3. Theory
4.1. Input Data
4.1.6. Reactive Porosity Specification
To add a reactive porosity (RPOR) to the project, click on Aftertreatment TNG in the parameter tree with the right mouse button and select Reactive Porosity: Insert from the submenu. To delete a RPOR from the project, click on the name of the RPOR (i.e. RP[1]) with the right mouse button and select Remove from the submenu.
The specification of a reactive porosity comprises data over its geometry, its fluid and thermodynamic behavior and the conversion reactions taking place.
Figure 47. Reactive Porosity Specification Parameter Tree
Copy from RPOR allows the complete set of input data to be copied from RPOR[X] to the present reactive porosity.
Figure 48. Copy from RPOR Function
4.1.6.1. General Reactive Porosity Specification
Select RPOR specification in the parameter tree to access the following input fields.
4.1.6.1.1. Reactive Porosity Specification
Typical Values
and Ranges Cell selection Supply a cell selection that defines the geometry
of the reactive porosity.
NoSelection (default) Mesh requirements
fulfilled
Specify if the mesh requirements for the RPOR cell selection which are summarized in section Mesh Requirements page [175]
are fulfilled or not.
The options available are: Yes and NO.
Yes (default)
Specified inlet/outlet of reactive porosity
Select this option for directed porosities.
This option enables the user more heat and mass transfer models for selection including those are available for catalysts. Also, enables specification of an inlet and outlet face selection for additional 2D output.
Active (default)
Inlet face selection If the geometry allows it, supply a face selection NoSelection
166
porosity. Only available for activated Specified inlet/outlet of reactive porosity.
Outlet face selection If the geometry allows it, supply a face selection that defines the outlet plane of the reactive porosity. Only available for activated Specified inlet/outlet of reactive porosity.
NoSelection (default)
RPOR initialization temperature
Determines the initial temperature of the reactive porosity.
293.15-1500 (K)
4.1.6.1.2. Reactive Porosity Type
Typical Values
and Ranges Fluid volume fraction
(porosity)
Determines the fluid volume fraction (=porosity) of the RPOR porosity block.
0.1-0.95 (-)
Geometric surface area (GSA)
Determines the geometric surface area. 100-10000 (m2/ m3)
4.1.6.2. Pressure Drop Specification 4.1.6.2.1. Pressure Drop Models
Two different pressure drop models and a user access are available to calculate the pressure drop within the RPOR block which is an undirected porosity.
4.1.6.2.1.1. Forchheimer
If Forchheimer is chosen as pressure drop model, the pressure gradients within the reactive porosity are calculated with following equation
(335)
The linear term and the quadratic terms take into account the viscous and the inertial losses, respectively, of the flow through the reactive porosity.
Pressure gradient within porous material
i Viscous loss coefficient (x-, y- and z-components) (1/m2) Molecular (laminar) dynamic viscosity of domain fluid (N·s/m2)
wi Interstitial (local) velocity components in porous medium according to the local volume-fraction
Inertial loss coefficient (x-, y- and z-components) (1/m)
Domain fluid density
To activate the Forchheimer pressure drop model, select Forchheimer from the Pressure drop model pull-down menu to access the following input fields:
Typical Values
and Ranges
Zeta-value This specifies the direction dependent parameters ( ) defining the dependency between the velocity and the pressure loss per unit length of porous material.
0-100 (1/m)
Alpha value This specifies the direction dependent parameters ( i) defining the dependency between the velocity in the i direction, the laminar viscosity, and the pressure loss per unit length of porous material.
0-107 (1/m2)
4.1.6.2.1.2. Carman-Kozeny
If Carman-Kozeny is chosen as pressure drop model, then the pressure gradients within the reactive porosity is calculated with following equation
(336)
CCK is the Carman-Kozeny constant usually 150, is the molecular dynamic viscosity of domain fluid in (N·s/m2), ui is the superficial and wi is the interstitial velocity in (m/s), is the fluid volume fraction (porosity) in (-), and dp is the equivalent solid particle diameter.
To activate the Carman-Kozeny pressure drop model, select Carman-Kozeny from the Pressure drop model pull-down menu to access the following input fields:
Typical Values
and Ranges Model constant C1 Specifies the Carman-Kozeny constant. 0-1500 (-) Equivalent particle
diameter
Specifies the diameter of an equivalent solid sphere for calculating the pressure drop.
0.0001-0.005 (m)
4.1.6.2.1.3. User
If User is chosen as pressure drop model, the pressure drop is calculated according to the coding in the user routine usepor_pres.f.
4.1.6.2.2. Turbulence Treatment
Within the interstices of the porosity the turbulence kinetic energy k is calculated by the standard transport equation. To take into account the laminarization process within the pores, the
dissipation rate is calculated from the algebraic equation shown below:
(337)
Crel is a relative turbulent length scale, which is multiplied with the hydraulic pore diameter dhyd and estimates the turbulence characteristics inside the porosity block. Crel is a problem dependent quantity which has to be specified by the user.
Typical Values
and Ranges Rel. turb. length
scale Crel
Relative turbulent length scale Crel in equation Eq.337 page [167]
to estimate the turbulence characteristics within the pores of the block.
0.0001-0.02 (-)
Hydraulic pore Hydraulic pore diameter dhyd in equation Eq.337 page 0.0001-0.005 (m)
168
4.1.6.3. Physical Properties of Reactive Porosities
Select RPOR Physical Properties in the parameter tree to access the following input fields.
4.1.6.3.1. RPOR Physical Properties
Typical Values
and Ranges Density Determines the density of the reactive porosity
material.
400-2000 (kg/
m3) Thermal conductivity Determines the thermal conductivity of
the reactive porosity material. The thermal conductivity can either be specified as a constant value or as a table where the value changes as a function of temperature. Click on to define table data.
0.1-50 (W/(m·K))
Specific heat Determines the specific heat of the reactive porosity material. The specific heat can either be specified as a constant value or as a table where the value changes as a function of temperature.
Click on to define table data.
500-2000 (J/
(kg·K))
Anisotropic cond.
Factor
Corrects the diffusion coefficients of the solid temperature equation normal to a preferential block direction. The default value of 1.0 means that there is no preferential block direction.
This is reasonable for packed beds, granulated materials, etc. However, for blocks with
preferential flow direction one can specify an anisotropic conductivity factor different from 1.
Then the thermal conductivity matrix is calculated so that there is different thermal diffusion
between block direction and the direction normal to the block direction. The preferential block direction vector is calculated from the center points of inlet and outlet face selection. (Inlet and outlet face selections have to be specified).
0-10 (-)
4.1.6.3.2. Mass Transfer Models 4.1.6.3.2.1. Constant
Constant values which have to be defined by the user are taken as mass transfer coefficients.
Typical Values
and Ranges Mass transfer
coefficient
Constant value of the species mass transfer coefficient.
0.1-10 (m/s)
4.1.6.3.2.2. VDI Packed Bed
The VDI packed bed correlation is used to calculate mass transfer coefficients.
Typical Values and Ranges Equivalent particle
diameter
Specifies the diameter of an equivalent solid sphere of the granulated material.
0.0001-0.005 (m)
Shape factor mass transfer
Specifies the shape factor of the Sherwood number for the mass transfer according to fe in section VDI Packed Bed page [30].
1-2.1 (-)
4.1.6.3.2.3. User
The user can specify the transfer coefficients in use_cattra.f.
4.1.6.3.3. Heat Transfer Models 4.1.6.3.3.1. Constant
Constant values which have to be defined by the user are taken as heat transfer coefficients.
Typical Values
and Ranges Heat transfer
coefficient
Constant value of the heat transfer coefficient. 5-500 (W/(m2·K))
4.1.6.3.3.2. VDI Packed Bed
The VDI packed bed correlation is used to calculate heat transfer coefficients.
Typical Values
and Ranges Equivalent particle
diameter
Specifies the diameter of an equivalent solid sphere of the granulated material.
0.0001-0.005 (m)
Shape factor heat transfer
Specifies the shape factor of the Nusselt number for the heat transfer according to fe in section VDI Packed Bed page [30].
1-2.1 (-)
4.1.6.3.3.3. User
The user can specify the transfer coefficients in use_cattra.f.
4.1.6.3.4. RPOR Segmentation
FIRE provides a simple model to take into account perforations in the reactive porosities. The setup is the same as for catalysts explained in section Catalyst Segmentation page [108]
. 4.1.6.3.5. External Heat Source
FIRE allows to specify constant heat sources for arbitrary cell selections. The setup is the same as for catalysts explained in section External Heat Source page [108]
. 4.1.6.4. Conversion Reactions
FIRE offers the possibility to compute chemical reactions inside the reactive porosity. Either no reactions are taken into account or the application of user defined models is possible.
4.1.6.4.1. User Defined Kinetic Reactions
170
4.1.6.5. Reactive Porosity Reaction Solver Specification
Select RPOR Reaction Solver Specification in the parameter tree to access the following input fields.
4.1.6.5.1. Reaction Solver Parameters
Typical Values
Reactive porosity solver: max.
number of iterations
Specifies the maximum number of sub-iterations that the solver carries out for the catalytic reactions.
Normally no changes are required.
20000 (-)
Reactive porosity solver: relative tolerance
Specifies the relative tolerance for the solution of the reaction rate equation system. Normally no changes are required.
1e-05 (-)
Reactive porosity solver: absolute tolerance
Specifies the absolute tolerance for the solution of the reaction rate equation system. Normally no changes are required.
Normally the reaction rate equation system is solved at the beginning of a time step. Depending on the problem (i.e. chemical equilibrium problems) it can be necessary to solve it within the time step also, i.e.
specify 5 to solve it every 5th iteration for large time steps. A value of 0 turns off implicit solver calls.
0-100 (-)
Reaction solver block size
In order to speed up the solution of the chemical kinetics, the corresponding equation system is not solved for each cell separately but more cells are considered for each solver call. The number of cells is given here.
1-50 (-)
Consider enthalpy sources from chemical reactions
Activates/deactivates the consideration of the enthalpy sources from the catalytic reactions in the enthalpy equation for the solid material ('isothermal').
If deactivated, only the species sources from the catalytic reactions are considered.
Active (default)
Activate user model for
catalytic reactions (use_catmod.f)
Activates/deactivates the user function
use_catmod.f. This user function is called by the CFD solver instead of the RPOR reaction model. Here the user defines the source terms for the species transport equations and the enthalpy equation. It is typically used by advanced users who have their own models available and need full flexibility for their implementation. Please contact FIRE support for more information on use_catmod.f.
Inactive (default)
4.1.6.6. Spray Particle Interaction
Select Spray particle interaction in the parameter tree. If the Spray module is deactivated, the button Activate is greyed out, otherwise one clicks on Activate to access the following input fields.
4.1.6.6.1. Collision
Typical Values
and Ranges O'Rourke based Selects the spray-porosity collision submodel based
on the O'Rourke spray particle-particle collision model
On (default)
User Selects a user-defined spray-porosity collision submodel. The user submodel must be coded in the user function cyuse_rpor.f
Off (default)
Collision factor Specifies the user-defined collision factor c. The higher the value is, the more probable a droplet-porosity collision is.
1 (-) (default)
4.1.6.6.2. Interaction with solid
Typical Values
and Ranges Kuhnke based Selects the spray-porosity interaction submodel
based on the Kuhnke spray-wall interaction model.
On (default)
User Selects a user-defined spray-wall interaction
submodel. The user submodel must be coded in the user function cyuse_rpor.f
Off (default)
Maximum deviation angle
Specifies the maximum deviation angle max from the gas direction that a particle can undergo after a collision with the solid part of the porous medium.
65-85 (deg)
Number of secondary droplets
Specifies the number of secondary droplets ns generated after a splashing of a particle on the solid part of the porous medium.
2-4 (-)
4.1.6.6.3. Enhancement of evaporation
Typical Values
and Ranges Enhancement
factor
Specifies the multiplication factor used for the evaporation massflow of each component.
1-5 (-)
Energy
redistribution factor
Specifies the factor e used in the redistribution of the energy sink required to evaporate the liquid spray.
The higher the factor is, the more energy is extracted from the solid for the evaporation.
2-6 (-)
4.1.6.7. 2D Output Specification
Select 2D Output Specification in the parameter tree to access the following input fields.
172
Activates/deactivates the output of the mean porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Maximum porosity temperature
Activates/deactivates the output of the maximum porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Minimum porosity temperature
Activates/deactivates the output of the minimum porosity temperature to the .fla file and to the .fl2 file.
Active (default)
Solid heat capacities
Activates/deactivates the output of the minimum, maximum and mean value of the solid specific heat capacity (J/(kg·K)) of the RPOR to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on to define table data.
Inactive (default)
Solid thermal conductivities
Activates/deactivates the output of the minimum, maximum and mean value of the solid thermal
conductivity (W/(m·K)) of the RPOR to the .fla file and to the .fl2 file. Data is only written for temperature dependent values. Click on to define table data.
Inactive (default)
Gradient of solid temperature
Activates/deactivates the output of the maximum and mean value of the solid temperature gradient (K/m).
Inactive (default)
Activates/deactivates the output of the total pressure drop (Pa) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active.
Active (default)
4.1.6.7.3. Flow Uniformities
Typical Values
and Ranges Uniformity index Activates/deactivates the output of the uniformity index
(-) of the RPOR to the .fla file and to the .fl2 file.
Output is only available if Specified inlet/outlet of reactive porosity is active.
The definition of the uniformity index is described in the 2D results of the catalyst in section 2D Output Specification page [139]
.
Inactive (default)
Centricity index Activates/deactivates the output of the centricity index (-) of the RPOR to the .fla file and to the .fl2 file.
Output is only available if Specified inlet/outlet of reactive porosity is active.
Inactive (default)
The definition of the centricity index is described in the 2D results of the catalyst in section 2D Output Specification page [139]
. Max./Min. inlet
velocities
Activates/deactivates the output of minimum and the maximum inlet velocity (m/s), and the position of the maximum inlet velocity (m) of the RPOR to the .fla file and to the .fl2 file. The max. and min. inlet velocity are determined in the last non-porous fluid cell layer in front of the RPOR. Output is only available if Specified inlet/outlet of reactive porosity is active.
Inactive (default)
High and low speed inlet area
Activates/deactivates the output of high and low speed inlet areas (-) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/
outlet of reactive porosity is active.
The definitions of the high and low speed inlet areas are described in the 2D results of the catalyst in section 2D Output Specification page [139]
.
Inactive (default)
Tangential inlet velocity
Activates/deactivates the output of the mean, the minimum, and the maximum tangential velocity (m/s) of the RPOR inlet to the .fla file and to the .fl2 file.
Output is only available if Specified inlet/outlet of reactive porosity is active.
The tangential inlet velocity is described in the 2D results of the catalyst in section 2D Output Specification page [139]
.
Inactive (default)
Tangential inlet pressure gradient
Activates/deactivates the output of the mean, the minimum, and the maximum tangential pressure gradient (Pa/m) of the RPOR inlet to the .fla file and to the .fl2 file. Output is only available if Specified inlet/outlet of reactive porosity is active.
The tangential inlet pressure gradient is described in the 2D results of the catalyst in section 2D Output Specification page [139]
.
Inactive (default)
Gas hourly space velocity (GHSV)
Activates/deactivates the output of the gas hourly space velocity at operation conditions (GHSV) (1/h) and the gas hourly space velocity at norm conditions (GHSVn) (1/h) of the RPOR to the .fla file and to the .fl2 file. Output is only available if Specified inlet/
outlet of reactive porosity is active.
The definition of the GHSV is described in the 2D results of the catalyst in section 2D Output Specification page [139]
.
Inactive (default)
4.1.6.7.4. Conversions
Typical Values
and Ranges Species Activates/deactivates the output of the species' Active (default)
174
The species conversion is described in the 2D results of the catalyst in section 2D Output Specification page
[139]
. Surface coverage fraction
Activates/deactivates the output of the mean surface coverage fractions (-) of the surface species of the RPOR to the .fla file and to the .fl2 file.
Inactive (default)
Excess oxygen ratio at inlet
Activates/deactivates the output of the excess oxygen ratio at the inlet to the .fla file and to the .fl2 file. The excess oxygen ratio is described in the 2D results of the catalyst in section 2D Output Specification page [139]
. Output is only available if Specified inlet/outlet of reactive porosity is active.
Inactive (default)
Redox ratio at inlet
Activates/deactivates the output of the redox ratio at the inlet to the .fla file and to the .fl2 file. The redox ratio is described in the 2D results of the catalyst in section 2D Output Specification page [139]
. Output is only available if Specified inlet/outlet of reactive porosity is active.
Inactive (default)
4.1.7. 3D Output Specification
Select 3D Output Specification in the parameter tree to access the following input fields.
4.1.7.1. Standard
Typical Values
and Ranges Monolith
temperature
Activates/deactivates the output of the monolith temperature.
Active (default)
Surface coverage fraction
Activates/deactivates the output of the surface coverage fraction.
Activates/deactivates the output of the heat transfer coefficient.
Inactive (default)
Solid heat capacity
Activates/deactivates the output of the specific solid heat capacity.
Inactive (default)
Solid thermal conductivity
Activates/deactivates the output of the solid thermal conductivity.
Inactive (default)
Mass transfer coefficients
Activates/deactivates the output of the mass transfer coefficients for each species.
Inactive (default)
Rates of user defined chemical reaction
Activates/deactivates the output of the rates for each user defined reaction.
Inactive (default)
Production/
depletion rates of chemical species
Activates/deactivates the output of the reaction rates for each species.
Inactive (default)
Tangential inlet velocity
Activates/deactivates the output of the velocity components perpendicular to the monolith direction.
The tangential velocity is plotted only in the fluid layer in front of the monolith inlet.
Inactive (default)
Tangential inlet pressure gradient
Activates/deactivates the output of the pressure gradient in the direction perpendicular to the monolith direction. The tangential pressure gradient is plotted only in the fluid layer in front of the monolith inlet.
Inactive (default)
Gradient of solid temperature
Activates/deactivates the output of the solid temperature gradient.
Inactive (default)
4.1.7.3. Washcoat Layer
The washcoat layer (WCL) model is available for catalysts only.
Note:
3D WCL results are plotted for every specified washcoat layer depth (YdPos). This may lead to a huge number of results and large result files.
Typical Values
and Ranges WCL Mole
Fraction
Activates/deactivates the output of the species' mole fractions for all cells over all washcoat layers
Inactive (default)
WCL Mass Fraction
Activates/deactivates the output of the species' mass fractions for all cells over all washcoat layers
Inactive (default)
WCL Species Concentration
Activates/deactivates the output of the species' concentrations for all cells over all washcoat layers
Inactive (default)
WCL Effective Diffusion Coefficient
Activates/deactivates the output of the species' effective diffusion coefficients for all cells over all washcoat layers
Inactive (default)
WCL Species Rate
Activates/deactivates the output of the species rates in
Activates/deactivates the output of the species rates in