Studies of High Frequency Combustion Instabilities with the Method of Pattern Dynamics

Abstract

The nonlinear high frequency combustion instability in liquid rocket engine is simulated in this paper. The gas governing Navier-Stokes equations are described under the Euler coordinate. The liquid phase governing equations are described under the Lagrangian coordinate. The two phase influences of gas and liquid are through the interaction of source terms of equations. The spray process in rocket engine is described with evaporation theory. The numerical method is MacCormack scheme which is two order accuracy in space and time direction. The two phase turbulent combustion steady process and high combustion instability in liquid rocket engine are simulated with the method of computational combustion dynamics. When there are spontaneous high frequency combustion instability in liquid rocket engine, the pressure in combustion chamber is oscillating near the steady state at the beginning, and as the simulated time passes, the pressure is exponentially increased until the high amplitude pressure oscillation is excited in combustion chamber because of nonlinear effects. In the three dimensional phase space of chamber pressure, mixed gas density and mixed gas velocity, the physics parameters are going round and round near the attractor, the six spiral main moving trajectories are created. There are lots of secondary moving trajectories between the main trajectories. The chaotic state is appeared far away from the attractor point. The same rule of moving trajectories is occurred in the three dimensional phase spaces of chamber pressure, mixed gas density, spray velocity and mixed gas density, mixed gas temperature, mixed gas velocity.