Incorporating Wake Effects in Data-Driven Transition and Turbulence Modeling for Multi-Stage Low-Pressure Turbines

The transitional and turbulent flow behaviors in multi-stage turbine environments are strongly influenced by the combined effects of varying pressure gradients, surface curvature, and unsteadiness. In particular, the deformation of upstream-shed wakes under acceleration and strong curvature results in a lag of turbulence response relative to the kinematic perturbation. Downstream blade rows are continuously subjected to unsteady wake disturbances, giving rise to wake-boundary layer and wake-wake interactions. These effects become even more complex with moving rotors and pose significant challenges for the transition and turbulence modeling in (Unsteady) Reynolds-Average Navier-Stokes calculations.  Accurate prediction of wake-induced transition remains difficult for transition models and wake-wake interaction challenges turbulence models, as these models have been tuned with data from steady inflow cases. Previous model-improvement efforts have focused primarily on turbine cascades without incoming wakes, employing symbolic regression-based models and reformulation (Fang et al., GT2023-102902; Metti et al., J. Turbomach. 148(2):021011). Therefore, none of these studies have incorporated wake-induced unsteadiness with the combined effects of pressure gradient and curvature on wake evolution in the physical modeling of the multi-stage environment. In this study, the transformer-based computational fluid dynamics (CFD)-driven training framework (Fang et al., GT2024-125550) is extended to incorporate unsteadiness information (phase-averaged pressure, friction coefficients and wake loss) into the cost function. Another contribution is the revision of a key term in the transition model, where a constant in the shear-sheltering function is replaced by a trained function that includes pressure-gradient and curvature-related input features to capture the wake-induced turbulent component. For the turbulence model development, the Boussinesq assumption is supplemented with an extra anisotropy stress term. A one-and-a-half low-pressure turbine stage configuration is employed as the training case. The trained explicit models are analyzed and simplified. Results demonstrate that the newly developed models successfully capture the increase of turbulent intensity across the blade rows. The unsteady wake interaction causes large-scale eddies shed from the blade wakes to break down into smaller fragments, sustaining elevated turbulence levels both within the boundary layer and in the free stream. It is observed that the trained models maintain minimal modification in the first stator region (without incoming wake) while correctly predicting the rise of turbulence downstream, thereby improving both transition and fully turbulent flow predictions. Finally, the generalizability of the trained models is validated using three additional test cases: (i) the same geometry at different Reynolds numbers, (ii) a distinct geometry at the same Reynolds number, and (iii) another geometry at a different Reynolds number.