AN ACOUSTIC ANALOGY MODEL FOR HELMHOLTZ RESONATORS WITH COOLING BIAS FLOW

Helmholtz resonators (HR), as a typical passive muffler device, are often installed in the combustor of aero engines and gas turbines to absorb noise and suppress combustion thermoacoustic oscillations. In practical applications, in order to prevent the high temperature gas in the combustion chamber from damaging the HR, a cooling airflow is often introduced from the back cavity of the HR into the combustor through its neck to protect the HR. The temperature of this cooling airflow is generally significantly lower than the temperature of the gas in the combustor. When such HR is installed on the combustor, the temperature difference may affect the relationship between the sound waves and entropy waves upstream and downstream of the HR in the combustor, and further affect the sound absorption performance of the HR. However, in previous models for studying the influence of HR on thermoacoustic oscillations in the combustor, the influence of this temperature difference is generally ignored. Based on the idea of acoustic analogy, we develop a theoretical model in this paper which can predict the acoustic performance of HR with cooling airflow. This HR is installed in a one-dimensional acoustic duct. The model is based on one-dimensional mass, momentum and energy conservation equations. Under the assumption of no viscous dissipation, ignoring volume forces, all external heat sources and thermal diffusion, we derived for the first time the wave equation with source term in a one-dimensional combustor with Helmholtz resonator with cooling airflow installed on the side wall.The source term on the right side of the equation reflects the effect of the resonator on the one-dimensional sound field in the combustor. It can be seen from this equation that the sound source/sink dissipation caused by the resonator is composed of entropy disturbance and mass disturbance terms. It can be further seen that the entropy disturbance generated by the temperature difference of the resonator will enter the one-dimensional sound wave equation in the combustor in the form of a sound source, significantly changing the effect of HR on the sound field in the combustor near its resonance frequency. By comparing with the existing jump condition model, we verified the accuracy of the model in predicting the effect of HR temperature difference on the sound field in the one-dimensional combustor.