基于奇点分布法的轴流泵叶片翼型设计与计算

为将奇点分布法这一有优势的流体机械叶片翼型设计方法应用于轴流泵叶轮叶片设计,以平面势流理论及数值计算为基础,推导了基于适合轴流泵叶片翼型边界条件的漩涡密度函数的系统应用性计算公式,所获结果将准确确定各翼型骨线关键节点位置,它们形成的翼型骨线在满足给定设计点泵的性能参数的同时,还能形成要求的流动奇点与驻点,由此产生流动损失最小的叶片翼型。以该方法改型设计的一台轴流泵的型式试验表明,设计泵在设计点的效率由原来的78%提升到85%,特性曲线符合要求。该研究深化了轴流泵叶轮叶栅流动理论,将奇点分布理论转化为轴流泵叶轮翼型的实用设计方法,为设计技术人员提供了开发新产品的工具。

Design and calculation of airfoil profile of blade in axial flow pump based on singularity approach

Abstract: Singularity calculating program is an important approach to design blade airfoils of axial flow machinery. This method is originally used in the runner design of propeller turbines. High efficiency and satisfactory performance of the runners has proved that this program has many advantages compared with other calculating methods for axial flow machines. To improve performance characteristics of axial flow pumps, it is valuable to introduce singularity calculating approach for the design of axial flow pumps. The principles in this program can be described briefly as follows. A vortex sheet is placed along a special curve in the uniform flow field with planar potential flow. If the induced velocity superimposed with the original planar uniform flow can ensure the curve to be a streamline and this streamline can meet all flowing boundary conditions, a solid curved thin plate can be used to replace the vortex sheet, for the flow field formed by the plate and the flow field without the plate are identical. Because velocity distribution of a potential flow is determined by its potential function, which satisfies the Laplacian equation. The solution to any Laplacian equation is solely determined by boundary conditions of the flow. As the induced velocity is developed by vortex sheet, the vortex density distribution along the sheet is very important. In a developed planar flow surface, for the same cascade, energy conversion and relative velocity in the runners and impellers are opposite, and stagnant point and singular point are also located in 2 opposite positions of the same airfoil. As a result, the vortex density distribution along the airfoil mean line can't be the same for the cascade when used for 2 kinds of hydraulic machines. However, there is only one distribution function presented in traditional approaches reported in all literatures. Further analysis showed that the traditional distribution function was only suitable for boundary conditions of runner airfoils. Later a new type of vortex density function was found. The induced velocity generated by new function along with the uniform flow can make the stagnant and singular points located in the required place, and the resultant velocity satisfies the Kutta-Joukowski law. The density function develops a curve with slight bending to form the mean line of airfoils. However, the vortex density function obtained cann't be used directly in the following calculation. It is only a starting point to deduce all formulae for later calculation. Since the vortex density function suitable for impellers is different from the corresponding function for runners, the conventional program formulated for runners cann't be applied in impeller airfoil calculation. According to the recently developed density function, potential flow theories and mathematical analysis, authors of this paper have obtained a series of formulae to locate 7 points in airfoil mean line and finally form the mean line of airfoil. In a primary planar straight cascade consisting of the airfoils of infinity, it takes an arbitrary one as the basic airfoil. Along the mean lines of all airfoils, the vortex sheets with the same density function are placed. On a given point among 7 points on the mean line of the basic airfoil, the vertical and horizontal velocity components are the superposition of 2 types of induced velocities, which are generated by continuous vortices on the basic airfoil mean line and by continuous vortices on all other airfoils. When the induced vertical and horizontal velocity components are calculated, superpose the velocity components of uniform flow on them. Thus, the actual relative velocity components can be achieved for all 7 points on basic mean line. The calculated relative velocity components then lead to the detection of the velocity direction at each point and 7 points can finally be located. A smooth curve passing all 7 fixed points will form the mean line of airfoil. In addition to calculating principles and obtained formulae, detailed designs are presented in this paper. All formulae for different kinds of velocity component calculation in this paper are different from the corresponding expressions in traditional approaches. The results presented in this paper make it possible to design axial flow pumps by using singularity approach, and will help pump design engineers use the new way in their design practice.