Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle

Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects. The expression for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instances it is important to have a single expression representing the whole flow. Recently Von Karman and Tsien constructed more general types of stream functions, but only by replacing the true pressure density relation by the linear pressure-specific volume relation so that their method is essential limited to flows the maximum Mach number of which is not too large. In a companion report the author derived a new formula for stream functions based on the true pressure density relation. It is not subject to the limitations of the Chaplygin method. In the present report this formula is employed to construct two-dimensional subsonic compressible fluid flows around a body similar in shape to a given symmetric obstacle. The methods described in the report are illustrated by numerical examples.