Two-dimensional unsteady leading-edge separation on a pitching airfoil

Abstract

The initial stages of two-dimension al unsteady leading-edge boundary-layer separation of laminar subsonic flow over a pitching NACA-0012 airfoil have been studied numerically at Reynolds number (based on airfoil chord length) Rec = 104, Mach number Mx = 0.2, and nondimensional pitch rate H£ = 0.2. Computations have been performed using two separate algorithms for the compressible laminar Navier-Stokes equations. The first method, denoted the structured grid algorithm, utilizes a structured, boundary-fitted C grid and employs the implicit approximate-factorization algorithm of Beam and Warming. The second method, denoted the unstructured grid algorithm, utilizes an unstructured grid of triangles and employs the flux-difference splitting method of Roe and a discrete representation of Gauss' theorem for the in viscid and viscous terms, respectively. Both algorithms are second-order accurate in space and time and have been extensively validated through comparison with analytical and previous numerical results for a variety of problems. The results show the emergence of a primary clockwise-rotating recirculating region near the leading edge which can be traced to a pair of critical points (a center and a saddle) that appear within the flowfield, followed by a secondary counterclockwise-rotating recirculating region and a tertiary clockwise-rotating recirculating region. The primary and secondary recirculating regions interact with each other to give rise to the unsteady separation (breakaway) of the boundary layer.