Unsteady Simulations of a Trailing-Edge Slot Using Machine-Learnt Turbulence Stress and Heat-Flux Closures

The trailing edge slot is a canonical representation of the pressure-side bleed flow encountered in high pressure turbines. Predicting the flow and temperature downstream of the slot exit remains challenging for RANS and URANS, with both significantly overpredicting the adiabatic wall-effectiveness. This over-prediction is attributable to the incorrect mixing prediction in cases where the vortex shedding is present. In case of RANS the modelling error is rooted in not properly accounting for the shedding scales while in URANS the closures account for the shedding scales twice, once by resolving the shedding and twice with the model for all the scales. Here, we present an approach which models only the stochastic scales that contribute to turbulence while resolving the scales that do not, i.e. scales considered as contributing to deterministic unsteadiness. The model for the stochastic scales is obtained through a data-driven machine learning algorithm, which produces a bespoke turbulence closure model from a high-fidelity dataset. We use the best closure (blowing ratio of 1.26) for the anisotropy obtained in the a priori study of Lav, Philip & Sandberg [A New Data-Driven Turbulence Model Framework for Unsteady Flows Applied to Wall-Jet and Wall-Wake Flows, 2019] and conduct compressible URANS calculations. In the first stage, the energy equation is solved utilising the standard gradient diffusion hypothesis for the heat-flux closure. In the second stage, we develop a bespoke heat-flux closure using the machine-learning approach for the stochastic heat-flux components only. Subsequently, calculations are performed using the machine-learnt closures for the heat-flux and the anisotropy together. Finally, the generalisability of the developed closures is evaluated by testing them on additional blowing ratios of 0.86 and 1.07. The machine-learnt closures developed specifically for URANS calculations show significantly improved predictions for the adiabatic wall-effectiveness across the different cases.