High frequency wave instability and combustion responses

This paper is concerned with the prediction of combustion instability in liquid-propeilant rocket engine represented by the temporal variation of the amplification factors of density, velocity, and pressure. Targeting the implementation of conventional analytical and computational approaches, computed Navier-Stokes solutions initializes spatial varying spray combustion, and freshly formulated ordinary differential equations(ODE's) in terms of amplification factors are time integrated. Combining the numerically calculated spray combustion and instability prediction formulation, linear and nonlinear wave instabilities in the liquid-propeilant rocket engine is attempted. Linear formulation showed the temporal variation of pressure amplification factor independent of magnitude of pressure perturbation and the system reaching the limiting cycle. In case of nonlinear analysis, the temporal variation of pressure amplification factor depends strongly on the magnitude of pressure perturbation. When the perturbation is sufficiently small, time trace of amplification factor resembles much with that due to linear analysis and repeatedly showed the limiting cycle, whereas when stronger perturbation is enforced, the system is driven to the unstable situation in nonlinear manner. Also attempted is the attenuation of instability with the amplification factors. Instability prediction method suggested in the present study requires accurate numerics of combusting flow variables with proper interpretations of dominating amplification parameters, and this remains as a future task.