Adaptive Detached Eddy Simulation of End-Wall Flow in a Linear Compressor Cascade

Reynolds-averaged Navier-Stokes methods tend to overpredict corner stall in an axial-flow compressor. Large Eddy Simulations are too expensive for large scale industry predictions. Recent approaches in applying Detached Eddy Simulation (DES) in Turbomachinery end wall flows have shown promising results. Xia et al. (2017) simulated the Ecole Centrale de Lyon (Gao, 2014) compressor cascade and showed improved prediction on corner stall characteristics, compared to RANS. However. With the steady Reynolds-averaged profile of the upstream turbulent boundary layer, it is challenging for the DES model to predict the bimodal instability, and thus the bimodal behavior of the separation. Extensive grid refinement near the horseshoe vortex region was reported to be necessary for revealing the unsteady nature. Suspecting that the `grey area’ issue, which commonly appears in DES simulations, may delay the development of shear layer instabilities, Xia et al. (2018) introduced the shear-layer adapted length scale (Shur et al., 2015) to accelerate the RANS-to-LES transition process. However, the horseshoe-vortex instability is still missing because the upstream flow and the shielded boundary layer near leading edge are solved by Reynolds-averaged equations. Therefore, there is still a gap between k-omega SST based DDES model (Gritskevich et al., 2012) and LES results (Gao, 2014).

The latest development of DES models (Travin et al., 2006; Yin et al., 2015) have the ability to perform Wall-modeled Large Eddy Simulation (WMLES), if realistic turbulent structures were provided at the inflow boundary condition. The motivation of the current research is to verify if the unsteady turbulent structures introduced to upstream can help the DES model to capture the bimodal instability, and consequently, to improve loss prediction accuracy. The recycling-rescaling method of Lund et al. (1998) is chosen for generating the time-dependent unsteady turbulent boundary layer at the inlet.

The Adaptive Detached Eddy Simulation model (Yin et al., 2015) is chosen for the current simulation. It was developed for the purpose of mimicking the dynamic Smagorisnky model (Lilly, 1991) in the eddy resolving regions. Fast RANS-to-LES transition is achieved by directly defining the eddy (subgrid) viscosity via length scale. Germano-identity is used in a dynamic procedure to determine the model constant. The model constant controls the subgrid viscosity and the thickness of shielded RANS region. The dynamic procedure has shown significant improvement on complex flow configurations.

A comparison of simulation results is made between the two inflow conditions: Reynolds-averaged inflow and synthetic eddy inflow. Detailed analysis of the sensitivity on inflow condition and grid resolution are carried out as the exploration of best practice in simulating end wall flows.