A fully three dimensional compressible inverse design method for the design of radial and mixed flow machines is described. In this method the distribution of the circumferentially averaged swirl velocity, or rV¯θ on the meridional geometry of the impeller is prescribed and the corresponding blade shape is computed iteratively. Two approaches are presented for solving the compressible flow problem. In the approximate approach, the pitchwise variation in density is neglected and as a result the algorithm is simple and efficient. In the exact approach, the velocities and density are computed throughout the three dimensional flow field by employing Fast Fourier Transform in the tangential direction. The results of the approximate and exact approach are compared for the case of a high speed (subsonic) radial-inflow turbine and it is shown that the difference between the blade shapes computed by the two methods is well within the manufacturing tolerances. The flow through the designed impeller is analysed by using three dimensional inviscid and viscous time marching programs and very good correlations between the specified and computed rV¯θ is obtained.

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