Large Eddy Simulations of a High-Speed Low-Pressure Turbine Cascade at Subsonic and Transonic Mach Numbers

High-speed low-pressure turbines (HS-LPTs) are one key turbomachinery component in ultra-high bypass ratio geared turbofan engines. The HS-LPT typically operates at transonic exit Mach numbers and low-Reynolds numbers. These flow regimes are prone to boundary layer instabilities such as separations on the suction side, leading to a significant increase in losses. It is therefore essential to understand the operation of LPTs and, more specifically, the behavior of the boundary layer on the blades in such environments. We present a numerical investigation of a high-speed low-Reynolds turbine cascade simulated at nominal and off-design Mach numbers. The study case is the SPLEEN C1 cascade tested in the transonic linear cascade rig S-1/C of the von Karman Institute. The cascade is numerically operated at the nominal test exit Reynolds number $Re2,is=70k$⁠, over a range of subsonic and transonic exit Mach numbers: $M2,is=0.70,0.80,0.90$⁠, and $0.95$⁠. All simulations are performed with the explicit compressible solver of the massively parallel code YALES2, using a wall-resolved large eddy simulations (WRLES) approach, and featuring a fourth-order finite volume spatial discretization. This scale-resolving approach allows to capture the turbine flow physics with high accuracy at an acceptable computational cost. The test case offers the possibility to assess the Mach and compressibility effects on the profile aerodynamics of HS-LPT: separation, transition mechanisms, unsteadiness, and passage choking, as well as trailing edge unsteady flows. The flow predictions show a substantial agreement with the available high-fidelity experimental data. Furthermore, the calculations suggest that the wake thins and loss increase with the Mach number. The experiments support this evidence, although discrepancies are observed in peak losses for Mach numbers above $0.70$⁠. The root cause is likely found in the laminar inflow used in the large eddy simulations (LES) compared to the freestream turbulence intensity level of $2.5%$ of the experimental test case. Compressibility effects are observed. In particular, a weak compression wave stands in the region of the cascade throat for the case $M2,is=0.90$⁠, whereas a shock appears for $M2,is=0.95$ with the cascade choked. The role of the shock on the separation and transition on the blade suction side is discussed.