跨音速透平叶栅速度面设计方法的研究

 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。

ON THE DESIGN OF TRANSONIC TURBINE CASCADE BY HODOGRAPH METHOD

The design and realization of a transonic turbine cascade with low energy loss is one of the crucial problems which should be solved for designing good transonic turbines. This paper deals with the inverse design problem of transonic turbine cascade in the hodograph plane by the finite area method.In the first part of the paper the governing equation is transformed into a symmetric form which can be adopted to obtain the upstream singular solution. The boundary condition connected with the existing discontinuity in the hodograph plane is also analyzed and afterwards vertified by numerical tests.The next part describes in detail the method of solving stream function field by means of finite area method, including the integral transformation of governing equation, the finite area scheme, the particular corner finite area schemes and so on. The accuracy of solution is then briefly discussed.The program is quite simple and quick-acting. Results of calculation prove that the solution is very stable and it is not necessary to modify the mesh near sonic line or other places.Moreover, calculation shows that the solution is rather sensitive to the position of the critical point on sonic line, which should be carefully selected by designers for obtaining good cascade profiles.