Hybrid finite element method-machine learning framework for radial pressure distribution analysis in inward flow between two rotating disks

This study examines the pressure distribution in inward flow between two rotating disks using a hybrid approach combining the finite element method (FEM) and machine learning (ML). Fluid enters through a peripheral gap between the two disks and leaves axially through the pipe at the center. A structured FEM mesh for an axisymmetric flow is considered, and the assumptions are laminar, steady, incompressible fluid flow. The governing equations are solved in a cylindrical coordinate system. Numerical simulations are performed for controlling parameters, such as throughflow Reynolds numbers (Re _q  = 1000–6000), rotational Reynolds numbers (Re = 10,000–50,000), gap ratios ( g  = 0.0020–0.0100), and speed ratios ( s  = −2 to 2), to generate a high-fidelity dataset. Regression Models, such as Linear Regression (LR), Random Forest (RF), Extreme Gradient Boosting (XGB), and Light Gradient Boosting Machine (LGBM), are trained to predict the pressure distribution (Pr) in rotating inward flow. These ML models evaluate the statistical parameters, such as coefficient of determination ( R ² ), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). XGB outperformed all models, achieving Train R ²  = 0.99998 and Test R ²  = 0.99959, with the lowest Test RMSE, MAE, and MAPE: 28.32, 17.95, and 0.31%, respectively. Scatter plots confirmed strong alignment between predicted and actual pressure distributions across training and testing datasets, demonstrating robust generalization. FEM, correlation, and regression model results confirm that the gap ratio, followed by the radial position, is the most statistically significant factor for determining the pressure distribution in inward flow.