Design of turbomachinery blading in three-dimensional flow by the circulation method

In this paper, we report on the progress of the further development and application of an analytical theory for the design of turbomachinery blading in three-dimensional flow. After a section describing the recent development of the theory, we discuss the various applications including the investigations of the design of radial inflow turbines. Numerical examples are also presented to illustrate the application of the theory to the design of a free vortex fan, an axial turbine rotor, a free vortex compressor stage for low and high Mach numbers, a non-free vortex fan with trailing vortex sheets, and a counter-rotating propeller in the limit of a large number of blades. Further possible applications of the theory to the design of other aero- and hydrodynamic devices are discussed.