Analytical investigation of non-adiabatic effects on the dynamics of sound reflection and transmission in a combustor

Acoustics of a simplified, non-adiabatic combustor chamber, including a duct followed by a downstream exit nozzle, are considered. This system features heat transfer to the environment, and therefore involves mean axial temperature gradient along the duct and the nozzle. The effect of heat transfer on the dynamics of the acoustic reflection and transmission in the duct and nozzle is investigated analytically. These involve the development of analytical expressions for the response of non-adiabatic nozzles through compact acoustic modeling and also the effective length approach. Further, an existing work on the dynamics of heat transferring ducts is extended and combined with that of the nozzles. The acoustic responses of the combined non-adiabatic system are, subsequently, characterized by analyzing the net reflection and transmission of an incident acoustic wave. The results show that heat transfer can considerably modify the dynamic behavior of the acoustic reflections and transmissions. Due to the multiple reflections in the system, the phase response features significant irregularities. It is argued that the observed modifications in the chamber acoustics can noticeably affect the thermoacoustics of the system.