Implicit unstructured Navier-Stokes simulation of leading edge separation over a pitching airfoil

Abstract

The two-dimensional laminar flow over a pitching airfoil is simulated using an implicit unstructured grid Navier-Stokes algorithm. The inviscid and viscous fluxes are represented using second-order accurate discretizations employing Roe's method and Gauss' theorem, respectively. The temporal integration is an implicit first-order backward Euler differencing. The linear system arising from the discretization for the governing equations is solved using preconditioned BI-CGSTAB, with the incomplete factorization of the Jacobian used as the preconditioning matrix. Computations are presented for a NACA0012 airfoil pitching about the quarter-chord at a freestream Mach number M ∞ = 0.2 and Reynolds numbers Re c = 10 4 and 2 × 10 4 at a dimensionless pitching rate Ω 0 + = 2.0 . The results for Re c = 10 4 are in excellent agreement with previous computations using an explicit unstructured Navier-Stokes algorithm. New results for Re c = 2 × 10 4 indicate that the principal effect of increasing Reynolds number is to reduce the angle at which the primary recirculation region appears, and to cause it to form closer to the leading edge. This trend, confirmed by a grid refinement study, is consistent with previous results obtained at M ∞ = 0.5.