The increase of the thrust/weight ratio of aircraft engines is extremely restricted by different 3-D flow loss mechanisms. One of them is the corner separation that can form at the junction between a blade suction side and a hub or shroud. In this paper, in order to further investigate the turbulent characteristics of corner separation, large-eddy simulation (LES) is conducted on a compressor cascade configuration using NACA65 blade profiles (chord based Reynolds number: 3.82 × 10⁵), in comparison with the previous obtained experimental data. Using the shear-improved Smagorinsky model as subgrid-scale model, the LES gives a good description of the mean aerodynamics of the corner separation, especially for the blade surface static pressure coefficient and the total pressure losses. The turbulent dynamics is then analyzed in detail, in consideration of the turbulent structures, the one-point velocity spectra, and the turbulence anisotropy. Within the recirculation region, the energy appears to concentrate around the largest turbulent eddies, with fairly isotropic characteristics. Concerning the dynamics, an aperiodic shedding of hairpin vortices seems to induce an unsteadiness of the separation envelope.

Based on physical arguments, the importance of separating the mean-flow from turbulence in the modeling of the subgrid-scale eddy-viscosity is emphasized. Therefore, two distinct time-domain smoothing algorithms are proposed to estimate the mean-flow as the simulation progresses, namely, an exponentially weighted moving average (or exponential smoothing) and an adaptive low-pass Kalman filter. These algorithms highlight the longer-term evolution or cycles of the flow but erase short-term fluctuations. Indeed, it is our assumption that the mean-flow (in the statistical sense) may be approximated as the low-frequency component of the velocity field and that the turbulent part of the flow adds itself to this “unsteady mean.” The cutoff frequency separating these two components is fixed according to some characteristic time-scale of the flow in the exponential smoothing, but inferred dynamically from the recent history of the flow in the Kalman filter. In practice, these two algorithms are implemented in large-eddy simulations that rely on a shear-improved Smagorinsky’s model. In this model, the magnitude of mean-flow rate of strain is subtracted from the magnitude of the instantaneous rate of strain in the subgrid-scale eddy-viscosity. Two test-cases have been investigated: a turbulent plane-channel flow (Rew=395) and the flow past a circular cylinder in the subcritical turbulent regime (ReD=4.7×104). Comparisons with direct numerical simulation and experimental data demonstrate the good efficiency of the whole modeling. This allows us to address nonhomogeneous unsteady configurations without adding significant complication and computational cost to the standard Smagorinsky’s model. From a computational viewpoint, this modeling deserves interest since it is entirely local in space. It is therefore adapted for parallelization and convenient for boundary conditions.

The flow induced by the clearance between the tip of an isolated airfoil and an end-plate is investigated numerically, using a zonal approach with large-eddy simulation in the region of interest. The results are analyzed in comparison with available experimental data, presented in a companion paper. The incoming boundary layer and the pressure distribution around the blade are evaluated. The description of the inflow-jet deviation, with an averaged approach, enables to represent the proper loading on the airfoil. Also, particular attention is paid to the powerful tip-leakage vortex. The vortex characteristics are investigated using specific functions to locate its center and quantify its width. Overall, good results are obtained for the flow statistics and spectra. Furthermore, a very good description of the far-field pressure is achieved using the acoustic analogy, and the results confirm that the tip-flow essentially radiates in the central frequency range (0.7 kHz, 7 kHz).