Porous Media

Porous media are continua that contain both fluid and fine-scale solid structures, for example: packed-bed chemical reactors, filters, radiators, honeycomb structures, or fibrous materials. The solid geometrical structures are too fine to be individually meshed and fully resolved by a computational grid.

Simcenter STAR-CCM+ provides two approaches to model the effects of the porous medium on the flow:

One way of modeling flow in a porous medium is to introduce source terms into the momentum transport equations to approximate the pressure losses. This approach is usually termed as superficial velocity formulation. In Simcenter STAR-CCM+, it is called porous region modeling.
The second modeling approach is more general in that it accounts for the increase in physical velocity when flow enters the porous medium. This approach is usually termed physical velocity formulation. In Simcenter STAR-CCM+, it is called phasic porous media modeling. The phasic porous media model provides the ability to have multiple solid phases in the porous medium, for each of which a separate energy equation can be solved.

Both modeling approaches use the porosity and add appropriate source terms to the governing equations. The porosity is defined as the ratio of the volume

V_{f}

that is occupied by the fluid and the total volume

V

of a cell:

Figure 1. EQUATION_DISPLAY

χ = \frac{V_{f}}{V}

(1837)

When flow enters a porous medium, the physical flow velocity rises at a given point, because there is less open area available to the flow. Porous region modeling does not compute this increase in physical velocity, instead basing the approach on a calculated superficial velocity. The superficial velocity is related to the physical velocity as:

Figure 2. EQUATION_DISPLAY

v_{s} = χ \cdot v

(1838)

The superficial velocity is the same in the fluid region and in the porous region. The superficial velocity is an artificial flow velocity that assumes that only fluid passes the cross-sectional area and neglects the solid portion of the porous medium.

Diffusion in porous media depends on the porosity of the medium and on the tortuosity $τ$ . Tortuosity is defined as the ratio between the actual (convoluted) path length through the porous medium from point to point and the straight-line distance between the same two points. Tortuosity reduces the rate of diffusion in a porous medium, so that the effective diffusion coefficient is:

Figure 3. EQUATION_DISPLAY

D_{e f f} = \frac{χ}{τ} D

(1839)

where $D$ is the diffusion coefficient of the fluid. Tortuosity can be a factor in cases involving species transport, passive scalars, Li-ion transport, and electrical conductivity in the context of electromagnetics.

For multiphase segregated flow simulations only, a blending is used to ensure a smooth transition from resistance-dominated to inertia/viscosity dominated regimes.

Turbulence in Porous Media

For RANS turbulence models, the SRH turbulence model, and DES, the turbulence transport equations are not solved in the porous regions. The effect of a porous region on turbulent flow depends on its internal structure. Where turbulence is present, the turbulence scales are dominated by the geometric structure of the porous medium. As Simcenter STAR-CCM+ does not predict these turbulence scales directly in the porous region, you must specify them directly in the form of either:

turbulent kinetic energy and dissipation rate
turbulence intensity and length scale
turbulence intensity and viscosity ratio

Turbulence quantities in the fluid leaving the porous region are constructed from the user-defined values; they are not transported from the upstream side of the porous region.

LES treats turbulence in porous regions the same way as in fluid regions.