3. Theory
4.1. Input Data
4.1.4. Catalyst Specification
To add a catalyst to the project, click on Aftertreatment TNG in the parameter tree with the right mouse button and select Catalyst: Insert from the submenu. To delete a catalyst from the project, click on the name of the catalyst (i.e. Catalyst[1]) with the right mouse button and select Remove from the submenu.
The specification of a catalyst comprises data over its geometry, its fluid and thermodynamic behavior and the conversion reactions taking place.
Copy from CAT allows the complete set of input data to be copied from Catalyst[X] to the present catalyst.
Figure 38. Copy from CAT Function
This input data is discussed in the following sub-sections.
4.1.4.1. Catalyst Specification
Select Catalyst specification in the parameter tree to access the following input fields:
4.1.4.1.1. Catalyst Specification
Typical Values
and Ranges Cell selection Supply a cell selection that defines the
geometry of the catalyst.
NoSelection (default) Inlet face selection Supply a face selection that defines the inlet
plane of the catalyst.
NoSelection (default) Outlet face selection Supply a face selection that defines the outlet
plane of the catalyst.
NoSelection (default) Monolith initialization
temperature
Determines the initial temperature of the catalyst.
293.15-1500 (K)
4.1.4.1.2. Catalyst Type: Square Cell Catalyst
Typical Values
and Ranges Cell density (cpsi) Determines the type of monolith: Number of
channels per in2 = N.
100-900 (1/in2)
Wall thickness Determines the thickness of the monolith's walls = Wall.
0.006-0.015 (in)
Washcoat thickness Determines the thickness of the washcoat =
WC. For activated Activate Washcoat Layer (WCL) Model a value greater than zero is required.
0-0.003 (m)
4.1.4.1.3. Catalyst Type: General Catalyst
Typical Values
and Ranges Open frontal area
(OFA)
Determines the open frontal area (= fluid volume fraction) of monolith ( ).
0.50-0.75 (-)
Hydraulic diameter
Determines the hydraulic diameter dhyd of the monolith.
0.001-0.005 (m)
102
4.1.4.2. Pressure Drop Specification
The pressure loss of the flow within a catalytic converter is determined by a flow-resistance model and corresponding parameters, which have to be supplied by the user. All necessary input data are summarized in the following sections.
4.1.4.2.1. Pressure Drop Models
Four different pressure drop models are available to calculate the pressure drop within the catalyst:
4.1.4.2.1.1. Tube Friction
The Tube Friction pressure drop model is especially applicable for flow through catalysts where empirical data of the pressure drop are not available. The pressure drop is based on the flow of fluid along the channels of the catalyst and the pressure drop is calculated due to the wall friction within pipes:
(328)
The notation used is as follows:
Pressure gradient within porous material
Mean hydraulic diameter =
A Non-circular cross-sectional area dh
Lper Wetted perimeter
wi Interstitial (local) velocity components in the tubes ( ) Laminar tube friction (HAGEN-POISEUILLE)
= 1.0 for cross sections with circular shapes = 0.89 for cross sections with quadratic shapes (user-supplied input)
Turbulent tube friction (BLASIUS)
Reynolds number
To activate the Tube friction pressure drop model, select Tube friction from the Pressure drop model pull-down menu to access the following input fields:
Typical Values
and Ranges Shape factor This specifies a shape factor for the laminar tube
friction. In the laminar case the tube friction is dependent on the shape of the cross-sectional area.
= 1.0 for cross sections with circular shapes.
= 0.89 for cross sections with quadratic shapes.
0.8-1 (-)
4.1.4.2.1.2. Forchheimer
If Forchheimer is chosen as pressure drop model, then the pressure gradients within the catalyst channels are calculated with following equation
(329)
The linear and the quadratic term take into account the viscous losses and the inertial losses, respectively, of the flow inside the catalyst channels.
Pressure gradient within porous material
i Viscous loss coefficient (x-, y- and z-components) (1/m2) Molecular (laminar) dynamic viscosity of domain fluid (Ns/m2)
wi Interstitial (local) velocity components in porous medium according to the local volume-fraction
Inertial loss coefficient (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 parameter ( ) 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 parameter ( i) defining the dependency between the velocity in the i direction, the laminar viscosity, and the pressure loss per unit length of porous material. Only if Undirected is selected for Porosity Type, direction dependent alpha values ( i) can be defined to simulate an unisotropic porous media.
0-107 (1/m2)
Instead of the direct specification of the pressure drop model parameters Alpha and Zeta, a set of corresponding measured pressure drop / velocity pairs and the corresponding reference density and viscosity could be specified. During a pre-processing step FIRE then fits Alpha and Zeta from this data.
Typical Values
and Ranges Reference Density This specifies the density of the medium which is
used in the experiment, where the pressure/velocity data specified in the table are evaluated.
0.5-50 (kg/m3)
Reference Viscosity
This specifies the viscosity of the medium which is used in the experiment, where the pressure/velocity data specified in the table are evaluated.
5.10-7-5.10-4(Ns/
m2)
104
Typical Values
and Ranges Interstitial velocity
w
This specifies the measured interstitial velocities (for fitting Alpha and Zeta, at least three different velocities are necessary).
0-50 (m/s)
Pressure Gradient dp/dx
This specifies the measured pressure gradients corresponding to the different velocities (for positive pressure drops over the monolith length, the pressure gradients are negative!)
-400000-0 (N/
m3)
4.1.4.2.1.3. Re formulation
If Re formulation is chosen as pressure drop model, the pressure gradients within the catalyst channels are calculated with following equation:
(330)
The notation used is as follows:
Pressure gradient within porous material
Mean hydraulic diameter =
A Non-circular cross-sectional area dh
Lper Wetted perimeter
wi Interstitial (local) velocity components in porous medium according to the local volume-fraction
General Re-number dependent correlation for the friction factor f
Reynolds Number
(square:0.89) Fanning friction factor
The friction factor f is described as a function of the Reynolds Number Re and changes depending on the flow regime (laminar, transition or turbulent):
(331) The bounds for the transition region from laminar to turbulent are set by Reynolds numbers of Relam = 2300 and Returb = 5000. In the turbulent region, fturb is considered as a constant input value. In the laminar region flam is given by
(332)
To activate the Re formulation pressure drop model, select Re formulation from the Pressure drop model pull-down menu to access the following input fields:
Typical Values
Coefficient a Input for the calculation of the general Re number dependent correlation for the friction factor.
64 (-)
Coefficient b Input for the calculation of the general Re number dependent correlation for the friction factor.
-1 (-)
Turbulent Turbulent Friction Factor 0.019
Channel Shape Input for the Fanning Friction Factor Square: 0.89 4.1.4.2.1.4. Power Law
For catalysts where empirical data of the pressure drop are available, the power law option may be suitable. The empirical pressure drop is used to prescribe the user-supplied pressure drop coefficients:
(333)
The notation used is as follows:
Pressure gradient within porous material
wi Interstitial (local) velocity components through porous material , Power law parameters
To activate the power law pressure drop model, select Power law from the Pressure drop model pull-down menu to access the following input fields:
Typical
Values and Ranges alpha-value This specifies the parameter defining the
dependency between velocity and the pressure loss per unit length of porous material.
0.1-1000 (-)
beta-value This specifies the parameter defining the
dependency between the velocity and the pressure loss per unit length of porous material.
0-2 (-)
4.1.4.2.1.5. 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.
4.1.4.2.2. Turbulence Treatment
Within the single channels of a catalytic converter, the turbulence kinetic energy k is calculated by the standard transport equation. To take into account the laminarization process within the single channels the dissipation rate is calculated from the algebraic equation shown below:
(334)
Crel is a relative turbulent length scale, which is multiplied with the hydraulic channel diameter dhyd and estimates the turbulence characteristics inside the monolith channels. Crel is a problem
106
Typical Values
and Ranges Rel. turb. length
scale Crel
Relative turbulent length scale which is multiplied with the hydraulic channel diameter to estimate the turbulence characteristics within monolith channels.
0.0001-0.02 (-)
4.1.4.3. Catalyst Physical Properties
Select Catalyst Physical Properties in the parameter tree to access the following input fields:
4.1.4.3.1. Catalyst Physical Properties
Typical Values
and Ranges Density Determines the bulk density of the monolith material
considering the volume in the pores.
400-2000 (kg/
m3) Thermal
conductivity
Determines the thermal conductivity of the monolith material (= bulk solid material considering the volume in the pores). 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 monolith material (= bulk solid material considering the volume in the pores). 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 axial direction. A value of 1.0 simulates an isotropic conductivity. A value of 0.5 would be a good choice for monoliths.
The anisotropic conduction factor is not used if the user-defined parameter ATM_ACTIV_RADIATION is specified and the current catalyst is selected as shown in the following figure. Then the effective thermal conductivity including radiation is used instead of the default anisotropic model (see section Anisotropic Heat Conduction Matrix page [10])
0-10 (-)
Figure 39. User Defined Parameters for Effective Heat Conduction Specification
4.1.4.3.2. Mass Transfer Model
FIRE allows to specify mass and heat transfer models independently. The following mass transfer models are available:
Typical Values and Ranges Sieder/Tate:
The Sieder/Tate correlation is used to calculate heat and mass transfer coefficients (Eq.78 page [29]).
Hawthorn:
The Hawthorn correlation is used to calculate heat and mass transfer coefficients (Eq.80 page [29]).
Hausen:
The Hausen correlation is used to calculate heat and mass transfer coefficients (Eq.79 page [29]).
constant:
Constant values which have to be defined by the user are taken as heat and mass transfer coefficients.
The Martin correlation is used to calculate heat and mass transfer coefficients (Eq.81 page [29]).
user:
The user can specify the transfer coefficients in use_cattra.f.
0.1-10 (m/s)
Mass Transfer Multiplier
Specify a factor by which the gas diffusion coefficient of the mass transfer model is scaled. Possible input is constant (mass transfer of every species is scaled in the same way) or table (mass transfer of selected species is scaled).
0.01-10 (-)
4.1.4.3.3. Heat Transfer Model
The following heat transfer models are available:
Typical Values
and Ranges Sieder/Tate:
The Sieder/Tate correlation is used to calculate heat and mass transfer coefficients (Eq.78 page [29]).
Hawthorn:
The Hawthorn correlation is used to calculate heat and mass transfer coefficients (Eq.80 page [29]).
Hausen:
The Hausen correlation is used to calculate heat and mass transfer coefficients (Eq.79 page [29]).
constant:
Constant values which have to be defined by the user are taken as heat and mass transfer coefficients.
108
user:
The user can specify the transfer coefficients in use_cattra.f.
Heat Transfer Multiplier
Specify a factor by which the heat transfer is scaled. 0.1-10 (-)
4.1.4.3.4. Catalyst Segmentation
FIRE provides a simple model to take into account perforations in the catalyst. If Repeat turbulent inlet region is activated, the distance to the channel inlet in the heat and mass transfer models (Sieder/Tate, Hausen, Hawthorn and Martin) is reset at every location of a perforation (see length l in section Transfer Coefficients page [28]).
Typical Values
and Ranges Repeating Length Determines the repeating length of the uniformly
distributed perforations.
0.001-0.2 (m)
4.1.4.3.5. External Heat Source
FIRE allows to specify constant heat sources for arbitrary cell selections. The specification is done for catalyst, reactive porosity and particulate filter separately. A warning check is performed, if a cell selection is specified more than one time.
Select Activate at External heat source and click New external heat source for every heat source selection to be specified:
Figure 40. Specification of External Heat Sources
Select HeatSource_X to open the window for the heat source specification. To delete a heat source select the check box at delete? and click Delete external heat source.
Figure 41. Specification of External Heat Sources
Typical Values
and Ranges Cell selection Determines the cell selections for which the constant
heat sources are applied. Click on to define table or formula data.
NoSelection
Heat Source Determines the quantity of heat introduced. 0-108 (W/m3)
4.1.4.4. Washcoat
Two different approaches are available to model heterogeneous reactions. In the standard model approach, the pore diffusion through the washcoat layer(s) is neglected. In the advanced model approach, pore diffusion is taken into account. Therefore, every washcoat layer is discretized in the direction perpendicular to the catalyst solid surface. The standard approach is equivalent to the advanced approach with only one washcoat layer of one computational cell. Therefore, the former specification at Conversion Reactions is now done at the My_Reaction branch. The advanced approach, taking into account pore diffusion through the washcoat layers, requires the specification of Transport Model and Reaction Model for each washcoat layer respectively.
Note:
For a deactivated button Activate Washcoat Layer (WCL) Model, the set-up of the Conversion Reactions is located in the first reaction branch My_Reaction. For the activated washcoat layer model one has to specify conversion reactions as well as a transport model for every layer separately.
Note:
The washcoat layer (WCL) model requires a Washcoat Thickness greater than zero to be specified at Catalyst Specification.
Figure 42. Washcoat - Activated Washcoat Layer (WCL) Model
If Activate Washcoat Layer (WCL) Model is selected, the following input data has to be specified:
Typical Values
and Ranges Layer Thickness Determines the dimensionless layer thickness
for every washcoat layer. The sum over all layer thicknesses must be 1.0. The dimensioned layer thickness is determined by multiplication with the Washcoat Thickness.
10-6-1 (-)
No. Grid Points Determines the number of computational cells of each washcoat layer.
1-10 (-)
110
Ref. WCL Volume Determines the specific reference washcoat layer thickness as described in section Pore Diffusion Model page [20]. With Calculate Spec.
Washcoat Layer Volume, a reasonable default value based on the geometrical specification is calculated.
0.01 (-)
Density Determines the bulk density of the washcoat layer materials. Together with the density specified at Catalyst Physical Properties, a solid mixture density is calculated.
400-2000 (kg/m3)
Reaction Model User-given name of the reaction model for each washcoat layer.
My_Reaction (default) Transport Model User-given name of the transport model for each
washcoat layer.
My_Transport (default) 4.1.4.4.1. Reaction Model (Conversion Reactions)
Several different reaction models are available. Either no reactions are taken into account, pre-defined reaction models are chosen or the application of user-defined models is possible.
If Activate Washcoat Layer (WCL) Model is selected, one has to specify a reaction model for each washcoat layer separately. More detailed information about the individual reaction mechanisms is given in Section DOC Catalyst Reactions page [77].
The pre-defined reaction models use global kinetic approaches given by Langmuir Hinshelwood equations and also transient mechanisms where adsorption and desorption steps are explicitly taken into account. All reaction models are supplied with default values for the individual kinetic parameters. The user can use the kinetic model and adjust all kinetic parameters. Note that the suggested reaction parameters have been successfully applied to several validation simulations, but they may have to be adjusted for use in other types of catalysts. In this case it is recommended to apply the pre-defined reaction model and to supply it with adequate reaction parameters.
The following pre-defined reaction models are available:
1. Diesel Oxidation Catalyst (DOC). This model is dedicated for DOCs comprising the three major oxidation reactions of CO, HC and NO.
2. Three Way Catalyst (TWC). This model is a dedicated TWC model comprising seven conversion reactions and surface storage reactions on cerium, rhodium and barium. By selecting specific reactions and adapting the related kinetic parameters, this model also can be applied to other catalysts such as DOCs.
3. Selective Catalytic Reduction (SCR), Steady Kinetics. This model comprises seven reaction rates which can be enabled/disabled individually for three different reaction sections in the catalyst. The SCR rates use Eley-Rideal mechanisms, thus it assumes steady-state conditions for the reaction steps of adsorption, catalytic reaction and desorption.
4. Selective Catalytic Reduction (SCR), Transient Kinetics. This model comprises nine reactions that can be enabled/disabled individually for three different reaction sections in the catalyst. The transient effect of ad-/desorption is explicitly taken into account.
5. NOx Trap Catalyst Reactions. This model comprises two conversion reactions for NO and the surface storage of NO2 on barium.
6. Lean NOx Trap. This model comprises ten conversion reactions and surface storage on cerium. Furthermore, it offers two approaches of storing nitric oxides: an ash core model approach, developed by ICVT Stuttgart, and a surface storage approach.
4.1.4.4.1.1. Diesel Oxidation Catalyst (DOC)
This reaction model offers a set of three oxidation reactions. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters.
More detailed information about this model is given in section DOC Catalyst Reactions page [77].
The different reactions can be en/disabled individually by clicking the corresponding check boxes. This enables sub-pages for the detailed specification of the reaction parameters.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of carbon monoxide.
The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5 Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R1: CO Oxidation
E1 - E5 Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
The Langmuir-Hinshelwood kinetic approach is commonly accepted in the literature for the oxidation of propane as representative of hydro carbons.
The denominator takes into account the different inhibition effects of all species involved and each reaction constant is evaluated using Arrhenius' law.
K1 - K5 Determines the frequency factors used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
R2: C3H6 Oxidation
E1 - E5 Determines the activation temperatures used in the pre-defined Langmuir-Hinshelwood conversion mechanism.
A reversible rate mechanism is commonly accepted in the
literature for the oxidation of nitric monoxide. Two rate approaches are available.
The reaction constant is evaluated using Arrhenius' law. The equilibrium constant is also a function of the temperature and is derived from the free Gibbs reaction enthalpy.
Approach 1
Approach 2
R3: NO Oxidation
K Determines the frequency factors used in the
112
E Determines the activation temperatures used in the pre-defined reversible power-law conversion mechanism.
A Determines the temperature dependency used in the pre-defined reversible power-law conversion mechanism.
4.1.4.4.1.2. Three Way Catalyst (TWC)
This reaction model offers a set of nine conversion reactions and surface storage mechanisms at three different surface sites. The rate equation and a set of default values of all kinetic parameters are given. The user can adjust all kinetic parameters.
More detailed information about this model is given in Section TWC Catalyst Reactions page [78]. The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. When enabled, several sub-pages for the detailed specification of the reaction parameters become enabled.
More detailed information about this model is given in Section TWC Catalyst Reactions page [78]. The different reactions can be enabled/disabled individually by clicking the corresponding check boxes. When enabled, several sub-pages for the detailed specification of the reaction parameters become enabled.