Numerical simulation studies of unsteady low Reynolds number separated flows

Numerical simulations were used to study unsteady low-Reynolds-number separated flows. The studies were focused on the instability of the separation bubbles, the associated vortex shedding, and the response to imposed disturbances. The simulations were performed for separation bubbles in both low Mach number compressible and incompressible flow regimes. The compressible study consisted of unsteady simulations of flows over the Eppler 387 airfoil and the APEX airfoil. For a sufficiently high Reynolds number the simulations showed that the flow over the airfoils is inherently unsteady, with associated vortex shedding. A Fourier analysis of the unsteady flowfield revealed the presence of a dominant frequency in the flow. The dominant frequency from the numerical solution was found to agree with the most unstable frequency calculated using linear stability theory. The vortex shedding was shown to be caused by the growth of the disturbance waves corresponding to the dominant mode calculated from the linear stability analysis.; In order to study the separation bubble and the vortex shedding in detail, a simpler two-dimensional (2-D) and three-dimensional (3-D) incompressible flow over a flat plate was considered. The onset of self excited vortex shedding, and the response of the separation bubble to 2-D and 3-D disturbances was studied in detail through numerical simulations. The incompressible Navier-Stokes equations were solved using a fifth order finite difference scheme for spatial discretization and a fourth order Runge-Kutta scheme for time advancement. A new high-order nonuniform grid finite difference scheme was also developed for the simulations. The incompressible simulation results showed that it was possible to induce vortex shedding by imposing disturbances upstream of the separation bubble. For a sufficiently large freestream velocity gradient the separation bubble was globally unstable, leading to a growth in the size of the separation bubble and the subsequent appearance of self-excited vortex shedding. The 3-D numerical simulations also showed the presence of 3-D global instability modes. The numerical results from simulations of 2-D and 3-D disturbances were found to be in good agreement with LST analyses. The simulations for the stationary 3-D disturbance wave agree with the linear stability results of Theofilis et. al. (2000).