Detached eddy simulation of flow over NACA0012 airfoil at high angle of attack with spectral difference method

A detached eddy simulation (DES) solver based on Spalart-Allmaras (SA) turbulence model is developed in this study. The high order spectral difference method is used for spatial discretization, and the multi-time-step method based on the optimized Adams-Bashforth scheme is utilized for time marching to speed up the simulation. When applying the multi-time-step time marching scheme, the computational domain is partitioned into a number of subdomains based on the mesh-size and flow scales. In each sub-domain the simulation is advanced with an independent time step which is determined with its local mesh size. A high order time interpolation is utilized for information exchanging between two adjacent sub-domains. A modified SA model is used to eliminate the instability of the nonlinear source terms in the turbulence model. A second order filter is also applied to the eddy viscosity on the flux points in the simulation to improve the stability of the solver. The developed solver is firstly validated with the viscous flow over a cylinder at low Reynolds number. The computed results with the multi-time-step method, including lift and drag forces, the far field pressure disturbances, the pressure coefficient on the cylinder surface, are all compared with the data calculated with the single time step method. A good agreement is obtained. The SA model is then validated with the high Reynolds number flow over a flat plate. The computed velocity profile is presented and compared with the experimental data. The good agreement indicates that the multi-time-step high order spectral difference solver with SA model is accurate to compute the turbulence boundary layer. Finally the developed DES solver is applied to simulate the flow over a NACA0012 airfoil at 45o and 60o angles of attack. The computed results are compared with the experimental data, as well as the URANS results. It shows that the DES method improves the prediction accuracy of turbulent flow with separations.