基于儒可夫斯基变换的轴流叶片翼型设计

为了改善轴流泵叶片翼型的水力性能,创新这类叶片的设计理论,给出了一种新颖的翼型骨线计算方法.以代表平面图形复变量的儒可夫斯基变换为基础,阐述了轴流翼型和叶片设计计算的原理与方法.通过复变量的定量计算,介绍了由偶极子、点涡和平面均匀流3种势流叠加后的复杂流动所产生的偏心圆的几何特性、流动特性及圆周上驻点的位置,讨论了以儒可夫斯基变换所得到的圆弧的几何性质和绕流动力特征,在此基础上,根据平面有势流动绕流变换曲线环量的不变性和变换前后复平面上无穷远来流速度大小和方向的不变性,给出了确定最终所得翼型骨线的方位及形态的应用性方法和步骤.导出的轴流式叶片翼型骨线计算的基本原理与方式,与升力法、奇点分布法、流线法等传统的叶片翼型设计准则有完全不同的理论基础和实施过程,易于设计人员在设计实践中应用,可为轴流叶片设计人员提供一种翼型设计新方法.

Design program for axial flow impeller blade based on Joukowski transform

To improve the performance of axial flow pumps and upgrade the design principle of the pump blades, a new approach for calculating the blade camber was proposed here. The principle and procedure that the approach designs the blades of axial flow impeller were presented based on the Joukowski transform. The geometrical properties of an eccentric circular cylinder, which was formed by the superposition of three two-dimensional potential flows--a doublet, a uniform plane flow and a point vortex, fluid dynamics around it and the position of stagnation point on it were described. Further, the geometrical properties of a circle arc, which was derived from Joukowski transform, and the fluid dynamics around it were discussed as well. Based on the above achievements, the method and producer for determining the direction and shape of a blade camber were developed in terms of the specified circulation and freestream velocity. The method and producer proposed here are completely different from the traditional ones, such as the singularity method, streamline method and so on for axial flow pump blades. The new approach is easily handled by pump engineers and it is hopeful that the approach can offer a new way for designing axial flow pump blades for the engineers.