A Method for Parametrically Representing the Aerodynamic Profiles of Axial Turbine Machinery Blades

Abstract

A parametric method for designing the cross sections of axial turbine machinery blade airfoils is described. Analytical Bezier curves are used for representing the profile generatrices and the skeleton line. Their shapes are uniquely determined by a set of 13 parameters that are related to the turbine cascade’s aerodynamic and strength characteristics. These parameters determine the main points through which the profile generatrices must pass at the specified tangent line angles. In general terms, the blade shape’s design calculation involves the following sequential stages: calculating the geometrical constraints based on 13 parameters, determining the skeleton line shape, and calculating the profile suction and pressure sides. By using the proposed method, it is possible to control the blade shape taking into account the imposed geometrical conditions, including the surface curvature distributions. A distinguishing feature of the proposed method is its adaptability: the degree of Bezier curves is determined during calculation by means of multidimensional minimization. This feature imparts flexibility to the method in terms of the possibility to specify the parameters in wide ranges of their values, thus making the method versatile in nature. An algorithm for iteratively determining the curve shape through calculating the skeleton line is presented. The proposed approach is supplemented by a procedure for automatically parameterizing the profiles specified as unevenly distributed point-wise coordinates of their generatrices. This opens up the possibility to represent the already existing blade shapes in the form of 13 parameters and to optimize them.