Inviscid-Viscous Interaction Method for Three-Dimensional Inverse Design of Centrifugal Impellers

Abstract

A three-dimensional design method for the design of the blade geometry of centrifugal compressor impellers is presented. In this method the blade shape is computed for a specified circulation distribution, normal (or tangential) thickness distribution, and meridional geometry. As the blade shapes are computed by using an inviscid slip (or flow tangency) condition, the viscous effects are introduced indirectly by using a viscous/inviscid procedure. The three-dimensional Navier–Stokes solver developed by Dawes is used as the viscous method. Two different approaches are described for incorporating the viscous effects into the inviscid design method. One method is based on the introduction of an aerodynamic blockage distribution throughout the meridional geometry, while in the other approach a vorticity term directly related to the entropy gradients in the machine is introduced. The method is applied to redesign the blade geometry of Eckardt’s 30 deg backswept impeller as well as a generic high pressure ratio (transonic) impeller. The results indicate that the entropy gradient approach can fairly accurately represent the viscous effects in the machine.