AN APPLICATION OF CROCCO'S STREAM FUNCTION TO THE STUDY OF ROTATIONAL SUPERSONIC FLOW PAST AIRFOILS

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Abstract
A method of successive approximations to the ideal flow around airfoils at high supersonic Mach numbers is developed, based on the concept of Crocco's stream function. Taking the undisturbed flow as a starting-point, a second approximation to the flow in the whole region surrounding the airfoil is derived, and the results for velocity and pressure distribution at the airfoil surface are compared with the corresponding expressions obtained by potential flow theory. The flow behind a plane shock wave is next chosen as zero-order approximation in order to obtain better results for the flow in the vicinity of the leading edge. The first approximation gives expressions for the shock-wave curvature and for the derivative of the pressure coefficient at the leading edge, which check similar results obtained by other investigators. The second approximation yields expressions for the derivative of the shock-wave curvature and for the second derivative of the pressure coefficient at the leading edge.

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