Time-dependent Navier-Stokes computations of separated flows over airfoils

Abstract

The application of both a central-difference and an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using the thin-layer approximation, both algorithms are employed to solve the low Reynolds number laminar flow around a circular cylinder with periodic shedding. Results agree with experimental Strouhal numbers to within about 10 percent. A grid refinement study is conducted using the upwind code for both the thin-layer and complete Navier-Stokes approximations. The circular cylinder solution is shown to be highly dependent upon both grid density outward from the body and grid extent. Finally, the thin-layer central-difference code is used to predict the time-accurate unsteady flow about two stalled airfoils. The NACA 0012 airfoil turbulent solutions are periodic with Strouhal numbers of about 0.1; a strong vortex is periodically shed from the leading edge. The LS(1)-0417 airfoil turbulent solution shows a high frequency oscillatory trailing edge separation. The 20 degree NACA 0012 airfoil solution is massively separated, but shows no evidence of periodicity.