FREE VORTEX THEORY FOR EFFICIENCY CALCULATIONS FROM ANNULAR CASCADE DATA

This paper describes a new three-dimensional theory to calculate the e fficiency or loss of nozzle guide vane annular cascades from experimen tal area traverse measurements of the compressible downstream pow. To calculate such an efficiency it is necessary to mix out the measured f low computationally to either a uniform state or one that is a fractio n 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 fr eedom 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 annul ar cascade efficiency is then uniquely defined as the ratio of the mix ed-out experimental kinetic energy flux to the ideal isentropic kineti c energy flux at the same mean radius static pressure. The mathematica l derivation of this method is presented. This new theory has been use d to process data obtained from a large, transonic, annular cascade in a blowdown tunnel. A four-hole pyramid probe, mounted on a computer-c ontrolled traverse, has been used to map the passage flowfield downstr eam of the nozzle guide vanes. Losses calculated by the new method are compared with those calculated from the same data using earlier analy sis methods.