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提出了关于叶轮机械中三维跨音速流动计算的一种高效率数值方法.设计了一种适合叶轮机械中三维流动特点的广义von Mises坐标系,并导出了该坐标系中的流线支配方程组.该坐标系的优点是易于选取较正确的初始值(流线的位置),从而使迭代过程具有很快的收敛速率;并能将正问题计算和反问题设计方便地统一在同一个算法之中.构造了流线支配方程组的旋转差分格式,以及提出了一种用来解决由于采用流函数坐标方法求解跨音速流动而出现的密度和速度双值问题的新方法.作为考核算例,计算了一个跨音速涡轮和一个跨音速压气机的典型直叶片排中的三维流动以及一个具有解析解的与轴流式叶轮机械叶栅流道内的流动相类似的三维流动.计算结果表明,该方法具有很快的收敛速率和精确度高等优点.
A high-efficiency numerical method for calculating transonic flow in three-dimensional turbomachinery is proposed.The generalized von Mises coordinate system which is suitable for three-dimensional flow in impeller machinery is designed and the governing equations of streamline in the coordinate system are derived The advantage of this coordinate system is that it is easy to select the correct initial value (the position of the streamline), so that the iterative process has a fast convergence rate, and the positive problem calculation and the inverse problem design can be conveniently unified in the same algorithm In this paper, the rotational difference scheme of streamline governing equations is constructed, and a new method is proposed to solve the problem of double value of density and velocity arising from the use of stream function coordinate method to solve transonic flow. As an example, The three-dimensional flow in a typical straight vane row of a transonic turbine and a transonic compressor is calculated and a three-dimensional flow with an analytic solution similar to the flow in an axial flow impeller cascade is calculated. The calculated results show that The method has the advantages of fast convergence rate and high accuracy.