Large eddy simulation of weakly compressible turbulent flows around an airfoil

The purpose of this study is to develop a numerical method for turbulent flows at low Mach number range. To account for the weak compressibility, we modify the time marching method of the usual incompressible scheme which is based on the elliptic equation for pressure. To deal with high Reynolds number flows appropriately, we propose a new one-equation subgrid scale model (SGS). In this model, the concept of coherent structure function model is introduced to treat the energy transfer from grid scale to SGS portion of turbulence kinetic energy. The feature of our one-equation SGS model is that the energy production rate of SGS kinetic energy is calculated without the dynamic procedure, and any parameters such as the friction velocity on the wall or distance from the wall are not necessary. The new one-equation SGS model is incorporated into the weakly compressible scheme to treat a small density variation. Computational examinations have been conducted for fully developed turbulent flows in a plane channel and turbulent flows around NACA0012 airfoil at low Mach number, and have shown satisfactory results. We show that the consideration of the density variation even in low Mach number flows is essential to reproduce the pressure fluctuation and vortical structure appropriately.