Improved prediction of film cooling effectiveness for flat-surface film holes in gas turbine endwalls and blades by considering turbulent Schmidt number modeling

Gas turbine efficiency relies on extreme turbine inlet temperatures, necessitating highly efficient cooling strategies where film cooling serves as the primary approach. As a key protective cooling technology in gas turbine engines, research on film cooling mainly focuses on cooling effectiveness, considering mass diffusion mechanisms. Conventional Reynolds-averaged Navier-Stokes simulations suffer from inaccurate scalar transport predictions due to oversimplified constant turbulent Schmidt number (Sc_t) models. To bridge this gap, this study focuses on flat-surface film holes in endwall/blades and proposes an improved physics-informed multi-parameter Sc_t model that incorporates the momentum ratio, density ratio, and streamwise distance to adapt to vortex evolution and balance momentum-mass diffusion through interpretable coefficients. Experimental data validated the model's accuracy using a comprehensive quantitative evaluation framework with metrics including SSIM, RMSE, and CCPS. Results demonstrate that at low momentum ratios, the optimized model mitigates excessive diffusion inherent in conventional constant Sc_t models, attributed to weaker vortex-induced mixing. Conversely, at high momentum ratios where vortex mixing intensifies, the optimized model enhances diffusion, achieving prediction accuracy improvements of up to 85.9 % compared to the standard Sc_t = 0.7 approach. This work establishes a mechanistic link between Sc_t and vortex evolution, providing a physics-based framework for high-fidelity gas turbine thermal management.