Perturbations on Hypersonic Wedge Flow

Citation

Malmuth, Norman David (1962) Perturbations on Hypersonic Wedge Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KE9Q-XN81. https://resolver.caltech.edu/CaltechETD:etd-12152005-133232

Abstract

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 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. Here, the outlying, uniform region solution is found to be trivial. 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 the Fourier series solution for the perturbation pressure indicating the surface loads associated with the perturbation as well as the shock distortion function. Integral representations are obtained for the downwash and sidewash perturbations using the pressure 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 [gamma] is close to one. This solution is specialized to the case considered previously and a qualitative evaluation of the physical significance of the results is made.

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