Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages—Part I: Stage Design and Preliminary Tip Optimization

Abstract

Rotor blade tip has significant influence on turbine stage aerodynamics and heat transfer. Most previous efforts have been based on low-speed cascade settings. However, more recent research on transonic blade tips exhibits distinctive flow features with qualitatively different performance sensitivities. These prompt two key issues of interest on the related flow conditioning. First, the contrast between a low-speed flow and a transonic regime highlights the less studied high-subsonic flow regime, closely relevant to many realistic turbine designs. Second, the relative casing movement and upstream inflow conditions, known to have non-negligible effects, indicate the need to examine a rotor blade tip in a realistic stator–rotor stage environment, which is also lacking. To elaborate the Mach number effect in the flow regimes of practical interest, we aim to examine a high subsonic stage in a direct and consistent comparison with a transonic one. To this end, a high subsonic stage (exit Mach number of 0.7) and a transonic (exit Mach number of 1.1) are designed at the same Reynolds number with a three-dimensional parameterization and meshing system. The tip squealer height is used as a representative parameter to investigate the sensitivity of the stage aerothermal performance. The multi-objective optimization using the Kriging surrogated model is employed to identify the Pareto fronts for the stage efficiency and the heat transfer. The comparison of the optimized results between these two stages shows distinctively different trends in the performance variation with the squealer height. The efficiency of the subsonic stage increases with the squealer height reaching a plateau. In contrast, the efficiency in the transonic stage first increases and then drops to the level comparable to that of a flat tip. Significantly, the present results indicate, for the first time, that the squealer tip in a transonic stage may not be as effective as in a subsonic stage. On the other hand, for heat transfer, sensitivity variations are more complex. The overall heat load and the local nonuniformity lead to qualitatively different sensitivities with the squealer height, as well as completely incomparable Pareto fronts. These observed heat transfer sensitivities raise the question on how to effectively conduct a combined aerodynamic and heat transfer performance design optimization. The authors subsequently resort further aerothermal physics analyses described in a companion paper as Part II of the two-part article. In Part II, the physical interpretation of the contrasting aero-efficiency sensitivities for the two stages, as well as a physical understanding leveraged selection of the objective function for such combined blade tip aerothermal optimization will be presented.