Implementation of Delayed Detached Eddy Simulation method to a high order spectral difference solver

The Delayed Detached Eddy Simulation (DDES) method based on Spalart-Allmaras (SA) turbulence model is implemented to a high order spectral difference solver for aeroacoustics problems in this study. A modified SA model by Crivellini et al. is used to eliminate the instability of the nonlinear source terms in the turbulence model. To speed up the unsteady simulation, the multi-time-step method based on the optimized Adams-Bashforth scheme is utilized for time marching. The perfectly matched layer absorbing boundary condition for Navier-Stokes equations is applied at the far-field and outflow boundary regions. The SA model is firstly validated with the high Reynolds number flow over a flat plate and the flow around a NACA0012 airfoil at 10° and 15° angles of attack. The numerical results are compared with the experimental or reference data by other researchers. The good agreement indicates that the high order spectral difference solver with SA model is accurate to compute the turbulence boundary layer. Then the developed DDES solver is validated with the backward facing step flow and the flow over a NACA0012 airfoil at 60° angle of attack. The computed results are compared with the experimental data, as well as the URANS results. The validation results show that the DDES solver is capable of computing the turbulence flow with boundary layer separations. Finally the noise from the flow past two cylinders in tandem is computed with the DDES solver. The computed results, including the time mean flow field, dynamic pressures on both cylinders and far field noise spectra are compared thoroughly with the experimental data provided by NASA, as well as the reference numerical results by other researchers. An assessment is made of the accuracy of the present high order SD solver versus the low order method. The results show that the high order SD solver with the DDES method is more accurate than low order solver for aeroacoustics numerical simulation with similar resolution, and capable of predicting accurately the noise for aeroacoustics problems with turbulence separations.