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

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 2.0×10^5 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

半開放形プロペラファンにおける翼端渦の三次元構造

The tip vortex has an important role on the aerodynamic performance and noise of half-ducted propeller fans. The present paper provides better understanding on the three-dimensional structure of the tip vortex in a half-ducted propeller fan, aiming at the effective control of it. A numerical analysis was carried out using a detached eddy simulation (DES). DES results were validated by the comparison with LDV measurement data. Vortex centers around the propeller fan were identified by the critical point theory. The numerical results show that the tip vortex in the opened region upstream of the shroud leading edge is advected nearly along main stream, whereas the tip vortex in the ducted region covered by the shroud is turned toward the tangential direction by the interaction of the tip vortex with the shroud wall. The behavior of the tip vortex in its inception region does not depend on the flow rate, because the relative inflow angle at the leading edge near the blade tip is independent of the flow rate. On the other hand, the behavior of the tip vortex in the ducted region is sensitive to the flow rate. As the flow rate is decreased, the tip vortex interacts more strongly with the shroud wall, and as a result, its trajectory is inclined more largely in the tangential direction in the ducted region. In the opened region, the core radius and circulation of the tip vortex increase rapidly at constant growth rate in the streamwise direction. In the ducted region, on the other hand, the tip vortex decays gradually in the downstream direction. The maximum circulation of the tip vortex amounts to 60～75% of the circulation of the bound vortices released from the near tip region of the blade. It is found that the jet-like axial velocity distribution is formed around the tip vortex center by the favorable pressure gradient along the tip vortex center resulting from its rapid growth in the opened region