基于气动载荷与叶片厚度分布的叶栅气动设计方法

Aerodynamic Design Method of Cascade Profiles Based on Load and Blade Thickness Distribution

建立一种以载荷与叶片厚度分布为约束的叶栅气动设计计算方法,约束条件体现了气动特性与强度两方面的要求,这些约束及其它所有边界条件,都包含在相应的变分原理的驻值条件中· 变分原理以周角函数为泛函的未知函数,周角函数定义在由流线坐标与流函数坐标(周向)构成的映象面上· 在映象面上,求解域———叶栅通道———化作一个矩形,叶片型线映射为一条水平直线,从而避免了叶片外形未知的困难· 利用有限元方法建立了计算程序,算例显示这种方法能有效地满足对叶片型线的设计要求。

A cascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints,which were correspondent to the demands from the aerodynamic characteristics and the blade strength.These constraints,together with all the other boundary conditions,were involved in the stationary conditions of a variational principle,in which the angle_function was employed as the unknown function.The angle_function (i.e.the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate (circumferential direction) and streamline coordinate.The solution domain,i.e.,the blade_to_blade passage,was transformed into a square in the image plane,while the blade contour was projected to a straight line; thus,the difficulty of the unknown blade geometry was avoided.The finite element method was employed to establish the calculation code.Applications show that this method can satisfy the design requests on the blade profile from both aerodynamic and strength respects.In addition,quite different from the most inverse_problem approaches that often encounter difficulties in the convergence of iteration,the present method shows a stable and fast convergence tendency.This will be significant for engineering applications.