Fluid (Porous Medium)
Use this node to specify the mass transport in a fluid phase filling the pores of a porous medium. It is used as a subnode to Porous Medium, Porous Catalyst, or Packed Bed (Moving Packed Bed).
Model Inputs
Specify the temperature and pressure in the fluid. The temperature model input is used when calculating the density from the ideal gas law, but also when thermal diffusion is accounted for by supplying thermal diffusion coefficients. The pressure model input is used in the diffusional driving force in Equation 3-6 (that is, when a Maxwell–Stefan Diffusion Model is used) and when calculating the density from the ideal gas law.
In a Porous Catalyst the temperature affecting is assumed to be the same in the fluid and the solid (thermal equilibrium). For temperature dependent reactions to use the same temperature as the fluid phase, the temperature is in this case given in the Porous Catalyst node.
Temperature
Select the source of the Temperature field T:
•
Select User defined to enter a value or an expression for the temperature.
•
When present, select a temperature defined by a Heat Transfer interface in the model. For example, select Temperature (ht) to use the temperature defined by the Heat Transfer in Fluids interface with the ht name.
Absolute Pressure
Select the source of the Absolute pressure p:
•
Select User defined to enter a value or an expression for the absolute pressure.
•
When present, select a pressure defined by a Fluid Flow interface present in the model. For example, select Absolute pressure (spf) to use the pressure defined in a Laminar Flow interface with spf as the name.
Density
Use this section to define the density of the fluid phase, and to specify the molar masses of the participating species.
Viscosity
When the Fluid node is present in a Packed Bed, use this section to define the viscosity of the fluid phase. The fluid viscosity is used when solving for the flow inside the pellets. Select From material to use the viscosity defined in the material, or select User defined to enter a constant or expression in the corresponding input field.
Mixture Density
Select a way to define the density from the Mixture density list — Ideal gas or User defined:
•
For Ideal gas, the density is computed from the ideal gas law in the manner of:
Here M is the mean molar mass of the mixture and Rg is the universal gas constant. The absolute pressure, p, and temperature, T, used corresponds to the ones defined in the Model Inputs section.
•
For User defined enter a value or expression for the Mixture density ρ.
Convection
Select the source of the Velocity field u:
•
Select User defined to enter values or expressions for the velocity components. This input is always available.
•
Select a velocity field defined by a Fluid Flow interface that solves for the velocity of the fluid. For example, select Velocity field (spf) to use the velocity field defined by in a Single-Phase Flow, Laminar Flow interface with spf as the Name.
When the interface is used in a reacting flow multiphysics coupling, the velocity is automatically defined and the input is disabled.
Diffusion
Specify the species molecular and thermal diffusivities in fluid phase in the manner described for the Fluid node.
To account for the effect of porosity in the diffusivities, select an Effective diffusivity model — Millington and Quirk model, Bruggeman model, Tortuosity model, or No correction. Using one of the first four models, the effective transport factor, fe, is defined from the porosity and the fluid tortuosity factor in the manner of:
(3-13)
For No correction, the effective transport factor is set to one.
•
For the Millington and Quirk model, the effective transport factor is .
•
For the Bruggeman model, the effective transport factor is .
•
For the Tortuosity model, specify the tortuosity factor τF. Select either Isotropic to define a scalar value, or Diagonal or Symmetric to define anisotropic tensor values.
The species diffusivities and mobilities are automatically adjusted for porous media transport using the effective transport factor.
Migration in Electric Field
This section is available when the Migration in electric field checkbox is selected in the Transport Mechanisms section of the interface. Select the source of the Electric potential V:
•
Select User defined to enter a value or expression for the electric potential.
•
When present, select an electric potential defined by an AC/DC interface that is present in the model. For example, select Electric potential (ec) to use the electric field defined an Electric Currents interface ec.
Settings for the mobilities are needed for the Mixture-averaged and Fick’s law diffusion models. By default the mobility is set to be calculated based on the species diffusivities (adjusted by the Effective diffusivity model in the Diffusion section) using the Nernst–Einstein relation. To manually specify the mobilities, select User defined for the mobility um,w and enter one value for each species.
The temperature (if you are using mobilities based or the Nernst–Einstein relation) is taken from the Model Inputs section.
Pore Wall Interactions
In porous media, it is possible to include Pore Wall Interactions. This accounts for species collisions with the surrounding media, that is, the pore walls.
For the Fick’s law and Mixture-averaged diffusion models, the diffusion coefficient is corrected with the Wall diffusion coefficient in the following way
For the Maxwell–Stefan diffusion model, the following term is added to the species force balance
For weakly adsorbing gases, the Knudsen formula can be applied for computing the wall diffusivities, based on the Pore diameter dpore (SI unit: m). For other cases, choose User defined.
For isobaric systems featuring concentration gradients in porous media, concentration gradients may give rise to nonzero fluid velocity as a result of the wall interactions. This effect can be modeled using the Maxwell–Stefan diffusion model in combination Pore Wall Interactions. For this case the wall velocity variable uW (tcs.uW) can be used to contribute to the fluid momentum balance (either as a Contributing Velocity in Darcy’s law, or as a Volume Force in either the Brinkman Equations or Free and Porous Media Flow, Brinkman interfaces. The multiphysics Reacting Flow nodes incorporates this contribution from uW automatically.