Effect of pore-structure on the Beaver-Joseph slip-coefficient for a free-flow and porous medium interface

Transport phenomena at the interface between a porous medium and an adjacent boundary layer play a significant role in various natural and industrial processes, such as soil evaporation, fuel cells, transpiration cooling, and aircraft wing noise reduction, among others. However, a fundamental understanding of exchange processes across scales, which is crucial for effective upscaling of hydrodynamic dispersion remains a challenge. In this thesis, steady-state numerical simulations are conducted in the laminar flow regime to investigate the interfacial dynamics of coupled free-flow and porous media systems. This study examines the effects of porosity (ranging from 50% to 85%), Reynolds number (from 0.1 to 200), and different pore structures (square and circular pillars) on flow characteristics, momentum transfer at the interface (y=0), and the Beaver-Joseph interface slip coefficient. The results show distinct flow patterns, including U-shaped flow fields and flow penetration across the interface. It was found that porosity and pore structure significantly impact the Beaver-Joseph constant, more so than the free-flow momentum. Furthermore, the effect of Reynolds number on velocity slip depends on porosity, with notable changes occurring only for Reynolds numbers above 50. As porosity increases, the average slip coefficient rises by 75% for square pillars and 133% for circular pillars, indicating that circular pillar configurations are more sensitive to changes in slip coefficients. An empirical correlation for the average Beaver-Joseph slip coefficient is also developed, which could help in scaling these phenomena from the micro- to macro-scale. Additionally, two-fluid flow simulations are performed to explore the effects of viscosity ratio and three-phase contact angles on momentum transfer. Significant recirculations are observed near the meniscus, with the depth of these recirculations being about 20-30% of the pore scale. The meniscus depth remains relatively unaffected by changes in Reynolds number and viscosity ratio. Overall, these findings provide valuable insights into flow dynamics within porous media systems, offering potential applications in both natural and industrial contexts. The results contribute to improved modelling of fluid dynamics and momentum transport in systems where free-flow and porous media interact.

The work is towards M.Sc. degree under the supervision of Assistant prof. Alexandros Terzis, Department of Aerospace Engineering, Technion – Israel Institute of Technology