Estimating turbulent heat flux by artificial intelligent models in comparison with diffusion hypothesis-based models

Accurately predicting turbulent heat flux remains a critical challenge in fluid dynamics, especially for complex flows like film cooling. Traditional models, such as the Gradient Diffusion Hypothesis (GDH), the Generalized Gradient Diffusion Hypothesis (GGDH), and the Higher-Order Generalized Gradient Diffusion Hypothesis (HOGGDH), have shown limitations in providing accurate predictions. This study aims to predict turbulent heat fluxes ( u i ′ T ′ ‾ ) directly using machine learning techniques, specifically random forest, and neural networks, from the known flow features without using the aforementioned assumptions (without using GDH, GGDH, and HOGGDH as a hypothesis to correlate turbulent heat flux to temperature gradient). Large eddy simulations (LES) with the dynamic Smagorinsky model for subgrid scales were conducted for flow over a flat plate with film cooling, with Re of 17382 and blowing ratio and density ratio of 1 and 2. A high-fidelity dataset of 130,000 data points with 34 features was extracted from four distinct zones. These features include adiabatic effectiveness, temperature gradients in three directions, directional velocity derivatives in three directions, six Reynolds stress components, six shear strain rate components, directional velocity in three directions, turbulent kinetic energy, laminar Prandtl number, the turbulent viscosity ratio, and the directional turbulent heat fluxes as the target. By Principal component analysis (PCA) the dataset was reduced to 8 key features. These reduced features were used to train both the random forest and the neural network models. Results demonstrate that the machine learning models provide more accurate predictions of turbulent heat flux compared with GDH, GGDH, and HOGGDH models.