Development of LES-high-order spectral difference method for flow induced noise simulation

The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modeled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm. The SD-LES method provides the acoustic sources for aerodynamic sound field simulation in the time domain. The numerical noise simulation is based on the Ffowcs-Williams Hawkings (FW-H) approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10³ and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional (3D) turbulent flow in a muffler at Re = 4.665 × 10⁴ and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately.