Hybridal Method for the Prediction of Wave Instabilities Inherent in High Energy-Density Combustors (1): Modeling of Nonlinear Cavity Acoustics and its Evolution

Lee, Gil-Yong;Yoon, Woong-Sup

  • Published : 2006.12.31


This paper targets a direct and quantitative prediction of characteristics of unstable waves in a combustion chamber, which employs the governing equations derived in terms of amplification factors of flow variables. A freshly formulated nonlinear acoustic equation is obtained and the analysis of unsteady waves in a rocket engine is attempted. In the present formalism, perturbation method decomposes the variables into time-averaged part that can be obtained easily and accurately and time-varying part which is assumed to be harmonic. Excluding the use of conventional spatially sinusoidal eigenfunctions, a direct numerical solution of wave equation replaces the initial spatial distribution of standing waves and forms the nonlinear space-averaged terms. Amplification factor is also calculated independently by the time rate of changes of fluctuating variables, and is no longer an explicit function for compulsory representation. Employing only the numerical computation, major assumptions inevitably inherent, and in erroneous manner, in up to date analytical methods could be avoided. With two definitions of amplification factor, 1-D stable wave and 3-D unstable wave are examined, and clearly demonstrated the potentiality of a suggested theoretical-numerical method of combustion instability.


Combustion Instability;Acoustic Wave;Rocket Engine


  1. Vigor Yang and Williams E. Anderson (eds), 1995, 'Liquid Rocket Engine Combustion Instability', AIAA
  2. Fred E. C. Culick, 1966, 'Acoustic Oscillations in Solid Propellant Rocket Chambers', Astronautica Acta, Vol. 12, No.2, pp. 113-126
  3. Crocco, L., and Cheng, S. I., 1956, 'Theory of Combustion Instability in Liquid Propellant Rocket Motors', AGARD Monograph, No.8, Butterworths, London, Chaps. 1-3
  4. Mitchell, C., 1989, 'Stability Design Methodology', TR 89-041, Astronautics Laboratory, Air Force Space Center
  5. Culick, F., and Yang, V., 1995, 'Combustion Instabilities in Liquid Rockets', AIAA Progress in Astronautics and Aeronautics, Vol. 169, pp. 3-37
  6. Culick, F., 1994, 'Some Recent Results for Nonlinear Acoustics in Combustion Chambers', AIAA J, Vol. 32, No.1, pp. 146-169
  7. Habiballah, M., Dubois, I., Vingert, L., Lourme, D., and Scherrer, D., 1992, 'High Frequency Combustion Instability in Liquid Propellant Rocket Engine - A Review of Studies Carried Out at ONERA for the Ariane Launcher', AlAA Paper 92-0774
  8. Dubois, I., and Habiballah, M., 1991, 'Numerical Simulation of High Frequency Instability in an Oxygen/Hydrogen Rocket Engine,' AIAA paper 91-1860
  9. Liang, P., Fisher, S., and Chang, Y., 1985, 'Comprehensive Modelling of a Liquid Rocket Combustion Chamber', AIAA Paper 85-0232
  10. Jeng, S., and Litchford, R, 1992, 'Liquid Rocket Spray Combustion Stability Analysis', AIAA Paper 92-3227
  11. F. E. C. Culick, 1968, 'A Review of Calculations for Unsteady Burning of a Solid Propellant', AIAA Journal, Vol. 6, pp 2241-2255
  12. Culick, F. E. C., and Yang. V., 1992, 'Prediction of the Stability of Unsteady Motions in Solid Propellant Rocket Motors', Nonsteady Burning and Combustion Stability of Solid Propellants, edited by L. Deluca and M. Summerfield, Vol. 143, Progress in Astronautica and Aeronautics, AIAA, Washington, DC, Chap. 8, pp. 719-780
  13. Tong, A.Y., and Sirignano, W.A., 1983, 'Analysis of a Vaporizing Droplet with Slip, Internal Circulation, and Unsteady Liquid-Phase and Quasi-Steady Gas-Phase Heat Transfer', ASME-JSME Thermal Engineering Joint Conference, Vol. 2, American Society of Mechanical Engineers, New York, pp. 481-487
  14. Yang, V., and Culick, F.E.C., 1990, 'On the Existence and Stability of Limit Cycles for Transverse Acoustic Oscillations in a Cylindrical Combustion Chamber. 1: Standing Modes', Combustion Science and Technology, Vol. 72, Nos. 1-3, pp. 37-65
  15. G.Y. Lee and W.S. Yoon, 2000, 'High Frequency Wave Instability and Combustion Responses', AIAA- 2000-3296
  16. F. E. C. Culick, 1976, 'Nonlinear Behavior of Acoustic Waves m Combustion Chambers-II', Acta Astronautica, Vol. 3, pp. 735-757.
  17. W.S. Yoon, 'Prediction and Evaluation of the High-Frequency Liquid Rocket Instabilities', Tech. Rept., 2002
  18. Yang, V., Kim, S., and Culick, F., 1987, 'Third-Order Nonlinear Acoustic Instabilities in Combustion Chambers, Part I : Longitudinal Modes', AIAA Paper 87-0152
  19. T'ien, J., and Sirignano, W., 1971, 'Unsteady Thermal Response of the Condensed-Phase Fuel Adjacent to a Reacting Gaseous Boundary Layer,' Thirteenth Symposium (International) on Combustion, The Combustion Institute
  20. Culick, F., 1971, 'Combustion Instabilities in Propulsion Systems', Combustion Science and Technology, Vol. 3, No.1, pp. 1-16
  21. Yoon, W.S., and Chung, T.J., 1993, 'Nonlinearly Unstable Waves Dominated by Entropy Mode', J of Acoust. Soc. Am, Vol. 96, No.2, pp. 1096-1103
  22. Kim, Y., Chen, C., and Ziebarth, J, 1992, 'Prediction of High Frequency Combustion Instability in Liquid Propellant Rocket Engines', AIAA Paper 92-0775