Combustion Instabilities In Solid Propellant Rocket Motors

Abstract : These notes for two lectures are intended to provide the basic ideas for understanding and interpreting coherent oscillations is solid propellant rocket motors. The discussion is concerned mainly with the dynamics of a system consisting of two coupled sub-systems: the chamber containing combustion products; and the combustion processes con ned almost entirely to a thin region adjacent to the surface of burning propellant. Coupling between the sub-systems is always present due to the sensitivity of the ocmbustion processes to local values of pressure and velocity. Thus the primary mechanisms for instabilities in solid rockets are related to those interactions. A second mechanism involves vortex shedding, a cause of instabilities mainly in large motors, notably the Space Shuttle and Ariene V boost motors. Following a brief review of the history of combustion instabilities in solid rockets, the mechanisms and their quantitative representations are discussed. The remainder of the lectures is devoted to an approximate analysis providing a general framework convenient for understanding, predicting and interpreting combustion instabilities.

[1]  E. Zukoski,et al.  Combustion instability sustained by unsteady vortex combustion , 1985 .

[2]  L. Strand,et al.  A theory of low-frequency combustion instability in solid rocket motors , 1964 .

[3]  R. S. Brown,et al.  Internal flow field studies in a simulated cylindrical port rocket chamber , 1990 .

[4]  Francois Vuillot,et al.  Numerical computations of hydrodynamic instabilities inside channels with wall injection , 1999 .

[5]  H. B. Mathes,et al.  Pressure oscillations in post-Challenger Space Shuttle redesigned solid rocket motors , 1993 .

[6]  Edward Harris Perry Investigations of the T-burner and its role in combustion instability studies , 1970 .

[7]  V. Yang,et al.  Overview of Combustion Instabilities in Liquid-Propellant Rocket Engines , 1995 .

[8]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[9]  S. Candel,et al.  A review of active control of combustion instabilities , 1993 .

[10]  J. F. Bird,et al.  AN EROSION MECHANISM FOR NON-LINEAR INSTABILITY IN THE AXIAL MODES OF SOLID PROPELLANT ROCKET MOTORS, , 1962 .

[11]  W. K. Van Moorhem,et al.  Experimental investigation of velocity coupling in combustion instability , 1991 .

[12]  Martin Summerfield,et al.  SOLID PROPELLANT COMBUSTION INSTABILITY: OSCILLATORY BURNING OF SOLID ROCKET PROPELLANTS , 1965 .

[13]  F. Culick Some recent results for nonlinear acoustics in combustion chambers , 1994 .

[14]  James S. T'ien,et al.  Oscillatory burning of solid propellants including gas phase time lag. , 1972 .

[15]  Leonard H. Caveny,et al.  Theory of dynamic extinguishment of solid propellants with special reference to nonsteady heat feedback law , 1970 .

[16]  Claude N. L. Seywert Combustion instabilities: Issues in modeling and control , 2001 .

[17]  F. Culick A Note on Rayleigh's Criterion , 1987 .

[18]  Merrill W. Beckstead,et al.  A REVIEW OF RIJKE TUBES, RIJKE BURNERS AND RELATED DEVICES , 1993 .

[19]  Fred E. C. Culick,et al.  Pulsed Instabilities in Solid-Propellant Rockets , 1995 .

[20]  W. G. Brownlee Nonlinear axial combustion instability in solid propellant motors , 1964 .

[21]  C. C. Jahnke,et al.  Application of dynamical systems theory to nonlinear combustion instabilities , 1994 .

[22]  Jay N. Levine,et al.  Pulsed instability in rocket motors - A comparison between predictions and experiments , 1984 .

[23]  M. D. Horton,et al.  The effect of compositional variables upon oscillatory combustion of solid rocket propellants , 1964 .

[24]  R. L. Coates,et al.  An interpretation of L' combustion instability in terms of acoustic instability theory. , 1967 .

[25]  R. S. Brown,et al.  Exploratory experiments on acoustic oscillations driven by periodic vortex shedding , 1981 .

[26]  F. Cozzi,et al.  Intrinsic combustion instability of solid energetic materials , 1995 .

[27]  Fred E. C. Culick,et al.  Combustion response of ammonium perchlorate , 2000 .

[28]  Fred E. C. Culick,et al.  The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers I. Exact Solution for Second Order Acoustics , 1989 .

[29]  Gary A. Flandro,et al.  Vortex generated sound in cavities , 1973 .

[30]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[31]  W. A. Wood,et al.  Oscillatory burning of solid composite propellants , 1963 .

[32]  Fred E. C. Culick,et al.  Analytical solution for composite solid propellant response functions , 2001 .

[33]  R. P. Smith,et al.  Combustion instability in solid-propellant rockets , 1953 .

[34]  Vladimir E. Zarko,et al.  Effect of Melting on Dynamic Combustion Behavior of Energetic Materials , 1999 .

[35]  Fred E. C. Culick,et al.  Modeling pressure oscillations in Ramjets , 1980 .

[36]  J. Baum,et al.  Numerical techniques for solving nonlinear instability problems in solid rocket motors , 1981 .

[37]  Michael Shusser,et al.  Combustion Response of AP Composite Propellants , 2000 .

[38]  Fred E. C. Culick,et al.  Calculation of the Admittance Function for a Burning Surface , 1967 .

[39]  Fred E. C. Culick,et al.  Combustion Instabilities in Propulsion Systems , 1996 .

[40]  Forman A. Williams,et al.  Influence of externally applied thermal radiation on the burning rates of homogeneous solid propellants , 1975 .

[41]  Vigor Yang,et al.  On the Existence and Stability of Limit Cycles for Transverse Acoustic Oscillations in a Cylindrical Combustion Chamber. 1: Standing Modes , 1990 .

[42]  E. Zukoski,et al.  NONLINEAR DYNAMICS OF LABORATORY COMBUSTOR PRESSURE OSCILLATIONS , 1991 .

[43]  S. Candel,et al.  Suppression of combustion instabilities by active control , 1987 .

[44]  Giorgio Carlo Isella Modeling and simulation of combustion chamber and propellant dynamics and issues in active control of combustion instabilities , 2001 .

[45]  James S. T'ien,et al.  Nonsteady burning phenomena of solid propellants - theory and experiments , 1968 .

[46]  Jay N. Levine,et al.  Pulse triggered instability in solid rocket motors , 1982 .

[47]  E. W. Price,et al.  Comments on "Role of Aluminum in Suppressing Instability in Solid Propellant Rocket Motors" , 1971 .

[48]  K. W. Dotson,et al.  Vortex driven pressure oscillations in the Titan IV solid rocket motor upgrade , 1995 .

[49]  V. Yang,et al.  Triggering of Longitudinal Pressure Oscillations in Combustion Chambers. I: Nonlinear Gasdynamics , 1990 .

[50]  Franck Cauty Solid-Propellant Combustion Response Function from Direct Measurement Methods: ONERA Experience , 1999 .

[51]  Fred E. C. Culick,et al.  A review of calculations for unsteady burning of a solid propellant. , 1968 .

[52]  Fred E. C. Culick,et al.  Comment on " Triggering of Longitudinal Combustion Instabilities in Rocket Motors: Nonlinear Combustion Response" , 2000 .

[53]  P. Kuentzmann,et al.  Response of a solid propellant to pressure oscillations , 1974 .

[54]  François Vuillot,et al.  Vortex-Shedding Phenomena in Solid Rocket Motors , 1995 .

[55]  James D. Sterling Longitudinal Mode Combustion Instabilities in Air Breathing Engines , 1987 .

[56]  A. Jankowski Combustion in solid-propellant rocket engines , 1968 .

[57]  Victor Scott Burnley,et al.  Nonlinear combustion instabilities and stochastic sources , 1996 .

[58]  R. W. Hart,et al.  Theory of acoustic instability in solid-propellant rocket combustion , 1965 .

[59]  S. S. Penner,et al.  Studies of the decomposition mechanism, erosive burning, sonance and resonance for solid composite propellants , 1958 .

[60]  Merrill W. Beckstead,et al.  A numerical model for temperature gradient and particle effects on Rijke burner oscillations , 1993 .

[61]  R. O. Hessler Prediction of finite pressure oscillations in stable rocket motors , 1980 .

[62]  Fred E. C. Culick,et al.  Nonlinear behavior of acoustic waves in combustion chambers. I, II. [stability in solid propellant rocket engine and T burner , 1976 .

[63]  Sin-I Cheng High-Frequency Combustion Instability in Solid Propellant Rockets. Part 2 , 1954 .

[64]  G. A. Flandro,et al.  Effects of vorticity on rocket combustion stability , 1995 .

[65]  L. D. Strand,et al.  An improved model for the combustion of AP composite propellants , 1981 .

[66]  Robert Beddini The role of turbulence interactions in solid propellant combustion instability , 1998 .

[67]  Harold Grad,et al.  Resonance burning in rocket motors , 1949 .

[68]  G. Avalon,et al.  NUMERICAL COMPUTATIONS AND VISUALIZATION TESTS OF THE FLOW INSIDE A COLD GAS SIMULATION WITH CHARACTERIZATION OF A PARIETAL VORTEX SHEDDING , 2000 .

[69]  N. Ananthkrishnan,et al.  Characterization of periodic motions in aircraft lateral dynamics , 1996 .

[70]  M. Q. Brewster,et al.  Theory of Unsteady Combustion of Solids: Investigation of Quasisteady Assumption , 1996 .

[71]  Fred E. C. Culick,et al.  A further Note on Active Control of Combustion instabilities Based on Hysteresis , 1997 .

[72]  Kenneth K. Kuo Transient Burning of Solid Propellants , 1984 .

[73]  Jay N. Levine,et al.  Nonlinear Analysis of Solid Rocket Combustion Instability. Volume II. , 1974 .

[74]  Boris V. Novozhilov Second harmonic nonlinear resonance in propellant combustion , 1992 .

[75]  S. I. Cheng Combustion Instability in Solid Rockets using Propellants with Suspended Metallic Powders , 1960 .

[76]  Hsue-shen Tsien,et al.  The transfer functions of rocket nozzles , 1952 .

[77]  R. D. Geckler,et al.  Unsolved problems in solid-propellant combustion , 1955 .

[78]  B. Zinn,et al.  Application of the Galerkin method in the solution of combustion-instability problems. , 1970 .

[79]  Fred E. C. Culick,et al.  An experimental investigation of pure tone generation by vortex shedding in a duct , 1982 .

[80]  Merrill W. Beckstead,et al.  A comparison of analysis and experiment for solid propellant combustion instability , 1971 .

[81]  G. A. Flandro,et al.  Vortex driving mechanism in oscillatory rocket flows , 1986 .

[82]  F. Culick,et al.  Modeling the combustion response function with surface and gas phase dynamics , 2000 .

[83]  Fred E. C. Culick,et al.  An Elementary Calculation for the Burning Rate of Composite Solid Propellants , 1969 .

[84]  Frank E. Marble,et al.  Sound attenuation in a condensing vapor , 1970 .

[85]  Vigor Yang,et al.  Prediction of the stability of unsteady motions in solid-propellant rocket motors , 1992 .

[86]  Paul Clavin,et al.  Theoretical Analysis of Oscillatory Burning of Homogeneous Solid Propellant Including Non-Steady Gas Phase Effects , 1992 .

[87]  M. D. Horton,et al.  Dynamic characteristics of solid propellant combustion , 1963 .

[88]  Vigor Yang,et al.  Stability and Acoustic Resonance of Internal Flows Generated by Side Injection , 2000 .

[89]  C. F. Price,et al.  A model of composite solid-propellant combustion based on multiple flames , 1970 .

[90]  F. Culick,et al.  On the Existence and Stability of Limit Cycles forLongitudinal Acoustic Modes in a Combustion Chamber , 1986 .

[91]  G. Avalon,et al.  Flow instabilities and acoustic resonance of channels with wall injection , 1998 .

[92]  R. S. Brown,et al.  Vortex Shedding as a Source of Acoustic Energy in Segmented Solid Rockets , 1981 .

[93]  L. Kovasznay,et al.  Non-linear interactions in a viscous heat-conducting compressible gas , 1958, Journal of Fluid Mechanics.

[94]  G. Evans,et al.  The suppression of combustion instability in smokeless solid propellant rocket motors , 1978 .

[95]  Fred E. C. Culick,et al.  Measurements of energy exchange between acoustic fields and non-uniform steady flow fields , 1978 .

[96]  Fred E. C. Culick,et al.  Excitation of acoustic modes in a chamber by vortex shedding , 1979 .

[97]  L. D. Luca,et al.  Theory of Nonsteady Burning and Combustion Stability of Solid Propellants by Flame Models , 1992 .

[98]  Fred E. C. Culick,et al.  Combustion Response of Ammonium Perchlorate , 2002 .

[99]  Fred E. C. Culick Acoustic oscillations in solid propellant rocket chambers , 1966 .

[100]  R. W. Hart,et al.  AMPLIFICATION AND ATTENUATION OF SOUND BY BURNING PROPELLANTS , 1963 .

[101]  Joseph Majdalani Vortical and acoustical mode coupling inside a two-dimensional cavity with transpiring walls , 1999 .

[102]  F. E. C. Culick Some Problems in the Unsteady Burning of Solid Propellants , 1969 .

[103]  Fred E. C. Culick,et al.  Stability of Longitudinal Oscillations with Pressure and Velocity Coupling in a Solid Propellant Rocket , 1970 .

[104]  R. S. Brown,et al.  Effect of surface reactions on acoustic response of solid propellants. , 1967 .

[105]  L. T. De Luca A critical review of solid rocket propellant transient flame models , 1990 .

[106]  Nicolai Minorsky,et al.  Introduction to non-linear mechanics : topological methods, analytical methods, nonlinear resonance, relaxation oscillations , 1947 .

[107]  Duane A. Smith An Experimental Study of Acoustically Excited, Vortex Driven, Combustion Instability within a Rearward Facing Step Combustor , 1985 .

[108]  Jay N. Levine,et al.  Modeling of nonlinear combustion instability in solid propellant rocket motors , 1982 .

[109]  Sin-I Cheng,et al.  Unstable combustion in solid-propellant rocket motors , 1961 .

[110]  Amable Liñán Martínez,et al.  Longitudinal acoustic instabilities in slender solid propellant rockets: linear analysis , 2001, Journal of Fluid Mechanics.

[111]  Merrill K. King Erosive Burning of Composite Solid Propellants: Experimental and Modeling Studies , 1979 .

[112]  L. D. Strand,et al.  Combustion response to compositional fluctuations , 1983 .

[113]  A Anurag Application of secondary bifurcations to large-amplitude limit cycles in mechanical systems , 1998 .

[114]  Steven F. Son,et al.  Quasi-steady combustion modeling of homogeneous solid propellants , 1995 .

[115]  Franklin K Moore,et al.  Transverse oscillations in a cylindrical combustion chamber , 1954 .

[116]  F. Vuillot,et al.  Propagation of an acoustic wave in a two-phase reactive medium , 1998 .

[117]  F. A. Williams,et al.  Response of a Burning Solid to Small-Amplitude Pressure Oscillations , 1962 .

[118]  H. B. Mathes,et al.  Entropy Waves Produced in Oscillatory Combustion of Solid Propellants , 1969 .

[119]  R. W. Hart,et al.  Linear Acoustic Gains and Losses in Solid Propellant Rocket Motors , 1964 .

[120]  Fred E. C. Culick,et al.  Influence of Random Excitations on Acoustic Instabilities in Combustion Chambers , 2000 .

[121]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[122]  J. Levine,et al.  A numerical study of nonlinear instability phenomena in solid rocket motors , 1981 .

[123]  Fred E. C. Culick A Note on Ordering Perturbations and the Insignificance of Linear Coupling in Combustion Instabilities , 1997 .

[124]  Fred E. C. Culick,et al.  Role of Condensed Phase Details in the Oscillatory Combustion of Composite Propellants , 1977 .

[125]  G. Marxman,et al.  Finite-amplitude axial instability in solid-rocket combustion , 1969 .

[126]  Ben T. Zinn A theoretical study of nonlinear combustion instability in liquid-propellant rocket engines. , 1968 .

[127]  K. N. Lakshmisha,et al.  Nonlinear Intrinsic Instability of Solid Propellant Combustion Including Gas-Phase Thermal Inertia , 2000 .

[128]  M. Tanno,et al.  Low Frequency Instability in Solid Propellant Rocket Motors , 1960 .

[129]  J. N. Levine,et al.  A numerical study of nonlinear instability phenomena in solid rocketmotors , 1983 .

[130]  H. B. Keller,et al.  NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS , 1991 .

[131]  J. F. Bird,et al.  Acoustic Resonance in Solid Propellant Rockets , 1960 .

[132]  Luigi T. DeLuca,et al.  Linear Stability and Pressure-Driven Response Function of Solid Propellants with Phase Transition , 1999 .

[133]  Vigor Yang,et al.  Comprehensive review of liquid-propellant combustion instabilities in F-1 engines , 1993 .

[134]  L. Crocco Theoretical studies on liquid-propellant rocket instability , 1965 .

[135]  K. Sudhakar,et al.  LARGE-AMPLITUDE LIMIT CYCLES IN RESONANTLY COUPLED OSCILLATORS , 2000 .

[136]  J. Sterling Nonlinear Analysis and Modelling of Combustion Instabilities in a Laboratory Combustor , 1993 .

[137]  F. T. McClure,et al.  Combustion Instability: Acoustic Interaction with a Burning Propellant Surface , 1959 .

[138]  G. Lengelle,et al.  Thermal degradation kinetics and surface pyrolysis of vinyl polymers , 1970 .

[139]  M. W. Beckstead Low frequency instability: A comparison of theory and experiment , 1968 .

[140]  D. R. Mason,et al.  Thrust oscillations of the Space Shuttle solid rocket Booster motor during static tests , 1979 .

[141]  M. W. Beckstead,et al.  NON-ACOUSTIC COMBUSTION INSTABILITY OF SOLID PROPELLANTS , 1966 .

[142]  W. Nachbar,et al.  Analysis of a Simplified Model of Solid Propellant Resonant Burning , 1959 .

[143]  L. T. De Luca,et al.  Nonsteady Burning and Combustion Stability of Solid Propellants , 1992 .

[144]  T. Lieuwen,et al.  Experimental investigation of limit cycle oscillations in an unstable gas turbine combustor , 2000 .

[145]  Thomas L. Jackson,et al.  Random propellant packs and the flames they support , 2000 .

[146]  Fred E. C. Culick Combustion Instabilities and Rayleigh’s Criterion , 1991 .

[147]  B. V. Novozhilov,et al.  Stability criterion for steady-state burning of powders , 1965 .

[148]  Gary A Flandro,et al.  Combustion Instability in Solid Propellant Rockets , 1989 .