Two-Dimensional Navier-Stokes Solution of the Flow over a Thick Supercritical Airfoil with Strong Shock-Induced Separation

摘要

This report describes a numerical solution of the Navier-Stokes equations for transonic flow over a thick supercritical airfoil with strong shock-induced separation on both the upper and lower surfaces. The separated flow region extends from the shock (approximately 50% chord) to the trailing edge on both surfaces. The report first reviews the processes involved in producing a computational solution of the Navier-Stokes equations for a two-dimensional airfoil in a perfect gas. A brief development of the Navier-Stokes equations is provided. The solution algorithm used (an explicit predictor-corrector method) is developed and described. An algebraic turbulence model used to model the turbulent Reynolds stresses is described and the need for such a model is discussed. A hyperbolic, two-dimensional procedure for producing a computational grid (mesh) is also described. The boundary conditions imposed at the outer regions of the computational domain (farfield) and at the airfoil surface are discussed and described. The second part of the report discusses the treatment of the eddy viscosity development through the shock, in the separated regions over the airfoil and in the near wake. This work was critical for obtaining a successful solution on the very difficult test case chosen. Modifications to an algebraic eddy viscosity model to include the effects of the thickness of the separated flow region downstream of the shock are described. Keywords: Transonic aerodynamics; Separated flow. (edc)