In film cooling flows, it is important to know the temperature distribution resulting from the interaction between a hot main flow and a cooler jet. However, current Reynolds-averaged Navier-Stokes (RANS) models yield poor temperature predictions. A novel approach for RANS modeling of the turbulent heat flux is proposed, in which the simple gradient diffusion hypothesis (GDH) is assumed and a machine learning algorithm is used to infer an improved turbulent diffusivity field. This approach is implemented using three distinct data sets: two are used to train the model and the third is used for validation. The results show that the proposed method produces significant improvement compared to the common RANS closure, especially in the prediction of film cooling effectiveness.

Measurement techniques such as Magnetic Resonance Velocimety (MRV) and Magnetic Resonance Concentration (MRC) are useful for obtaining 3D time-averaged flow quantities in complex turbulent flows, but cannot measure turbulent correlations or near-wall data. In this work, we use highly resolved Large Eddy Simulations (LES) to complement the experiments and bypass those limitations. Coupling LES and magnetic resonance experimental techniques is especially advantageous in complex non-homogeneous flows because the 3D data allow for extensive validation, creating confidence that the simulation results portray a physically realistic flow. As such we can treat the simulation as data, which "enrich" the original MRI mean flow results. This approach is demonstrated using a cylindrical and inclined jet in crossflow with three distinct velocity ratios, r = 1, r = 1.5, and r = 2. The numerical mesh is highly refined in order for the subgrid scale models to have negligible contribution, and a systematic, iterative procedure is described to set inlet conditions. The validation of the mean flow data shows excellent agreement between simulation and experiments, which creates confidence that the LES data can be used to enrich the experiments with near-wall results and turbulent statistics. We also discuss some mean flow features and how they vary with velocity ratio, including wall concentration, the counter rotating vortex pair, and the in-hole velocity.

Abstract

Current turbulent heat flux models fail to predict accurate temperature distributions in film cooling flows. The present paper focuses on a machine learning approach to this problem, in which the Gradient Diffusion Hypothesis (GDH) is used in conjunction with a data-driven prediction for the turbulent diffusivity field αt. An overview of the model is presented, followed by validation against two film cooling datasets. Despite insufficiencies, the model shows some improvement in the near-injection region. The present work also attempts to interpret the complex machine learning decision process, by analyzing the model features and determining their importance. These results show that the model is heavily reliant of distance to the wall d and eddy viscosity vt, while other features display localized prominence.

The design of film cooling systems relies heavily on Reynolds-averaged Navier–Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion with a fixed turbulent Prandtl number (Prt), fail to accurately predict heat transfer in film cooling flows. In the present work, machine learning models are trained to predict a non-uniform Prt field using various datasets as training sets. The ability of these models to generalize beyond the flows on which they were trained is explored. Furthermore, visualization techniques are employed to compare distinct datasets and to help explain the cross-validation results.