We are pleased to announce that our guest researcher Prof. Costanza Aricò from the University of Palermo (Italy) will give the SFB 1313 "Pretty Porous Science Lecture" #22. Her talk will be on "Investigation of free fluid over porous media. A novel numerical solver for One-Domain-Approach".
Date: Tuesday, 13 September 2022
Time: 4:00 pm CET
Speaker: Costanza Aricò from the University of Palermo (Italy)
Lecture title:"Investigation of free fluid over porous media. A novel numerical solver for One-Domain-Approach".
Place: The lecture will be a hybrid lecture. A small audience is possible in Pfaffenwaldring 61 MML, additionally the lecture is offered online. After registration, you will receive the meeting information.
Registration: If you are interested in participating in the lecture, please contact melanie.lipp@iws.uni-stuttgart.de
Abstract
Transport phenomena of combined free fluid (ff) and porous medium (pm) flow occur in several industrial, environmental and biological applications (e.g., surface and groundwater flow, contaminant transport from lakes by groundwater, fuel cells, oil filters, blood flow in vessels and tissue, transfer of therapeutic agents).
The related mass, momentum and energy transport mechanisms at the ff–pm interface have been intensively investigated during the last decades applying two main approaches, the formulations at the micro- and macro-levels, respectively.
At the microscopical level, the porous medium is assumed as a connected domain of pore spaces filled with the fluid. The flow is governed by Navier–Stokes (or Stokes) equations, and no–slip boundary conditions are imposed on the interfaces between fluid and solid particles of the porous medium. The main drawback of this approach is its application for real problems, due to the huge amount of CPU time and computer memory storage, as well as the lack of an exact knowledge of the real porous geometry.
At the macroscopical level, the sets of the governing equations are obtained by averaging or upscaling the equations at the microscopic level over a Representative Elementary Volume (REV) [1]. The REV size is much larger than the characteristic size of the pore, but much smaller than the representative size of the domain. Two general different approaches have been derived at the macroscale, namely the Two-Domain Approach (TDA) and the One-Domain Approach (ODA) [1].
In TDA, the domain is split into two regions, and, in the most general case, the Navier–Stokes equations describe the fluid flow in the ff domain, while the Darcy’s law is applied in the pm region. This is the most difficult approach from a mathematical point of view, since the two sets of governing equations are completely different systems of Partially Differential Equations (PDEs) and need interface conditions (IFCs). A sharp interface is assumed, where appropriate boundary conditions are imposed (typically, the conservation of mass, the balance of normal forces and the Beavers–Joseph condition (BJC) for the tangential velocity components [2]).
On the contrary, in ODA, the porous layer is regarded as a pseudo-fluid and the composite region free fluid-porous medium is treated as a continuum. One set of PDEs is assumed, typically the Brinkman or the (Navier)-Stokes-Brinkman equations (e.g., [1, 3]). The transition from the fluid to the porous medium is achieved through a continuous spatial variation of physical properties, such as permeability and porosity inside a transition layer (TL) which separates the homogeneous ff region from the bulk porous medium. The major drawback of the ODA is related to the knowledge of the size of the TL between the two homogeneous regions and how the physical parameters of the porous medium change inside it.
In the recent literature, some ODA have been proposed for the Brinkman equations [4] or a momentum equation having a Darcy form, including inertial and slip effects [5].
In the present talk, a novel numerical solver for ODA for incompressible and single-phase fluid over a saturated anisotropic porous medium is presented. The governing equations, derived by averaging the pore scale microscopic Navier-Stokes equations, are the Incompressible Navier-Stokes-Brinkman equations (INSBEs), discretized over general unstructured meshes. Preliminary model results are shown.
References
[1] B. Goyeau, D. Lhuillier, D. Gobina, M.G. Velarde, Momentum transport at a fluid–porous interface, Int. J. Heat and Mass Transfer 46 (2003) 4071–4081
[2] G.S. Beavers, D. D. Joseph, Boundary conditions at a naturally permeable wall, J. Fluid Mech. 30(01) (1967) 197–207
[3] L. Wang, L.-P. Wang, Z. Guo, J. Mi, Volume-averaged macroscopic equation for fluid flow in moving porous media, Int. J. Heat and Mass Transfer 82 (2015) 357–368
[4] H. Chen, X.-P. Wang, A one-domain approach for modeling and simulation of free fluid over a porous medium, J. Comp. Phys., 259 (2014) 650–671
[5] F. J. Valdés-Parada, D. Lasseux, A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects, Phys. Fluids 33, 022106 (2021)