Aeroacoustic simulation of broadband sound generated from low-Mach-number flows using a lattice Boltzmann method

Abstract

The present paper demonstrates the capability of a numerical method based on the lattice Boltzmann method (LBM) with wall-resolved grid to predict the broadband sound generated from the turbulent boundary layer at low Mach numbers. The present method is based on the lattice BGK equation with the D2Q9 and D3Q15 models, and a multi-scale approach using hierarchically refined grids is proposed to efficiently and simultaneously capture the multi-scale phenomena of turbulent eddies near walls and far-field sound waves. Numerical instabilities caused by the lack of grid resolution are suppressed with a fourth-order implicit filtering scheme. This numerical method is discussed in two benchmark problems and an application to the prediction of the broadband sound generated from the turbulent boundary layer. First, the computational accuracy and speed of the LBM scheme are assessed with a pulse-propagating problem. The results indicate that the LBM can achieve accuracy comparable to the fourth-order central scheme with the four-stage Runge-Kutta method for the compressible Navier-Stokes (N-S) equations and compute 12.3 times faster. These findings suggest that the LBM is an efficient computational method for aeroacoustic simulations. Second, the proposed method is validated by simulating the Aeolian tone generated by the flow past a circular cylinder at Reynolds number of 150 and Mach number of 0.2. The present simulation is compared with a compressible N-S simulation using a high-order finite difference scheme in terms of the wave profile and the propagation speed of the tonal sound. This validation result suggests that the present method is available for direct aeroacoustic simulations of low-Mach-number flows. Finally, the capability of the present method to predict the broadband sound is demonstrated by conducting a wall-resolved simulation for the turbulent flow generated by a short separation bubble over an isolated airfoil at Reynolds number of 2.0×105 and Mach number of 0.058. This simulation shows a good agreement with measurements of the surface pressure distributions, the wake velocity profiles, and the far-field sound spectrum. In contrast to hybrid approaches based on the incompressible N-S equations, the present method can accurately predict the broadband sound in the high-frequency range by simulating the acoustic scattering on the airfoil.