2-DIMENSIONAL UNSTEADY LEADING-EDGE SEPARATION ON A PITCHING AIRFOIL

The initial stages of two-dimensional unsteady leading-edge boundary-l ayer separation of laminar subsonic flow over a pitching NACA-0012 air foil have been studied numerically at Reynolds number (based on airfoi l chord length) Re(c) = 10(4), Mach number M(infinity) = 0.2, and nond imensional pitch rate OMEGA0+ = 0.2. Computations have been performed using two separate algorithms for the compressible laminar Navier-Stok es equations. The first method, denoted the structured grid algorithm, utilizes a structured, boundary-fitted C grid and employs the implici t approximate-factorization algorithm of Beam and Warming. The second method, denoted the unstructured grid algorithm, utilizes an unstructu red grid of triangles and employs the flux-difference splitting method of Roe and a discrete representation of Gauss' theorem for the invisc id and viscous terms, respectively. Both algorithms are second-order a ccurate in space and time and have been extensively validated through comparison with analytical and previous numerical results for a variet y of problems. The results show the emergence of a primary clockwise-r otating recirculating region near the leading edge which can be traced to a pair of critical points (a center and a saddle) that appear with in the flowfield, followed by a secondary counter-clockwise-rotating r ecirculating region and a tertiary clockwise-rotating recirculating re gion. The primary and secondary recirculating regions interact with ea ch other to give rise to the unsteady separation (''breakaway'') of th e boundary layer.