TABLE 10-1: THE POROUS MEDIA FLOW DEFAULT SETTINGS

The Porous Media Flow Interface Options

Figure 10-1 shows the Brinkman Equations Settings window with a drop-down list to select either Compressible or Incompressible flow, and a check box available to select either normal or Stokes Brinkman flow. Combinations are also possible.

D A R C Y ’ S L A W

The Darcy’s Law Interface () is used for modeling fluid movement through interstices in a porous medium where a homogenization of the porous and fluid media into a single medium is done. Together with the continuity equation and equation of state for the pore fluid (or gas) this interface can be used to model low velocity flows, for which the pressure gradient is the major driving force. The penetration of reacting gases in a tight catalytic layer, such as a washcoat or membrane, is a classic example for use of Darcy’s Law.

Darcy’s law can be used in porous media where the fluid is mostly influenced by the frictional resistance within the pores. Its use is within very low flows, or media where the porosity is very small. Where the size of the interstices are larger, and the fluid is also influenced by itself, the kinetic potential from fluid velocity, pressure, and gravity must be considered. This is done in the Brinkman Equations interface. Fluid penetration of filters and packed beds are applications for this mode.

B R I N K M A N E Q U A T I O N S

The Brinkman Equations Interface () is used to model compressible flow at speeds of less than 0.3 Mach, but you have to maintain control over the density and any of the mass balances that are deployed to help with this. You can also choose to model incompressible flow, and simplify the equations to be solved. Furthermore, you can select the Stokes-Brinkman flow feature to reduce the equations’ dependence on inertial effects (see Figure 10-1).

T H E M E C H A N I S M S F O R M O D E L I N G P O R O U S M E D I A A N D S U B S U R F A C E F L O W | 309

Figure 10-1: The Settings window for the Brinkman Equations interface. You can model compressible or non-compressible flow and Stokes flow. Combinations are also possible.

The Brinkman equations extend Darcy’s law to describe the dissipation of the kinetic energy by viscous shear, similar to the Navier-Stokes equation. Consequently, they are well suited to transitions between slow flow in porous media, governed by Darcy’s law, and fast flow in channels described by the Navier-Stokes equations. The equations and boundary conditions that describe these types of phenomena are to be found in the Free and Porous Media Flow interface.

The Brinkman equations also contains the possibility to add a Forchheimer drag term, which is a viscous drag on the porous matrix proportional to the square of the flow velocity.

F R E E A N D P O R O U S M E D I A

The Free and Porous Media Flow Interface () is useful for equipment that contain domains where both free flow is connected to porous media, such as packed-bed reactors and catalytic converters. It should be noted that if the porous medium is large in comparison to the free channel, and you are not primarily interested in results in the

310 | C H A P T E R 1 0 : P O R O U S M E D I A A N D S U B S U R F A C E F L O W B R A N C H