Multiscale Data-Driven RANS Closure for Trailing Edge Cutback Film Cooling Flows

Abstract This article addresses the steady Reynolds-averaged Navier–Stokes (RANS) simulation of turbomachinery flows with spectral overlap. A multiscale RANS closure model is proposed and applied to trailing edge (TE) cutback film cooling flows, featuring deterministic vortex shedding and its interaction with stochastic turbulence. The model consists of three transport equations that solve the deterministic kinetic energy kd, stochastic kinetic energy ks, and stochastic specific energy dissipation rate ω, hence referred to as the k2–ω model. The key terms are the deterministic anisotropy tensor ad,ij that controls the production of kd, the deterministic length scale Ld that controls the kd-to-ks energy transfer, and the deterministic Prandtl number Prd that controls the deterministic heat flux, all of which are closed by data-driven algebraic models with high-fidelity simulation data. The model is trained on one geometry under two operating conditions, and it is tested in a range of unseen geometries with different TE thicknesses and wall inclination angles under different operating conditions. The k2–ω model predicts the near-wake velocity and temperature field with sufficient accuracy at the cost of 1% of scale-resolving simulations. It is capable of capturing the change of wall cooling effectiveness with respect to the change of geometries and operating conditions, whereas the conventional RANS closure models fail to do so due to the inherent limitation of the Reynolds averaging process in the presence of both deterministic flow structures and turbulence. The presented model is a useful tool for future turbine cutback trailing-edge aerothermal design.