Analysis of Unsteady Tip and Endwall Heat Transfer in a Highly Loaded Transonic Turbine Stage

In a previous study, vane-rotor shock interactions and heat transfer on the rotor blade of a highly loaded transonic turbine stage were simulated. The geometry consists of a high pressure turbine vane and a downstream rotor blade. This study focuses on the physics of flow and heat transfer in the rotor tip, casing, and hub regions. The simulation was performed using the unsteady Reynolds-averaged Navier–Stokes code MSU-TURBO. A low Reynolds number $k-ε$ model was utilized to model turbulence. The rotor blade in question has a tip gap height of 2.1% of the blade height. The Reynolds number of the flow is approximately $3×106/m$⁠. Unsteadiness was observed at the tip surface that results in intermittent “hot spots.” It is demonstrated that unsteadiness in the tip gap is governed by inviscid effects due to high speed flow and is not strongly dependent on pressure ratio across the tip gap contrary to published observations that have primarily dealt with subsonic tip flows. The high relative Mach numbers in the tip gap lead to a choking of the leakage flow that translates to a relative attenuation of losses at higher loading. The efficacy of new tip geometry is discussed to minimize heat flux at the tip while maintaining choked conditions. In addition, an explanation is provided that shows the mechanism behind the rise in stagnation temperature on the casing to values above the absolute total temperature at the inlet. It is concluded that even in steady (in a computational sense) mode, work transfer to the near tip fluid occurs due to relative shearing by the casing. This is believed to be the first such explanation of the work transfer phenomenon in the open literature. The difference in pattern between steady and time-averaged heat fluxes at the hub is also explained.