Volumetric and Entropic Sound Sources of Helmholtz Resonators with Different Temperatures

Abstract

This study proposes an acoustic analogy model for the Helmholtz resonator (HR)–combustor system, considering the temperature difference between the bias flow from the HR and the grazing flow inside the combustor duct. The model highlights how the mass flux of the bias flow and the temperature difference serve as mass and entropic sound sources, respectively, influencing the HR’s sound absorption performance. To validate the model, we conducted numerical simulations using the Reynolds-averaged Navier–Stokes shear stress transport model to obtain the mean flow, followed by solving the frequency-domain linearized Navier–Stokes equations in COMSOL. The model was tested with HRs attached to combustor ducts under open–open and open–closed boundary conditions. Theoretical results agree well with numerical simulations, confirming the model’s accuracy. Results indicate that when the bias flow temperature is lower than the grazing flow temperature, the entropic sound source negatively affects duct acoustics, reducing sound absorption performance. Conversely, higher bias flow temperatures enhance sound absorption by superimposing entropic and mass-related sound sources. Additionally, the overall effect of the mass-related and entropic sound sources is equal to a volumetric source which depends on the mean sound speed and density of the HR instead of those of the combustor.