A compressible three‐dimensional design method for radial and mixed flow turbomachinery blades

Abstract A fully three‐dimensional compressible inverse design method for the design of radial and mixed flow turbomachines is described. In this method the distribution of the circumferentially averaged swirl velocity r V 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 a 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 method was validated by calculating the flow through a designed high‐speed radial‐inflow turbine by using a three‐dimensional inviscid Euler solver. Very good correlation was obtained between the specified and computed r V θ ‐distributions.