

be constant too. In general, the heat transfer in the economizer is cheaper than

the heat transfer in the evaporator. This fact leads designers to increase the

heating capacity of the economizer and decrease the heating capacity of the

evaporator. Comparing the pinch and approach points of the existing and

optimized HRSG, the pinch point of the optimized evaporator is larger than the

pinch point of the existing boiler. But the approach point of the optimized

economizer is smaller than the approach point of the existing economizer. This

fact shows that optimization program increased the heating capacity of the

economizer and reduced the heating capacity of the evaporator. It means that a

bigger economizer has been selected in the optimization to reduce the total

cost of the HRSG.

In 4.2.1, the flue gas draft loss has been explained as an important constraint

that affects the performance of the gas turbine. Considering table 7.14, the flue

gas draft loss of the optimized HRSG is lower than the flue gas draft loss of the

existing HRSG. Therefore, the flue gas pressure drop is acceptable and the

allowable back pressure of the gas turbine was met in the first case of the HRSG

optimization.

Both steam and water pressure drop are the other constraints explained in

4.2.4. Steam and water pressure drops of the optimized HRSG are 2.27 and 1.18

bar respectively. Therefore, both steam and water pressure drops are

acceptable and the optimization program meets the requirements of table 7.5.

Selecting better optimization variables, overall heat transfer has been increased

in optimized superheater no. 1, evaporator and economizer. Compared to the

existing HRSG, the heat transfer surface of these sections was decreased.

Therefore, the weight of the optimized HRSG and consequently its capital cost

were decreased significantly. Considering the data of table 7.14, total weight

and cost of the optimized HRSG have been decreased by 23.1 % and 24.3 %

respectively compared to the existing HRSG.


98


optimized HRSGs, case 1

For better comparison of the existing and the optimized HRSG, the heat transfer

surfaces of all the sections are shown in Fig. 7.2. Except superheater no. 2, the

heat transfer surfaces of all the sections were decreased in the optimized HRSG

by simply selecting better variables.

Fig. 7.1: Heat transfer surface of the HRSG and its sections, case 1

7.3. HRSG optimization, case 2

In 7.2, the first case of optimization was presented with the variation ranges of

variables and constraints that were considered close to the parameters of the

existing boiler. But based on engineering judgments, design recommendation

and manufacturing capabilities of the fin tubes, using a wider range of variables

0

10,000

20,000

30,000

40,000

50,000

60,000

1 2 3 4 5

Hea

t tr

ansf

er s

urf

ace

, m²

HRSG and its sections, case 1

Existing HRSG

Optimized HRSG

SH2 SH1 EVA. ECO HRSG


99

and constraints compared to optimization case 1 is allowed and recommended.

In optimization case 2, the variation ranges of variables and constraints are

considered wider than in case 1. For instance, more fins per meter were

considered for the fin tubes. Design variables, constraints, design parameters

and thermal design of the existing and optimized HRSGs (case 2) are presented

in the following.

7.3.1. Variation ranges of the optimization variables, case 2

Table 7.15 and 7.16 show the optimization variables (genes) and relevant

acceptable ranges of variations for all sections of case 2. Compared to the

variation ranges of the optimization variables of case 1, higher values of tube

diameter, fins per meter, transverse pitch, longitudinal pitch, steam velocity and

number of rows were considered the optimization variables of case 2.


100

Table 7.15 Design variables and variation range for superheater no. 2 and

superheater no. 1, case 2

Superheater no. 2 Superheater no. 1


Tube diameter, mm 31.8, 33.7, 38.1, 44.5 - 31.8, 33.7, 38.1, 44.5 -

Tube arrangement in line, staggered - in line, staggered -


Fin thickness, mm 0.8,0.9,1,1.1,1.2 - 0.8,0.9,1,1.1,1.2 -





Steam velocity, m/s 10 30 7 40




header 2, 3 2, 3


101

Table 7.16 Design variables and variation range for evaporator and economizer, case 2

Evaporator Economizer


Tube diameter, mm 33.7, 38.1, 44.5 - 31.8, 33.7, 38.1 -


staggered -

in line, staggered

-


Fin thickness, mm 0.8,0.9,1,1.1,1.2 - 0.8,0.9,1,1.1,1.2 -





Water velocity, m/s - - 0.6 1.5




1, 2, 3 2, 3

7.3.2. Constraints and their range of variation, case 2

The main constraints of the optimization (case 2) and their range of variations

are shown in Table 7.17. The variation range of the constraints affects the

optimization results significantly. Due to the wider range of constraints in case 2

of the optimization, it is expected to achieve a better fitness and lower cost than

case 1. Considering table 7.17, the acceptable range of the overall dimensions,


102

steam pressure drop, pinch point and approach point are wider than the

constraints of case 1. But due to the requirement of the gas turbine back

pressure, allowable flue gas draft loss is similar to optimization case 1 . As in

case optimization 1, the acceptable fin tip temperature was defined according

to the requirements of the ASME code [21].

Table 7.17 Constraints and their variation range, case 2

Constraint From To

Allowable flue gas draft loss, mbar - 13

Tube length, mm 14,000 22,000

Width of HRSG, mm 3,000 10,000

Fin tip temperature of carbon steel, °C - 449

Fin tip temperature of alloy steel, °C 450 650

Economizer water pressure drop, Bar - 5

Pinch point, °C 8 28

Approach point, °C 8 28

Steam pressure drop, bar - 5

Maximum spray water flow as Percentage of total steam flow, %

- 5

7.3.3. Optimization results and comparison, case 2

The results of the HRSG optimization (case 2) are presented hereafter. In

7.3.3.1, the optimization variables and thermal design results of the HRSG

sections are presented. Also, the optimized variables are compared to the

parameters of the existing heat recovery steam generator. The general data,

cost (objective function) of the optimized heat recovery steam generator


103

(case 2) are compared with the data of the existing heat recovery steam

generator in 7.3.3.2. Finally, the heat transfer surfaces of the optimized (case 2)

and existing HRSG are compared in 7.3.3.3.

7.3.3.1. Optimization variables and thermal design results of the HRSG

sections, case 2

For the second case of optimization, the variables and thermal design results of

the HRSG sections (superheater no. 2, superheater no. 1, evaporator and

economizer) are presented hereafter. Then for each optimized section, relevant

optimized variables and thermal design results are compared to the parameters

of the existing HRSG.


design results of the optimized and existing superheaters no. 2. Compared to

existing superheater no. 2, number of rows, fins per meter, fin thickness,

longitudinal pitch ( ) and transvers pitch ( ) of optimized superheater no. 2

were decreased, but fin height was increased. Also, in line arrangement and

serrated fins have been selected in optimization. Due to the selection of the in

line arrangement in optimized superheater no. 2, both longitudinal pitch ( )

and transvers pitch ( ) of the optimized superheater no. 2 are smaller than the

longitudinal pitch and transvers pitch of existing superheater no. 2. But, the

ratio of ( ) has been increased in order to increase factor in equation

(19). Consequently the outside heat transfer coefficient will be improved in this

section.

The number of rows in optimized superheater no. 2 is the main variable that

decreased significantly. Considering the optimization variables, the transverse

pitch of optimized superheater no. 2 is smaller than the transverse pitch of

existing superheater No. 2. Therefore, the number of tubes per row has been

increased in optimized superheater no. 2. The optimized number of rows is

lower than the number of rows in existing superheater no. 2. Therefore, the

total quantity of tubes in optimized superheater no. 2 is lower than the total

quantity of tubes of existing superheater no. 2. Moreover, fins per meter and fin


104

thickness of optimized superheater no. 2 were decreased compared to existing

superheater no. 2. Considering above mentioned points, due to the lower total

quantity of tubes and also the lower fin weight, the total weight of optimized

superheater no. 2 was decreased to reduce the cost of superheater no. 2 and

obtain better fitness in this section. Considering the optimization results, all

variables have been selected properly to meet the requirements of the fin and

tube wall temperatures that are the main constraints of this section.

Table 7.18 Variables of the existing and optimized superheaters no. 2, case 2

Unit Existing


superheater no. 2

Tube arrangement staggered in line


Transverse pitch, mm 96 78


Fin type - solid serrated

Fin height, mm 10 13





Steam velocity, m/s 15 18


- 3 2


105

Table 7.19 Thermal design results of the existing and optimized superheaters no. 2, case 2

Unit Existing

superheater no. 2


no. 2


Gas pass length mm 15,736 16,533




W/m²·K 61.8 55.88





and existing superheaters no. 1 are shown in Table 7.20 and 7.21. As explained

before, the same length and width will be considered for all sections. Therefore,

the best transverse pitch has been found in optimization case 2. Comparing the

parameters of the optimized and the existing superheater no. 1, tube diameter,

fin height, fin thickness and fins per meter of the optimized superheater no. 1

are smaller than the parameters of the existing superheater no. 1. The ratio

( ) has been decreased in optimized superheater no. 1. Therefore, factor

was increased in equations (18) and the outside heat transfer coefficient of

superheater no. 1 was increased in equation (15). Based on the ASME code [22],

the thickness of the tube wall and the weight of superheater no. 1 were

decreased due to the smaller tube diameter of optimized superheater no. 1.

Due to the better bundle arrangement and better fin geometry of optimized

superheater no. 1, the overall heat transfer coefficient of optimized

superheater no. 1 was increased by 43.6% compared to that of existing

superheater no. 1. The required heat transfer surface and weight of optimized


106

superheater no. 1 have been decreased. Consequently, the cost of this section

has been reduced. Similar to superheater no. 2, the fin tip and tube wall

temperatures are within the allowable range.

Table 7.20 Variables of existing and optimized superheater no. 1, case 2

Unit Existing


superheater no. 1











Steam velocity, m/s 9.6 12.2


header - 3 2


107

Table 7.21 Thermal design results of the existing and optimized superheaters no. 1, case 2

Unit Existing

superheater no. 1


no. 1






W/m²·K 40.4 58.03





design results of the optimized and existing evaporators. Due to the necessity of

the same length and width of all sections, the transverse pitch has been

optimized properly and the number of rows has been rounded in the optimized

evaporator. Comparing the variables of the optimized and the existing

evaporators, the number of the rows is the main variable that has been

decreased in the optimization. It is related to the value of the optimized pinch

point. The pinch point of the optimized evaporator is significantly higher than

the pinch point of the existing evaporator. Therefore, the heat transfer in the

optimized evaporator is lower than the heat transfer in the existing evaporator

and a lower heat transfer surface is required for the optimized evaporator.

Consequently, weight and cost of the optimized evaporator are lower than

weight and cost of the existing evaporator.


108

Table 7.22 Variables of the existing and optimized evaporators, case 2

Unit Existing












Water velocity, m/s - -


- 3 3


109

Table 7.23 Thermal design results of the existing and optimized evaporators, case 2

Unit Existing







W/m²·K 49.2 46.22





and existing economizers are presented in tables 7.24 and 7.25. Similarly to the

evaporator and superheater no. 1, the length and width of the economizer need

to be equal to the other sections. Therefore, the best transverse pitch was

found through optimization and the number of rows was rounded properly.

Considering the ASME code [22], the thickness of the tube wall was decreased

due to the smaller tube diameter of the optimized economizer. Also, the fin

thickness of the optimized economizer is smaller than the fin thickness of the

existing economizer. Therefore, the weight and consequently the cost of the

economizer were decreased in optimization.


110

Table 7.24 Variables of existing and optimized economizer, Case 2

Unit

Existing economizer

Optimized economizer











Water velocity, m/s 0.67 0.89


- 2 2



111

Table 7.25 Thermal design results of the existing and optimized economizers, case 2

Unit Existing

economizer Optimized

economizer






W/m²·K 39.2 35.79



Water pressure drop Bar 4.8 0.51


7.3.3.2. General data and cost (objective function) comparison of the

optimized and existing HRSGs, case 2

Table 7.26 presents the general data and cost (objective function) of the existing

and optimized HRSGs. In optimization case 2, the variation ranges of the

constraints have been defined wider than in optimization case 1. Therefore, the

better fitness was achieved in optimization. The flue gas outlet temperature of

the optimized HRSG (245.7°C) is lower than the flue gas outlet temperature of

the existing HRSG (245.9°C). Therefore, the guaranteed steam capacity will be

met in optimization case 2.


112

Table 7.26 Comparison of the existing and optimized HRSGs, case 2

Unit Existing HRSG

Optimized HRSG






Flue gas outlet temperature °C 245.9 245.7

Flue gas pressure drop, mbar 12.68 12,38



Economizer water pressure drop bar 4.8 0.51

Total weight t 281 199.6

Capital cost (Objective function) USD 2,113,428 1,496,960

The heat transfer occurring in the economizer is cheaper than that occurring in

the evaporator. Also, the variation ranges of the approach point and pinch point

in optimization case 2 is wider than that in optimization case 1. In case 2, the

optimization program selected a lower approach point than in case 1.

Considering the data of according to tables 7.14 and 7.26, the approach point of

case 1 is 16.17°C, while the approach point of case 2 was reduced to 12.51°C.

Compared to the optimization case 1, the results show that optimization

program increased the heating capacity of the economizer and reduced the

heating capacity of the evaporator. This means that a bigger economizer was

selected in optimization case 2 to reduce total cost of the HRSG further.


113

Due to the requirement of the back pressure of the gas turbine, the flue gas

draft loss in optimization case 2 is lower than that of the existing HRSG.

Therefore, the flue gas pressure drop is acceptable and the allowable back

pressure of the gas turbine is met in the second case of HRSG optimization. Also,

both steam and water pressure drops are acceptable and the optimization

program met the requirements of table 7.17.

Compared to the existing and optimized HRSGs in case 1, better optimization

variables have been selected and a better fitness has been achieved in

optimization case 2. Therefore, the weight of the optimized HRSG in case 2 and

consequently the relevant capital cost decreased significantly. As per table 7.26,

total weight and cost of the optimized HRSG in case 2 were decreased by 28.9%

and 29.2% respectively compared to the existing HRSG.

As per tables 7.14 and 7.26, total weight and cost of the optimized HRSG case 2

were decreased by 7.6% and 6.3% respectively compared to optimization

case 1. The results of the second case of optimization show the effects of the

constraints and variables in optimization. By considering wider ranges of

constraints and variables, better fitness and lower cost were achieved in the

optimization of the HRSG.


optimized HRSGs, case 2

Fig. 7.3 illustrates the heat transfer surface of all sections of the existing and

optimized HRSGs in optimization case 2.

The heat transfer surface of optimized superheater no. 2 is approximately equal

to the heat transfer surface of existing superheater no. 2. Also, the heat transfer

surface of optimized superheater no. 1 and the optimized evaporator is lower

than the heat transfer surface of existing superheater no. 1 and the existing

evaporator. But compared to the existing economizer, the heat transfer surface

of the optimized economizer was increased in optimization case 2. This is due to

the effect of the approach point. Because of the cheaper heat transfer in the

economizer, the optimization program decreased the approach point and


114

increased the heat transfer of the optimized economizer. According to

table 7.26, the cost of the sections has been decreased significantly.

Fig. 7.2: Heat transfer surface of the HRSG and its sections, case 2

0

10,000

20,000

30,000

40,000

50,000

60,000

1 2 3 4 5

He

at t

ran

sfe

r su

rfac

e, m

²

HRSG and its sections, case 2

Existing HRSG

Optimized HRSG

SH2 SH1 EVA ECO HRSG

Chapter 8 Conclusion

115

CHAPTER 8

8. Conclusion

Combined cycle power plants currently have the highest efficiency for power

production. In this regard, heat recovery steam generators are the main and

most important component of combined cycle power plants and cogeneration

systems. The role of heat recovery steam generators in combined cycle power

plants and industrial economy is profound. Suitable design and optimization of

heat recovery steam generators is one of the key factors to improve the

efficiency of combined cycle power plants.

In general, the optimization of heat recovery steam generators is divided into

two levels. The first level obtains the main thermodynamic and operating

parameters of the heat recovery steam generator, while the second level

provides the thermal and detail designs of the heat recovery steam generator

sections. The output of the first level is the input of the second level. Apart from

the thermodynamic parameters, economic considerations are very important in

HRSG design. Many authors proposed several methods for the thermodynamic


116

optimization of HRSGs and obtained the relevant optimized thermodynamic

parameters.

This work demonstrated both the thermal design and the cost optimization of a

heat recovery steam generator. Exergy costing was applied to a heat recovery

steam generator and the corresponding result leads us to focus on the

minimization of capital investment in the heat recovery steam generator as a

target of the cost optimization.

Four sections (two superheaters, an evaporator, and an economizer) were

included in the HRSG optimization. Two superheaters were included in the

HRSG design to prevent any simplification and also to optimize actual HRSGs

that are used in existing power plants. Actually, steam is superheated in the two

superheaters and spray water is injected between them to control the outlet

steam temperature.

A comprehensive program was developed for the thermal design of all the

sections of HRSG. Then, a genetic algorithm was applied to minimize the HRSG

cost.

HRSG steam generation and temperature profiles cannot be arbitrarily defined.

The thermal design of the HRSG should be based on the concepts of pinch point

and approach point that specify the temperature profiles of flue gas, water and

steam. Pinch and approach points affect both thermodynamic and economic

viewpoints of the HRSG optimization.

Usually, the values of pinch and approach points are derived from practical

experience. But in this work, the pinch and approach points are variables to be

optimized.

Approach point, water and steam velocity and also all geometric parameters of

each section (including tube diameter, tube arrangement [staggered or in-line],

transverse pitch, longitudinal pitch, number of tube rows, number of tubes on

the circumference of a header, fin height, fin thickness, fin density, fin type

[solid or serrated], segment width) were the variables of optimization.

Also, the main constraints (including minimum required thermal efficiency,

allowable flue gas draft loss, water and steam pressure drop, minimum

allowable gap between fin tubes, fin tip temperature, tube wall temperature,


117

minimum and maximum allowable values of pinch and approach points, overall

dimensions of the HRSG) were satisfied in the optimization.

Focusing on the thermal design of HRSG, this work obtains the best pinch point,

approach point, geometric parameters and arrangement of the HRSG to

minimize the cost. Moreover, the optimization program satisfies all of the

design constraints.

The proposed optimization method was applied to optimize an HRSG that is

operated in a combined cycle power plant. The existing HRSG was optimized

twice with different variation ranges of variables and constraints.

To show the capabilities of the optimization program, the variation range of the

variables and constraints of optimization case 1 were chosen close to the values

of the existing HRSG, while in optimization case 2, the variation range of

variables and constraints are chosen wider than case 1.

Compared to the existing HRSG, capital cost of the optimized HRSG in case 1

decreased by 24.3%. But cost of the optimized HRSG in case 2 decreased by

29.2%. The significant cost reduction was achieved by finding the best variables

of the HRSG.

Considering the optimization results, pinch point and approach point are the

main variables that have been significantly changed in the thermal design and

optimization of the HRSG. Comparing pinch point and approach point of the

existing and optimized HRSGs, the optimization program has reduced the

approach point and increased the pinch point of the optimized HRSG in both

cases of optimization. This optimization result is related to the heat transfer in

the evaporator. Optimized HRSGs have bigger economizers, but the total cost of

economizer and evaporator is lower. This leads designers to decrease the

approach point and increase the pinch point to reduce the cost of the HRSG.

Focusing on the heat transfer of each section, the product of the overall heat

transfer coefficient and the heat transfer surface affects the rate of heat

transfer. For similar variation ranges of variables and constraints, the overall

heat transfer coefficient should be increased by selecting the best fin tube

arrangements, geometry and specifications. Therefore, the heat transfer surface

will be reduced to minimize the weight and cost of the HRSG sections.


118

Serrated fins provide higher heat transfer coefficients than solid fins. Therefore,

serrated fins are preferred in all sections to improve the heat transfer

coefficients. But, the fin tip temperature, tube wall temperature and flue gas

pressure drop should be controlled by a suitable selection of the fin tube

arrangement and specifications.

The thickness of the fins is an important variable in cost minimization.

Considering the optimization results of both cases, fin thickness was reduced in

all sections of the HRSG. By selecting thinner fins, the heat transfer surface will

decrease slightly. But the weight of the fin tubes will decrease significantly and

lower cost is expected.

Increasing the number of fins per meter will increase the heat transfer surface

of the unit length of fin tubes. Therefore, the number of tubes will decrease and

a lower cost will be achieved in economizer and evaporator. In case of selecting

more fins per meter, the pressure drop of the flue gas should be controlled to

be kept below the gas turbine back pressure.

Considering the optimization results, a staggered tube arrangement and

serrated fins were selected in most sections. In this regard, lower ratios ( )

and ( ) are recommended to increase the overall heat transfer coefficient

and consequently minimize cost.

The results of optimization case 2 show the effect of variation ranges of

variables and constraints. Due to wider variation ranges of variables and

constraints, better fitness and lower cost were achieved compared to

optimization case 1. The optimization program selected a lower approach point

and more fins per meter in the second case of optimization to reduce the cost.

The lowest allowable approach point is recommended in optimization to

achieve minimum cost. But, steaming should be prevented in any case of

operation.

As an advantage of the existing work and the optimization program, the

complete thermal design of the HRSG was provided. Therefore, various

optimization strategies and objective functions (such as minimizing the flue gas

pressure drop) can be chosen by defining the objective function. Furthermore,

the program can be developed for the optimization of multi-pressure HRSGs by

adding modules for a second or third drum.

Glossary

119

GLOSSARY

Cost function: function to be optimized

Cost: output of the cost function

Crossover rate: a number between zero and one that indicates how frequently

crossover is applied to a given population

Elitism: the chromosome with the best cost is kept from generation to

generation

Evolution: a series of genetic changes in which living organisms acquire the

characteristics that distinguish them from other organisms

Evolutionary algorithm: any computer program that uses the concept of

biological evolution to solve problems; examples include genetic algorithms,

genetic programming, evolutionary strategies, and evolutionary programming

Fitness: opposite of cost; a value associated with a chromosome that assigns a

relative merit to that chromosome

Fitness function: has the negative output of the cost function; mathematical

subroutine that assigns a value or fitness to a set of variables

Genetic algorithm (GA): A type of evolutionary computation devised by John

Holland; it models biological genetic processes by including crossover and

mutation operators.

Mutation rate: percentage of bits in a population mutated in each iteration of

the GA

Optimization: the process of iteratively improving the solution to a problem

with respect to a specified objective function

Reproduction operator: the algorithmic technique used to implement

reproduction

Natural selection: The most-fit individuals reproduce, passing their genetic

information on to their offspring.

Reference

120

REFERENCES

[1] Attala L, Facchini B, Ferrara G. Thermoeconomic optimization method as

design tool in gas-steam combined plant realization. Energy Conversion and

Management. 42 (2001) 2163–2172.

[2] Dechamps P J. Incremental cost optimization of heat recovery steam

generators. ASME COGEN-TURBO. 1995.

*3+ Franco A, Russo A. Combined cycle plant efficiency increase based on the

optimization of the heat recovery steam generator operating parameters. Int. J.

Thermal Sci. 2002; 41:843–59.

[4] Casarosa C, Donatini F, Franco A. Thermoeconomic optimization of heat

recovery steam generators operating parameters for combined plants. Energy

2004; 29:389–414.

[5] Valdés M, Rapún J. Optimization of heat recovery steam generators for

combined cycle gas turbine power plants, Applied Thermal Engineering 21

(2001) 1149-1159.

[6] Valdés M, Durán MD, Rovira A. Thermoeconomic optimization of combined

cycle gas turbine using genetic algorithms. Appl Therm Eng 2003; 23(17): 2169–

82.

*7+ Valdes M, Rovira A, Durán MD. Influence of the Heat Recovery Steam

Generator Design Parameters on the Thermoeconomic Performances of

Combined Cycle Gas Turbine Power Plants. Int. J. Energy 2004; 28:1243–1254.

[8] Franco A, Giannini N. A general method for the optimum design of heat

recovery steam generators. Energy 31 (15) (2006) 3342e3361.

Reference

121

[9] Manassaldi J, Mussati S, Scenna N. Optimal synthesis and design of Heat

Recovery Steam Generation (HRSG) via mathematical programming. Energy 36

(1) (2011) 475-485.

[10] Durán MD, Valdés M, Rovira A, Rincón E. A methodology for the geometric

design of heat recovery steam generators applying genetic algorithms. Applied

Thermal Engineering 52 (2013) 77-83.

[11] Rayaprolu K. Boilers for power and process. Boca Raton (Florida): CRC

Press; 2009.

[12] ALSTOM, Heat Recovery Steam Generators for combined-cycle power

plants,

http://www.mcilvainecompany.com/Decision_Tree/subscriber/Tree/Descriptio

nTextLinks/heat-recovery-steam-generators-hrsg.pdf

[accessed 20.04.2017]

[13] Babcock & Wilcox power generation group, https://www.babcock.com/en/products/-

/media/7c6e4f303c294816afd85bee65564b63.ashx [accessed 20.04.2017]

[14] Victory energy, Heat Recovery Steam Generators,

http://www.victoryenergy.com/pdf/VEO_HRSG_BRO_WEB.pdf

[accessed 20.04.2017]

[15] Amec Foster Wheeler, Heat Recovery Steam Generators,

https://www.amecfw.com/documents/brochures-publications/brochures/heat-

recovery-steam-generators-brochures.pdf , [accessed 20.04.2017]

[16] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New

York: Wiley; 1996.

http://www.mcilvainecompany.com/Decision_Tree/subscriber/Tree/DescriptionTextLinks/heat-recovery-steam-generators-hrsg.pdf

http://www.mcilvainecompany.com/Decision_Tree/subscriber/Tree/DescriptionTextLinks/heat-recovery-steam-generators-hrsg.pdf

https://www.babcock.com/en/products/-/media/7c6e4f303c294816afd85bee65564b63.ashx

https://www.babcock.com/en/products/-/media/7c6e4f303c294816afd85bee65564b63.ashx

http://www.victoryenergy.com/pdf/VEO_HRSG_BRO_WEB.pdf

https://www.amecfw.com/documents/brochures-publications/brochures/heat-recovery-steam-generators-brochures.pdf

https://www.amecfw.com/documents/brochures-publications/brochures/heat-recovery-steam-generators-brochures.pdf

Reference

122


Press; 2009.

[18] Wagner W, Kretzschmar H. International Steam Tables, Properties of Water

and Steam Based on the Industrial Formulation IAPWS-If97. Berlin: Springer;

1988.

[19] Reid R C, Prausnitz J M, Poling B E. The properties of gases and liquids. 4th

ed. New York: Mc Graw-Hill; 1988.

[20] ASME PTC 4, Fired Steam Generators, Performance Test Codes. New York:

The American society of mechanical engineers; 2008.

[21] ASME boiler and pressure vessel code, Rules for Construction of Power

Boilers, Sec. II. New York: The American society of mechanical engineers; 2010

Edition.

[22] ASME boiler and pressure vessel code, Rules for Construction of Power

Boilers, Sec. I. New York: The American society of mechanical engineers; 2010

Edition.

[23] Annaratone D. Steam generators description and design. Berlin: Springer;

2008.

[24] Rohsenow WM, Hartnett J P, Cho Y I. Handbook of heat transfer. 3th ed.

New York: McGraw-Hill; 1998.

[25] Holman JP. Heat Transfer. 6th ed. New York: McGraw-Hill; 1986.

[26] ESCOA Corp, ESCOA Fintube Manual, Oklahoma, ESCOA, 1979.

[27] Crane Co., Flow of fluids through valves, fittings and pipe, Woodlands,

North America, Crane Co. 1999

Reference

123

[28] Moody, L. F. (1944). Friction Factors for Pipe Flow, Trans. ASME, 66, 671–

684.


Press; 2009.

[30] Yogesh J. Design and optimization of thermal systems. Boca Raton (Florida):

CRC Press; 2008.

[31] Kreith F. The CRC handbook of thermal engineering. Boca Raton (Florida):

CRC Press; 2000.

[32] Gosselin L, Tye-Gingras M, Mathieu-Potvin M. Review of utilization of

genetic algorithms in heat transfer problems. International Journal of Heat and

Mass Transfer 52 (2009) 2169–2188.

[33] Bagley JD. The behavior of adaptive systems which employ genetic and

correlation algorithms. Ph.D. thesis. University of Michigan. Ann Arbor. 1967.

[34+ Holland JH, Adaptation in Natural and Artificial Systems, University of

Michigan Press, Ann Arbor, 1975.

[35] De Jong KA, An analysis of the behavior of a class of genetic adaptive

systems, Dissertation Abstracts International, vol. 36, no. 10, 1975, 5140B

(University Microfilms No. 76-9381).

[36] Grefenstette JJ, Optimization of control parameters for genetic algorithms,

IEEE Transactions on Systems, Man and Cybernetics (1986) 122–128.

[37+ Baker JE, Reducing bias and inefficiency in the selection algorithm, in:

Genetic Algorithms and Their Applications: Proc. 2nd Int. Conf. Genetic

Algorithms, 1987, pp. 14–21.

Reference

124

[38] Goldberg D. Genetic Algorithms in Search Optimization and Machine

Learning. Michigan: Addison-Wesley; 1996.

[39] Bäck T, Hammel U, Schwefel HP, Evolutionary computation: comments on

the history and current state, IEEE Transactions on Evolutionary Computation 1

(1997) 3–17.

[40] R. Selbas, O. Kizilkan, M. Reppich, A new design approach for shell-and-tube

heat exchangers using genetic algorithms from economic point of view,

Chemical Engineering and Processing 45 (4) (2006) 268–275.

[41] P. Wildi-Tremblay, L. Gosselin, Minimizing shell-and-tube heat exchanger

cost with genetic algorithms and considering maintenance, International Journal

of Energy Research 31 (9) (2007) 867–885.

[42]A.C. Caputo, P.M. Pelagagge, P. Salini, Heat exchanger design based on

economic optimisation, Applied Thermal Engineering 28 (10) (2008) 1151–

1159.

[43] Y. Ozcelik, Exergetic optimization of shell and tube heat exchangers using a

genetic based algorithm, Applied Thermal Engineering 27 (11–12) (2007) 1849–

1856.

[44] H. Peng, X. Ling, Optimal design approach for the plate-fin heat exchangers

using neural networks cooperated with genetic algorithms, Applied Thermal

Engineering 28 (5–6) (2008) 642–650.

[45] I. Ozkol, G. Komurgoz, Determination of the optimum geometry of the heat

exchanger body via a genetic algorithm, Numerical Heat Transfer Part A –

Applications 48 (3) (2005) 283–296.

Reference

125

[46] Sirikum J, Techanitisawad A, Power generation expansion planning with

emission control: a nonlinear model and a GA-based heuristic approach,

International Journal of Energy Research 30 (2) (2006) 81–99.

[47] H. Li, R. Nalim, P.A. Haldi, Thermal-economic optimization of a distributed

multi-generation energy system – a case study of Beijing, Applied Thermal

Engineering 26 (7) (2006) 709–719.

[48] M. Valdes, M.D. Duran, A. Rovira, Thermoeconomic optimization of

combined cycle gas turbine power plants using genetic algorithms, Applied

Thermal Engineering 23 (17) (2003) 2169–2182.

[49] X. Qin, L. Chen, F. Sun, C. Wu, Optimization for a steam turbine stage

efficiency using a genetic algorithm, Applied Thermal Engineering 23 (18) (2003)

2307–2316.

[50] S. Obara, Operating schedule of a combined energy network system with

fuel cell, International Journal of Energy Research 30 (13) (2006) 1055–1073.

[51] N. Oldenburg, G. Gruhn, J. Stoldt, Capacity analysis of multi-product plants

integrating energy consumption, Applied Thermal Engineering 21 (13–14) (2001)

1283–1298.

*52+ G.A. Efthimeros, D.T. Tsahalis, Intensified energy-saving technologies

developed in EU-funded research: a review, Applied Thermal Engineering 20

(15–16) (2000) 1607–1613.

[53] D.A. Manolas, C.A. Frangopoulos, T.P. Gialamas, D.T. Tsahalis, Operation

optimization of an industrial cogeneration system by a genetic algorithm,

Energy Conversion and Management 38 (15–17) (1997) 1625–1636.

[54] F. Pettersson, J. Soderman, Design of robust heat recovery systems in paper

machines, Chemical Engineering and Processing 46 (10) (2007) 910–917.

Reference

126

[55] K.M. Bjork, R. Nordman, Solving large-scale retrofit heat exchanger network

synthesis problems with mathematical optimization methods, Chemical

Engineering and Processing 44 (8) (2005) 869–876.

[56] J. Jezowski, R. Bochenek, G. Poplewski, On application of stochastic

optimization techniques to designing heat exchanger- and water networks,

Chemical Engineering and Processing 46 (11) (2007) 1160–1174.

[57] M.A.S.S. Ravagnani, A.P. Silva, P.A. Arroyo, A.A. Constantino, Heat

exchanger network synthesis and optimisation using genetic algorithm, Applied

Thermal Engineering 25 (7) (2005) 1003–1017.

[58] J. Dipama, A. Teyssedou, M. Sorin, Synthesis of heat exchanger networks

using genetic algorithms, Applied Thermal Engineering 28 (14–15) (2008) 1763–

1773.

[59] X. Ma, P. Yao, X. Luo, W. Roetzel, Synthesis of multi-stream heat exchanger

network for multi-period operation with genetic/simulated annealing

algorithms, Applied Thermal Engineering 28 (8–9) (2008) 809–823.

[60] L. Lu,W.J. Cai, Y.C. Soh, L. Xie, Global optimization for overall HVAC systems

Part II problem solution and simulations, Energy Conversion and Management

46 (7–8) (2005) 1015–1028.

[61] L. Lu,W.J. Cai, Y.S. Chai, L. Xie, Global optimization for overall HVAC systems

Part I problem formulation and analysis, Energy Conversion and Management

46 (7–8) (2005) 999–1014.

[62] L. Lu, W. Cai, L. Xie, S. Li, Y.C. Soh, HVAC system optimization – in building

section, Energy and Buildings 37 (1) (2005) 11–22.

[63] N. Nassif, S. Kajl, R. Sabourin, Optimization of HVAC, control system

strategy using two-objective genetic algorithm, HVAC&R 11 (3) (2005) 459–486.

Reference

127

[64] L. Lu, W.J. Cai, Y.C. Soh, L. Xie, S. Li, HVAC system optimization – condenser

water loop, Energy Conversion and Management 45 (4) (2004) 613–630.

[65] X. Jin, H. Ren, X. Xiao, Prediction-based online optimal control of outdoor

air of multi-zone VAV air conditioning systems, Energy and Buildings 37 (9)

(2005) 939–944.

*66+ G. Fabbri, A genetic algorithm for fin profile optimization, International

Journal of Heat and Mass Transfer 40 (9) (1997) 2165–2172.

[67] M. Younes, A. Potiron, A genetic algorithm for the shape optimization of

parts subjected to thermal loading, Numerical Heat Transfer Part A–

Applications 39 (5) (2001) 449–470.

*68+ M. Sasikumar, C. Balaji, Optimization of convective fin systems: a holistic

approach, Heat and Mass Transfer 39 (1) (2002) 57–68.

[69] K. Jeevan, G.A. Quadir, K.N. Seetharamu, I.A. Azid, Z.A. Zainal, Optimization

of thermal resistance of stacked micro-channel using genetic algorithm,

International Journal of Numerical Methods for Heat & Fluid Flow 15 (1) (2005)

27–42.

*70+ G. Fabbri, Heat transfer optimization in internally finned tubes under

laminar flow conditions, International Journal of Heat and Mass Transfer 41 (10)

(1998) 1243–1253.

*71+ G. Fabbri, Optimum profiles for asymmetrical longitudinal fills in cylindrical

ducts, International Journal of Heat andMass Transfer 42 (3) (1999) 511–523.

*72+ G. Fabbri, Optimization of heat transfer through finned dissipators cooled

by laminar flow, International Journal of Heat and Fluid Flow 19 (6) (1998) 644–

654.

Reference

128

[73+ G. Fabbri, Optimum performances of longitudinal convective fins with

symmetrical and asymmetrical profiles, International Journal of Heat and Fluid

Flow 20 (6) (1999) 634–641.

[74] H. Pedro, M.H. Kobayashi, C.F.M. Coimbra, A.K. da Silva, Effectiveness of

complex design through an evolutionary approach, Journal of Thermophysics

and Heat Transfer 22 (1) (2008) 115–118.

[75] A.J. Goupee, S.S. Vel, Two-dimensional optimization of material

composition of functionally graded materials using meshless analyses and a

genetic algorithm, Computer Methods in Applied Mechanics and Engineering

195 (44–47) (2006) 5926–5948.

[76] J.V. Wolfersdorf, E. Achermann, B. Weigand, Shape optimization of cooling

channels using genetic algorithms, Journal of Heat Transfer – Transactions of

the ASME 119 (2) (1997) 380–388.

[77] M. Krol, R.A. Bialecki, Optimization of a window frame by BEM and genetic

algorithm, International Journal of Numerical Methods for Heat & Fluid Flow 13

(5–6) (2003) 565–580.

[78] R.A. Bialecki, T. Burczynski, A. Dlugosz, W. Kus, Z. Ostrowski, Evolutionary

shape optimization of thermoelastic bodies exchanging heat by convection and

radiation, Computer Methods in Applied Mechanics and Engineering 194 (17)

(2005) 1839–1859.

[79] E. Nobile, F. Pinto, G. Rizzetto, Geometric parameterization and

multiobjective shape optimization of convective periodic channels, Numerical

Heat Transfer Part B – Fundamentals 50 (5) (2006) 425–453.

[80] P. Wildi-Tremblay, L. Gosselin, Layered porous media architecture for

maximal cooling, International Journal of Heat and Mass Transfer 50 (3–4)

(2007) 464–478.

Reference

129

[81] M. Tye-Gingras, L. Gosselin, Thermal resistance minimization of a fin-and-

porous medium heat sink with evolutionary algorithms, Numerical Heat

Transfer-Part A 54 (4) (2008) 349–366.

[82] A.K. da Silva, L. Gosselin, Evolutionary placement of discrete heaters in

forced convection, Numerical Heat Transfer – Part A 54 (1) (2008) 20–33.

[83] T. Dias, L.F. Milanez, Optimal location of heat sources on a vertical wall

with natural convection through genetic algorithms, International Journal of

Heat and Mass Transfer 49 (13–14) (2006) 2090–2096.

[84] R. Hilbert, G. Janiga, R. Baron, D. Thevenin, Multi-objective shape

optimization of a heat exchanger using parallel genetic algorithms, International

Journal of Heat and Mass Transfer 49 (15–16) (2006) 2567–2577.

[85] T.S. Schmit, A.K. Dhingra, F. Landis, G. Kojasoy, A genetic algorithm

optimization technique for compact high intensity cooler, Journal of Enhanced

Heat Transfer 3 (4) (1996) 281–290.

[86] K. Foli, T. Okabe, M. Olhofer, Y.C. Jin, B. Sendhoff, Optimization of micro

heat exchanger: CFD, analytical approach and multi-objective evolutionary

algorithms, International Journal of Heat and Mass Transfer 49 (5–6) (2006)

1090–1099.

[87] G. Fabbri, Heat transfer optimization in corrugated wall channels,

International Journal of Heat and Mass Transfer 43 (23) (2000) 4299–4310.

[88] D. Rakshit, C. Balaji, Thermodynamic optimization of conjugate convection

from a finned channel using genetic algorithms, Heat and Mass Transfer 41 (6)

(2005) 535–544.

Reference

130

[89] H.W. Lee, Y.J. Teng, I.A. Azid, K.N. Seetharamu, Neuro-genetic optimization

of micro compact heat exchanger, International Journal of Numerical Methods

for Heat & Fluid Flow 17 (1) (2007) 20–33.

[90] B. Ozcelik, T. Erzurumlu, Determination of effecting dimensional

parameters on warpage of thin shell plastic parts using integrated response

surface method and genetic algorithmic, International Communications in Heat

and Mass Transfer 32 (8) (2005) 1085–1094.

[91] M. Cavazzuti, M.A. Corticelli, Optimization of a buoyancy chimney with a

heated ribbed wall, Heat and Mass Transfer 44 (4) (2008) 421–435.

[92] S.M.H. Sarvari, Optimal geometry design of radiative enclosures using the

genetic algorithm, Numerical Heat Transfer Part A – Applications 52 (2) (2007)

127–143.

[93] M.N. Ozisik, H.R.B. Orlande, Inverse Heat Transfer, Taylor & Francis, 2000.

[94] M.R. Jones, M.Q. Brewster, Y. Yamada, Application of a genetic algorithm to

the optical characterization of propellant smoke, Journal of Thermophysics and

Heat Transfer 10 (2) (1996) 372–377.

[95] H.Y. Li, C.Y. Yang, A genetic algorithm for inverse radiation problems,

International Journal of Heat and Mass Transfer 40 (7) (1997) 1545–1549.

[96] M.R. Jones, A. Tezukaa, Y. Yamada, Thermal tomographic detection of

inhomogeneities, Journal of Heat Transfer – Transactions of the ASME 117 (4)

(1995) 969–975.

*97+ M. Raudensky, J. Horsky, J. Krejsa, L. lama, Usage of artificial intelligence

methods in inverse problems for estimation of material parameters,


19–29.

Reference

131

[98] E. Divo, A. Kassab, F. Rodriguez, Characterization of space dependent

thermal conductivity with a BEM-based genetic algorithm, Numerical Heat

Transfer Part A – Applications 37 (8) (2000) 845–875.

[99] S. Orain, Y. Scudeller, S. Garcia, T. Brousse, Use of genetic algorithms for the

simultaneous estimation of thin films thermal conductivity and contact

resistances, International Journal of Heat and Mass Transfer 44 (20) (2001)

3973–3984.

[100] S. Garcia, E.P. Scott, Use of genetic algorithms in thermal property

estimation. Part I: Experimental design optimization, Numerical Heat Transfer

Part A –Applications 33 (2) (1998) 135–147.

[101] S. Garcia, J. Guynn, E.P. Scott, Use of genetic algorithms in thermal

property estimation. Part II: Simultaneous estimation of thermal properties,

Numerical Heat Transfer Part A – Applications 33 (2) (1998) 149–168.

[102] A.R. Hanuska, E.P. Scott, K. Daryabeigi, Thermal characterization of

aerospace structures, Journal of Thermophysics and Heat Transfer 14 (3) (2000)

322–329.

[103] S. Verma, C. Balaji, Multi-parameter estimation in combined conduction–

radiation from a plane parallel participating medium using genetic algorithms,

International Journal of Heat and Mass Transfer 50 (9–10) (2007) 1706–1714.

[104] K. Daryabeigi, Heat transfer in high-temperature fibrous insulation,

Journal of Thermophysics and Heat Transfer 17 (1) (2003) 10–20.

*105+ G.R. Liu, J.H. Lee, A.T. Patera, Z.L. Yang, K.Y. Lam, Inverse identification of

thermal parameters using reduced-basis method, Computer Methods in Applied

Mechanics and Engineering 194 (27–29) (2005) 3090–3107.

Reference

132

[106] M. Raudensky, K.A. Woodbury, J. Kral, T. Brezina, Genetic algorithm in

solution of inverse conduction problems, Numerical Heat Transfer Part B –

Fundamentals 28 (3) (1995) 293–306.

[107] X. Xu, S. Wang, Optimal simplified thermal models of building envelope

based on frequency domain regression using genetic algorithm, Energy and

Buildings 39 (5) (2007) 525–536.

[108] S.W. Wang, X.H. Xu, Parameter estimation of internal thermal mass of

building dynamic models using genetic algorithm, Energy Conversion and

Management 47 (13–14) (2006) 1927–1941.

[109] P. Lauret, H. Boyer, C. Riviere, A. Bastide, A genetic algorithm applied to

the validation of building thermal models, Energy and Buildings 37 (8) (2005)

858–866.

[110] K.H. Cho, S. Kim, Y.J. Lee, A fast EIT image reconstruction method for the

two-phase flow visualization, International Communications in Heat and Mass

Transfer 26 (5) (1999) 637–646.

[111] Y.H. Guo, G.B. He, A.T. Hsu, Application of genetic algorithms to the

development of a variable Schmidt number model for jet-in-crossflows,


744–760.

[112] Randy L. Haupt, Sue Ellen Haupt, Practical genetic algorithms, second

edition, John Wiley & Sons,2004.

[113] Bentley P. An Introduction to Evolutionary Design by Computers: Morgan

Kaufmann; 1999.

Reference

133

[114] IAPWS, Revised Release on the IAPWS Formulation 1995 for the

Thermodynamic Properties of Ordinary Water Substance for General and

Scientific Use (2009).

[115] Kitto J B, Stultz S C. Steam Its Generation and Use. 41th ed. Ohio: Babcok

and Wilcox Co; 2005.

[116] Toffolo A, Lazzareto A. Evolutionary algorithms for multi-objective

energetic and economic optimization in thermal system design. Energy 27

(2002) 549–567.

[117] Kakaç S. Boilers Evaporators and Condensers. 1st ed. New York: Wiley;

1991.

[118] Boyce M P. Handbook for cogeneration and combined cycle power plant.

New York: ASME Press; 2002.

[119] Ganapathy V. Heat-Recovery Steam Generators, Understand the Basics,

Chemical engineering progress, 1996.

http://www.angelfire.com/md3/vganapathy/hrsgcep.pdf [accessed 06.07.2016]

[120] Ganpathy V. Industrial Boilers and Heat Steam Generators, Design

Applications and Calculations. 1st ed. New York: Marcel Deker Inc; 2002.

[121] Queipo N, Devarakonda R, Humphrey JAC, Genetic algorithms for

thermosciences research – application to the optimized cooling of electronic

components, International Journal of Heat and Mass Transfer 37 (6) (1994) 893–

908.

http://www.angelfire.com/md3/vganapathy/hrsgcep.pdf

Documents

Thermal Design and Optimization of Heat Recovery … Thermal Design and Optimization of Heat Recovery Steam Generators and Waste Heat Boilers Ali Rezaie Navaie Berlin 2017 Technische