PRESSURE OSCILLATIONS IN ROCKET COMBUSTION CHAMBERS

Abstract

The launching of space shuttle and probes for space exploration, firing of surface to surface/air, air to air/ground missiles for defense shield and launching of communication, weather and surveying satellites for commercial projects can only be achieved with reliable rocket propulsion system. The rocket scientists and engineers face an immense challenge of undesirable pressure oscillations in solid as well as liquid propellant rocket combustion chambers. The ultimate goal is, ideally, to design rocket propulsion system devoid of pressure oscillations in its combustion chamber and really, to control these oscillations. For both of these ideal and real scenarios the accurate and efficient prediction of pressure oscillations is essential. Over the years, researchers have employed various perturbation techniques to solve the pressure oscillation problem. The Multiple Time Scales (MTS) is a promising method because its results using first order perturbation terms coincide with numerical simulations. Moreover, it gives mathematical relations for amplitude and phase of oscillations which helps to understand the effect of various parameters. In this study acoustic pressure oscillations for single (uncoupled) and first two coupled longitudinal acoustic modes in Solid Rocket Motor (SRM) are investigated using MTS method. Two independent time scales, i.e. fast and slow are introduced. The oscillations occur on fast time scale whereas the amplitude and phase changes on slow time scale. The comparison of analytical expression with numerical method demonstrates an excellent agreement. Hopf bifurcation is employed to investigate the properties of solution. For single and coupled acoustic modes, the bifurcation point is found to lie at the point where linear stability / instability of solid rocket motor toggles. The supercritical bifurcation and hence the limit cycle is observed for linearly unstable system. It is established that in case of coupled modes the limited amplitude owes to equal energy gain and loss rates of mode one and two respectively. The effect of linear instability and frequency of longitudinal modes on amplitude and phase of oscillations are determined for both single and coupled modes. For both cases, the maximum amplitude of oscillations decreases with the increasing frequency of longitudinal acoustic mode and linear stability of SRM.