Physics-Informed Neural Network for Turbulent Flow Reconstruction in Composite Porous-Fluid Systems

This study explores the implementation of Physics-Informed Neural Networks (PINN) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The segregated PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-Averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e., porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features, including flow leakage, channeling effect and wake recirculation was investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data was considered in this study. Results showed that the PINN model predictions with second-order internal training data achieved high accuracy for the prominent flow features compared to the RANS data, within a 20% L2 norm error of second-order statistics in the solid block case. In addition, for the porous block case, providing training data at the porous-fluid interface showed errors of 18.04% and 19.94% for second-order statistics, representing an increase in prediction accuracy by 7% compared to without interface training data. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.