Abstract
Interfacial boundary conditions determined from empirical or ad hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using a multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (J. Fluid Mech., vol. 30 (01), 1967, pp. 197–207). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscale problems and computes the velocity boundary condition without free parameters over any porous bed.
Highlights
Surfaces found in nature are generally non-smooth with complex hierarchical structural features (Liu & Jiang 2011)
Valdés-Parada et al (2013) used the same technique to analyse both stress and velocity jump across the interface. They identified a fixed location of the interface that yields best results when imposing a velocity jump. This is in contrast to both the theoretical findings by Marciniak-Czochra & Mikelic (2012) and the numerical results presented in this paper, which show that the accuracy of the velocity jump condition is independent of the interface location
Boundary conditions at interface between free fluid and a porous medium 871 For example Rosti et al (2015) recently showed that slip velocities below 3 % had a significant effect on the flow statistics in a turbulent channel
Summary
Surfaces found in nature are generally non-smooth with complex hierarchical structural features (Liu & Jiang 2011). Boundary conditions at interface between free fluid and a porous medium 871 For example Rosti et al (2015) recently showed that slip velocities below 3 % had a significant effect on the flow statistics in a turbulent channel. The condition for slip velocity us is us This expression is similar to the condition obtained empirically by Beavers and Joseph, except that Ks is the interface permeability (e.g. Ks = Kcyl), related to a semi-permeable transition layer between the porous medium and the free fluid.
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