Numerical study of unsteady low-Reynolds-number separation bubbles using a new high order scheme

Low-Reynolds-number flows over airfoils are often characterized by the presence of separation bubbles, which can be unsteady with vortex shedding. The separation bubbles are unstable and their structure depends on the ambient disturbances present. Hence, it is important to understand the receptivity to disturbances and its effect on the separation bubbles. The objectives of this paper are two fold: 1) to develop and validate a new high-order (of arbitrarily high order) explicit finite difference scheme with stable boundary closure for solving the unsteady incompressible Navier-Stokes equations in the vorticity-velocity form; 2) to present results of numerical simulations of unsteady separation bubbles induced on a flat plate. The first part of this paper presents a new method for solving unsteady incompressible Navier-Stokes equations, which uses arbitrarily high-order finite difference schemes with stable boundary closure schemes derived directly on a nonuniform stretched grid. The second part of the paper presents results from separation bubble simulations, computed using a fifth order accurate method in the streamwise and wall normal direction and a spectral method in the spanwise direction. The separation bubbles on the flat plate are induced by specifying a velocity gradient in the freestream or by suction at the freest ream. The freestream velocity distributions are varied to obtain different sizes of separation bubbles. The unsteady separation bubbles are studied by introducing wall blowing and suction disturbances, of varying frequencies and amplitudes.