Full-scale numerical model of a Rijke-type pulse combustor

Abstract

In this paper a numerical model is developed to investigate the thermoacoustic conversion of heat into sound inside a Rijke tube. This study is carried out in an attempt to better understand the internal coupling between heat addition, pressure and velocity oscillations inside pulse combustors. In fact, similar coupling is believed to exist in other combustion devices including rocket motors at the verge of instability. In light of the recent progress in computational fluid dynamics (CFD), it is now possible to model quite effectively the compressibility effects bridging the gap between thermal and pressure oscillations. Our CFD results have been favorable in that they concurred with experimental observations. Self-sustained thermal oscillations near the heat source are found to be responsible for driving the acoustic pressure excitation. When acoustic velocity and pressure have maximum additive amplitudes, an optimal conversion of thermal energy into mechanical energy occurs. The latter is manifested in the form of acoustic intensity, which is the product of acoustic velocity and pressure. Below a threshold value in power input to the internal heat source, no self-sustained acoustic oscillations have been observed. Conversely, when a critical power input to the heater is exceeded, resonance is triggered in the form of pronounced acoustic amplification. The acoustic pressure and velocity mode shapes concur with classic theory except near the heater source where a local increase in the velocity amplitude is noted. During limit-cycle oscillations, the acoustic pressure is found to lead thermal fluctuations by a 45 degree angle. This result may be used to specify the phase angle in Carvalho's analytical formulation which predicted a value under 90 degrees. Overall, numerical results indicate a strong pressure dependence on heat fluctuations. In fact, the modulus of thermal oscillations is found to be directly proportional to the modular product of acoustic velocity and pressure. In relation to solid and hybrid rocket motors, they predict a strong thermoacoustic, noise generating coupling in the forward half of the motor.