Refined k-ϵ Turbulence Model Q3D-Predictions in Compressor Cascades at Design and Off-Design

The performance of two refinements (non-equilibrium and non-linear) to the Low-Reynolds-Number Launder and Sharma (1974) k-ε–turbulence model in the framework of a turbomachinery Navier-Stokes code is evaluated for subsonic and transonic compressor cascades at design and off-design conditions. The non-equilibrium treatment originally developed by Rodi (1972) for extending the standard high Re-number k-ε–model to account for the imbalance of production and dissipation in far-field wakes has been applied, in combination with the well-established Kato and Launder (1993) modification, to the entire flow field by extending the scaling of the eddy viscosity to the production term of turbulent kinetic energy in its transport equation. Accounting for non-equilibrium (spectral) effects such as non-local strain history in adverse pressure gradients has been found to be essential a) in predicting early separation on the DCA blade of the subsonic compressor cascade at design conditions and b) in obtaining a more accurate position of a swallowed shock in the transonic compressor cascade at off-design. The former improvement has resulted in a better prediction of the flow exit angle and the latter is essential in capturing the physics of the shock/boundary-layer interaction but further refinements are required to improve the overall flow field and hence loss predictions. The potential of the cubic two-equation non-linear stress-strain model extension developed by Suga (1995) has been investigated. This is shown to provide a better baseline for non-equilibrium modeling than the Kato and Launder modified k-ε–model, since it accounts additionally for the misalignment of turbulence and strain tensor principal axes, streamline curvature and partially for non-equilibrium effects at very little additional computational cost. The non-linear model is found to demonstrate the correct trends, though it requires recalibration over a wider range of turbomachinery flows.