Airfoil computation at high angles of attack, inviscid and viscous phenomena

HE existence of flow separation and recirculation is usually associated with viscous flows. The physical basis is fairly well understood and has been extensively studied. There are a number of physical phenomena that cause flow separation and recirculation. In all cases in which recirculation is present, vorticity must also be present and, thus, there must exist some mechanism that generates vorticity. In a viscous wall-bounded flow, the boundary layer generates a velocity gradient, vorticity, and momentum losses. In the presence of an adverse pressure gradient, separation can occur with the subsequent development of a recirculating reverse flow region and possible reattachment. A shock impinging on a boundary layer can cause flow separation. The governing equations for these types of flows are the NavierStokes equations or some subset of them. Recently, there has been considerable interest in the numerical solution of the inviscid flow equations (the Euler equations). For most of the work reported in the literature, the accuracy of the results is quite good and the solutions obtained are representative of the physical flow of interest. For instance, when viscous effects are negligible, such as for thin boundary layers, the inviscid solutions are a good approximation to the solution of the full Navier-Stokes equations. In this situation, certain quantities, such as the pressure along the body, can be predicted well by the Euler equations. In contrast, numerical solutions to the Euler equations have been reported that do not have a straightforward physical interpretation. In particular, flow separation and recirculation for solutions to the Euler equations have been reported by a number of researchers (e.g., Salas1). The question naturally arises as to the physical interpretation of these flows in the absence of physical viscosity. In trying to attach any physical meaning to these flows, we must first examine the possible mechanisms that could generate vorticity. Actual fluid flow is never truly inviscid, although in some cases the viscous effects are negligible. In computations, however, we can solve numerical approximations to the Euler equations. The solution of the Euler equations is