Free Vortex Theory for Efficiency Calculations From Annular Cascade Data

This paper describes a new three-dimensional theory to calculate the efficiency or loss of nozzle guide vane annular cascades from experimental area traverse measurements of the compressible downstream flow. To calculate such an efficiency, it is necessary to mix out the measured flow computationally to either a uniform state or one that is a function of radius only. When this is done by conserving momentum, mass, and energy flow, there is a remaining degree of freedom in that the radial distribution of circumferential velocity can be chosen. This extra freedom does not arise in two-dimensional cascades. The new method mixes the flow out to a free (i.e., irrotational) vortex. This is preferred to existing methods in that it gives a physically realistic flow and also provides a unique, lossless, isentropic reference flow. The annular cascade efficiency is then uniquely defined as the ratio of the mixed-out experimental kinetic energy flux to the ideal isentropic kinetic energy flux at the same mean radius static pressure. The mathematical derivation of this method is presented. This new theory has been used to process data obtained from a large, transonic, annular cascade in a blowdown tunnel. A four-hole pyramid probe, mounted on a computer-controlled traverse, has been used to map the passage flowfield downstream of the nozzle guide vanes. Losses calculated by the new method are compared with those calculated from the same data using earlier analysis methods.