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INTERNAL COMBUSTIONPROCESSES OF LIQUIDROCKET ENGINES

INTERNAL COMBUSTIONPROCESSES OF LIQUIDROCKET ENGINESMODELING AND NUMERICALSIMULATIONS

Zhen-Guo WangNational University of Defense Technology Changsha China

This edition first published 2016copy 2016 National Defense Industry Press All rights reserved

Published by John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 under exclusive license granted by National Defense Industry Press for all media and languages excludingChinese and throughout the world excluding Mainland China and with non-exclusive license for electronic versions inMainland China

Registered OfficeJohn Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore 138628

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

All Rights Reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in anyform or by any means electronic mechanical photocopying recording scanning or otherwise except as expresslypermitted by law without either the prior written permission of the Publisher or authorization through payment of theappropriate photocopy fee to the Copyright Clearance Center Requests for permission should be addressed to thePublisher John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 tel 65-66438000 fax 65-66438008 email enquirywileycom

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The Publisher is not associated with any product or vendor mentioned in this book This publicationis designed to provide accurate and authoritative information in regard to the subject matter covered It is sold onthe understanding that the Publisher is not engaged in rendering professional services If professional advice orother expert assistance is required the services of a competent professional should be sought

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparingthis book they make no representations or warranties with respect to the accuracy or completeness of the contentsof this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purposeIt is sold on the understanding that the publisher is not engaged in rendering professional services and neitherthe publisher nor the author shall be liable for damages arising herefrom If professional advice or other expertassistance is required the services of a competent professional should be sought

Library of Congress Cataloging-in-Publication data applied for

ISBN 9781118890028

A catalogue record for this book is available from the British Library

Set in 10 12pt Times by SPi Global Pondicherry India

1 2016

INTERNAL COMBUSTIONPROCESSES OF LIQUIDROCKET ENGINES

INTERNAL COMBUSTIONPROCESSES OF LIQUIDROCKET ENGINESMODELING AND NUMERICALSIMULATIONS

Zhen-Guo WangNational University of Defense Technology Changsha China

This edition first published 2016copy 2016 National Defense Industry Press All rights reserved

Published by John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 under exclusive license granted by National Defense Industry Press for all media and languages excludingChinese and throughout the world excluding Mainland China and with non-exclusive license for electronic versions inMainland China

Registered OfficeJohn Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore 138628

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

All Rights Reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in anyform or by any means electronic mechanical photocopying recording scanning or otherwise except as expresslypermitted by law without either the prior written permission of the Publisher or authorization through payment of theappropriate photocopy fee to the Copyright Clearance Center Requests for permission should be addressed to thePublisher John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 tel 65-66438000 fax 65-66438008 email enquirywileycom

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The Publisher is not associated with any product or vendor mentioned in this book This publicationis designed to provide accurate and authoritative information in regard to the subject matter covered It is sold onthe understanding that the Publisher is not engaged in rendering professional services If professional advice orother expert assistance is required the services of a competent professional should be sought

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparingthis book they make no representations or warranties with respect to the accuracy or completeness of the contentsof this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purposeIt is sold on the understanding that the publisher is not engaged in rendering professional services and neitherthe publisher nor the author shall be liable for damages arising herefrom If professional advice or other expertassistance is required the services of a competent professional should be sought

Library of Congress Cataloging-in-Publication data applied for

ISBN 9781118890028

A catalogue record for this book is available from the British Library

Set in 10 12pt Times by SPi Global Pondicherry India

1 2016

INTERNAL COMBUSTIONPROCESSES OF LIQUIDROCKET ENGINESMODELING AND NUMERICALSIMULATIONS

Zhen-Guo WangNational University of Defense Technology Changsha China

This edition first published 2016copy 2016 National Defense Industry Press All rights reserved

Published by John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 under exclusive license granted by National Defense Industry Press for all media and languages excludingChinese and throughout the world excluding Mainland China and with non-exclusive license for electronic versions inMainland China

Registered OfficeJohn Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore 138628

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

All Rights Reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in anyform or by any means electronic mechanical photocopying recording scanning or otherwise except as expresslypermitted by law without either the prior written permission of the Publisher or authorization through payment of theappropriate photocopy fee to the Copyright Clearance Center Requests for permission should be addressed to thePublisher John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 tel 65-66438000 fax 65-66438008 email enquirywileycom

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The Publisher is not associated with any product or vendor mentioned in this book This publicationis designed to provide accurate and authoritative information in regard to the subject matter covered It is sold onthe understanding that the Publisher is not engaged in rendering professional services If professional advice orother expert assistance is required the services of a competent professional should be sought

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparingthis book they make no representations or warranties with respect to the accuracy or completeness of the contentsof this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purposeIt is sold on the understanding that the publisher is not engaged in rendering professional services and neitherthe publisher nor the author shall be liable for damages arising herefrom If professional advice or other expertassistance is required the services of a competent professional should be sought

Library of Congress Cataloging-in-Publication data applied for

ISBN 9781118890028

A catalogue record for this book is available from the British Library

Set in 10 12pt Times by SPi Global Pondicherry India

1 2016

This edition first published 2016copy 2016 National Defense Industry Press All rights reserved

Published by John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 under exclusive license granted by National Defense Industry Press for all media and languages excludingChinese and throughout the world excluding Mainland China and with non-exclusive license for electronic versions inMainland China

Registered OfficeJohn Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore 138628

For details of our global editorial offices for customer services and for information about how to apply for permission toreuse the copyright material in this book please see our website at wwwwileycom

All Rights Reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in anyform or by any means electronic mechanical photocopying recording scanning or otherwise except as expresslypermitted by law without either the prior written permission of the Publisher or authorization through payment of theappropriate photocopy fee to the Copyright Clearance Center Requests for permission should be addressed to thePublisher John Wiley amp Sons Singapore Pte Ltd 1 Fusionopolis Walk 07-01 Solaris South Tower Singapore138628 tel 65-66438000 fax 65-66438008 email enquirywileycom

Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be availablein electronic books

Designations used by companies to distinguish their products are often claimed as trademarks All brand namesand product names used in this book are trade names service marks trademarks or registered trademarks of theirrespective owners The Publisher is not associated with any product or vendor mentioned in this book This publicationis designed to provide accurate and authoritative information in regard to the subject matter covered It is sold onthe understanding that the Publisher is not engaged in rendering professional services If professional advice orother expert assistance is required the services of a competent professional should be sought

Limit of LiabilityDisclaimer of Warranty While the publisher and author have used their best efforts in preparingthis book they make no representations or warranties with respect to the accuracy or completeness of the contentsof this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purposeIt is sold on the understanding that the publisher is not engaged in rendering professional services and neitherthe publisher nor the author shall be liable for damages arising herefrom If professional advice or other expertassistance is required the services of a competent professional should be sought

Library of Congress Cataloging-in-Publication data applied for

ISBN 9781118890028

A catalogue record for this book is available from the British Library

Set in 10 12pt Times by SPi Global Pondicherry India

1 2016

Contents

Preface x

1 Introduction 111 Basic Configuration of Liquid Rocket Engines 2

111 Propellant Feed System 2112 Thrust Chamber 6

12 Internal Combustion Processes of Liquid Rocket Engines 13121 Start and Shutdown 13122 Combustion Process 15123 Performance Parameters in Working Process 18

13 Characteristics and Development History of Numerical Simulation of theCombustion Process in Liquid Rocket Engines 19131 Benefits of Numerical Simulation of the Combustion Process in

Liquid Rocket Engines 19132 Main Contents of Numerical Simulations of Liquid Rocket Engine

Operating Process 19133 Development of Numerical Simulations of Combustion Process

in Liquid Rocket Engines 2114 Governing Equations of Chemical Fluid Dynamics 2215 Outline of this Book 24References 25

2 Physical Mechanism and Numerical Modeling of Liquid Propellant Atomization 2621 Types and Functions of Injectors in a Liquid Rocket Engine 2722 Atomization Mechanism of Liquid Propellant 28

221 Formation of Static Liquid Droplet 28222 Breakup of Cylindrical Liquid Jet 29223 Liquid Sheet Breakup 36

224 Droplet Secondary Breakup 4323 Characteristics of Atomization in Liquid Rocket Engines 48

231 Distribution Function of the Droplet Size 51232 Mean Diameter and Characteristic Diameter 53233 Measurement of Spray Size Distribution 55

24 Atomization Modeling for Liquid Rocket Engine Atomizers 59241 Straight-flow Injector 60242 Centrifugal Injector 60243 Impinging-stream Injectors 64244 Coaxial Shear Injector 70245 Coaxial Centrifugal Injectors 70

25 Numerical Simulation of Liquid Propellant Atomization 75251 Theoretical Models of Liquid Propellant Atomization 75252 Quasi-fluid Models 80253 Particle Trajectory Models 81254 Simulation of Liquid Jet Atomization Using Interface Tracking Method 85255 Liquid Jet Structure ndash Varying Flow Conditions 91

References 94

3 Modeling of Droplet Evaporation and Combustion 9731 Theory for Quasi-Steady Evaporation and Combustion of a Single Droplet at

Atmospheric Pressure 97311 Quasi-Steady Evaporation Theory for Single Droplet in the Static

Gas without Combustion 98312 Quasi-Steady Evaporation Theory for Droplet in a Static Gas with

Combustion 103313 Non-Combustion Evaporation Theory for a Droplet in a

Convective Flow 107314 Evaporation Theory for a Droplet in a Convective Medium with

Combustion 10832 Evaporation Model for a Single Droplet under High Pressure 109

321 ZKS Droplet High Pressure Evaporation Theory 110322 Application of the Liquid Activity Coefficient to Calculate the

GasndashLiquid Equilibrium at a High Pressure 11533 Subcritical Evaporation Response Characteristics of Propellant Droplet in

Oscillatory Environments 117331 Physical Model 118332 Examples and the Analysis of Results 120

34 Multicomponent Fuel Droplet Evaporation Model 123341 Simple Multicomponent Droplet Evaporation Model 124342 Continuous Thermodynamics Model of Complex Multicomponent

Mixture Droplet Evaporation 13535 Droplet Group Evaporation 145

351 Definition of Group Combustion Number 146352 Droplet Group Combustion Model 146

References 149

vi Contents

4 Modeling of Turbulence 15141 Turbulence Modeling in RANS 152

411 Algebraic Model 153412 One-Equation Model 154413 Two-Equation Models 156414 Turbulence Model Modification 161415 Nonlinear Eddy Viscosity Model 165416 Reynolds-Stress Model 170417 Comments on the Models 173

42 Theories and Equations of Large Eddy Simulation 174421 Philosophy behind LES 174422 LES Governing Equations 175423 Subgrid-Scale Model 176424 Hybrid RANSLES Methods 182

43 Two-Phase Turbulence Model 187431 HinzendashTchen Algebraic Model for Particle Turbulence 187432 Two-Phase Turbulence Model k-ε-kp and k-ε-Ap 188

References 189

5 Turbulent Combustion Model 19251 Average of Chemical Reaction Term 19252 Presumed PDFmdashFast Chemistry Model for Diffusion Flame 194

521 Concepts and Assumptions 195522 κminusεminusZminusg Equations 197523 Probability Density Distribution Function 197524 Presumed PDF 198525 Truncated Gaussian PDF 200

53 Finite Rate EBUmdashArrhenius Model for Premixed Flames 20154 Moment-Equation Model 202

541 Time-Averaged Chemical Reaction Rate 203542 Closure for the Moments 203

55 Flamelet Model for Turbulent Combustion 204551 Diffusion Flamelet Model 205552 Premixed Flamelet Model 206

56 Transported PDF Method for Turbulent Combustion 208561 Transport Equations of the Probability Density Function 208562 The Closure Problem of Turbulence PDF Equation 211563 Transport Equation for the Single-Point Joint PDF with

Density-Weighted Average 212564 Solution Algorithm for the Transport Equation of Probability

Density Function 21257 Large Eddy Simulation of Turbulent Combustion 214

571 Governing Equations of Large Eddy Simulation forTurbulent Combustion 214

572 Sub-Grid Scale Combustion Models 218References 226

viiContents

6 Heat Transfer Modeling and Simulation 22861 Convective Heat Transfer Model of Combustor Wall 228

611 Model of Gas Convection Heat 229612 Convection Cooling Model 232

62 Heat Conduction Model of Combustor Wall 235621 Fourier Heat Conduction Law 235622 1D Steady Heat Conduction 235623 2D Steady Heat Conduction 237624 Unsteady Heat Conduction 237

63 Radiation Heat Transfer Model 238631 Basic Law of Radiation 238632 Empirical Model of Radiation Heat Flux Density Calculation 245633 Numerical Simulation of Combustion Heat Radiation 246

References 254

7 The Model of Combustion Instability 25571 Overview 255

711 Behavior of Combustion Instability 256712 Classification of Combustion Instability 257713 Characteristics of Combustion Instability 259

72 Acoustic Basis of Combustion Instability 260721 Rayleigh Criterion for Acoustic Oscillations Arising from

Heat or Mass Supply 260722 Acoustic and Acoustic Oscillations 261723 Acoustic Modes in the Combustion Chamber 263724 Self-Excited Oscillations in Rocket Engines 267

73 Response Characteristics of Combustion Process in Liquid Rocket Engines 269731 Response Characteristics of the Propellant Supply System 269732 Response Characteristics of Spray Atomization Process 271733 Response Characteristics of Droplet Evaporation Process 272

74 Sensitive Time Delay Model nminusτ 272741 Combustion Time Delay 272742 Sensitive Time Delay Model 273

75 Nonlinear Theory for Combustion Stability in Liquid Rocket Engines 283751 Nonlinear Field Oscillator Model 286752 Continuous Stirred Tank Reactor Acoustic Model 287753 Spatio-Temporal Interaction Dynamic Model 291754 General Thermodynamic Analysis of Combustion Instability 293

76 Control of Unstable Combustion 295761 Passive Control 295762 Active Control 297763 A Third Control Method 298

References 300

viii Contents

8 Numerical Method and Simulations of Liquid Rocket EngineCombustion Process 30281 Governing Equations of Two-Phase Multicomponent Reaction Flows 302

811 Gas Phase Governing Equation 303812 Liquid Particle Trajectory Model 305813 Turbulence Model 308814 Droplets Atomizing Model 309815 Droplet Evaporation Model 311816 Chemical Reaction Kinetics Model 313

82 Numerical Methodology 314821 Overview 314822 The Commonly-Used Discretization Scheme 315823 Discrete Equations 320824 Discretization of the Momentum Equation Based on the

Staggered Grid 323825 The SIMPLE Algorithm of Flow Field Computing 326826 PISO Algorithm 329

83 Grid Generation Techniques 334831 Structured Grid Generation Technology 334832 Unstructured Mesh Generation Techniques 338

84 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340841 Numerical Analysis of Dual-States Hydrogen Engine Combustion

and Heat Transfer Processes 340842 Numerical Heat Transfer Simulation of a Three-Component

Thrust Chamber 349843 Numerical Simulation of Liquid Rocket Engine Combustion

Stability 356References 376

Index 377

ixContents

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

224 Droplet Secondary Breakup 4323 Characteristics of Atomization in Liquid Rocket Engines 48

231 Distribution Function of the Droplet Size 51232 Mean Diameter and Characteristic Diameter 53233 Measurement of Spray Size Distribution 55

24 Atomization Modeling for Liquid Rocket Engine Atomizers 59241 Straight-flow Injector 60242 Centrifugal Injector 60243 Impinging-stream Injectors 64244 Coaxial Shear Injector 70245 Coaxial Centrifugal Injectors 70

25 Numerical Simulation of Liquid Propellant Atomization 75251 Theoretical Models of Liquid Propellant Atomization 75252 Quasi-fluid Models 80253 Particle Trajectory Models 81254 Simulation of Liquid Jet Atomization Using Interface Tracking Method 85255 Liquid Jet Structure ndash Varying Flow Conditions 91

References 94

3 Modeling of Droplet Evaporation and Combustion 9731 Theory for Quasi-Steady Evaporation and Combustion of a Single Droplet at

Atmospheric Pressure 97311 Quasi-Steady Evaporation Theory for Single Droplet in the Static

Gas without Combustion 98312 Quasi-Steady Evaporation Theory for Droplet in a Static Gas with

Combustion 103313 Non-Combustion Evaporation Theory for a Droplet in a

Convective Flow 107314 Evaporation Theory for a Droplet in a Convective Medium with

Combustion 10832 Evaporation Model for a Single Droplet under High Pressure 109

321 ZKS Droplet High Pressure Evaporation Theory 110322 Application of the Liquid Activity Coefficient to Calculate the

GasndashLiquid Equilibrium at a High Pressure 11533 Subcritical Evaporation Response Characteristics of Propellant Droplet in

Oscillatory Environments 117331 Physical Model 118332 Examples and the Analysis of Results 120

34 Multicomponent Fuel Droplet Evaporation Model 123341 Simple Multicomponent Droplet Evaporation Model 124342 Continuous Thermodynamics Model of Complex Multicomponent

Mixture Droplet Evaporation 13535 Droplet Group Evaporation 145

351 Definition of Group Combustion Number 146352 Droplet Group Combustion Model 146

References 149

vi Contents

4 Modeling of Turbulence 15141 Turbulence Modeling in RANS 152

411 Algebraic Model 153412 One-Equation Model 154413 Two-Equation Models 156414 Turbulence Model Modification 161415 Nonlinear Eddy Viscosity Model 165416 Reynolds-Stress Model 170417 Comments on the Models 173

42 Theories and Equations of Large Eddy Simulation 174421 Philosophy behind LES 174422 LES Governing Equations 175423 Subgrid-Scale Model 176424 Hybrid RANSLES Methods 182

43 Two-Phase Turbulence Model 187431 HinzendashTchen Algebraic Model for Particle Turbulence 187432 Two-Phase Turbulence Model k-ε-kp and k-ε-Ap 188

References 189

5 Turbulent Combustion Model 19251 Average of Chemical Reaction Term 19252 Presumed PDFmdashFast Chemistry Model for Diffusion Flame 194

521 Concepts and Assumptions 195522 κminusεminusZminusg Equations 197523 Probability Density Distribution Function 197524 Presumed PDF 198525 Truncated Gaussian PDF 200

53 Finite Rate EBUmdashArrhenius Model for Premixed Flames 20154 Moment-Equation Model 202

541 Time-Averaged Chemical Reaction Rate 203542 Closure for the Moments 203

55 Flamelet Model for Turbulent Combustion 204551 Diffusion Flamelet Model 205552 Premixed Flamelet Model 206

56 Transported PDF Method for Turbulent Combustion 208561 Transport Equations of the Probability Density Function 208562 The Closure Problem of Turbulence PDF Equation 211563 Transport Equation for the Single-Point Joint PDF with

Density-Weighted Average 212564 Solution Algorithm for the Transport Equation of Probability

Density Function 21257 Large Eddy Simulation of Turbulent Combustion 214

571 Governing Equations of Large Eddy Simulation forTurbulent Combustion 214

572 Sub-Grid Scale Combustion Models 218References 226

viiContents

6 Heat Transfer Modeling and Simulation 22861 Convective Heat Transfer Model of Combustor Wall 228

611 Model of Gas Convection Heat 229612 Convection Cooling Model 232

62 Heat Conduction Model of Combustor Wall 235621 Fourier Heat Conduction Law 235622 1D Steady Heat Conduction 235623 2D Steady Heat Conduction 237624 Unsteady Heat Conduction 237

63 Radiation Heat Transfer Model 238631 Basic Law of Radiation 238632 Empirical Model of Radiation Heat Flux Density Calculation 245633 Numerical Simulation of Combustion Heat Radiation 246

References 254

7 The Model of Combustion Instability 25571 Overview 255

711 Behavior of Combustion Instability 256712 Classification of Combustion Instability 257713 Characteristics of Combustion Instability 259

72 Acoustic Basis of Combustion Instability 260721 Rayleigh Criterion for Acoustic Oscillations Arising from

Heat or Mass Supply 260722 Acoustic and Acoustic Oscillations 261723 Acoustic Modes in the Combustion Chamber 263724 Self-Excited Oscillations in Rocket Engines 267

73 Response Characteristics of Combustion Process in Liquid Rocket Engines 269731 Response Characteristics of the Propellant Supply System 269732 Response Characteristics of Spray Atomization Process 271733 Response Characteristics of Droplet Evaporation Process 272

74 Sensitive Time Delay Model nminusτ 272741 Combustion Time Delay 272742 Sensitive Time Delay Model 273

75 Nonlinear Theory for Combustion Stability in Liquid Rocket Engines 283751 Nonlinear Field Oscillator Model 286752 Continuous Stirred Tank Reactor Acoustic Model 287753 Spatio-Temporal Interaction Dynamic Model 291754 General Thermodynamic Analysis of Combustion Instability 293

76 Control of Unstable Combustion 295761 Passive Control 295762 Active Control 297763 A Third Control Method 298

References 300

viii Contents

8 Numerical Method and Simulations of Liquid Rocket EngineCombustion Process 30281 Governing Equations of Two-Phase Multicomponent Reaction Flows 302

811 Gas Phase Governing Equation 303812 Liquid Particle Trajectory Model 305813 Turbulence Model 308814 Droplets Atomizing Model 309815 Droplet Evaporation Model 311816 Chemical Reaction Kinetics Model 313

82 Numerical Methodology 314821 Overview 314822 The Commonly-Used Discretization Scheme 315823 Discrete Equations 320824 Discretization of the Momentum Equation Based on the

Staggered Grid 323825 The SIMPLE Algorithm of Flow Field Computing 326826 PISO Algorithm 329

83 Grid Generation Techniques 334831 Structured Grid Generation Technology 334832 Unstructured Mesh Generation Techniques 338

84 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340841 Numerical Analysis of Dual-States Hydrogen Engine Combustion

and Heat Transfer Processes 340842 Numerical Heat Transfer Simulation of a Three-Component

Thrust Chamber 349843 Numerical Simulation of Liquid Rocket Engine Combustion

Stability 356References 376

Index 377

ixContents

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

4 Modeling of Turbulence 15141 Turbulence Modeling in RANS 152

411 Algebraic Model 153412 One-Equation Model 154413 Two-Equation Models 156414 Turbulence Model Modification 161415 Nonlinear Eddy Viscosity Model 165416 Reynolds-Stress Model 170417 Comments on the Models 173

42 Theories and Equations of Large Eddy Simulation 174421 Philosophy behind LES 174422 LES Governing Equations 175423 Subgrid-Scale Model 176424 Hybrid RANSLES Methods 182

43 Two-Phase Turbulence Model 187431 HinzendashTchen Algebraic Model for Particle Turbulence 187432 Two-Phase Turbulence Model k-ε-kp and k-ε-Ap 188

References 189

5 Turbulent Combustion Model 19251 Average of Chemical Reaction Term 19252 Presumed PDFmdashFast Chemistry Model for Diffusion Flame 194

521 Concepts and Assumptions 195522 κminusεminusZminusg Equations 197523 Probability Density Distribution Function 197524 Presumed PDF 198525 Truncated Gaussian PDF 200

53 Finite Rate EBUmdashArrhenius Model for Premixed Flames 20154 Moment-Equation Model 202

541 Time-Averaged Chemical Reaction Rate 203542 Closure for the Moments 203

55 Flamelet Model for Turbulent Combustion 204551 Diffusion Flamelet Model 205552 Premixed Flamelet Model 206

56 Transported PDF Method for Turbulent Combustion 208561 Transport Equations of the Probability Density Function 208562 The Closure Problem of Turbulence PDF Equation 211563 Transport Equation for the Single-Point Joint PDF with

Density-Weighted Average 212564 Solution Algorithm for the Transport Equation of Probability

Density Function 21257 Large Eddy Simulation of Turbulent Combustion 214

571 Governing Equations of Large Eddy Simulation forTurbulent Combustion 214

572 Sub-Grid Scale Combustion Models 218References 226

viiContents

6 Heat Transfer Modeling and Simulation 22861 Convective Heat Transfer Model of Combustor Wall 228

611 Model of Gas Convection Heat 229612 Convection Cooling Model 232

62 Heat Conduction Model of Combustor Wall 235621 Fourier Heat Conduction Law 235622 1D Steady Heat Conduction 235623 2D Steady Heat Conduction 237624 Unsteady Heat Conduction 237

63 Radiation Heat Transfer Model 238631 Basic Law of Radiation 238632 Empirical Model of Radiation Heat Flux Density Calculation 245633 Numerical Simulation of Combustion Heat Radiation 246

References 254

7 The Model of Combustion Instability 25571 Overview 255

711 Behavior of Combustion Instability 256712 Classification of Combustion Instability 257713 Characteristics of Combustion Instability 259

72 Acoustic Basis of Combustion Instability 260721 Rayleigh Criterion for Acoustic Oscillations Arising from

Heat or Mass Supply 260722 Acoustic and Acoustic Oscillations 261723 Acoustic Modes in the Combustion Chamber 263724 Self-Excited Oscillations in Rocket Engines 267

73 Response Characteristics of Combustion Process in Liquid Rocket Engines 269731 Response Characteristics of the Propellant Supply System 269732 Response Characteristics of Spray Atomization Process 271733 Response Characteristics of Droplet Evaporation Process 272

74 Sensitive Time Delay Model nminusτ 272741 Combustion Time Delay 272742 Sensitive Time Delay Model 273

75 Nonlinear Theory for Combustion Stability in Liquid Rocket Engines 283751 Nonlinear Field Oscillator Model 286752 Continuous Stirred Tank Reactor Acoustic Model 287753 Spatio-Temporal Interaction Dynamic Model 291754 General Thermodynamic Analysis of Combustion Instability 293

76 Control of Unstable Combustion 295761 Passive Control 295762 Active Control 297763 A Third Control Method 298

References 300

viii Contents

8 Numerical Method and Simulations of Liquid Rocket EngineCombustion Process 30281 Governing Equations of Two-Phase Multicomponent Reaction Flows 302

811 Gas Phase Governing Equation 303812 Liquid Particle Trajectory Model 305813 Turbulence Model 308814 Droplets Atomizing Model 309815 Droplet Evaporation Model 311816 Chemical Reaction Kinetics Model 313

82 Numerical Methodology 314821 Overview 314822 The Commonly-Used Discretization Scheme 315823 Discrete Equations 320824 Discretization of the Momentum Equation Based on the

Staggered Grid 323825 The SIMPLE Algorithm of Flow Field Computing 326826 PISO Algorithm 329

83 Grid Generation Techniques 334831 Structured Grid Generation Technology 334832 Unstructured Mesh Generation Techniques 338

84 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340841 Numerical Analysis of Dual-States Hydrogen Engine Combustion

and Heat Transfer Processes 340842 Numerical Heat Transfer Simulation of a Three-Component

Thrust Chamber 349843 Numerical Simulation of Liquid Rocket Engine Combustion

Stability 356References 376

Index 377

ixContents

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

6 Heat Transfer Modeling and Simulation 22861 Convective Heat Transfer Model of Combustor Wall 228

611 Model of Gas Convection Heat 229612 Convection Cooling Model 232

62 Heat Conduction Model of Combustor Wall 235621 Fourier Heat Conduction Law 235622 1D Steady Heat Conduction 235623 2D Steady Heat Conduction 237624 Unsteady Heat Conduction 237

63 Radiation Heat Transfer Model 238631 Basic Law of Radiation 238632 Empirical Model of Radiation Heat Flux Density Calculation 245633 Numerical Simulation of Combustion Heat Radiation 246

References 254

7 The Model of Combustion Instability 25571 Overview 255

711 Behavior of Combustion Instability 256712 Classification of Combustion Instability 257713 Characteristics of Combustion Instability 259

72 Acoustic Basis of Combustion Instability 260721 Rayleigh Criterion for Acoustic Oscillations Arising from

Heat or Mass Supply 260722 Acoustic and Acoustic Oscillations 261723 Acoustic Modes in the Combustion Chamber 263724 Self-Excited Oscillations in Rocket Engines 267

73 Response Characteristics of Combustion Process in Liquid Rocket Engines 269731 Response Characteristics of the Propellant Supply System 269732 Response Characteristics of Spray Atomization Process 271733 Response Characteristics of Droplet Evaporation Process 272

74 Sensitive Time Delay Model nminusτ 272741 Combustion Time Delay 272742 Sensitive Time Delay Model 273

75 Nonlinear Theory for Combustion Stability in Liquid Rocket Engines 283751 Nonlinear Field Oscillator Model 286752 Continuous Stirred Tank Reactor Acoustic Model 287753 Spatio-Temporal Interaction Dynamic Model 291754 General Thermodynamic Analysis of Combustion Instability 293

76 Control of Unstable Combustion 295761 Passive Control 295762 Active Control 297763 A Third Control Method 298

References 300

viii Contents

8 Numerical Method and Simulations of Liquid Rocket EngineCombustion Process 30281 Governing Equations of Two-Phase Multicomponent Reaction Flows 302

811 Gas Phase Governing Equation 303812 Liquid Particle Trajectory Model 305813 Turbulence Model 308814 Droplets Atomizing Model 309815 Droplet Evaporation Model 311816 Chemical Reaction Kinetics Model 313

82 Numerical Methodology 314821 Overview 314822 The Commonly-Used Discretization Scheme 315823 Discrete Equations 320824 Discretization of the Momentum Equation Based on the

Staggered Grid 323825 The SIMPLE Algorithm of Flow Field Computing 326826 PISO Algorithm 329

83 Grid Generation Techniques 334831 Structured Grid Generation Technology 334832 Unstructured Mesh Generation Techniques 338

84 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340841 Numerical Analysis of Dual-States Hydrogen Engine Combustion

and Heat Transfer Processes 340842 Numerical Heat Transfer Simulation of a Three-Component

Thrust Chamber 349843 Numerical Simulation of Liquid Rocket Engine Combustion

Stability 356References 376

Index 377

ixContents

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

8 Numerical Method and Simulations of Liquid Rocket EngineCombustion Process 30281 Governing Equations of Two-Phase Multicomponent Reaction Flows 302

811 Gas Phase Governing Equation 303812 Liquid Particle Trajectory Model 305813 Turbulence Model 308814 Droplets Atomizing Model 309815 Droplet Evaporation Model 311816 Chemical Reaction Kinetics Model 313

82 Numerical Methodology 314821 Overview 314822 The Commonly-Used Discretization Scheme 315823 Discrete Equations 320824 Discretization of the Momentum Equation Based on the

Staggered Grid 323825 The SIMPLE Algorithm of Flow Field Computing 326826 PISO Algorithm 329

83 Grid Generation Techniques 334831 Structured Grid Generation Technology 334832 Unstructured Mesh Generation Techniques 338

84 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340841 Numerical Analysis of Dual-States Hydrogen Engine Combustion

and Heat Transfer Processes 340842 Numerical Heat Transfer Simulation of a Three-Component

Thrust Chamber 349843 Numerical Simulation of Liquid Rocket Engine Combustion

Stability 356References 376

Index 377

ixContents

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

Preface

Liquid rocket engines are the main propulsion system for a spacecraft The widespread appli-cations of liquid rocket engines in the future demands further studies of combustion mechan-isms in liquid rocket engines to improve their performance Numerical modeling of thecombustion process can improve our understanding of the incorporated physical mechanismand help in the design of liquid rocket engines Since the 1970s numerical simulations of com-bustion in liquid rocket engines have developed into a new interdisciplinary subject involvingcomputational fluid dynamics computational heat transfer computational combustion soft-ware design and flow visualization Owing to its significance in engine design this new subjecthas attracted many researchers With the rapid development of computer techniques andnumerical methods numerical modeling and simulations of atomization and combustion inliquid rocket engines will become an ever important research areaThe author has dedicated himself to the area of Aeronautical and Astronautical Science and

technology since the 1980s The present book is based on the teaching and supervision ofundergraduate and postgraduate students in the past 30 years The book highlights the advancedresearch work in the field of combustion modeling in liquid rocket engines such as liquid pro-pellant atomization evaporation of liquid droplets turbulent flows turbulent combustion heattransfer and combustion instability All these will contribute to our understanding of the com-bustion mechanism and to the improvement of combustion modeling facilitating numericalsimulations of combustion process in liquid fuelled enginesThe book consists of eight chapters Chapter 1 describes the configuration and fundamentals

of liquid rocket engines and presents an overview of numerical simulations of combustion inliquid rocket engines Chapters 2ndash7 detail the modeling of combustion sub processes in liquidrocket engines ie atomization modeling evaporation modeling turbulence modeling com-bustion modeling heat transfer modeling and combustion instability modeling Chapter 8 pre-sents a full description of numerical models for combustion numerical methodology forgoverning equation solution and grid generation Finally three applications are run to demon-strate the capability of the numerical models to predict the combustion process in liquid rocketengines

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

1Introduction

A liquid rocket engine which is also called a liquid propellant rocket engine is a chemicalrocket engine using liquid chemicals (liquid propellant) as the energy source and the workingfluid Liquid rocket engine technology has drawn researchersrsquo attention and been quite a hottopic in aerospace and aeronautic research during the last 70 years In the short long history ofhuman aviation ie from the A-4 engine of the German V2 missile to the F-1 engine of theUS lunar landing rocket ldquoSaturn 5rdquo and further to reusable space shuttle main engines everymilestone event is closely linked with the progress made in liquid rocket engine technologyBecause liquid rocket engines have the characteristics of high specific impulse repeatablestarting arbitrary working hours setting multiple usage adjustable thrust etc they are boundto occupy the dominant position in the area of aerospace propulsion long into the futureThe liquid rocket engine uses liquid fuels as the propellant In a liquid rocket engine the

liquid chemical propellants combust in the combustion chamber and produce very high pres-sure gas The gas is accelerated when it flows downstream through the nozzle and producesimpulse ie thrust for the aircraft There are several types of liquid propellants The schemestructure ignition and thermal protection etc of the liquid rocket engine have a close relation-ship with the characteristics of the propellants used by the engine systemThe expansion of liquid rocket application requires more in-depth studies on the basic theory

and design method of the liquid rocket engine Numerical simulation of the combustion processin a liquid rocket engine is also an important research direction This chapter introduces thebasic configuration and working process of liquid rocket engines and then discusses the mainobjective and research method of the numerical simulation of the combustion process in aliquid rocket engine

Internal Combustion Processes of Liquid Rocket Engines Modeling and Numerical SimulationsFirst Edition Zhen-Guo Wangcopy 2016 National Defense Industry Press Published 2016 by John Wiley amp Sons Singapore Pte Ltd

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

11 Basic Configuration of Liquid Rocket Engines

A liquid rocket engine consists of a thrust chamber (which consists of an injector a combustorand a nozzle) a propellant feed system propellant tanks and various automatic regulators etcThis section mainly introduces the propellant feed system and the thrust chambers which areclosely associated with the combustion process

111 Propellant Feed System

The propellant feed system is employed to deliver the propellants from the containing tanks tothe thrust chamber and can be divided into two categories according to the working modenamely the pressure feed system and the turbo-pump feed system

1111 Pressure Feed System

The pressure feed system pushes the propellants to the thrust chamber or the propellant gasgenerator by the high pressure gas in the tanks of the propellants The high pressure gasie the pressed gas can be pre-stored in cylinders as the storage gas and can also be generatedby a liquid or solid gas generator during the working process of the liquid rocket engine Themain requirements for the pressed gas are as follows (i) high density while under the pressedstate (ii) low relative molecular mass under the pressed state (iii) minor solubility with pro-pellant (iv) no or minor chemical reaction with the propellants and (v) no solid and liquidimpuritiesThe pressure feed system can employ inert gases as the pressed gas This kind of pressure

feed system has two type of working mode namely the regulated pressure mode and the blow-down mode The former employs a pressure regulator to maintain the pressure in the propellanttank and also maintains the thrust at a constant value The latter stores the propellant and thepressed gas in one tank The pressure drops during the adiabatic expansion of gas fewer pro-pellants are injected into the combustor and therefore the pressure in the combustion chamberalso drops Typical pressure feed systems are (i) those with high-pressure gas cylinders and(ii) those with gas generators The former can employ air nitrogen helium and some otherinert gas as the pressed gas The main drawback of air is that the contained oxygen has a rela-tively high boiling point and therefore it cannot be used to press cryogenic propellants Heliumcan be used to press all existing liquid propellants Although such a pressure feed system has arelatively large size and heavy mass it has the characteristics of a simple structure and highreliability It is also simple to employ and ensures repeatable starting of the engineIn pressure feed systems with a gas generator a single-component liquid fuel gas generator

using a monopropellant as the source of the driven pressure and the propellant decompositioncan be realized by catalysis or heating according to the kind of propellant In dual-componentliquid fuel gas generators the high pressure gas can be obtained from the two propellant com-ponents by burning under oxygen-rich or fuel-rich conditions The temperature of the gas isdetermined by the propellant component mixed ratio in the gas generatorThe structure of the pressure feed system is simple and reliable However as the propellant

tanks must withstand high internal pressure the pressure feed system is relatively bulky and it isoften employed by spacecraft-attitude-control engines Sometimes to ensure the reliability of

2 Internal Combustion Processes of Liquid Rocket Engines

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction

manned flight although the engine thrust is large a pressure feed system is also employed suchas the service module engine drop class and upgraded engines of Apollo spacecraft

1112 Turbo-Pump Feed System

A turbo-pump feed system employs pumps to deliver propellants and the pump acquires thedriven force from a turbo In the turbo-pump feed system a turbo-pump assembly is necessaryThe basic requirements for a liquid rocket engine turbo-pump are as follows

1 If the mass flow rate of a given propellant is given we need to ensure the pressure at theengine outlet matches the requirement of the engine system

2 The turbo-pump should be as small and light as possible3 The turbo-pump is to have as high an efficiency as possible4 The turbo-pump should ensure stable operation at all engine operating conditions and the

pressure pulsation and mechanical vibration must be minor5 The turbo-pump is to be compatible with corrosive liquid and cryogenic liquids Friction is

not allowed between the components of the oxidizer pump because the heat created by thefriction may produce a local high temperature even an explosion

6 The turbo-pump is to be capable of sucking propellants that contain a small amount of gasor steam

There are three common types of cycle program for the turbo-pump feed system namely gasgenerator cycle expansion cycle and staged combustion cycle The gas generator cycle and thestaged combustion cycle can employ most of the commonly used liquid propellants Theexpansion cycle engine is commonly used in an engine that employs liquid hydrogen as thrustchamber coolant because liquid hydrogen is a good absorbing-heat medium and it does notdecomposeIn the gas generator cycle the turbine inlet gas is from an independent gas generator turbine

exhaust gas by passing through a small area ratio turbine nozzle or by injecting in the mainstream of the engine through the opening of a nozzle divergence cone The gas generator pro-pellant can be monopropellant or bipropellant both of which are from the main propellant feedsystem Figure 11 shows the bipropellant gas generator cycle turbo-pump feed system the fuelin the pump portion is injected into the bipropellant gas generator and combust producingworking fluid to drive the turbine To make sure that the temperature of the combustion prod-ucts in the gas generator is suitable for the requirements of the turbine we need to control thepropellant mixing ratio in the gas generator and the gas temperature should be in the range700ndash900 C Since a bipropellant gas generator system does not require an auxiliary propellantor another tank its structure is certainly simple and it is widely employed in liquid rocketenginesThe gas generator cycle is relatively simple The pressure in the fluid pipes and pumps is

relatively low Therefore it is the most commonly used turbo-pump cycle For an engine usingthe gas generator cycle the specific impulse of the thrust chamber is slightly higher than thatof the engine However the thrust of the thrust chamber is always slightly lower than that ofthe engine

3Introduction