Discussion Forum

Hello,

I focus now on the flow and solute transportation simulation in the free flow and porous media. There are traditionally one singe formulation, typically Brinkman and two-domain coupling with Navier-Stokes/Stokes and Darcy's or Brinkman's. For the former unified one I guess as exerted in fp (free flow and porous media), there is no need to specify the boundary conditon along the interface between the two medias, which provides continuous velocity profile across the transition zone. However, I would also like to try the coupling with specification of a slip jump velocity across the interface. There is some literature in comsol conference proceedings. Could anyone explain to me in detail how to impose this jump boundary condition? What is the difference between the choices of 'slip conditon' and ''slip velocity'', could ''slip velocity'' be prescribed as experssion like the Beaver&Joseph boundary dU/dy=α/√k(Uf-Ud), or necessarily assign a value? What is the difference with the maxwell boundary conditon? Could anyone explain to me more in detail or find me some reference?

Best

Yuexia

Hello Ali

Finally I didn't use slip interfacial boundary condition, as no-slip boundary was justified for my physical model. If you want to apply a slip boundary in COMSOL, for examp, add a 'wall' in N-S module, and you could choose 'boundary condition' to be 'slip velocity'. For the prescription of the slip velocity, you could read in detail the help manual. I tried it out before, but the formula of calculating the slip length is somehow different with the classical B-J boundary condition. Then you could compare the velocity profile across your N-S and Dl or Br, you will find obiviously the jump of velocity at the interface.


Here is the way if you estimate uB with B-J boundary condition. I just attached some literature on the estimation of the parameters.

du/dy= β (uB-Q) (7)
β=α/√k


Where uB is the slip velocity at the interface, Q is the filter velocity within the porous region, k is permeability of porous media, du/dy is the velocity gradient, (in comsol, you could estimate with dtang(u,y) at the interface), β is in a length scale characterizing the depth – δ (referred to as the boundary layer thickness) , up to which the velocity inside the fluid region is extrapolated. Theoretical studies suggest the thickness δ is on the order of √k (Kaviany, 1995). However, it is observed that from experimental studies that δ is of the order of the grain diameter, which is much larger than the theoretical prediction (Goharzadeh et al., 2005; Gupte and Advani, 1997). The measured δ from (Goharzadeh et al., 2005) for different types of material and grain size is 40-100 times of the theoretical estimation. α is an empirical slip parameter, a dimensionless quantity depending on the structure of permeable material, with a wide range from 0.1 to 4. A widely used mathematical representation for α is √(μ ̃/μ) (Neale and Nader, 1974). However, the literature exhibits a remarkable disagreement in terms of the ratio of μ ̃/μ, from <1 to >10 (Alazmi and Vafai, 2001; Shavit et al., 2004).

But you could first try with the slip length 'tick the option' using √k of your porous media to give a value of the slip length (transitional thickness).

Good luck

Yuexia