TWO-DIMENSIONAL NUMERICAL VERIFICATION OF THE UNSTEADY THERMOACOUSTIC FIELD INSIDE A RIJKE-TYPE PULSE COMBUSTOR

Abstract

In this article a numerical model is developed to investigate the thermoacoustic conversion of heat into sound in a Rijke tube. This study is carried out in an attempt to better understand the internal coupling among heat addition, pressure, and velocity oscillations inside a Rijke-type pulse combustor. 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), we are now able to incorporate the compressibility and acoustic wave effects bridging the gap between thermal and pressure oscillations. When acoustic velocity and pressure have favorable time phases in the lower tube section, their synchronously alternating motions in the upward or downward directions give rise to acoustic excitation. As a result, an optimal conversion occurs whereby thermal energy is converted into mechanical energy. The latter is manifested in the form of acoustic intensity, a by-product of acoustic velocity and pressure. Below a threshold value in power input to the internal heat source, no self-sustained acoustic oscillations are observed. Conversely, when a critical power input to the heater is exceeded, resonance is triggered in the form of pronounced acoustic amplification. Self-sustained thermal oscillations near the heat source are found to be responsible for driving the acoustic pressure excitation. The acoustic pressure and velocity mode shapes along the centerline concur with one-dimensional acoustic theory except near the heater source where a local increase in the velocity amplitude is noted. Our two-dimensional CFD results agree with experimental observations reported in other studies. 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 smaller than 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, our findings can be extrapolated to predict a strong thermoacoustic, noise generating coupling in the forward half of the motor.