Theory of Blade Design for Large Deflections: Part I—Two-Dimensional Cascade

As a step in the development of an analytical method for designing highly loaded, three-dimensional blade profiles for axial compressors and turbines, a simple two-dimensional method was first investigated. The fluid is assumed to be incompressible and inviscid, the blades of negligible thickness, and the mean tangential velocity is prescribed. The blades are represented by a distributed bound vorticity whose strength is determined by the prescribed tangential velocity. The velocity induced by the bound vortices is obtained by a conventional Biot-Savart method assuming a first approximation to the blade profile. Using the blade surface boundary condition, the profile is then obtained by iteration. It is shown that this procedure is successful even for large pitch-chord ratios and large deflections. In order to develop a method for use in three dimensions, the velocity is divided into a pitchwise mean value and a value varying periodically in the pitchwise direction. By using generalized functions to represent the bound vorticity and a Clebsch formulation for the periodic velocity, series expressions are obtained which can be adapted to three-dimensional problems. Several numerical results were obtained using both approaches.