Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate mathematical modeling of various applications described by coupled free-flow and porous-medium problems. To model single-fluid-phase flows at low Reynolds numbers in such coupled systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the fluid-porous interface, the balance of normal forces and the Beavers-Joseph condition on the tangential component of velocity. In the latter condition, the value of the Beavers-Joseph slip coefficient is uncertain, however, it is routinely set equal to one that is not correct for many applications. In this paper, three flow problems (pressure-driven flow, lid-driven cavity over porous bed, general filtration problem) with different pore geometries are studied. We determine the optimal value of the Beavers-Joseph parameter for unidirectional flows minimizing the error between the pore-scale resolved and macroscale simulation results. We demonstrate that the Beavers-Joseph slip coefficient is not constant along the fluid-porous interface for arbitrary flow directions, thus, the Beavers-Joseph condition is not applicable in this case.
翻译:流体- 浮质界面与正确确定的有效参数的物理一致的结合条件对于以自由流和多孔- 介质问题描述的各种应用的精确数学模型的精确模型来说是必要的。为了在这种混合系统中以低Reynolds数量模拟单流流阶段流,通常使用Stoks/Darcy方程式,同时在流体- 浮质界面中保护质量、正常力量的平衡和比弗斯- 约瑟夫条件与速度的正切部分。在后一种情况下,比弗斯- 约瑟夫滑移系数的价值不确定,但通常被设定为在许多应用中不正确的。在本文中,对三种流问题(压动流、浮质驱动于多孔床之上、一般过滤问题)进行了研究。我们确定单向流中比弗斯- 约瑟夫参数的最佳值,以最小化孔- 溶度和宏观模拟结果之间的误差。我们证明,贝弗斯- 浮体- 滑度- 滑度系数通常等同于许多应用不正确的数值。在本文件中, 三次流流中, 任意- 流体- 流体- 流体- 误系数是不固定的。