A Numerical Study of Flow Around an Oscillating Airfoil with High-Order Spectral Difference Method

A high-order spectral difference flow solver for compressible three-dimensional NavierStokes (N-S) equations has been utilized to numerically simulate the unsteady flow over the NACA 0012 airfoil undergoing a sinusoidal pitching motion at the Reynolds (Re) number of 12600. The effects of the reduced frequency and Strouhal number on the wake vortex structure and force coefficient have been studied. The force coefficients under different aerodynamic conditions agree well with experimental results. It was found that the wake vortex structure and thrust coefficient can be attributable to the combined effects caused by the reduced frequency and the Strouhal number. A relatively larger Strouhal number can easily induce moderate leading edge separation, which can generate larger thrust; A relatively smaller reduced frequency corresponds to a lower shear strain rate in the wake, which can also generate larger thrust. A deflected wake appears at large Strouhal numbers and the behavior of the deflected wake is greatly influenced by the initial conditions. A simple model was developed to explain the generation of the deflected wake, and it appears that the dipole acceleration could serve as a reason for the larger thrust generation at a larger Strouhal number. In addition, it was found that the compressibility of the fluid has an influence on the force coefficient. Based on this observation, all numerical simulations are performed with an inlet Mach number of 0.1, which has been verified to be reasonable for the present study. Moreover, in order to minimize the errors from dynamic grids, the effect of the Geometric Conservation Law (GCL) has been investigated in the ongoing research.