Modeling the Effects of Velocity Coupling on the Global Dynamics of Combustion Chambers

Abstract

Considerable data exists suggesting that the response functions for many solid propellants tend to have higher values, in some ranges of frequencies, than predicted by the conventional QSHOD theory. It is a familiar idea that such behavior is associated with dynamical processes possessing characteristic times shorter than that of the thermal wave in the condensed phase. The QSHOD theory, and most of its variants, contains only the dynamics of that process, which normally has a characteristic frequency in the range of a few hundred hertz. Two previous works seeking to correct this deficiency (T'ien, 1972; Lazima and Clavin, 1992) have focused their attention on including the dynamics of the thermal wave in the gas phase. Both include effects of diffusion that complicate the analysis although the second achieves some simplification by applying the ideas of 'activation energy asymptotics'. While their results differ in detail, both works show influences at frequencies higher than those near the broad peak of the response due to the thennal wave. Recent theoretical work and simulations show that a combustion response function based on simple pressure coupling is not enough to explain the characteristics of the instability observed experimentally. Namely, differences in the shape of the response function fail to reproduce the differences observed experimentally in the characteristics of the limit cycle reached by combustion chambers with propellants of different chemical (or physical) composition. On the other hand, velocity coupling in the combustion response seems a promising mechanism able to predict the changes in the unstable modes observed experimentally and to produce considerable effect on the shape of the resulting limit cycle. The Baum and Levine model is used as a starting point in the investigation of velocity coupling. Other models, in which the mass burning rate is modified by some function of the velocity, are also investigated through direct time-simulation and by the use of a continuation method. Modeling of particle damping at high frequency constitutes a serious consideration in the modeling of the interaction of combustion dynamics and chamber acoustics. The effect of particle size distribution is analyzed by considering an experimental particle size distribution. The ultimate goal of this work is to find a link between the global dynamics of the combustion chamber and small changes in the combustion dynamics, caused by differences in propellant chemical composition or physical characteristics (for example, particle size and distribution). Response functions are shown for realistic ranges of the chief parameters characterizing the dynamics of the propellant. The results are also incorporated in the dynamical analysis of a small rocket motor to illustrate the consequences of the combustion dynamics for the stability and nonlinear behavior of unsteady motions in a motor.

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