Vortical Structures and Loss Mechanism of Tip Leakage Flow In Subsonic and Transonic Turbine Stages
Authors: Duan P. H. , He L. 
Published: October 2022

Abstract
Aerothermal behavior and performance of turbine blade squealer tip has been extensively studied, but previously mainly confined to very low speed flows. Some recent research efforts have revealed some distinctive tip heat transfer as well as aerodynamic characteristics in a transonic flow, many of which are confined to a linear cascade setting. There is a need to identify driving mechanisms for such configurations and to quantify corresponding performance characteristics in general, and in the process address how those drivers would relate to some specific issues of interest such as:
1) the differences between a cascade and a rotor tip, thus the impact of relative casing movement?
2) The difference between a transonic and a high subsonic flow condition?
3) the difference between a squealer tip and flat tip?
In this study, the vortical structures and the loss mechanism of the Over Tip Leakage (OTL) flow in a high-subsonic stage and a transonic stage are analyzed using a proposed vortex model and Denton’s loss model. The two stages are specifically designed to work in the same Reynolds number with the efficiency comparable to the one predicted in the Smith’s chart. Two counter-rotating vortices, the Pressure-side Separation Vortex (PSV) and the Casing-driven Cavity Vortex (CCV), are identified as key drivers as inside a squealer cavity strongly impacting aerothermal performance (OTL mass flow and the heat transfer distribution). The cavity flow pattern results from the balancing between the CCV primarily driven by the relative casing movement, and the PSV originating from the flow separation around the pressure side rim. Consequently a detoured flow path is created within the squealer cavity when the leakage flow separating on the pressure side is entrained by the two vortices to the squealer bath and finally leaves the cavity along the suction side of the squealer wall. The entrainment of the leakage flow induces a signature of a high HTC strip on the squealer floor.
Without the relative casing movement, the CCV is absent in the majority of the cavity so that the leakage flow can directly cross the tip which increases the leakage mass flow rate and reduce the HTC value on the cavity floor. Due to the distinct difference in vortical structures, the change of the HTC with and without relative casing movement can be interpreted by the vortex model. The vortex model is also able to explain the variation of the leakage mass flow rate and the HTC contours with the increasing squealer height. From the best knowledge of the authors, this is the first-of-its kind effort in using in the cavity vortices to systematically and quantitatively study the effect of the relative casing movement and the aerothermal performance of the tip with varying squealer height.
In counting the aero losses for the two stages, three sources are attributed to the total loss generation: the baseline loss which assumes there is no leakage, the in-tip loss which is generated within the tip gap and the out-tip loss which accounts for the mixing loss between the OTL flow and the main passage flow. The out-tip loss is found to be the major source of the loss caused by the tip leakage flow. Denton’s loss model is used to calculate the out-tip loss quantitatively. The model predicted loss agrees in trend with the one calculated from the CFD results. According to the model, the out-tip loss is related to the main flow Mach number, the OTL mass flow rate and the velocity difference between the main flow and the OTL flow. From the distribution of these terms along the tip, the loss is mainly generated at the rear portion of the tip. The reduction of the leakage mass flow rate by the squealer is mainly at the zones where the CCV and the PSV are leaving the squealer cavity. The present analysis and results indicate that the squealer in the transonic stage tends to be less effective in reducing the out-tip loss compared to the subsonic one. The region of the tip where the CCV has already left the cavity with the PSV remaining shows the highest entropy generation rate, due to locally both the high mainstream velocity and the high OTL mass flow given the PSV being left as the only sealing vortex there.