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.

中文翻译：

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参数化表示轴流涡轮机叶片气动轮廓的方法

摘要-

描述了一种设计轴向涡轮机叶片翼型截面的参数化方法。Bezier解析曲线用于表示轮廓母线和骨架线。它们的形状由一组13个参数唯一地确定，这些参数与涡轮机叶栅的空气动力学和强度特性有关。这些参数确定轮廓母线必须在指定的切线角处通过的主要点。一般而言，叶片形状的设计计算包括以下连续阶段：基于13个参数计算几何约束，确定骨架线形状以及计算轮廓吸力侧和压力侧。通过使用建议的方法，考虑到所施加的几何条件，包括表面曲率分布，可以控制叶片形状。该方法的一个显着特点是它的适应性：在计算过程中通过多维最小化确定贝塞尔曲线的程度。就可以在较宽范围内指定参数的可能性而言，此功能为该方法赋予了灵活性，从而使该方法本质上具有通用性。提出了一种通过计算骨架线来迭代确定曲线形状的算法。所提出的方法由一个程序自动补充，该程序用于自动将轮廓指定为其母线的不均匀分布的点状坐标。