A SOLUTION OF SHOCK-INDUCED BOUNDARY LAYER PROBLEMS BY AN INTEGRAL METHOD.
AEROSPACE CORP SAN BERNARDINO CALIF SAN BERNARDINO OPERATIONS
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An integral technique is developed to solve a general class of shock-induced boundary layer problems. Included in this class are the boundary layer which grows near the leading edge of a semi-infinite flat plate with a shock wave propagating over it and the boundary layer region in a shock tube which is dependent upon both the shock wave and the expansion wave. The assumed boundary layer profile used to solve the Howarth transformed incompressible momentum equation is a linear combination of two exact solutions to the boundary layer equations, with the relative proportion of these two solutions controlled by a shape factor similar to the Karman-Pohlhausen shape factor. The present shape factor differs from that of Karman and Pohlhausen in that it is controlled by the dgree of unsteadiness in the boundary layer rather than by the pressure gradient. The solutions generated by the present technique are in good agreement with published exact solutions. The incompressible values of the momentum and displacement thicknesses are within 5 percent of the exact value and the wall shear stress is within 1 percent. While this accuracy should be satisfactory for most purposes, certain refinements are possible which will reduce all errors associated with the integral technique to values on the order of 1 percent. Author
- Fluid Mechanics