Pore-scale flow mechanisms in three-dimensional heterogeneous porous channels: Topology optimization and critical pore diameter effects

This paper presents a method for modeling three-dimensional heterogeneous porous channels using the variable density topology optimization technique. This approach allows for parametric control over porosity and pore throat dimensions, enabling the creation of a highly accurate geometric model. Additionally, the Navier–Stokes equations are employed to examine the pore-scale flow behavior, revealing the microscopic mechanisms through which pore structure parameters affect flow velocity, pressure drop, and nonlinear flow transition characteristics. Ultimately, a revised model for effective permeability (Keff) is introduced, enhancing the precision of macroscopic models in the cross-scale analysis of flow in porous media. The results indicate that the method of generating porous flow channels through topology optimization demonstrates high accuracy. The design error decreases as the porosity increases, reaching a minimum of 0.2% at a porosity of 0.5. It has been found that a critical pore diameter of 150 μm maximizes fluid flow velocity and minimizes critical mass flux. The effect of pore diameter on fluid velocity and vortex strength is significant, while the influence of porosity becomes apparent only at the critical pore diameter. As mass flux increases, effective permeability continuously decreases, whereas the number of vortex structures initially increases before stabilizing. The modified Keff model links pore-scale structure with macroscopic predictions, reducing the prediction error of the pressure gradient to 0.04% in cross-scale simulations. These findings provide new insights for optimizing porous media in microfluidic and energy applications.