Rigorous Solution of Compressible Potential Flow Past Two-Dimensional Cascades of Airfoils : Especially for High Subsonic Flow

抄録

A rigorous solution of complex velocity of a compressible potential flow past two-dimensional cascades of airfoils is obtained by introducing a pseudoanalytical function with respect to complex coordinates. A basic differential equation about complex velocity is derived from a continuous relation and an irrotational flow condition and then reduced to an inhomogeneous complex singular integral equation. Using successive substitution which depends on theorems of quasi-conformal mappings a solution of the equation can be numerically given with the help of results of an incompressible potential flow, since the complex velocities of compressible and incompressible flows are in one-to-one correspondence with each other. Using this function-theoretic means the solution is applicable both to axial and to radial flows and also to inverse problems. Numerical illustrations of the method are given for high subsonic potential flows through A₃K₇ turbine blades in cascade.