Iterative Solution of Transonic Flows over Airfoils and Wings,

Transonic aerodynamics is the focus of strong interest at the present time because it is known to encompass one of the most efficient regimes of flight. While current transport aircraft operate just below the speed of sound, more radical aerodynamic designs, such as R. T. Jones’ proposal for a yawed wing in [1], favor operation at low supersonic speeds in the range from Mach 1 to 1.3 (a regime in which the sonic boom should pose no serious problem). The hodograph method of generating a flow together with the corresponding boundary shape has been perfected by Bauer, Garabedian and Korn [2]. It now provides a flexible tool for the design of supercritical wing sections which produce shockfree flow at a specified speed and angle of attack. Since, however, it yields no information about the flow at off design conditions, and is restricted to two dimensions, it needs to be complemented by a method for calculating the flow over specified shapes in two and three dimensions throughout the desired range of speed and angle of attack. An accurate and reliable method would eliminate the need to rely on massive wind tunnel testing, and should lead to more rational designs. Following the initial success of Murman and Cole [3], substantial progress has recently been made in the development of finite difference methods for the calculation of transonic flows (cf. [4], [5], [6], [7]). These methods have generally been restricted, however, either to flows which are subsonic at infinity, or to small disturbance theories. The present paper describes a method using a new ‘rotated’ difference scheme, which is suitable for the calculation of both twoand three-dimensional flows without restriction on the speed at infinity, and which has been successfully applied to a variety of flows over airplane wings, including the case of flight at Mach 1.