A Three-Dimensional Inverse Method for Turbomachinery: Part I—Theory

There are surprisingly few inverse methods described in the literature that are truly three dimensional. Here, one such method is presented. This technique uses as input a prescribed distribution of the mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the machine. In the present implementation the flow is considered inviscid and incompressible and is assumed irrotational at the inlet to the blade row. In order to evaluate the velocity field inside the turbomachine, the blades (supposed infinitely thin) are replaced by sheets of vorticity, whose strength is related to the specified mean swirl. Some advice on the choice of a suitable mean swirl distribution is given. In order to assess the usefulness of the present procedure, it was decided to apply it to the design of an impeller for a low-speed radial-inflow turbine. The results of the tests are described in the second part of this paper.