A Finite-Difference Method for Transonic Airfoil Design

Abstract

This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain, and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.

Airfoil design and optimization by the one-shot method

“…For convenience, n is the unit normal on the boundary. The far-field boundary condition given by ( 9) is consistent with the infinity condition stated by (3).…”

“…Although significant progress has been made in developing computational methods for fluid flow analysis, the methods for the design and optimization of aircraft configuration are still in their infancy. Among the many techniques that have been developed, the inverse design method [1][2][3][4][5][6] is perhaps the most widely used. This method is severely restrictive because its depends on the experience and knowledge of the designer to establish desirable velocity or pressure distributions.…”

Efficient Transonic Shock-Free Wing Redesign Procedure Using a Fictitious Gas Method

“…Iterative finite difference methods have been explored by Steger and Klineberg, 12 Tranen, 13 Carlson, 14 Shankar et al, 15 and Volpe,16 wherein the design problem is treated as an inverse problem, i.e., the airfoil shape that supports a given pressure distribution is found by iteration.…”