Calculation of three-dimensional transonic flows in turbomachinery with generalized von Mises coordinate system

An efficient numerical method for calculating the three-dimensional transonic flow in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mises coordinate system to reflect the flow feature in turbomachinery. Its main advantage is that it is easier to specify more reasonable initial values, i.e.:initial streamsurface position, thus accelerating the convergence rate of the iteration process. Moreover, to use the generalized von Mises coordinates makes the present method capable of incorporating;the calculation of the flow field, design and modification of the blade contour into a unified algorithm. A rotated finite difference scheme for the streamsurface-governing equations is constructed, and a new measure is presented to deal with the double-value problem of the velocity and density caused by the application of the stream functions as coordinates in the transonic flow. Three test cases were considered with the present approach to demonstrate the solution method for 3-D inviscid flow analysis. Numerical results confirm that the present method has rapid convergence and high accuracy.