liquid rocket propulsion instabilities

NASA SP-194

NATIONAL AERONAUTICS AND

SPACE ADMINISTRATION

NASA SP-194

LIQUID PROPELLANT ROCKET COMBUSTION INSTABILITY

.

Editor DAVID HARRJE T. Princeton University

Associate Editor FREDERICK REARDON H. Sacramento State College

Scientific and Technical information Ofice

1972

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Washington, D.C.

-

For sale by thc Supcrintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402Price$5.50

Library of C O ~ ~ TCahlog Card Number 70-170324 PSS Stock nrirnbcr 3300-0450

PREFACEThis reference book originated in the concern of a number of engineers engaged in the solution of problems of combustion instability for more effective communication between the various workers in this field. I n December 1962 an ad hoc working group was formed by the JANNAF Interagency Propulsion Committee (then the Interagency Chemical Rocket Propulsion Group, ICRPG) to study the extent of combustion instability problems in liquid propellant rocket engines and to make recommendations as to their solution. This ad hoc group urged that a more permanent working group be established to promote an integrated research and technology plan, which could provide stability design criteria, and to promote a better exchange of technical information among scientists and engineers interested in combustion instability in liquid propellant rockets. The ICRPG formed a Working Group on Liquid Propellant Combustion Instability in January 1964. Beginning that year, annual conferences have been held by the Working Group. These conferences, the proceedings of which are published promptly in the form of expanded abstracts (with illustrations), have proven to be extremely effective in enhancing the exchange of up-to-date information. I t was recognized from the beginning, honever, that much of the theoretical and experimental combustion instability information was scattered in numerous progress reports and technical papers in various journals and conference proceedings. I n its first year, the Working Group recommended the preparation of a book that would help to train new ~vorkcrs the field, as well as providing a reference in for others. I n 1964 a reference book committee was appointed by the Working Group to outline the content. At the 1965 Working Group meeting, the committee presented its recommended reference book outline, and means of implementing the writing and publication of the book were discussed. Further deliberations by the committee during 1966 resulted in the recommendation that a prime contract be given to a general editor, someone well acquainted with the combustion instability field, who could subcontract the variety of subject matter to a number of specialized authors. This recommendation was adopted by the Working Group; work \\-as initiated in 1967 under a SASA contract with Princeton University, with Richard J. Priem, of the ?;Ash-Lewis Research Center, as contract monitor. Funds for the contract were provided by SASA, the Air Force, the Army, and the Itavy. The excellence of the work done by the Reference Book Committee is evidenced by the fact that their suggested outline has been rather closely followed. I t is hoped that this reference book will prove to be useful to all ~vorkers the in liquid propellant combustion instability field, whether they are engaged in research, design, or development. The philosophy followed in compiling this book is that the prime importance is to provide the main outline of the most significant developments, both theoretical and experimental, with emphasis on fundamental principles and relationships between alternative approaches. For detailed information, the reader is supplied with an extensive list of references, which should help guard against rapid obsolescence of the reference book, a danger faced by any text in a fast-developing field.

iv

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There are four main parts to the book: (1) background information, including an introduction to the phenomenon of combustion instability and a discussion of pertinent aspects of the combustion and flow processes that take place in a liquid propellant rocket engine (Chs. 1 to 3), (2) analytical models of both low and high frequency instability, with the theoretical basis of each model given first and the use of the models in design and development following in a separate chapter (Chs. 4 t o 6 ) , (3) a practical guide for designers, including aspects of excitation and damping, with experiential information integrated as much as possible with the results of theoretical studies (Chs. 7 and 8), and (4) experimental aspects of the study of combustion instability, that is, techniques used to identify and investigate oscillatory processes in both research and developmental hardware, and methods of rating the stability of a giver] engine (Chs. 9 and 10). The reference book is designed to allow the reader to quickly look up information on combustion instability and related topics. The detailed index provided by the authors and editors as well as the extensive table of contents should greatly aid the reader in this respect. The General Somenclature, supplemented by specialized nomenclature when required, should provide thc required information to interpret the equations accurately. Each equation, figure, and table is uniquely numbered by section to avoid confusion. We arc greatly indebted to the many authors and reviewers (whose names are listed elsenhere in the book) for the generally high quality of their manuscripts and their cooperativeness during the editorial process. Special thanks go to Robert J. Hefncr and I,. Paul Combs, who took responsibility for compiling Chapters 9 and 10, respectively, arid to 01ven W. Dykema, who edited Section 7.4. The Editors David '1'. EIarrjc Frederick 11. Iteardon

CONTENTSCHAPTER

PAGE

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF EDITORS. AUTHORS. A N D REVIEWERS . . . . . . . . . . . .1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1 LIQUID ROCKET ENGINE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Conventional Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1.1 Press~~re-fed engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1.2 P11mp-fed engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Advanced Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2.1 Aerospike cngine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2.2 St.aged combustion engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Performance Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3.1 External performance parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3.2 Intcrr~al processes in rocket thrust chambers . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3.3 Ileal rocket performance calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 CORZBUSTION INSTABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Physical RIanifcstat.ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1.1 Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1.2 Effect on combustion efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2.1 Low frequency, chug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2.2 High frcqucncy instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2.3 Intermcdiatc frequency, buzz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Initiation of Combustion Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3.1 Spontaneously initiated linear instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3.2 Indr~ced nonlinear combustion instability . . . . . . . . . . . . . . . . . . . . . . . . . or 1.2.4 Dynamic Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4.1 Ilynamic versus statistical stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4.2 Dynamic stability in engine development programs . . . . . . . . . . . . . . . . . . 1.2.4.3 Demonstrating dynamic stability in engine development programs . . . . . 1.3 HISTOItICAL SUltVEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 CUItItENT STATUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

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xvii11 I 2 3 5

.5 6 7 8X 14 14 15 15 16 16 17 17 19 20 21 22 23 24 26 27 30 34

2 STEADY-STATE PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1

3737 37 38 39 39 40 41 42 42 45 45 . 46 49 49 50 51 52

GENERAL DESCItIPTION OF COMBUSTION AND FLOW PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Overall 1)escription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Conversion Time and Izesidence Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Characteristic Length and Characteristic Velocity . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Gas-Phase Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Condensed-Phase and Gasification Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Spray Comb~~stion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.1.7 Experimental Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.8 Elaborntior~on 1)escription of Spray-Combustion Modela . . . . . . . . . . . . . . . . . 2.2 INJECTION AND ATOllIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 JIanifold Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 J e t Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 JIechanisms of Atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.1 Liquid surface instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.2 Liquid jet breakup, low velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.3 Liquid jet breakup, high velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.4 St~mmary jet breakup results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of

LIQUID PROPELLANT ROCKET COMBUSTION INSTABILITYCHAPTER PAGE

2.2.3.5 Surface breakup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.6 Liquid sheet breakup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.7 Secondary drop breakup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Spray Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 SPATIAL DISTRIBUTION OF PROPELLANTS . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 hlass Flux Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Mixture Ratio Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Mixing Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.1 Liquid phase mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.2 1)roplct transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3.3.3 Vapor mlxlng. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Itecirc111.ttion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 LIQUIII 1)ItOPLET VAPOItIZATION AND COMBUSTION . . . . . . . . . . . . 2.4.1 1)roplet IIc~at-Up and Vaporizat.ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Biprop~11:~11t 1)ropIet Cornk)listion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2.1 Envc. lope flarnc model for sltbcritic:tl prcssurcs-theory and experiment . . . 2.4.2.2 1~:nvclopcflame model for srtpcrcritic:tl pressures-theory and experiment . .. 2.4.3 Monopropellant 1)roplet Comb~~stion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3.1 Monopropellant droplet decomposition in an atmosphere comprised solely of inert gases or decomposition products-theory and experiment . 2.4.3.2 %lonopropellant droplet fuel decomposition in an oxidizing atmospheretheory and experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 FLOW PIIOCESSI'S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Corc! Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1.1 Effects of injector design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 ..5.1.2 R1cchanic:~lt~~rbrllence generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 I3nrtnd:~rvFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2.1 Film or t)o~~nd:try coolant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2.2 Wall effects . . . . . . . . . . . ......................... 2..5.2.3 Off-design opctration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Energy Jteleasc 1)istribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3.1 I':lrment dcsign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 ..5. 3.2 Combustion volume and length effects . . . . . . . . . . . . . . . . . . . . . . . . . . .

52 54 55 55 99 ~59 60 63 6569

70 72 74 77 83 84 9194

9590

100 100 100 102 102 102 103 103103

103 104

3 DYIVAJIICS OF COLIIBCSTION AND FLOW PROCESSES . . . . . .3.1 1NTIIOI)UCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 FLOW I N PROPELLANT F E E D SYSTlChlS . . . . . . . . . . . . . . . . . . . . . .. . . 3.2.1 Fved S!.stcm Aror~stics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Component 1)ynsmics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2.1 Lumped-parameter approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2.2 Continuo~~s-parameter approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2.3 Modal techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 System Itesponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Comparison of Analysis and Experi~nent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......................................... 3.3 INJECTION PIS OF SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Mechanization of thc I31igine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Represer~t:ttiorl of u. Time Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.3 Obtaining the Solr~tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 234 234 236 236 237 238 240 241 242 242 243 243 243 243 244 244 246 247 249 249 251 253 253 254 257 258 259 260 260

6

U S E OF ANALYTICAL MODELS I N DESIGN A N D DEVELOPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

265

6.1 1NTIlOI)UCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 6.2 LOW AND INT151 GAS FLOWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Typical Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Effect. of 1)esign V.tri.tb1c.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s 10.4.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 FEIj:I> SYST15M PICI1TUIt.BATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Siren (Continr~or~s Osc+illatior~s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10.5.2 Pulscr (Singlc P111sc( h e r a t o r ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 OTITEll RATIN(; TE.CIrNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.1 Liquid ITydrogcrl Ten~pcratrlre Iiamping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.2 Variable Frc!c!rlc>nc.y T(,st.ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.3 Cornb~lstiotrAlt.c.r.ttiotrs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.4 Prcssurc Lcvcl Charlgc.s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 COMPAItISON OF ItATIN(; TI', C1TNIQUIj:S . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.1 Corrcbl:~tions I3cat.wc.c.11T(a(.hniqllcs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2 IJinlit~ntions Av:~il:~l)l(~ of Tcrhlliqllcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.1 I)is(.~~rl).~nec. c.ffccsts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [)rofilcs

539539 -539 540 540 541 542 543 546 546 547 548 548 550 55'2 555 556 557 557 558 5.51) 559 . 59 5 561 56:< 565 570 572 572 574 575 577 578 580 583 583 586 587 588 588 588 580 5O X

CONTENTSCHAPTER PAGE

Xlll

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10.7.2.2 Access ports through chamber walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.3 Shrapnel damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.4 Multiple pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.5 Thermal initiation of detonation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.6 Acoustic interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.7 External engine access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2.8 Handling characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.3 Criteria for Selection of a Rating Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.3.1 Program considerations . . . . . . . . . . . . ..................... 10.7.3.2 Engine design and operational considerations . . . . . . . . . . . . . . . . . . . . . . .

_

589 591 591 591 .591 591 592 592 593 593

GENERAL NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599 629

EDITORS, AUTHORS, AND REVIEWERS

Abbe, Charles J . Captain, USAF Formerly: Senior Project Engineer Air Force Rocket Propulsion Lab. Agosta, Vito D. Professor of Aerospace Engineering Aerospace Engineering and Applied Mechanics Polytechnic Institute of Brooklyn Bastress, E. Karl Director, Applied Sciences Group Northern Research and Engineering Corp. Bickford, Landis L. Supervisor, Control Dynamics Aerojet Liquid Rocket Company Bloomer, Harry E. Aerospace Engineer V/STOL and Noise Division NASA-Lewis Research Center Bracco, Frediano V. Member of the Research Staff Dept. of Aerospace and Mechanical Sciences Princeton University Breen, Ben P. Vice President I W B Engineering Burge, Harland L. Manager, Applied Technology Dept. TRW Systems Campbell, David T. Manager, Propulsion Technology Advanced Programs Rocketdyne Campbell, John, Jr. Manager, Production Thrust Chamber Unit Engineering Dept. Rocketdyne

Contributor, Sects. 6.4.3, 7.4.2, and 7.4.3 Reviewer, Chapter 4

Author, Sects. 3.5.2.1 to 3.5.2.3

Author, Sects. 4.4.2 and 6.6

Author, Sects. 5.5.3, 6.2.3.4, 7.5.2, and 7.5.3 Author, Sect. 10.3

Author, Sect. 7.2.4 Reviewer, Chapter 4

Contributor, Sect. 6.4.3


Contributor, Sects. 4.3.1 and 6.4.1 to 6.4.3 Reviewer, Chapter 2 Contributor, Sect. 7.4.4

xvi

LIQUID PROPELLANT ROCKET COMBUSTION

INSTABILITY

Carpenter, Thomas W. Assistant Professor Aeronautical Dept. California State Polytechnic College Chew, Thomas J. C. Senior Project Engineer Air Force Rocket Propulsion Laboratory Clayton, Richard M. Member of the Technical Staff Liquid Propulsion Section Jet Propulsion Laboratory Clinger, Eugene C. Engineering Manager Liquid Rocket Division Rocketdyne Combs, L. Paul Member of the Technical Staff Advanced Programs Rocketdyne Coultas, Thomas A. Program Manager Combustion and Materials Technology Advanced Programs Rocketdyne Crocco, Luigi Robert H. Goddard Professor of Aerospace Propulsion Aerospace and Mechanical Sciences Dept. Princeton University Culick, Fred E. C. Associate Professor of Engineering Mechanical Engineering Dept. California Institute of Technology Dobbins, Richard A. Professor of Engineering Division of Engineering Brown University Dykema, Owen W. Member of the Technical Staff Applied Mechanics Division The Aerospace Corporation Erbs, Joseph E. Project Engineer, Lance Liquid Rocket Division Rocketdyne

Reviewer, Chapter 2

Reviewer, Chapter 10

Author, Sect. 7.2.6 Contributor, Sect. 7.6 Reviewer, Chapter 10 Contributor, Sect. 7.4.3

Editor, Chapter 10 Author, Sects. 10.1 to 10.4 and 10.7 Reviewer, Chapter 9 Author, Sects. 1.2.1 to 1.2.3, 7.2.3, 8.3.6, 8.5.3, 9.2.2, 9.4.1, 9.4.2, and 9.4.3.2

Author, Sects. 4.2 and 5.3.2

Author, Sect. 4.5

Author, Sect. 8.5.2

Editor, Section 7.4 Author, Sects. 1.2.4, 4.4.1.3, 6.5.2, 7.4, 7.4.1, and 7.4.6 Reviewer, Chapter 3 Reviewer, Chapter 7

EDITORS,

SUTHORS,

AND REVIEWERS

xvii

Faeth, Gerard M. Associate Professor Mechanical Engineering Dept. Pennsylvania State University Fairchild, David A. Engineering Manager, Mechanical Design Aerojet Liquid Rocket Co. Feiler, Charles E. Head, Acoustics Section V/STOL and Noise Division NASA-Lewis Research Center Fenwick, James R. Member of the Technical Staff Liquid Rocket Division Rocketdyne Ford, Wayne M. Member of the Technical Staff Advanced Programs Rocketdyne Garrison, Gary D. Assistant Project Engineer Florida Research and Development Center Pratt and Whitney Aircraft Co. Goelz, Ralph R. Aerospace Engineer Chemical Rocket Division NASA-Lewis Research Center Groeneweg, John F. Aerospace Engineer V/STOL and Noise Division NASA-Lewis Research Center Hammer, Sandford S. Associate Professor Engineering Sciences Dept. Hofstra University Harris, George H. Operations Research Analyst Management Sciences Division Arthur D. Little, Inc. Harrje, David T. Senior Research Engineer and Lecturer Dept. of Aerospace and Mechanical Sciences Princeton University

Reviewer, Chapter 2

Author, Sect. 10.5

Author, Sects. 4.4.1.2 and 6.5.1

Author, Sects. 3.2, 5.4.3, and 7.5.1 Contributor, Sect. 3.3.1

Author, Sects. 9.4.1 and 9.6.4



Author, Sect. 2.2.4

Reviewer, Chapter 4

Author, Sects. 4.4.2 and 6.6

Editor, Reference Book Editor, Chapters 1,2,7, and 8 Author, Sects. 1.3, 1.4, 3.3.1,3.3.2, 7.1, 7.2.4, 8.5.1, 10.3, and 10.6.2 to 10.6.4 Contributor, Sects. 7.4.2 and 7.4.3

xviii


Hefner, Robert J. Director o Engineering Consumer Products Group f Bell and Howell Company Formerly : Manager, Combustion Dynamics Dept. Liquid Rocket Operations Aerojet-General Corp. Heidmann, Marcus F. Research Scientist Chemical Rocket Division NASA-Lewis Research Center Hewitt, Ross A. Engineering Specialist Combustion Dynamics Dept. Aerojet Liquid Rocket Company Howells, Edgar Senior Engineer Research and Development McGram-Edison Power Systems Division Formerly : Member of the Combustion Devices Group Bell Aerospace Company Kesselring, Robert C. Member of the Technical Staff Advanced Programs Rocketdyne Kosvic, Thomas C. i ineer Test C ng' IiVB Engineering Lazar, Robert S. l'roject Engineer Systems Center Naval Under~vater Leeper, Charles K. Assistant General Manager Itesearch and Engineering Aerojet Nuclear Company Levine, Robert S. Staff Scientist Space Tecahnology Division NASA-1,angley 1iesearc.h Center Lewis, J. Dudley Superintendent, Liquid Engines Division Rocket l'ropl~lsion Establishment Grcat Rrit,ain

Editor, Chapter 9 Author, Sects. 9.1, 9.2.1, 9.2.3, 9.3.3, 9.3.5, 9.4.1, 9.6.1, 9.6.2, 9.7.1, 10.2, 10.3, and 10.7 Contributor, Sect. 8.5.1 Reviewer, Chapter 10 Author, Sects. 4.4.1.2, 6.5.1, and 10.4 Reviewer, Chapter 7 Reviewer, Chapter 3

Author, Sect. 9.5

Author, Sects. 9.2.2, 9.4.2, 9.4.4.1, and 9.4.4.3


Reviewer, Chapter 1

Author, Sects. 4.4.1.4 and 6.5.3

Reviewer, Chapter 1


EDITORS,

AUTHORS, AND

REVIEWERS

xix

Lovingham, Joseph J. Director of Engineering The McIntire Company Formerly: Chief, Systems Engineering Reaction Motors Division Thiokol Chemical Corporation Lytle, Archie D. Principal Engineer Bell Aerospace Company Masters, Arthur I. Senior Assistant Project Engineer Florida Research and Development Center Pratt Bz IVhitney Aircraft Company Matthews, Birch J. Member of the Technical Staff TRW Systems McBride, James M. Supervisor Combustion Dynamics Aerojet Liquid Rocket Company Miller, Irwin Senior Staff llanager Alanagement Sciences Division A. D. Little Co. Miller, Joseph Manager, Propulsion Systems Engineering Dept. TRW Systems Mitchell, Charles E. Assistant Professor Dept. of Mechanical Engineering Colorado State University Monteil, Vernon H. Manager, Booster Propulsion Applied Mechanics Division The Aerospace Corporation Morgan, C. Joe Aerospace Engineer Chemical Rocket Division NASA-Lewis Research Center Nestlerode, James A. Member of the Technical Staff Liquid Rocket Division Rocketdyne


Author, Sect. 5.6


Author, Sect. 9.4.5

Author, Sects. 8.2.2 and 8.2.3 Contributor, Sect. 7.4.2 Author, Sects. 4.4.2 and 6.6

Reviewer, Chapter 5

Reviewer, Chapter 7

Author, Sect. 1.2.4

Reviewer, Chapter 8

Author, Sects. 3.2, 5.4.3, and 7.5.1 Contributor, Sect. 3.3.1 Reviewer, Chapter 6

XX


Nicholls, J. A. Professor Dcpt. o Aerospace Engineering f The University of Michigan Oberg, Carl L. Manager, Combustion Advanced Programs Rocketdyne Oshorn, John R. Professor of Mechanical Engineering Purduc University Phillips, Bert R. Aerospace Engineer Chemical Rocket Division NASA-Ilewis Research Center Powell, Walter R. Member of the Technical Staff Liquid Propulsion Section Jet Propulsion Laboratory Priem, Richard J . Head, Iiocket Combustion Section Chemical Rocket Division NASA-Lewis Research Center Proffitt, Robert L. Principal Scientist, Mechanics and Optics Rcscarch Division Rocketdyne Ranger, Arthur A. Assistant Professor School of Aeronautics, Astronautics, and Engineering Sciences Purdue University Reardon, Frederick H. Associate Professor of Mechanical Engineering Sacramento State College

Author, Sects. 3.3.3, 3.4.3.2, and 3.4.4.3


Author, Sect. 7.2.5 Reviewer, Chapter 9 Author, Sects. 8.3.2 and 8.3.3

Author, Sect. 1.1.3

Contract Monitor on Reference Rook Author, Sects. 4.3, 6.4, and 6.7 Author, Sect. 9.4.3.2

Reviewer, Chapter 3

Associate Editor, Reference Book Editor, Chapters 3, 4, 5, 6 Author, Sects. 3.3.1, 3.3.2, 3.4.4.1, 3.4.4.2, 3.5.3.3, 5.1, 5.2, 5.3.1, 5.4.1, 5.4.2, 5.5.1, 5.5.2, 6.1, 6.3, 6.7, 7.3, and 8.2.1 Author, Sect. 2.2.3

Rice, Edward J . Aerospace Engineer V/S'I'OII and Noise Ilivision NASA-1,ewis Iicscarch Center

EDITORS, AUTHORS, Richmond, Robert J. Technical Assistant Propulsion and Power Branch Astronautics Laboratory hlarshall Space Flight Center Rogero, Steve Senior Research Engineer Instrumentation Section Jet Propulsion Laboratory Rosner, Daniel E. Associate Professor Dept. of Engineering and Applied Science Yale University and Consultant to Aerochem Research Laboratories Rupe, Jack H. Research Group Supervisor Liquid Propulsion Section Jet Propulsion Laboratory Sack, Larry E. Member of the Technical Staff Liquid Iiot-ket Division Rocketdyne

AND REVIEWERS

XX1


Author, Sect. 9.3.3

Author, Sect. 2.4

Author, Sects. 2.2.1, 2.3.1, and 2.3.2

Author, Sects. 3.2, 5.4.3, and 7.5.1 Contributor, Sect. 3.3.1

Sanscrainte, Willard A. Technical Director of Advanced Agena Rocket Engines Bell Aerospace Company Senneff, John M. Assistant Chief Cng'ineer Combustion .Devices Bell Aerospace Company Sirignano, Jliilliam A. Associate I'rofessor Dept. of Aerospace and Mechanical Sciei~ces Princeton IJniversity Smith, Allan J . Jr. Research Engineer Georgia Institute of Technology Formerly : Design Engineer Aerojet-General Corp. Sokolo~vski, Daniel E. Aerospace C ng'lneer ' Chemical Rocket Division NASA-Lewis llesearch Center

Reviewer, Chapter 9

Author, Sects. 8.3.6 and 10.2 Contributor, Sects. 7.4.2 and 8.5.1 Reviewer, Chapter 8 Author, Sects. 3 . 1 3.5.2.4, 3.5.3.1, 3.3.3.2, 3.6, 4.1, 8.1, and 8.4.1 Reviewer, Chapter 8 Author, Sects. 7.2.1 and 8.4.4 Contributor, Sects. 7.4.2 and 7.6 Reviewer, Chapter G

Author, Sect. 10.6.1 Revie\vcr, Chapter 5

xxii

LIQUID PROPELLANT ROCKET COMBUSTION

INSTABILITY

Strahle, Warren C. Associate Professor of Aerospace Engineering Georgia Institute of Technology Formerly : Member of the Professional Staff Science and Technology Division Institute for Defense Analyses Szuch, John R. Project Engineer Advanced Systems Division NASA-Lewis Research Center Thibodaus, Joseph G. Jr. Chief, Propulsion and Power Division NASA-Manned Spacecraft Center Tonon, Thomas S. NASA Fellow Dept. o Aerospace and Mechanical Sciences f Princeton University Valentine, Ralph S. Director, Engineering Research Dept. Atlantic Research Corporation Van IIuff, Norman E. llanager, Design and Analysis Dept. Engineering Aerojet Liquid Rocket Company Van Wyk, Rod llanngcr, SysLerrl iZrlttlysis Section Winchester Group Research Olin Corporation Varma, Ashok K. Guggenheim Fellow Dept. of Aerospace and Mechanical Sciences Priilceton University Vincent, Joseph Membcr of the Technical Staff Liquid Rocket Division Rocketdyne Wanhainen, ,John P. Aerospace Engineer Chcmical Rocket Division NASA-1,rwis Rescarrh Center Waugh, I:_,,_4_,_ / heat transfer)_

.....

/

i!!

_

ti:_P" _!_._ I_I_'_"

I I I

\ rhi,(O/F)f \ -d_--_Stream

_\. _ tubes

"\

/ \

_ .Arbritrary \,/exit surface

I....._:" T -!Drmlbl::tivoprlzatln

i

', I

....Supersonic flowreglon--_

\

_ -

T

-!-

(Energy / I__

release)

l-Transonic

flow region :_

Injection, primary atomization, _istribution of droplets stream tube formation)

-_--Additional energy release, chemical kinetic rate limited equilibrium shift during expansion through nozzle

Fro =_FIGURE l.t.3b.--Internal

rhLVLcos O_L+J'PeLdAeLprocesses in the real rocket motor.

stream of the injector face is sampled.* Alternatively, a careful analysis based on the hydraulic flow characteristics of the injector propellant passages and orifices can give a useful indication of the delivered distributions. It has been found that regions of identifiable mass and mixture ratio which are larger than a typical molecular mixing distance (about inch) tend to maintain their separate identity as they react and progress through the thrust chamber and nozzle. Thus the rocket motor can be idealized as a group of separate, non-mixing, rocket motors (stream tubes) operating in parallel, and constrained to coexist within the overall chamber and nozzle contour. As a tirst order approximation, the performance

of the

stream

tube

rocket

motor

is the

mass-

averaged performance of each of its stream tubes, each presumed to expand through a nozzle having the shape and exit area ratio of the overall nozzle. The net effect of the variation in mixture ratio from stream tube to stream tube is a decrease mance in performance compared to the perforthat would have been obtained at a uniratio. NOZZLE FLOW:

form average mixture TWO-DIMENSIONAL

The two-dimensional shape of the de Laval nozzle affects the flow in two ways. Near the throat, curving of the flow distorts the pressure distribution, leading to curved constant-pressure surfaces. This causes a decrease in the mass flow through the nozzle, comlmred to one-dimensional sonic flow through the geometrical throat area; and the diw;rgence of the exit flow results in a loss of axial momentum, and thus a loss in specific impulse.

* llowew'r, c_m :tlter

il is recognized l.h(, nott-re:tctive-fluid

that

tim

clu'lnic'tl

re.ration

spray

distributions.

INTRODUCTION

1.1

11

TABLE

I.I.3b.--llEAL

ROCKET AND LOSSI'S

MOTOR

PROCESSES

stream of the throat. The supersonic flow for an inviscid fluid can be developed by a method-ofcharacteristics calculation, point a transonic solution above. Such the surface using as such as that a starting mentioned on the

Process

Typical percent

loss

a calculation gives the pressure of the nozzle downstream of

Nonuniform mixture ratio distribution (stream tubes) Incomplete energy release Multi-phase flow (solid particles) Two-dimensional flow (curvature and divergence) Finite reaction rates (kinetics) Boundary layer (friction and heat transfer)

Oto5 1 to5 Not treated 0.1 0.1 0.5 to3 Iol0 to 5 here

starting line, and/or the pressure, density, velocity, and direction of flow through any chosen nozzle exit surface. The total thrust of the nozzle determined and axial from either the momentum flux starting line pressure plus the axial comin the superthe exit surflux, is the momentum gases motor that taken

ponent of the surface pressure forces sonic region of the nozzle, or from face pressure and same, and reflects due to divergence axial momentum the loss in axial of the exit flow.

Various approaches to determining the effect of throat curvature on the pressure distribution in the transonic flow field and on the mass flow through the nozzle are given in the literature. When two or more stream tubes coexist in a given nozzle flow, additional constraints, beyond the fundamental assumption that the static pressure is everywhere continuous, are needed to define the sonic surface and to determine the relative flow areas occupied by the stream tubes in the region of the nozzle throat. Kliegel and Quan 49 have presented an analysis of the flow of two concentric stream tubes within a rocket nozzle. Propellant injection conditions were not specified. They concluded that the sonic surfaces of the stream tubes must lie on a common constant-pressure tion maximizes the throat. surface, total mass since this condiflow through the

FINITE REACTION RATES: The in the combustion chamber of a rocket are generally at a high enough some dissociation of molecular temperature species has

place. As the hot gases expand through the nozzle, the pressure and temperature decrease. At the reduced pressure and temperature, the dissoeiated species tend to recombine, and to liberate energy as they do so. However, these recombination reactions are rate-limited, and are only partly completed during transit through a typical rocket nozzle. With a knowledge of the rate constants for the particular reactions involved, and a specific nozzle size or time scale, the kinetic effects can be incorporated in the nozzle flow and performance calculation. The effect is always a decrease in the otherwise attainable performance. MULTI-PHASE FLOW: Some propellants yield combustion products which contain solid particles in the combustion chamber, or which form condensed species during expansion through the nozzle. The magnitude of the effect of solid particle flow on the rocket motor performance depends on the state and number of the particles as well as on their drag and heat transfer coefficients. The two-phase flow process effects on performance are complex, and the basic data needed to analyze the process is difficult to obtain. Some existing computer programs approximate the effect of two-phase flow in one-dimensional nozzles, but no two-dimensional treatment is available at the present time. For these reasons no estimate of the magnitude flow loss is given in Table 1.1.3b. of the two-phase

Norton _'gb studied the flow of multiple stream tubes through a nozzle with the injection conditions (mass, momentum, energy) specified for each stream tube, and found that the sonic surface was, in general, discontinuous. In either case, if the properties of the gases in two stream tubes differ, then the stagnation pressures of the two stream tubes differ. This causes the difficulty, which was mentioned earlier, in the definition and evaluation of the characteristic velocity. The development of the supersonic flow field and the divergence of the exit flow are determined by the shape of the two-dimensional nozzle down-

12INCOMPLETE

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

ENERGY

RELEASE: and reaction occur instan-

Atomization, mixing, evaporation, of the injected propellant do not

taneously or completely in a rocket motor. Typically, most of the combustion is completed within the combustion chamber, before the products of combustion enter the nozzle convergence section. Some droplets may evaporate and some reaction may occur during transit through the nozzle.* However, some propellant droplets may not evaporate within the confines of the thrust chamber, and some evaporated molecules may not find "partners" with which they can react. The result in either case is an energy deficiency and a small change in the composition and properties of the combustion products, with a reduction in the realized performance. A distinction should be made between the stream tube process and the incomplete energy release process. A stream tube is a macroscopic region of uniform mixture ratio, distinguishable from other macroscopic regions having other uniform mixture ratios. Energy release efficiency is a measure of the completeness of the reaction within a stream tube; it is related to the degree of mixing and vaporization of the drops produced by the individual injector elements and to the microscale processes by which molecules mix and react. The real distributed energy release process has not been completely described and modeled as yet, although some analytical and experimental investigations are under way and others have been proposed. In the absence of a capability of analytically describing the energy release process and predicting its effect on performance, an empirical interim model and procedure 23 has been found useful. Incomplete energy release is modeled analytically by reducing the total energy of the system through a reduction in the stagnation enthalpy. Prior to expansion, 100% of the propellant is presumed to be in thermodynamic equilibrium at the reduced enthalpy level. The chemical and fluid dynamAc calculations are then made in their usual manner. The calculated per-

formance is reduced as a result of the lower energy available to the expansion process. The reduced enthalpy also provides a different base condition from which the kinetic loss is reckoned. This empirical single-parameter model was selected for interim use because it is simple and unambiguous. While this simplified energy release model cannot exactly duplicate the effect of the real distributed energy release process, it has proven, empirically, to give useful overall performance correlations and extrapolations when used with several conventional propellant systems. BOUNDARY LAYER FRICTION AND HEAT TRANSFER: The effect of surface friction and of heat transfer from the combustion gases to the wall is confined to a relatively thin layer of gases next to the wall. The core of the gas flow can be considered to be remote from viscous or heat transfer effects. The influence of the bdundary layer on rocket motor performance is given by a model which replaces the real flow with an equivalent completely inviscid and isentropic potential flow. A displacement thickness, _*, is evaluated which defines the size and shape of the potential flow nozzle with respect to the real nozzle, so that the mass flow through the potential flow nozzle is the same as that through the real nozzle. This is shown in Fig. 1.1.3c. The excess momentum flux through the equivalent potential flow nozzle over the momentum flux of the real flow is given by a momentum thickness, 0, of the potential flow, such that an annular layer of the potential flow of thickness 0 has this amount of momentum. Then, as shown on Fig. 1.1.3c, the thrust of the real motor is obtained by correcting the thrust of the equivalent potential flow motor for the excess momentum flux and for the exit pressure acting on the displacement thickness. The propellant mass flow as computed for the throat of the equivalent potential flow motor is used with the calculated real motor thrust to obtain the specific impulse. The derivation of the expressions for the disp!ncement and momentum thicknesses from the basic heat transfer, friction, and fluid flow relationships is given by Elliott, Bartz, and Silver 24' and by Alber% A unique Bartz, and feature Silver of the treatment is the simultaneous by Elliott, solution

* A study the area supersonic ratio,

I) 3, Mitchell portion still can

4n has of the

shown nozzle

that flow,

combustion even at

in high

contribute

to performance.

INTRODUCTION

1.1

13

Surface

of real nozzle--,

e_

_--_

I

"1"

'_-Surfoce

of potential

flow nozzle

__ll__ 1' _treol =l"n'potentiol flow nozzle =

having equal moll flow 8 = Displacement thickneu 8 = Momentum eXCell thicknell l_e

AFIre.

[._.

2

_r

_.,

e e Pe-2a're_ePeVe_" ....

2_C

Freal = Fpotentiol nozzle

flow

- [ 27rreOeCS ,

, (ePeVe,t]Je

E ]_'_e

Pe

__

Oee/v;,eand kinetics is a decrease in

FIGURE

1.1.3c.--Boundary

layer

model

and

performance

correction.

of the integral momentum and energy equations for the thin boundary layer. This results in the losses due to heat transfer to the wall appearing indirectly, as part of the total boundary layer loss, rather than appearing separately, as in earlier boundary layer treatments. Thus all interactions between shear drag and heat loss from the gases are taken care of within the boundary layer model. Alber 6 takes an overall look at this approach to the evaluation of the boundary layer losses and shows that the displacement thickness-momentum thickness approach is exactly equivalent to a correct accounting of the axial component of the pressure forces acting on the interior of the nozzle. INTERACTIONS BETWEEN PROCESSES: In principle, each process in the real thrust chamber interacts occurring with each

plete energy

release

the vacuum specific impulse. Further, thermodynamic nature of the nozzle process, the percentage performance given energy deficiency increases with area ratio, and the magnitude of this creases with increasing energy loss. (2) The effect of two-dimensional and other losses. Two-dimensional

due to the expansion loss for a the nozzle effect in-

flow on kinetic flow affects the

magnitude and rate of change of the properties of the expanding gas. Small nozzles and nozzles having small radius of curvature throats and/or high expansion angles just downstream of the throat may expand the combustion gases so rapidly that there is not enough time for ratelimited equilibrium shifts to occur. Nozzle contour curvature, located near the exit of a "bell" nozzle, can cause local changes in pressure, density, velocity, and direction which enter into calculation of the boundary layer loss and the divergence loss. (3) The effect of nonuniform mass and mixture ratio distribution on kinetic losses. Stream tubes having different mixture ratios will produce combustion gases having different properties and temperatures, and thus the kinetic losses will be different in each stream tube. (4) The effects of incomplete energy release, kinetics, stream tube flow, and two-dimensional flow on the boundary layer loss. The properties used in calculating the boundary layer corrections are those of the stream tube closest to the wall. The properties of the gases in this stream tube

other process. These interactions must be accounted for in a valid performance calculation procedure. Some of the more important of these interactions (1) The are discussed here effect of incomplete in general terms: energy release on

kinetic losses and on the nozzle expansion process. Incomplete evaporation, mixing, and reaction result in a loss of energy and a change in the composition of the combustion products, compared to complete reaction. The temperature of the gases entering the expansion nozzle is reduced, and associated with this is a reduction in the fraction of dissociated that part of the total kinetics may decrease, species present. While loss directly ascribable to the net effect of incom-

14

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

are determined by the local mixture ratio and by the energy release, kinetics, and two-dimensional interaction effects. 1.1.3.3 Real rocket performance calculations.-Calculation of the performance of a real rocket motor must be based on an integrated physical model that is a composite of models describing each of the physical processes or effects occurring in the real rocket motor. Separate inputs should define each effect, and the calculated performance should reflect the result of all interactions. If all of the real rocket motor processes are identified and appropriately modeled, and if the input information is available to accurately specify each process or loss, then the computed performance will be identical to the performance of the real rocket motor as measured on a test stand (presuming accuracy of the test data). In practice, this degree of perfection has not yet been achieved. Some processes have still not been adequately modeled, some needed physical data are not as yet known with sufficient accuracy, and present computational procedures are limited. Because of these present limitations, the capability to predict the performance of the general case of a real rocket motor does not now exist. However, a practical methodology for correlating and predicting the performance of a useful class of rocket motors has been developed by the Performance Standardization Working Group* of the ICRPG TM _'_'_'.This class of rocket motors is limited to those that a. Use propellants whose combustion products are entirely gas phase, with no solid partides. (Currently only the chemical elemerits C, H, O, C1, F, and N can be handled.) Are large enough so that the flow is not dominated by viscous effects (i.e., above about 100 lbf thrust)I'erform'mcc Standardization Chemic-d 1965 _md Working Group

c. d.

Have

conventional

de Laval

nozzles

Have conventional upstream-end propellant injection techniques; no mass addition in the supersonic region e. Are in steady-state operation These restrictions correspond to the capabilities of existing computer programs, and to processes which are relatively well understood. Despite these seeming limitations, there is a wide and important field of applicability for the developed performance calculation capability; i.e., most rocket motors used for space propulsion applications use propellants composed of the six listed elements, produce more than 100 lbf thrust, and have de Laval nozzles. The rocket motor performance calculation capability developed by the Performance Standardization Working Group is based on two computer programs and on the use of the empirical model for the incomplete energy release process, (discussed under Sect. 1.1.3.2). The two computer programs were selected by the Working Group from among all those that were available to it in June 1967. These computer programs, selected on the basis of technical validity, computation time, documentation, and other factors _, have since been modified and improved to meet the needs of a standardized performance calculation and prediction procedure and to be compatible with each other, and have been made available as reference programs) 7,22,23,",4_(These and other related computer programs can be obtained through CPIA (Chemical Propulsion Information Agency), The Johns Hopkins University, 8621 Georgia Avenue, Silver Springs Maryland 20910.) 1.2 COMBUSTION INSTABILITY*

b.

* The

Combustion instability problems have been experienced dm'ing nearly every rocket engine development program. Since these problems severely impair tim operation of the engine and vehicle system, there is considerable incentive to seek an understanding of this undesirable phenomenon. Combustion in_t_bi!ity results from coupling between the combustion and the fluid dynamics of the system. Through this coupling, oscillatory energy is supplied by the combustion* T. A. Coultas, Author, Sects. 1.2.1 to 1.2.3.

of the intcragcncy was org_mized in three aml ante

Rocket Propulsion Group h'_s functioned through its s, TheoreIie:tl The ICllPG Prol)(,ll_mt Mel hods, PerformRocket Overall

COlllnliI tees ; Overall Concel)t Expcrim(mt_d Measu,'emenls. Ewdualion M:muaI for of 2s is tim l)roducL _m(l tile Theoretical

Liquid

Engilms Concet)is

joint, efforls of the MeI hods committees.

INTRODUCTION

1.2 bration measurements often do not correlate

15

to sustain the oscillations. Only if the damping processes present in the system are sufficiently large to dissipate the oscillatory energy more rapidly than it is supplied, will the oscillations decay. Thus, combustion instability may be prevented by either increasing the damping or decreasing the coupling with the driving forces. Several distinct types of instability have been observed and their physical manifestations have caused a variety of picturesque names to be generated for each of them. A common trait is that all types of combustion instability are characterized by chamber pressure oscillations, although the frequency and amplitude of these oscillations and their external manifestations normally vary with the type of instability. Oscillatory operation of a rocket engine is undesirable for many reasons. One of the most important of these effects is the severe vibration. Vibration levels in excess of 1000 g have been experienced. Such vibration levels can impair the operation of sensitive guidance components and have severe effects upon payloads and even relatively massive structural members. Another severe effect is the grossly increased heat transfer due to the oscillatory operation. This increase is often sufficient to melt and destroy portions of the rocket system. Other less drastic effects include decreased performance, uncontrolled impulse, variation in thrust vector, and the effects of oscillatory propellant flow rates. 1.2.1 Physical Manifestations

well with the corresponding chamber pressure measurements. Frequently, however, there will be similarities in frequency as well as in severity or amplitude (sec Sect. 9.5). Temperature and heat transfer monitoring has also been successful in indicating the onset of combustion instability. Thermocouples buried in the chamber wall respond to the rapid increase in wall temperature. Faster response is afforded by measuring the transducer coolant or the local regenerative coolant temperature changes (see Sect. 9.6.5). Combustion instability also causes oscillations of the axial position of the Mach diamonds in the exhaust plume and speed photography. this can be detected by high The oscillations of the Mach

diamonds will usually correspond in frequency to the chamber pressure oscillations. Monitoring of the luminosity variations from the exhaust plume is another optical technique sometimes used. These variations in luminosity may be very weak. For instance, it has been estimated for one case that the relative amplitude of brightness oscillations in the plume would be only 0.1 percent of the relative oscillations in chamber pressure (optical measurements are discussed in Sect. 9.4). Flow rate variations and thrust variations have also been observed as an indication of combustion instability.

1.2.1.1

Damage.--In

addition

to

the

destruc-

Combustion instability is manifested in many ways. The most satisfactory method of detection and study of combustion instability is the mensurement of chamber pressure (see Sect. 9.3). Pressure measurements made in the propellant feed system show similar oscillations, and in some cases the amplitude measured here may be greater than that measured in the combustion chamber. In the combustion chamber, frequencies from less than 100 to over 15,000 hertz have been measured at amplitudes of from 10 to 1000 percent of steady-state chamber pressure. In addition to pressure measurements, instabilities are often shown by means of vibration measurements. The very high vibration levels often measm'ed have given rise to the term "rough combustion," meaning in that case unstable combustion. Vi-

tive vibration, thrust magnitude and direction vibrations, and uncontrolled impulse caused by an oscillating system, combustion instabilities may result in extensive damage to the thrust chamber and injector itself. High frequency instabilities result in grossly increased convective heat transfer coefficients in the chamber walls. With the prevalent tangential mode instabilities this increase occurs at all axial positions in the chamber. Since the heat transfer rate is normally highest near the nozzle throat, this is a very sensitive location. In one rocket engine development program it was found that combustion instability caused the nozzle to be neatly severed at the throat and dropped into the exhaust flame deflector. In another program, where considerable unreacted together oxidizer was present with the maximum near the injector, tangential mode

16

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

amplitude, increased in chemically burning

heat transfer rates the thrust chamber

resulted at that

location. This can become a chain reaction, burning not only the chamber and the injector, but propellant lines and thrust stand structure as well. Combustion instability is not always so dramatically destructive. Lower frequency modes of instability may do no damage at all. Even some high frequency instabilities are nondestructive if the injector and thrust chamber are satisfactorily cooled and sufficiently strong. In fact, at high frequencies, a quite sophisticated set of instrumentation is often required to determine if the combustion is unstable. At very high frequencies, the amplitude of the oscillations may be quite low and the damage incurred negligible over the short periods of times (3 to 4 seconds) typically used to obtain performance data. 1.2.1.2 Effect on, combustiw_ e_cien.cy.--The apparent performance of a particular rocket system may either increase or decrease during a combustion instability. At high frequencies, the high transverse pressure and velocity gradients enhance both factors which control the steadystate rocket engine performance. These factors are mixing (distribution), and vaporization of the propellants. In engines where either of these factors has not been very thoroughly optimized for steady-state operation, it, might be expected that the performance would increase during an instability. In contrast, for the case of an optimally designed injector configuration displacement of the propellants may actually result in a performance loss. Considerable design efforts are usually put forth to assure that the propellant mixtm'e ratio is made as uniform as possible at each point on the injector face. In spite of these efforts, however, combustion may occur locally at mixture ratios considerably off design or optimum value, particularly for propellants which vaporize at grossly different rates. It has been found that if the propellants have not been properly distributed within about an inch down_uc_,H of the injector, any * ........... ;"_""e ratio variations tend to persist, since gas phase mixing is (;xeeedingly sh)w. In the presence of a strong a('oustic lid(I, however, the gas-l)hase mixing is (umsidcrahly enh.mced, minimizing this source of inefficiency.

Effort is also expended to assure that the propellants will be atomized into droplets sufficiently small that they will be completely vaporized in the chamber prior to expansion through the nozzle. Propellant vaporization is governed by heat and mass transfer between the propellant droplets and the hot combustion gases. Additional convective effects generated by the acoustic or oscillatory pressure field will enhance the combustion efficiency by accelerating the vaporization of the propellants. In spite of these factors, which sometimes increase the combustion efficiency, other effects of combustion instability may override them and decrease the apparent or overall combustion efficiency. The presence of low frequency or longitudinal mode high frequency oscillations may result in a decided increase in the axial mixture ratio variations. This is particularly true with injectors having unequal injection pressure drops across the two propellant systems. Here, a temporarily lowered chamber t)ressure will cause a much larger quantity of one propellant to be injected during the low pressure portion of the cycle than of the other propellant. Thus, alternatively high and low mixture ratio injection rates will result in wide variations in mixture ratio along the length of tile chamber, resulting in poor performance. Further, the grossly increased injection rates during the low pressure part of the cycle can result in a portion of both propellants being exhausted from the chamber unburned. Thus, even though the mixing and vaporization may be very complete during one portion of the cycle, (high chamber pressure and low injection rate) the chamber is flooded during the low chamber pressure portion of the cycle. Other less important losses occurring during combustion instability include increased heat transfer and friction. As a rule of thumb, it may be stated that high frequency instabilities tend to increase the combustion efficiency if the combustor is not initially a high performer, while low frequency oscillations tend to decrease performance. 1.2.2 Classification

Several different cl,tsses of instability have been identified and studied experimentally. Usually the instability driving mechanisms differ among the classes such th:tt different methods are re-

INTRODUCTION 1.2 quired to controlor eliminatethe instability. Historically,instabilitieshave been classified by their frequency range,but thereis not a sharpdividing line between so-called the low, intermediate ndhighfrequency a classes. Classificationof combustion instability,merely its by frequency, hasled to muchconfusion. would It appearthat a better methodwouldrelatethe classes f instabilityto their effects, he most o t important couplingmechanisms, to the and devices toeliminate used them.1.2.2.1 Low freque_cy, ckug.--Of the various types of combustion instability the low-frequency type, or chug, also called putt-putt, groaning, and motor-boating, is perhaps the easiest to handle both from an analytical and experimental or developmental standpoint (see Chapters 5 and 6). It is generally accepted that the frequency range which might be encountered in the chugging mode is less than several hundred hertz. In this frequency range, the wavelength is usually much larger than characteristic dimensions of either the chamber or the feed system. In some cases, however, there may be wave motion in the propellant feed lines. This instability usually begins with a low amplitude, sinusoidal wave shape, growing in a linear fashion to higher amplitude. Analytically, tile chamber may be simulated by a lumped vohnne element, the combustion represented by a and the propellant glected, although simple, constant time delay feed system resistance nefeed system inertance and time delay have met with mixed success.

17These

changes, even if successful in eliminating chug, may decrease the system performance or bring about a high frequency instability. Other low frequency instabilities have been caused by coupling of the combustion process with the injector structure. The injector may act as a diaphragm and oscillate in an "oil can" mode. This can cause nonuniform propellant injection and atomization which results in a low frequency instability. Still other cases can allow coupling between the combustion, or chamber pressure, and the structural system. One instance was found where pressure oscillations in the propellant contained in the regenerative cooling jacket were being caused by chamber pressure perturbations flexing the jacket wall structure with the resultant coupling causing a low frequency instability. Another rocket system instability, of very low frequency (order of a few hertz), is caused by propellant flow rate oscillations which result from pump amplification of the fluctuations of the pump inlet pressure (the pump inlet pressure variations are due to the g-loading of the liquid column extending back to the tank). Although this "pogo" instability is driven by thrust modulations that are transferred to the structure, the combustion turbed so slowly as to remain essentially and hence this is not generally considered bustion instability. is persteady a com-

capacitance may become important in the analysis. The combustion time delay is defined as the time required for' the liquid propellant to enter the chamber, travel at injection velocity to an impingement point, then be totally vaporized and burned. Usually an empirical average can be found for each propellant. A value which has often been used is simply the liquid flight time from injector face to impingement point, usually for the least volatile of the propellants since this constitutes a major portion of the total time lag. Methods of elimination of chug instabilities include: increasing the pressure drop in the injector, increasing fluid inertance (i.e., longer L/D in the injector or feed system), decreasing chamber volume, etc. Attempts to change the

1.2.2.2 Hi q]_ freque,_cy i,_stabilily--The most destructive type of instability is referred to as high fre(luency instability, resonant combustion, or acoustic instability. The latter is a generic term derived froni the observed correspondence in frequency and phase between experimentally observed chamber pressure oscillations and those calculated for the acoustic resonances of the chamber (see (longitudinal) gential) modes High frequency Chapters 4 and 6). Both and transverse (radial and are included instability axial tan-

in this terminology. has also been called

by such names as "screaming," "squealing," "organing," "screeching," and just plain "rough." It is generally conceded that the effect of the propellant feed system is usually unimportant in tire study of high frequency instability. The frequencies are often so high as to preclude coup-

18

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

ling with the relatively sluggish feed system. It should be noted, however, that in large combustion chambers the fundamental acoustic frequency may be so low that the feed system can easily couple. Combinations of resonant combustion and chug instability have also been observed. In some cases the elimination of the chug by feed system of the changes resonant has also resulted in elimination combustion. In other cases, the

than that required for sustaining the oscillations; and (2) making changes in the dynamic energy losses or damping so that they exceed the energy gains from the combustion response (see Chapters 7 and 8). Into the first category fall the very common developmental attempts to achieve stability by varying the injector hole pattern, hole size, pressure drop, etc. Of the thousands of postulates or design criteria for achieving combustion stability, the following is an example of an injector design rule that has worked out quite well. In nearly every case, "the stability of a rocket engine will be improved if the two phases, i.e., liquid and combustion gases, move at grossly different axial velocities." This rule of thumb indicates that if the most volatile propellant is injected at higher velocity, the engine will become more stable. Also, if the less volatile propellant is injected at lower velocities, further increases in stability will be found. This "relative velocity" criterion is probably responsible for the generally observed good stability characteristics of engines using gaseous hydrogen fuel. Like all generalizations in the study of combustion instability, there have been exceptions to the rule and certain limits must be set. Often it is not practical for performance, compatibility, or other system reasons to increase the relative injection velocities (see Sect. 7.4). The predominant effect of combustion chamber baffles places them in this first category as well, because their stabilizing influence primarily results from simultaneously increased resonant frequency (i.e., a shift to higher modes) and lowered acoustic displacement of the combustion gases within a baffle compartment. Some of their effectiveness may also stem from disruption of wave propagation and droplet shattering. In addition, there may be some effect of the baffles in energy dissipation due to vortex shedding, but the extent of this contribution to effectiveness of baffles is not currently known. Although it is known that engines may be stabilized by the use of baffles on the injector face, less .... u _1_ ..... _ ....:_,,,.; .... ;,'* for defining how many baffles are required, i.e., the necessary baffle spacing, or baltic length required to achieveI_ ULL--UbLILLk, U (,| t U_I try _,xl_)t,

opposite has been true. An oscillatory source of energy is required for sustaining an instability. For high frequency instabilities, this energy must come from the propellant combustion and is usually only weakly dependent upon the feed system. Further, the sustaining energy addition must be properly time-phased with respect to the oscillating pressure. In most high frequency instabilities the coupling appears to be direct. Each wave affects the propellant combustion strongly enough so that sustaining energy is added directly to that wave (i.e., within a time no longer thal_ the period). come from Effects of secondary importance transient change in propellant can in-

jection rates, in propellant impingement and atomization characteristics and from residual effects from one cycle influencing the amplification of the next. In general, however, these simply affect the equilibrium amplitude bility. SUSTAINING MECHANISMS: mechanisms which have been of the insta-

Sustaining for high

proposed

frequency include: loss of ignition, sensitive chemical preparation time, physical time delays, detonation processes, pressure or temperature sensitive chemical kinetics, the "exploding" of droplets heated to above their critical temperature and pressure and the shattering and mixing of the streams, fans, or drops by the gas particle motion. These are only a few of the more recurrent explanations which are advanced to explain the sustained combustion instabilities. Many of these will be discussed in detail in later chapters. METH()I)S OF ELIMINATION: Two lUllUaHtcm,_tt lnc{,ttocl8 of emmn_tmg quency coml)ustion chaml)er instal)ility been employed: (1) making changes in t)ellant sl)ray combustion tield or in the wave character* so that the coml)ustion to thc wave motion relcascs less oscillatory high-frehave the propressure response encrgy

*

F

'e(]u('n(*y through

or

W:tVt'

sha[)o ()t' lhe

:tlh'l':tli,)llS ('ham|)('v

llllty geometry.

be

,'teonl-

plished

(.hang('s

INTRODUCTION

1.2 or other Acoustic

19 types of acoustic absorbers (Sect. 8.2). absorbers are also often considered to

dynamic stability in the engine (see Sects. 3.5.3.3 and 8.2). Although some empirical rules have been developed which seem applicable to some propellant combinations over narrow ranges of injector variation, these rules are based only upon experience. When they fail in practice they must be replaced by other rules which accommodate the most recent failures of the old ones. Generally, it has been thought that if a baffle is made long enough to "shield" the region in the chamber wherein the major portion of the combustion occurs, and if the baffle spacing is such that the baffle cavity frequency is above about 5000 Hz, the engine would be stable. Unfortunately, there is much evidence which contradicts this rule. In one case it was found that longer baffles made the engine stable. In most cases, however, it that if the baffles are made long they are spaced closely enough, stabilize. even more unhas been found enough, and if the engine will

be a panacea. It is noted that if "enough" highly absorbing resonators are inserted into a chamber, it will be stable. Similar to the case of baffles, questions remain as to the correct design criteria, and together with other operational factors it is desirable to minimize the use of acoustic absorbers. It has also been found that the inclusion of particulate matter into the combustion gas acts as an absorbing device by dissipation of oscillatory energy through frictional processes associated with particle drag. This damping method has been widely acclaimed as the solution to high frequency instability problems in solid propellant motors (see Sect. 8.5.2). 1.2.2.3 Intermediate frequency, buzz.--Between

the two extreme types of combustion instability is the intermediate frequency. It is unfortunate, but most of the combustion instabilities which are not obviously either low or high-frequency are lumped into this intermediate category. This propensity is so strong that often many chugging instabilities at higher than usual frequency are referred to as buzz (see Chapters 5 and 6). The beginning of an intermediate frequency instability usual y shows a growing coherence of the combustion noise at a particular frequency with slowly increasing amplitude. There is usually wave motion in the propellant feed system. Although there may be wave motion in the chamber, the phase and frequency does not usually correspond to an acoustic mode. If chug and buzztypes are to be distinguished, it is by spatial chamber pressure variations present during buzz instability. The pressure wave shape is very nearly sinusoidal and one or both of the propellant feed systems may be highly coupled. Buzz-type instabilities are not particularly damaging if they remain at low amplitude, but may degrade performance, total impulse or thrust vector. In some cases the amplitude increases to triggering a high frequency mode. In very large chambers motion which approximates instability. and phase the point of

Baffles are not generally regarded as a panacea for promoting combustion stability. Even if sufficient and proper baffles did assure stability, it would still be desirable to minimize the length and number of baffles used. The presence of baffles on the injector face represent a discontinuity in the most important combustion region. It has been shown that baffles can have significant and deleterious effects on both combustion efficiency, and the effectiveness of nozzle thrustthe the vector-control baffle length injection*. is increased, Furthermore, as the heat losses from

combustion gases can become large enough to lower combustion efficiency, and the heat loads to the baffles may become prohibitive. Thus, it is desirable from the standpoint of cost, complexity, performance, thermal compatibility and thrust vector control to minimize the number and length of baffles used in a combustion chamber to achieve dynamic combustion stability. In the second category fall various types of damping devices. Items of this nature have been noted to be effective when metal-walled combustion chambers chambers were replaced with ablative (Sect. 8.5.1) or lined with Helmholtz

there may be wave that of acoustic

* This effects nozzle.

effectiveness associated with

loss the

is

because which

of

mixture into

ratio the

In one buzz instability the amplitude relationships in the combustion cham-

baffle

persists

ber were the same as for a first tangential acoustic mode, but the frequency was 20 to 30 percent

20

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

lower than had previously been observed for this mode. This particular instability was cured by the use of quarter-wave tubes placed on the propellant feed system. Some instances of longitudinal high-frequency instability, although by definition an acoustic mode, probably should be called buzz. This is because this acoustic instability has the feed system feed system A type of intermediate linear buzz characteristics, is usually coupled, and may be eliminated by rather than combustion changes. instability which also falls into the category is the so-called "entropy

amplitude. The combustion either triggered unstable by turbance taneously. or the instability

chamber may be some artificial dismay develop spon-

wave." Here axial mixture ratio gradients passing the sonic plane in the nozzle may emit a pressure wave which travels upstream toward the injector. The reflected wave influences tile mixture ratio and hence travels back downstream as an entropy discontinuity overall effect is that oscillation. Buzz programs is at the gas velocity. The of an intermediate frequency in are development designed to

often encountered on engines which

throttle over a wide thrust range. It is almost axiomatic that if the throttling range is to be very wide, buzz or chug will be encountered at some thrust condition. This is because the combustion is given a continuously varying set of conditions; e.g., velocity of propellants, impingement time, atomization effectiveness, etc. It is nearly certain that at least one condition will be found which is favorable for coupling with wave motion in the propellant feed system. This is particularly true if the engine is fairly large, allowing many possible resonances in manifolds, domes, feed lines and other parts of the feed system. This type of instability has been noted on many engines which were designed to be throttled. Not only will the engine buzz at some operating condition, but often these os('illations will increase in amplitude frequency instability. 1.2.3 Initiation_(ILllbl()ll _O bllg

The initiation of an acoustic instability is frequently a nonlinear phenomenon; that is, there may be a threshold value of perturbation amplitude above which a sustained instability is caused, and below which the perturbation will damp. Thus a single pressure disturbance can be amplified and result in sustained combustion instability. A rocket engine's inherent stability determines its ability to absorb large disturbances and yet return to its steady-state operation. This was the impetus for combustion stability rating devices which provide artificial disturbances to a combustion chamber (see Chapter 10). Prior to the introduction of stability rating devices, a rocket engine's inherent stability was determined by reliance upon the occurrence of spontaneous stability. This required very many tests and one system was deemed more stable than another if, in many tests, the superior system exhibited fewer occurrences of combustion instability. In other cases, the operational conditions were varied from the nominal. The system which remained stable through the widest excursion of operating conditions such as mixture ratio, chamber pressure, fuel temperature, etc., was alleged to be the more stable. The technique of relying upon spontaneously occurring combustion instability was desirable in that the rating found was clearly associated with naturally occurring disturbances and the combustion was not changed because of the insertion of foreign rating devices into the system. However, using that approach, either a very large number of tests was required for rating, or the rating obtained might not be typical of the occasional large trigger source (for instance, a hard start). Furthermore, there was no method for determining the size of perturbation to which the system would be stable. If the rating was obtained by changing the operating conditions, it may ha-'e been obtained at conditions remote from actual operating conditions. At the offnomin:d conditions there might be completely different driving "m(l damping than at the desired ol)erating of these severe limitations, nmchanisms (,onditions. coml)ustion i)resent Bccause stability

sufficiently

to initiate

a high

of CombustionUll{tlgt;t,.3 ,'_l(,_

Instabilityof _-I... fit,L j-

developed instability discussed in the previous section, the manner in whi('h the instability starts can also furnish an iml)ortant (_lue to the diagnosti('ian, l(nowlcdge of how the inslal)ility began may be as iml)ortant as its mode, fre(luency and

INTRODUCTION 1.2 rating devices havebeendeveloped perturb to stable,steady-stateombustion c upon demand, andthuseliminate some the disadvantages of of the naturally occurringinstability rating approach. Rating devices havehelpedto shortenthe development cycleof rocketengines. rior to P extensiveseof these u devices waspossible it to arriveat theflightteststage andencounter small systemchanges whichgaveperturbationsufs ficientlydifferentthan thosepreviously experienced soasto cause sustained a instability. In additionto the methods f initiation,the o beginning the combustion instability is quite ofdifferent instability for the may two be cases. The remarkably fully-developed similar even though this initiation stage is distinctly different. These characteristics are contrasted by a variety of name pairs; such as, sinusoidal versus steep-fronted waves, spontaneous gered or pulsed, small amplitude amplitude, nonlinear. and more generally, This latter distinction versus versus trigfinite or small perturbation boundary. Pressure perturbations analysis on the at the stability

21

order

of a few

percent of the steady-state chamber pressure and exhibiting a sinusoidal shape are deemed linear. Transition to a distorted wave shape and amplitudes increased to above ten percent of chamber pressure imply a nonlinear regime has been reached. Should this latter wave shape be present from the onset of resonant combustion then a nonlinear analysis is required. All classes of combustion instability are distinguished from random turbulent fluctuations or combustion noise by coherence of a particular frequency or set of frequencies and in most cases by a much greater amplitude. Turbulent or randora chamber pressure oscillations in rocket engines may have amplitudes on the order of one to three percent. It should be noted that these "random" oscillations, show many preferred quencies, usually be tics such length or when spectrally analyzed, frequencies. These fre-

linear versus is derived from

the type of analysis which is believed applicable to the mathematical modeling of at least the onset of these instabilities. Because of this fundamental difference in the initiation characteristics, two rather distinct veloped (see Chapter schools 4). of thought have de-

even in a stably operating system, can attributed to some system characterisas pump speed, propellant feed line combustion chamber dimensions.

The lower frequency instabilities such as chug and buzz, and even most longitudinal mode highfrequency instabilities, were historically found to be linearly initiated. The high frequency nonlinear instabilities were not generally recognized. This was probably due to the relatively crude pressure transducers which were available at the time and the absence of rating devices. Further, the early engines were usually characterized by low injection density and were prone to a linear, or slowly building instability. Exceptions to this may have been found on some start sequences which resulted in a finite perturbation or "hard start." Linear, low-frequency instabilities acting as triggers for high frequency instabilities are often prevalent during engine start-up. As noted, an engine operating over a wide range of thrusts, flowrates, and chamber pressures is much more likely to experience an intermediate frequency instability. Thus, if an engine's start transient is very gradual, i.e., full thrust is achieved only after several seconds, some set of operating conditions is likely to be prone to a linear buzz or chug instal>ility. This linear instability can grow

Linear instabilities are nearly ahvays considered to be spontaneous, but devices have been constructed which sometimes can enhance the occurrence of linear instabilities. Nonlinear instabilities, on the other hand, are ahvays triggered by a finite disturbance. The disturbance may occm" naturally, or may be artificiaUy triggered by a combustion stability rating device. 1.2.3.1 Spontaneously iniliated linear instabiIity.--Spontaneous instabilities require no initial disturbance, but rather grow out of the noise inherent in the combustion process. If an engine is to experience a linear instability, it might be expected to begin immediately upon reaching normal operating conditions, since no trigger is required. However, variations in test conditions as well as the closeness to a stability could delay that occurrence somewhat. appear stability boundary It would

that if an engine has experienced an inof this type, it should yield to a linear

22and this trigger resonant occurrence upon

LIQUID

PROPELLANT

ROCKET

COMBUSTION

INSTABILITY

combustion. engine start,

To prevent the start se-

affect

the

guidance

sensor

systems.

Further,

for

quence is typically shortened to a few milliseconds (while still avoiding overshoot or hard start). In this manner, the linear growth of any oscillations is curtailed since the "sensitive" portion 1.2.3.2 of the start or is quickly nonli_war passed through. i_.-

small engines used for intermittent the resultant thrust or total impulse altered from that of a smooth start. engines, this for sustained ignition spike can result resonant combustion

operation, is severely For larger in a trigger which may

cause subsequent NATURALLY

hardware destruction. OCCURRING TRIGGERS:

b_duced

combustions,

stabilily.--It would appear that most of the bustion instabilities which are encountered are initiated by finite disturbances. These disturbances may take the form of several of natural disturbances or artificial triggers are used to determine dynamic stability engine system. The naturally occurring disturbances

comtoday finite types which of an ac-

have

Hypergolic liquid bipropellant rocket engines may operate over a wide range of conditions, ranging from a highly pulsed mode of operation to long duration tirings. In either situation, the ignition and start transients must be compatible with the propulsion system. For example, high pressure spikes resulting from explosions of accumulated propellants may result in the complete failure of a radiation cooled chamber. Propellants are said to be "beneficially hypergolie" if the chemical reaction initiated by contact of the two propellants is sufficiently energetic to establish steady-state combustion with a smooth pressure buildup in a specified period of time. Because of low chemical reactivity, the chemical reaction may build up slowly for a period of time allowing unreaeted propellant accumulation to occur in the chamber. This period of time may result in undesirable spiking when true tion ignition actually occurs because the propagaflame front passes through premixed proMuch by inand

quired the descriptive names of "spikes" and "pops." Although there is no universal agreement in the rocket industry, it is generally conceded that a "spike" is a significant chamber overpressure upon ignition of the engine. A "pop" is defined as a similar over-pressure, but occurring spontaneously during mainstage operation (i.e., operation at nominal chamber pressure). For many years the sources of pops and spikes were the subject of intensive research during rocket recent bance engine development programs. In more years, however, the source of the disturhas become of less interest due to the

development of stability rating devices. Engine systems which have withstood a variety of artificial combustion perturbations and quickly returned to stable operating conditions have been assumed to damp natural perturbations rapidly. This has been found to be the case in many engine systems and natural perturbations have thus been rendered innocuous, although wherever possible the bances are still removed. sources of such distur-

pellants and lmilds into a detonn,tion wave. of the experience with spiking is clouded strumental problems. Very sophisticated

high frequency response instrumentation is required to make a careful study of spiking. 4a_ A typical spike pressure amplitude may be ten times steady-state chamber pressures, but with pulse duration of only a few microseconds. This spike may either decay in a single cycle or show linear damping, lasting through several cycles of an acoustic mode of the chamber. High frequency instability but not always, following a spike will usually, damp very quickly as steadyto e_.n

Under conditions of high altitude operation, hypergolic bipropellant combinations may characteristically start with an extremely high chamber pressure spike. This spike may be atbl'llJtlbetl bO bill2 t2.\|)lUblUlt/ u.,,,_;,_t,t,,,t

of

tile

state operating conditions are approached. Pops are not usually severely damaging combustion eha,nbers, but