Supercavitating Cascade Flow Analysis

Abstract

An exact mathematical theory of supercavitating flow in cascades with arbitrary blade shapes is developed. Applying conformal mapping methods to the potential flow problem involved, a general mapping procedure is established. The geometric interpretation of the obtained mappings is discussed in general and completed in the case of the flat-plate cascade. Furthermore, for this case, a procedure has been established for computing the shape of the free streamline issuing from the leading edge. All results assume infinitely long cavities. The application of the established mapping procedure to the case of a cascade with arbitrary blade shape requires the solution of a nonlinear integral equation for one of the mapping functions, or the approximation of this mapping function by a Fourier series whose coefficients must be determined from implicit conditions imposed by the blade shape. In the case of a circular-arc blade, the integral equation may be rearranged in a form suitable for numerical evaluation of the integral involved, thereby opening the way for its solution by numerical iteration.