基于椭圆拓扑变换的叶片二维叶型参数化方法

A Parametrization Method of Blade Section Based on Topological Transformation of Ellipse

叶型参数化方法服务于叶片设计、制造和再制造全生命周期。针对目前叶型参数化方法难以兼顾造型参数几何含义直观和叶型曲率及曲率导数的连续性问题,提出了一种基于椭圆拓扑变换的二维叶型参数化方法。该方法基于椭圆与叶型曲率分布特征与拓扑结构的一致性,通过构造多个拓扑变换使椭圆变形成二维叶型。在变形过程中,建立了叶型主要几何特征参数与造型参数的一一对应关系且自然地保持了椭圆的高阶连续性。为验证该方法的有效性,对不同几何特征的叶型进行了反演验证。结果表明,与现有方法相比,该方法可用更少的造型参数实现更高的拟合精度;反演叶型曲率及曲率的导数均连续变化;反演叶型和原始叶型气动性能保持很好的一致性;改变单个造型参数可直观地改变叶型几何特征。因此,该参数化方法更易设计出低损失高负荷的叶型,传递的设计意图也更易被制造和再制造环节理解使用,有利于保障叶片的最终服役性能。

The parametrization method of the blade section serves the whole life cycle of the blade,including design,manufacturing and remanufacturing.However,it is difficult for the current parametric methods to take into account the intuitive geometric meaning of modeling parameters and the continuities of the curvature and the slope of curvature.To solve the problem,a parameterization method based on the ellipse topology transformation is proposed.The method is based on the consistency of the curvature distribution and that of the topological structure between the ellipse and the blade section and the ellipse is transformed into the blade section by applying several designed topological transformations.Meanwhile,one-to-one correspondences between the blade key geometry parameters and the modeling parameters are established and the high-order continuity of the ellipse is maintained.To verify the effectiveness of the proposed method,the inversions of several blade sections with different geometrical characteristics are carried out respectively.The results show that compared with the existing method,the proposed method achieves higher fitting accuracy with fewer modeling parameters;the curvature and the curvature derivative of the inversion sections are both continuous;the aerodynamic performance of the inversion sections is consistent well with that of the original ones;modifying a single modeling parameter can intuitively change the corresponding blade geometry.Therefore,the proposed method facilitates the design of lower-loss higher-loading blade sections and the transmitted design intentions are easier to be understood and used in the manufacturing and remanufacturing process,which are both conducive to guarantee the final service performance of the blade.