This paper studies the acoustic behavior inside the deep annular and cylindrical cavity at low Mach number. The turbulent shear layer above the cavity acts as a broadband noise source and drives resonant standing waves inside the cavity for various modes. According to previous investigation, those resonant standing waves inside the cavity play an important role in the aeroacoustic resonance of cavity noise, which gives perfect prediction of tonal frequency from the solution of wave equation. From the perspective of engineering application, it is more important to predict the spatial distribution of tonal intensity. It is needed to point out that the solution of the linear wave equation also provides the relative spatial distribution tonal intensity and the absolute value of tonal intensity can be determined from the acoustic experiments that is measured only at some locations. Based on this idea, a scheme is setup and validated to predict the amplitude spatial distribution of tonal intensity of aeroacoustic resonance. For example, an analytical model is established to provide the relative mode shape of aeroacoustic resonance in a simple geometry of cavity, which is realized by solving the wave equation with boundary conditions in a semi-closed space. This model considers the freestream velocity scaling and the depth correction factor varying with the Helmholtz number. The experimental aeroacoustic result is acquired by measuring the pressure fluctuation at some locations of cavity internal wall with the use of surface microphones. The experimental results are used to supplement and validate this analytical model. The amplitude spatial distribution at any freestream velocity (low Mach number) can be acquired by measuring the pressure fluctuation once at the leading edge or trailing edge of cavity bottom at an arbitrary Mach number, as the amplitude of most modes reaches its maximum here.
Analysis of an asymptotic preserving low mach number accurate IMEX-RK scheme for the wave equation system
