Convection in Porous Media
Convection (also called advection) describes the movement of a species, such as a pollutant, with the bulk fluid velocity. The velocity field u corresponds to a superficial volume average over a unit volume of the porous medium, including both pores and matrix. This velocity is sometimes called Darcy velocity, and defined as volume flow rates per unit cross section of the medium. This definition makes the velocity field continuous across the boundaries between porous regions and regions with free flow.
The velocity field to be used in the Model Inputs section on the physics interface can, for example, be prescribed using the velocity field from a Darcy’s Law or a Brinkman Equations interface.
The average linear fluid velocities ua, provides an estimate of the fluid velocity within the pores:
where εp is the porosity and θ = sεp the liquid volume fraction, and s the saturation, a dimensionless number between 0 and 1.
Figure 4-1: A block of a porous medium consisting of solids and the pore space between the solid grains. The average linear velocity describes how fast the fluid moves within the pores. The Darcy velocity attributes this flow over the entire fluid-solid face.
Convective Term Formulation
The Transport of Diluted Species in Porous Media interface includes two formulations of the convective term. The conservative formulation of the species equations in Equation 4-17 is written as:
(4-21)
If the conservative formulation is expanded using the chain rule, then one of the terms from the convection part, ci∇·u, would equal zero for an incompressible fluid and would result in the nonconservative formulation described in Equation 4-17.
When using the nonconservative formulation, which is the default, the fluid is assumed incompressible and divergence free: ∇ ⋅ u = 0. The nonconservative formulation improves the stability of systems coupled to a momentum equation (fluid flow equation).
To switch between the two formulations, click the Show button () and select Advanced Physics Options. In the section Advanced Settings select either Nonconservative form (the default) or Conservative form. The conservative formulation should be used for compressible flow.