Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages—Part II: Flow Physics and Augmented Aerothermal Integral Objective Function

In Part I, a companion paper of the two-part article, a subsonic turbine stage and a transonic one conditioned at the same Reynolds number, flow coefficient, loading coefficient and reaction, but two different exit Mach numbers are designed to provide a direct contrast between a high-subsonic and a transonic flow conditioning for rotor blade squealer tips. In this paper as Part II, further analyses are carried out to address the main issues of interest arising from Part I: first, to identify the driving flow physical mechanisms for the contrasting aerodynamic efficiency sensitivities of the two stages; second to seek a more suitable heat transfer objective function for the tip aerothermal design optimization, given the seemingly strong conflicts among those conventionally adopted heat transfer objective functions. Two counter-rotating tip vortical structures, the pressure side vortex (PSV) and the casing-driven cavity vortex (CCV), are shown to impact the aero-performance differently between the two stages. For the subsonic stage, the leakage flow is strongly affected by a stronger residual PSV at the squealer cavity exit. For the transonic stage however, the tip choking in limiting the over tip leakage (OTL) mass flow and favorable pressure gradient in a transonic flow over a separation bubble led to a much stronger and more persistent CCV and thus lower aero-effectiveness of squealer tip for the transonic stage. The two vortices also show major heat transfer signatures on the cavity surfaces by impingement. For the PSV, the impingement impact is mainly on the cavity floor. For the CCV, on the other hand, its impact is mainly on the inner side-wall of the suction side rim. The latter is found to be mainly responsible for the overall linear variations of the heat load with the squealer height. Again, the relative strength between PSV and CCV serves as an effective differentiator in the heat transfer performance. The stronger and more persistent CCV in the transonic stage results in a strong signature on a large portion of the suction side cavity inner sidewall, thus a much higher increment in heat transfer with the squealer height than that for the subsonic stage. In seeking to establish a more consistent heat transfer objective function for combined aerothermal design and optimization, a coolability weighted nonuniformity parameter is proposed to integrate the local heat transfer and the coolability. The proposed objective function is shown to lead to consistent Pareto fronts for the combined aerothermal performance sensitivities, particularly for the present cases with strong heat transfer nonuniformity which are particularly challenging to those conventional treatments as shown in Part I. The coolability-augmented objective function should thus serve as an enabler to help practical applications of blade tip aerothermal design optimizations.