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低能量损失系数跨音速透平叶栅的设计和实现是提高跨音速透平性能的关键问题之一。本文给出了基于有限面积法的跨音速透平叶栅速度面反问题设计方法。首先推导了基本方程的对称形式,用于上游奇点处理,并对速度面上不连续边界条件作了分析和数值验证说明。然后详细叙述了流函数场的有限面积解法包括主方程的积分变换,基本有限面积格式和边角有限面积格式处理以及解精确度的粗略分析。所编制的程序简明快速。计算结果表明解相当稳定并且不需要在音速线附近等处加密网格或作其他处理。算例也指明音速线上临界奇点位置的选取,对流场及叶型型线形状有一定影响,应在设计时注意。
The design and implementation of transonic turbo cascades with low energy loss coefficients are one of the key issues in improving the performance of transonic turbines. In this paper, the design method of transversal velocity cascade inverse problem based on the finite area method is given. Firstly, the symmetrical forms of the basic equations are deduced and used to deal with the singularities of the upper reaches. The discontinuous boundary conditions on the velocity surface are analyzed and verified. Then the finite area method of stream function field is described in detail, including the integral transform of the main equation, the basic finite-area format and the finite-area method of corner and the rough analysis of the solution accuracy. The preparation of the program is concise and rapid. The result of the calculation shows that the solution is fairly stable and does not require the mesh to be encrypted or other processing near the sonic line. The example also indicates that the selection of the critical singularity position on the sonic line has some influence on the flow field and the shape of the leaf profile line, which should be noticed in design.