Brinkman double-layer model for flow at a free-porous interface

The phenomenon of the Stokes-Darcy flow in coupled systems comprising a clear channel and a complex 3D porous medium is investigated through both numerical and theoretical approaches. A quartet structure generation set (QSGS) method is used to generate random complex 3D porous structures imitating real structures in nature. Pore-scale flow simulations are performed using the Lattice Boltzmann method, enabling detailed analysis and characterization of the interfacial flow phenomena. Four key parameters with clear physical meanings are introduced to quantitatively capture essential aspects of the flow dynamics, revealing intriguing linear relationships with the square root of permeability - a fundamental characteristic length scale dominating the phenomenon. Several existing models are examined by these parameters. To address the limitations of existing models, a Brinkman double-layer(BDL) model is proposed. By comparing with several classic models, the present BDL model stands out due to its simplicity, accuracy and robustness, providing a comprehensive understanding of the complex flow behavior in the coupled system.