Compressor Cascade Optimization based on Inverse Boundary Layer Method and Inverse Cascade Method : 1st Report, An Inverse Cascade Method for Incompressible Two-dimensional Potential Flow

An aerodynamic approach to an optimum compressor cascade in a two-dimensional incompressible flow is described on the basis of two inverse problems; namely, inverse boundary layer problem to produce the optimum velocity distribution and inverse cascade problem to obtain a blade section which realizes a prescribed velocity distribution. A new method for the latter problem is developed in this report. In this method a cascade is transformed into a row of circular cylinders and the blade section is calculated for prescribed velocity distribution, velocity triangle and solidity by solving simultaneous equations about the mapping function. The mapping distortion is exceedingly small in this transformation, and so the inverse problem about the potential flow through a cascade whose solidity, stagger angle and load per blade are high can be solved accurately even near the leading- and trailing-edge.