Two-dimensional transonic aerodynamic design and analysis using the Euler equations

Abstract

A method is developed for the solution of the steady two-dimensional Euler equations with viscous corrections for transonic design and analysis problems. The steady finite volume integral equations are formulated on an intrinsic streamline grid, and are solved using a global Newton method. Conservative differencing together with artificial bulk viscosity in supersonic regions permit correct shock capturing. The design capability of the method stems from the streamline-based grid and Newton solution method, which allow both direct and inverse boundary conditions and constraints to be readily applied to the governing equations. For all boundary condition types, the effects of boundary layers and wakes on the inviscid flow are modeled by the displacement thickness concept. The boundary layer and wake parameters are described by compressible integral boundary layer equations which are coupled to the inviscid flow and are included in the global Newton solution scheme. This coupling procedure gives stable convergence for flows with limited separation regions. A transition criterion based on the Orr-Sommerfeld equation is developed and applied to transitional separation bubbles. Accurate drag predictions are obtained for subsonic and shocked transonic airfoils. Design examples involving airfoils and cascades are presented.