A New Approach for Predicting the Pressure Drop in Various Types of Metal Foams Using a Combination of CFD and Machine Learning Regression Models

The present study investigates the effects of the geometric properties of porous media on fluid flows and uses a combination of computational fluid dynamics (CFD) and machine learning (ML) methods to develop new models for predicting the coefficients in the Forchheimer equation (Delta P/L = alpha v + beta v(2)). For this purpose, CFD simulations are performed to assess the effects of foam structural properties on fluid flows for each of the 217 foam types tested. In this research, the Voronoi tessellation method is used to investigate such foam physical properties as porosity, pore diameter, strut diameter, and specific surface area. In all the simulations, air is used as the fluid entering the metallic foams at different superficial velocities but at a constant temperature of 300 K. Pressure gradient as well as Darcy (alpha) and non-Darcy (beta) flow coefficients are then calculated for each foam using the equation and the simulation results. It is shown that the values thus obtained strongly depend on the geometric properties of the porous medium. A second aspect of the study involves resolving the problems of the computation cost due to the complex geometries of foams that result in too many computational grids in the proposed method. This was addressed via machine learning (ML) regression models to develop a continuous model based on foam intrinsic properties. In this approach, models are proposed for estimating alpha and beta coefficients to be used in calculating pressure drop in different metallic foams. The results show that the ridge regularization regression and ordinary least squares are robust models for predicting the coefficients based on foam geometric properties. Moreover, the model is capable of calculating both the values for Reynolds number and friction factor in the continuous range, whereby the flow type can also be determined. Finally, the results obtained from the models indicate the efficacy of the proposed approach for the study of fluid flows in large-scale porous media with minimum errors and satisfactory accuracy.