Integration of Machine Learning and Computational Fluid Dynamics to Develop Turbulence Models for Improved Turbine Wake Mixing Prediction

Accurately predicting the wake mixing in gas turbines is of utmost importance from the perspective of blade designers as this phenomenon governs the stagnation pressure loss. Existing Reynolds Averaged Navier-Stokes (RANS) based turbulence models struggle to offer good predictions of the wake-mixing, especially close to the blade trailing edge. One of the primary reasons why these models fail is due to the use of the Boussinesq approximation. Explicit algebraic Reynolds stress models (EARSM) are a computationally efficient approach to address the deficiencies of the Boussinesq approximation. This study employs a novel CFD-driven machine learning framework for EARSM development which is an extension of the gene expression programming method. The developed framework evaluates the ‘fitness’ of candidate models by running RANS calculations in an integrated way, rather than evaluating an algebraic cost function. The resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in subsequent RANS calculations across a range of turbine operating conditions and blade geometries.

Firstly, this study analyses the influence of the inclusion of the near-wake area in the training region on the performance of the CFD-driven models. In essence, it was found that the greater the deterministic unsteadiness in the flow, the greater the portion of the wake near the TE that has to be excluded from the training region in order to obtain a model that performs well in the far-wake. In order to ensure that the models from the CFD-driven approach are actually improving the accuracy of the wake mixing prediction and not just inserting another error to correct the original error from a RANS calculation, CFD-driven model development was conducted for a region downstream of a low pressure turbine blade trailing edge (which excludes the near-wake region completely) by prescribing inlet profiles from a well-validated direct numerical simulation (DNS). When the correct inflow conditions from DNS were prescribed, the CFD-driven models had the ability to closely match the DNS wake evolution. It can therefore be said with increased confidence that CFD-driven models capture the right trends in physics to improve the overall wake mixing for full-blade scenarios.

This approach has also been extended to full-blade scenarios wherein CFD-driven EARSMs have been developed to enhance the wake mixing prediction for low and high pressure across different engine operating conditions. In order to assess the robustness of the models developed, they have been tested across different operating conditions and geometries, other than the ones they were trained for. It has been found that the CFD-driven models are able to bring about significant improvements across all the geometries and operating conditions in the wake loss and shear stress profiles, which shows that the CFD-driven model generation process has the ability to capture physics that can reliably improve wake mixing predictions across completely different operating conditions. The improved wake prediction is mainly due to the extra diffusion introduced by the CFD-driven model as compared to the Boussinesq approximation.