Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot

A form of supervised machine learning was applied to highly resolved large-eddy simulation (LES) data to develop non linear turbulence stress and heat flux closures with increased prediction accuracy for trailing-edge cooling slot cases. The LES data were generated for a thick and a thin trailing-edge slot and shown to agree well with experimental data, thus providing suitable training data for model development. A Gene Expression Programming (GEP) based algorithm was used to symbolically regress novel nonlinear Explicit Algebraic Stress Models (EASM) and heat-flux closures based on either the gradient diffusion or the generalized gradient diffusion approaches. Following a-priori assessment, the new models were used for steady RANS calculations of both thin and thick trailing-edge slot geometries, testing their performance and robustness. Overall, the best agreement with LES data was found when training the RANS model in the near wall region where high levels of anisotropy exist and using the mean squared error of the anisotropy tensor as cost function. In the case of the thin lip geometry, combining an improved EASM model with the standard eddy-diffusivity model predicted the adiabatic wall effectiveness in good agreement with the LES and experimental data. Crucially, the obtained model was also applied to different blowing ratios of the thin lip geometry and a significant improvement in the predictive accuracy of adiabatic wall effectiveness was observed for those cases not previously seen in the training process. For the thick lip case the match with reference values deteriorated due to the presence of large-scale, relative to the slot height, vortex shedding. The machine-learning algorithm was therefore also used to ‘learn’ an appropriate closure for the turbulent heat flux vector. The constructed scalar flux model, in conjunction with a trained RANS model, was found to have the capability to further improve the prediction of the adiabatic wall effectiveness.