Acoustic Scattering by a Localized Thermal Disturbance

Abstract

Direct aeroacoustic simulation, which simulates acoustic radiation associated with unsteady fluid flows, involves capturing waves in both aerodynamic and acoustic scales. The presence of a thermal field further complicates this simulation. There are few analytical thermal-acoustic problems that could serve as benchmark to validate computational aeroacoustics schemes. This paper attempts to seek a theoretical solution of a simple problem involving scattering of acoustic plane waves by a localized zero-heat-gain/loss thermal disturbance and use it as a benchmark to verify the validity and extent of a numerical gas-kinetic scheme based on the modeled Boltzmann equation for the study of aeroacoustics resulting from thermal-flow/acoustic interaction. Two limiting cases with different acoustic wavelengths are attempted. Theoretical solutions are established for both cases, with the center of an axisymmetric thermal disturbance located at the origin of the physical domain. The incident acoustic wave has a dimensionless amplitude given by 1 x 10 -4 and is propagated from left to right of the coordinate system. The simulation of the gas-kinetic scheme is carried out using the same computational setting as for the theoretical solutions. Riemann invariants are stipulated at the open boundaries. Numerical results are compared with the theoretical solutions and good agreement is obtained for the short-wavelength case only. The discrepancy for the long-wavelength case could be partially attributed to the inappropriateness of the Riemann invariants for oblique waves at the boundaries.