Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages - Part I: Stage Design and Preliminary Tip Optimization
Authors: Duan P. H. , He L. 
Published: October 2022

Abstract
Rotor blade tip has significant influence on turbine stage aerodynamics and heat transfer. Although most previous work on turbine tip was largely based on a low speed cascade settings, more recent research on transonic turbine tip has on the other hand exhibited distinctive flow features with qualitatively different performance sensitivities. Questions arise in relation to two flow conditioning aspects. Firstly, the contrasting observations in either a low speed incompressible flow regime or a transonic flow regime indicate the gap in a high subsonic regime relevant to many realistic turbine designs. Secondly, the relative casing movement and upstream inflow conditions are known to have non negligible effects, and they together suggest the need to examine a rotor blade tip in a realistic stator-rotor stage environment, which is also lacking. In this study, two turbine stages (a high subsonic one at exit Mach number of 0.7 and a transonic one with exit Mach number of 1.1) with the same Reynolds number are designed to provide such direct contrast for elaborating the Mach number effect in the flow regimes of practical interest. The stage configurations are designed as research vehicles and constrained as such with a specific blade count and constant-area annulus. The parameterization can automatically generate the 3D turbine blade mesh using assigned design parameters. The designed baseline stages have comparable aerodynamic efficiency to those predicted in the Smith’s Chart.
The rotor squealer tip height is used as a representative parameter to investigate the sensitivity of the stage aerothermal performance to the tip geometry in these two stages respectively. The multi-objective optimization procedure using the Kriging surrogated model is employed to identify the Pareto fronts for the high efficiency and the low heat load. The comparison of the optimized results between these two stages shows the distinctively different trends in the variation of the aerothermal performance with the squealer height. The efficiency of the subsonic stage increases with the squealer height reaching a plateau, while the efficiency in the transonic stage firstly increases and then drops to the level comparable to that of a flat tip, indicating that the squealer in the transonic stage may not be as effective as in the subsonic stage. On the other hand, for heat transfer, sensitivity variations are more complex, or even contradicting depending on the objective function selected. The overall heat load and the non-uniformity are considered as the objective function respectively, leading to qualitatively different sensitivities with the squealer height, as well as completely incomparable Pareto fronts. This raises the question on how to effectively conduct a combined aerodynamic and heat transfer performance design optimization. The authors thus resort some further detailed aerothermal physics analyses as presented in Part II, a companion paper of the two-part article, to provide a physical understanding-based leverage in both gaining insights into the contrasting aero-efficiency sensitivities between the two stages and in selecting an appropriate objective function for such blade tip aerothermal optimization.