Studies of the double-wedge and biconvex airfoils in hypersonic flow

Abstract

Through the development of the high altitude rocket interest has turned to the investigation of aerodynamic problems beyond the supersonic regime. This domain of speed has been termed hypersonic, meaning high Mach number flight in a homogeneous medium whose molecules describe negligible mean free paths with respect to a chosen characteristic dimension. The thesis presented given an extension of two-dimensional supersonic airfoil theory to attack the problem of getting aerodynamic coefficients for the double-wedge and biconvex airfoils. The shock wave equations along with those for Prandtl-Meyer flow have been modified by making approximations based on the hypersonic Mach numbers. These equations have been used to treat the following three cases: (A) The Mach angle is much less than the deflection angle. (B) The Mach angle is much greater than the deflection angle. (C) The Mach angle is of the same order of magnitude as the deflection angle. A brief discussion is made of the assumptions involved in the development of each of these flows to show that they do not violate basic principles. The hypersonic approximations already mentioned are then applied to these equations. In case (A) formulas are derived giving a quick approximation to the lift, drag, and moment coefficients. In case (B) formulas are found to be similar to those already obtained by the small perturbation method for supersonic flow. The results of case (C) show that a singular investigation must be made of each airfoil. The results of each of these cases are presented in the section titled Applications to the Double-wedge and Biconvex Airfoils. Results for symmetrical double-wedge airfoils, whose maximum thicknesses are 10 per cent of the chord and are located at 25, 50, and 75 per cent of the chord, are plotted in the appendix.