Triggering and Restabilization of Combustion Instability with Rocket Motor Acceleration

The probability of a liquid-propulsion rocket motor to develop screeching instability is studied computationally. The combustion chamber is accelerated as a rigid body using a prescribed acceleration time history; it is found that accelerations of proper magnitude, duration, and frequency induce a pressure wave inside the combustion chamber that grows to a screeching acoustic wave limit cycle. For a rectangular rocket motor, a reciprocating transverse acceleration leads to the development of a transverse pressure wave limit cycle; for a cylindrical rocket motor, the limit cycle may be either a standing wave, for a transverse reciprocating acceleration, or a spinning wave, for a transverse rotating acceleration. It is found that a limit cycle may be induced by either a large acceleration pulse of short duration or a smaller acceleration pulse of a longer duration. The polynomial chaos expansion method is used to study the probability of growth to a limit-cycle oscillation when the amplitude and frequency of the transverse acceleration pulse are random.