Simple Blade Design

Abstract

Flow deflection in turbomachines is established by stator and rotor blades with prescribed geometry that includes inlet and exit camber angles, stagger angle, camber line, and thickness distribution. The blade geometry is adjusted to the stage velocity diagram which is designed for specific turbine or compressor flow applications. Simple blade design methods are available in the open literature (see References). More sophisticated and high efficiency blade designs developed by engine manufacturers are generally not available to the public. An earlier theoretical approach by Joukowsky [1] uses the method of conformal transformation to obtain cambered profiles that can generate lift force. The mathematical limitations of the conformal transformation do not allow modifications of a cambered profile to produce the desired pressure distribution required by a turbine or a compressor blade design. In the following, a simple method is presented that is equally applicable for designing compressor and turbine blades. The method is based on (a) constructing the blade camber line and (b) superimposing a predefined base profile on the camber line. With regard to generating a base profile, the conformal transformation can be used to produce useful profiles for superposition purposes. A brief description of the Joukowsky transformation explains the methodology of symmetric and a-symmetric (Cambered) profiles. The transformation uses the complex analysis which is a powerful tool to deal with the potential theory in general and the potential flow in particular. It is found in almost every fluid mechanics textbook that has a chapter dealing with potential flow. While they all share the same underlying mathematics, the style of describing the subject to engineering students differ. A very compact and precise description of this subject matter is found in an excellent textbook by Spurk [2].