A Nonlinear Sub-grid Scale Model for Compressible Turbulent Flow

The governing equations for large eddy simulation (LES) are obtained by filtering the Navier-Stokes (N-S) equations with standard (non-Favre filtering) spatial filter function. The filtered scale stress due to the standard filtering is then reconstructed by using the Taylor series expansion. The loss of information due to truncating the expansion up to the first derivative term is modeled by a dynamic nonlinear model (DNM), which is free from any empirical constant and wall damping function. The DNM avoids the singularity of the model and shows good local stability. Unlike the conventional dynamic Smagorinsky model (DSM), the DNM does not require the plane averaging and reduces the computational cost. The turbulent flow over a double ellipsoid for Reynolds number of 4.25 × 106 and Mach number of 8.02 is simulated numerically to validate the proposed approach. The results are compared with experiment data, as well as the data of Reynolds averaged numerical simulation (RANS).