Data-driven turbulence and heat flux closure corrections for TPMS effusion cooling

Triply periodic minimal surface (TPMS) effusion cooling provides a promising route for advanced turbine thermal protection, but its complex three-dimensional pore-scale outflow, near-wall shear-layer mixing, and spatially non-uniform turbulent heat diffusion remain difficult to predict using conventional RANS models. In this study, gene expression programming (GEP)-based explicit closure-correction strategies for turbulence and heat transfer are implemented in ANSYS Fluent and applied to a Solid-Diamond TPMS effusion cooling configuration. The turbulence correction follows Pope’s tensor-basis framework to represent nonlinear Reynolds-stress anisotropy, while the heat-transfer correction replaces the constant turbulent Prandtl number assumed in the simple gradient diffusion hypothesis with a local explicit expression. This study compares three strategies including correcting the turbulence closure alone, the heat-transfer closure alone, and both closures simultaneously. For the injection ratio used during closure training, all three GEP-corrected models reduce the cooling-effectiveness prediction error relative to the baseline Realizable k - ε model. Among the three strategies, the coupled correction yields the largest reduction in the overall RMSE, by approximately 35%, and most effectively mitigates the downstream overprediction, reducing the downstream RMSE and MAE by approximately 83% and 86%. This improvement is associated with a more coordinated prediction of near-wall momentum transport and turbulent heat diffusion. A posteriori tests at unseen injection ratios show that the corrections remain effective when the baseline error pattern is similar to that in training, but their performance degrades when the error pattern changes. These results demonstrate the feasibility of deploying GEP-based explicit closure corrections in a commercial CFD solver and highlight the need for multi-condition training to improve robustness in TPMS effusion cooling predictions.