Assessment of the DDES-\gamma Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract

The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using Delayed Detached Eddy Simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales and it incorporates the one-equation \gamma-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation \gamma-transition model against experimental data and a benchmark LES. The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier-Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved Large Eddy Simulations (LES). Additionally, the results of the transitional DDES model are compared to DDES without a transition model, RANS eddy viscosity model and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation \gamma-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation \gamma-transition model becomes particularly evident when predicting the separated shear layer, transition process and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation \gamma-transition model can be a good compromise in terms of predictive accuracy and computational costs.