Analysis and design of transonic airfoils using streamwise coordinates

A new approach is developed for analysis and design of transonic airfoils. A set of full potential equivalent equations in von Mises coordinates is formulated from the Euler equations under the irrotationality and isentropic assumptions. This set is composed of a main equation for the main variable, y, and a secondary equations for the secondary variable, R. The main equation is solved by type dependent differencing combined with a shock point operator. The secondary equation is solved by marching from a non-characteristic boundary. Sample computations on NACA 0012 and biconvex airfoils show that, for the analysis problem, the present approach achieves good agreement with experimental C sub p distributions. For the design problem, the approach leads to a simple numerical algorithm in which the airfoil contour is calculated as part of the flow field solution.