New Supersonic Loss Model for the Preliminary Design of Transonic Turbine Blades and the Influence of Pitch

Abstract

In order to produce a more efficient design of a compact turbine driving a cryogenic engine turbo-pump for a satellite delivering rocket, a new supersonic loss model is proposed. The new model was constructed based on high-quality published data, composed of Schlieren photographs and experimental measurements, that combined provided a unique insight into the mechanisms driving supersonic losses. Using this as a cornerstone, model equations were formulated that predict the critical Mach number and shock loss and shock-induced mixing loss as functions of geometrical (i.e., blade outlet and uncovered turning angle and trailing edge thickness) and operational parameters (i.e., exit Mach number). A series of highly resolved CFD numerical simulations were conducted on an in-house designed state-of-the-art transonic turbine rotor row (around unity aspect ratio (AR)) to better understand changes in the shock system for varying parameters. The main outcome showed that pitch to chord ratio has a powerful impact on the shock system, and thus on the manner by which shock loss and shock-induced mixing loss is distributed to compose the overall supersonic losses. The numerical loss estimates for two pitch to chord ratios—t⁄c = 0.70 and t⁄c = 0.98—were compared with absolute loss data of a previously published similar blade with satisfactory agreement. Calibrated equations are provided to allow hands-on integration into existing overall turbine loss models, where supersonic losses play a key role, for further enhancement of preliminary turbine design.