Three-dimensional perturbations on hypersonic wedge flow
The hypersonic inviscid flow over a configuration representing a small perturbation about a two-dimensional wedge is analyzed. Equations and boundary conditions are obtained for a class of general perturbations within the framework of hypersonic small disturbance theory. A specialization of this formulation is made to the case where the resultant perturbation consists of two semi-infinite flat plates of slightly different incidence to the freestream. The flow over such a shape is divided into an outlying uniform region and a central conefield. The determination of the conefield gives rise to an elliptic boundary-value problem, which is solved with the aid of the Tschaplygin transformation and other conformal mappings. Calculations are presented using a Fourier series solution for the perturbation pressure which yields the surface loads associated with the perturbation as well as the shock distortion function. Integral representations are obtained for the down wash and sidewash perturbations from the pres^ sure solution. The results are compared qualitatively with an analogous linear supersonic flow. Finally, a solution for more general profiles is obtained under the further restriction that the specific heat ratio y is close to one. This solution is specialized to the configuration considered previously.