GAS TURBINES AND JET AND ROCKET PROPULSION Dr. M.L. MATHUR AND R.P. SHARMA ST AND ARD PUBLISHERS DISTRIBUTORS 1705-B, Nai Sarak, DELHl-110006 Phone : 1262700, 3215791 Post Box : 1066 l'llilillml by: Nern Chand Jait1 (Prop.), Standard Publishers Distributors, 1705-8, Nai Sarak, Delhi-110006 Second Edition 2007 Edition: 2010 'Edition 2014 This bo0k, or parts thereof, may not be reproduced in any form or traru.lated without the written permission of the Authors a~ publisher. Price : Rs.125. ISBN 81-8014-062-8 Prirrud at: Lomus f)ff"-Ct Pr~s. nl·!i1i. PREFACE Gas turbine is relatively a new power plant which has been originated and developed in the last half a century. World War n inducted this.power plant into aircrafts as a jet propulsion engine. Today turbojet engine and its variants are th~ most important power plants for aircraft and missile propulsion. Basically th.ere are two types of propulsive device1, : air breathfog engines and rockets. Initially the rocket technology developed due to the requirements ofmilitary but in recent times the requirements of space travel forced a· tremendous development in rocket propulsion. In this background, Gas Turbines and Jet and Rocket Propul sion has bec:>me a very important subject for mechanical engineers and many institutions have included this subject at under-graduate and post-graduate levels. This !hook has been written. to serve as a text· book for the Gas Turbine and Jet and Rocket Propulsion courses taught to engineer ing studeuts and not for specialists in propulsion. The book is based on Gas Turbine and Jet Propulsion courses given by authors to students for several years. The book is divided into nine chapters. Chapter l compares gas turbine plant with highly developed reciprocating internal combustion engine and steam turbine plants, and describes various applications of gas turbines. Chapter 2 gives the thermodynamic analysis of theor;;:tical and actual gas turbine plants-for .nuckar power generation, total energy systems and automotive field. For the study of propulsiou systems a basic knowledge of gas dynamics is essential and Chapter 3 is dtvoted to this topic. Compressor forms a very important component of a gas turbine plant as it absorbs almost two-thirds of the power developed by the turbine. The overall efficiency of a gas turbine plant heavily depends on the performance of tha compressor. As an introduction to compressors, Chapter 4 is devoted to positive displacement compressors-both reciprocating and rotary types. Chapter 5 deals with theory of dynamic compressors used in gas turbine plants, an.d compares the two basic type of compressors-the C<Jntrifugal and axial flow types including their design. Chapter 6 deals with gas turbine combustion chambers. The turbine design is a vast subject. Chapter 7 gives in.tro<luction to gas turbine design. Chapter 8 is devoted to jet propulsion. It deals with turbojet, turboprop and thrust argum~n tation devices. The athodoydsr;J.m jet and pulse jet, are also discussed. Finally, a comparison of different jet propulsion devices is given. ( iv) Chapter 9 is devoted to rocket propulsion and deals with solid and. liquid propellant chemical rockets. Possible future develop ments in rocket technology-nuclear, electrostatic and electromag netic rockets ar-e also discussed. The ~uthors have tried to present the subject matter in a simple can · and clear. manner so that the student learn subject with mi~immn help from the teacher. The,figures have been given as simple reproducible line diagrams. The theory has been illustrated with a large number of solved examnles, which are graded and titled, Sufficient examples for practic¢ have also been given. B0th S()lved and unsolved examples have been taken from various university examinations. A large nu,mber of theory qu~stions are given at the end of each chapter for self-testing of students. \Vith the rapid developments iln science and technol ."gy, knowkJgc and information be.comes dut of date very soon, and each .new bcok should justify its birth on the basis of presentation of new matedal. In this book an attempt has been made to draw deep into the latest literature available .. It is hoped that this feat~re will justify this book and it will be useful to practising engineers also. It is with great pleasure that . the authors express their gratitud~ t? many colleagues for ~ssista. ¢ce. . Thank~ are_particu]arly due to Shn F.S. Mehta, Reader m lllecpamcal engmeermg, Univer sity of Jodhpur, for critical comments and assistance in workirg out everal of the illustrative cxamp le~. Thanks are due to Shri 5 P.S. Kachhawa and ·S.N. · Garg for pre.paring the drawings. Authors also thank Shri Nem Chand Jain of M/s. St~ndard Publishers Distributors for·an help and co-operation in pulilishing this.book. !n the fir~t edition of" book some mistakes invariably creep in. Th,fauthors will be gr...eful if these are called to their atten tion. Also the authors will be hap}W to receive si.Iggestipns from students .and teachers for imprO\ inglthe book in sub:;-:quent editions. New Year Day M.L. Mathur · 1st January 1976 R;P. Sharma PREF ACE TO THE SECOND EDITION In the second edition of the book, the subject matter has been revised and upto date. 1st Oct. 1987 M.L. ~fathur R.P. Sha1 .na CONTE1VTS Preface V xi Glossary of Symbols 1-18 CHAPTER 1. Introduction -J 'l. Development of gas turbine 1 ... 1'2. Classification of ga~ turbines < 1·3. Gas turbine vs. reciprocating I C. ,--ngi"le~ 5 1'4, Gas turbine v.s. steam turbine 8 1·5. Applications of gas tuibinc 9 References 16 Exercises 1 17 l9-97 CHAPTER 2. Analysis of gas Turbine Cycles 2· 1. The '6asic cycle 19 2·2. Analysis of simple gas turbine cycle 19 .2'3. .Effect of thermodynamic variables on the performance of simple gas turbine plant · 24 24. Improvements in simple gas turbine cycle 2.9 2·5. Actual gas turbi'le cycle 41 2 6. Closed cyi;le gas turbine 4'.\ 2·1. Helium cooled.closed gas tu~bine for nuclear power plants 49 2°8. Total _energy system incorpO! a ting gas turbine 51 54 2'9, Semi-closed cycle gas turbine 55 2'10. Gas turbine plant arrangements 57 2' 11. Automotive gas turbine , Illustrative examples 61 Exercises 2 91 References 95 CHAPTER 3. Basic gas Dynamics 98-119 3'1, Introduction 98 3'2. Propagation of small disturban.ce-the velocity of sound 98 :j•.3, Mach number, Mach cone ar,d Mach angle 00 3·~. Total or st.igoation properties 10:? 3'$, One-dimensional adiabatic flow 104 3 6. I,sentropic ftow 106 3'7. Isentropic ftow in a passage of variabie cross-section u~ IM J·S. Flow ti.rough a convergent t:ozzle-cfTcct of pressure ratio 109 3 9. Flow through .a convergent-divergent nozzle l 10' ( ;,i) mustrative examples 112 Exerches 3 117 Rfferences U9 CHAPTER 4. Positive Displacement Compressors 120-14%. 4·1. Introduction 120 4'2, Classification of air compressors 121 4·3. Compressor efficiencies 121 4·4. He ciprocating compreswr 123 4'5. Roots blower 129 4'6, Lysholm compressor 132 4'7. Vane type compressor U2 4"8. L:quiJ piston rotary compressor 134 4 9. Reciprocating vs. rotary p;Jsitive oisp!acement compressors 135 Illustrative examples 136 Exerci '.Cf 4 140 References 142 CHAPTER 5. Dynamic Coimpressors 143-213 S'l. Dyri..:mic or steady flow compres,ors 143 s·:z. Total head or stagnation properties 145 5"3. Werk done in compre~sion in a dynamic compressor 146 5'4. Etfa iencies of dynamic compressors 148 5'5. Veloc;ty diagrams 152 5'6. Design uf cen!rifugal compressors 160 5"1. De~rce ol,' rcac!ion 172 5\8. Vetiex theory 174 5·9, A,rofoH theory 176 s·H•. Cc:scade th~ory !80 5 11. Surg;ng in compressors and its control 182 5·12. Characterhlic curves of dynamic compre·sors 185 5'13. Centrifugal vs. Axia( flow compressors 186 l i 1.ustrntiw e:xsmp!es 189 Exercises 5 210 References 212 CHAPTER 6. Gas Turbine Co:mbusdon Chamber 2141-239' 6·1. Introduction 214 6·2. Requirements 214 6·3. Combustion p1ocess in gas tmbir;e, 215 6'4. Types of combustion chamber 217 ~- 6"" Flow pattern in a combustion chamber 220 6"6. Performance and ope ating characteristics of combus• 0 t.ion chambers 223 6·7. Fuel injection in combustion chamber 234 (vii) ~·s. Conclusion 237 Exercises 6 237 References 238 CHAPTER 7. Eiem.enta1·y Turbines DHiga 240-303 1·1. I.,trcduction 240 7·2. !mplu~e and reaction turbine 240 1·:, C,,mpounding of turbines 241 "1"4. Efficien..:y of a turbine 242 1"5. Velocity diagrams work and efficiency 243 1 6. Degree of reaction 246 7.7. Flow and blade loading coefficients 248 7·g. \i elocity ratio 248 '!"9. Design for various degrees of reaction 249 1·10. Design with axial velocity outlet 2S2 7·11. Off-design performance 253 7'12. i, adia! equilibrium theory 254 7· B. Actuator disc theory 265 7·14 Factors limitin; the turbine design 265 1"15. Materials for gas turbines 271 716. Cooling of gas turbine blades 280 Il!ustrative examples 2,1 References 300 CHAPTER 8. Jet Propu1!!1ion 304-365 s·L Introduction .... :,. 304 8'2, Th:ust 306 8·3. Thrust vs. thrust hOise power :109 8·4. Efficiencies 311 s·s. Airscrew 317 8"6. Turbojet 319 11·1. Thrust augumentation 327 g·s. Turboprop engine 332 8·9. Bypass and ducted fan engines 334 s· 10. Regenerative ducted fan engine 336 s· H. T11rboshaft en>,line 338 8"12. Ram jet 338 8"13. Pulsejet 341 8"14. R·im rocket 345 11· 15. Comp:mson of various propulsion devices 345 l!lu-trativc cxampks 348 Exercises 8 361 Referenc•:s 364 CHAPTER. 9. Rocket Prop111lid.o:o ~-389 9.l. In1rnduc1ion 366 9·2. cia~sification of rocke1s 361 ( viii ) 9·3. Principle of rncket propulsion 369' 9"4. Analysis of an ideal chemical rock.et 371 9·s. Op,imum expansion ratio for rocket 374 9 6. The chcmi~dl rocket 375 . 9·7. Advantages of liquid propellant rockets lWi:r so: id propelli!nt rockets 383 9'8. Free radiC/iloi propulsio:, 383 9·9. Nude.r p opulsion 384 9·!0. Inn propulsion 38? 9 11. Plasma propulsion 38? 9·12. Pho:on propubi0r. 384 Exercises 9 388 Referenc.:s 389 INDEX 390 at't'tl v.,,nJtti'Nd a••~•i-'if·i«' ~on. ,. , ~1,u·•·•·· Cj •tiiiM'fat. i",&tam Pf~sff:t.; Ci s}lit-•t'il~ TI>ft1ffle b,tJ diiiffi1ffet I itttetwr: nerD t! s,Cti~ mte't'rtiJ ti:i:llfi)'J t,asG of t{jftn'al loptitltffit fern ,. ' F. ,.~ f g fftv)lit~J fit~FW4tiiilil ,. cffltst1aiit'~f j,t'e,att~1utifft Jf h &pt'tiff€ enthalpy, h~igl1f of blade J .fwt(t\ tijuivafou · · 1' afrsOiitte· ttffrtyetthtre tKetvin)~ work ,don;;: faciot, L,I Ienttli~ tkftft5 fift M m4'ifftilttt \ttf~lff:. Mith n-umoex 111· mliil. tti~Jtiifiwti-, ffttirrtJtr ~:f bia~ts · · m DHtsf ti¥ft N retati('Jftat &p'e'eth rlvofwfrd1 p, r mintltir ff polyU''epie index p ptJWer P;p absoh1tlt ptdsute fl, q heat; tatr of beat, transfer R ga:s c0rl'stant, titgree of tcactivr; Ro unihirsat gas cbnstant t, , ra:tlius, comptess!on rati0. st~ed· ratio ptes:sut~ ratfo s enttofJy