PDF
NOx Reduction in a Monolithic Reactor
Introduction
This example illustrates the detailed process modeling of selective catalytic reduction of NO with NH3, that occurs as flue gases pass through the channels of a monolithic reactor in the exhaust system of a diesel car. The optimal dosing of NH3 to minimize the NO emission, as found in Analysis of NOx Reaction Kinetics, is utilized.
Figure 1: Catalytic converters reduce the NOx levels in the exhaust gases emitted by combustion engines.
This application is set up in 3D to unravel the full space-dependency of the system.
Model Definition
The single channel model in Analysis of NOx Reaction Kinetics shows that temperature plays a central role in affecting the optimal dosing of NH3. Because the temperature distribution is sure to vary from channel to channel in a full reactor monolith, a full 3D reactor model is called for.
Model Geometry
The monolithic reactor has a modular structure made up of reactive channel blocks and supporting solid walls. The reactor is 0.36 m long with a 0.1 m radius. Each reactive channel has a cross-sectional area of 12.6 mm2, and the void fraction of a channel block is 0.75.
Figure 2: NO reduction chemistry takes place in the channel blocks. Supporting walls hold together the full reactor geometry. Symmetry reduces the modeling domain to one eighth of the full reactor geometry.
Model Equations
The present example takes a pseudo-homogeneous approach to model the hundreds of channels present in the monolith reactor. No mass is exchanged between channels, so each channel is described by 1D mass-transport equations. Furthermore, assume fully developed laminar flow in the channels, such that the average flow field is proportional to the pressure difference across the reactor. The fluid flow transports mass and energy only in the channel direction. The energy equation describes the temperature of the reacting gas in the channels, as well as the conductive heat transfer in the solid parts of the monolith structure. Because the temperature affects not only the reaction kinetics but also the density and viscosity of the reacting gas, the energy equation is what really connects the channels in the reactor structure, turning this into a 3D model.
Mass Transport
The mass balances describing transport and reaction in the monolith channels are given by diffusion-convection equations at steady state:
(1)
Here Di denotes the diffusion coefficient (SI unit: m2/s), ci is the species concentration (SI unit: mol/m3), and u equals the velocity vector (SI unit: m/s). The term  Ri (SI unit: mol/(m3·s)) corresponds to the species’ rate expression, which is a function of the reaction rates and the reaction stoichiometry.
Mass transport is only allowed in the direction of the channels, corresponding to direction of the x-axis in the 3D geometry used in this example. For the diffusive transport, this is accomplished by setting the y- and z-components of the diffusivity matrix to zero. The pressure-driven flow in the monolith is also defined in the direction of the x-axis, hereby restricting the convective mass transport to the channel direction as well. Each monolith channel thus behaves like a 1D plug flow model with included diffusion. These separate channel models are connected through the heat transfer equations for the reactor monolith.
Species concentrations are defined at the reactor inlet boundaries:
At the outlet, use the Outflow condition:
Fluid Flow
The flow of reacting gas through the monolith is modeled using a Darcy’s Law interface with the governing equations:
The monolith block is treated as a porous matrix with the effective permeability κ (SI unit: m2). Similarly to the diffusivity, the y- and z-components of the permeability matrix are set to zero. The density, ρ (SI unit: kg/m3), and viscosity, μ (SI unit: Pa·s), of the gas are assumed to be well represented by the temperature-dependent properties of nitrogen, as only relatively small concentrations of NO and NH3 are present.
Pressure conditions are set at the reactor inlet and outlet boundaries.
Heat Transfer
A single temperature equation describing the heat transfer in the porous monolith reactor can be written as:
(2)
where ρf (SI unit: kg/m3) is the fluid density, Cpf (SI unit: J/(kg·K)) is the fluid heat capacity, (ρCp)eff (SI unit: J/(m3·K)) is the effective volumetric heat capacity, and keff (SI unit: W/(m·K)) is the effective thermal conductivity. Furthermore, u (SI unit: m/s) is the fluid velocity field, which in this model is calculated in the Darcy’s Law interface. Q (SI unit: W/m3) is the heat source, which is due to exothermic chemical reactions:
Above, H1 and H2 (SI unit: J/(mol·K)) are the heats of reaction.
In the stationary case this implies
(3)
The effective conductivity of the solid-fluid system, keff, is related to the conductivity of the solid, ks, and to the conductivity of the fluid, kf, by
Here Θs denotes the solid material’s volume fraction, which is related to the volume fraction of the fluid Θf (or porosity) by:
The Heat Transfer interface sets up Equation 3 for a fluid domain. For the supporting walls in the reactor, only heat transfer by conduction applies:
where ks (SI unit: W/(m·K)) is the thermal conductivity for the solid walls.
The temperature is specified at the reactor inlet walls boundary:
,
and the Inflow condition, i.e.
is used at the inlet of the geometry. ΔH (SI unit: J/(kg)) is the sensible enthalpy.
At the outlet, use the Outflow condition:
For the reactor walls the heat flux through the boundaries is given by
where h (SI unit: W/(m2·K)) denotes the heat transfer coefficient, and Tamb (K) equals the ambient temperature.
As mentioned, the temperature affects not only reaction kinetics but also the density and viscosity of the reacting gas. In this way the heat transfer equation connects the channels in the reactor structure.
Thermodynamic and Transport Properties
Accurate thermodynamic data is required as input to energy balance equations, both in the plug flow model and the 3D monolith model (Equation 2). In addition to thermodynamic properties, the model equations also require transport properties to accurately describe the space dependent reactor model. For instance, the mass transport (Equation 1) needs species specific diffusion coefficients as input.
The Thermodynamics feature provides all necessary properties for the simulation. Different models are available for calculation of thermal and transport properties (see Thermodynamic Models and Theory). The viscosity of the system is calculated based on the Brokaw model. The thermal conductivity and diffusivity are calculated from Kinetic Theory and Fuller Schettler Giddings, respectively.
In this model, to simplify the problem, nitrogen is modeled as a solvent. This means that the gas properties are not composition dependent. Another way to speed up the calculations, also used in this model, is to use Generate Material from Thermodynamics. Information about how to efficiently use the Thermodynamics feature is available at Using Thermodynamic Properties.
Results
Figure 3 shows the conversion of NO in the monolith channel blocks. The isosurfaces in the plot show how a channel’s performance depends on its position in the reactor, clearly pointing to the 3D nature of the problem.
Figure 3: Isosurfaces showing the conversion of NO in the reactor. Fluid flow from left to right.
The average conversion at the outlet is 97% (not seen in Figure 3, see Modeling Instructions, Surface Average, page 25). This is somewhat lower than the 99% conversion predicted by the single channel model (see results from Analysis of NOx Reaction Kinetics).
The individual channels, although they do not exchange mass, are connected through the temperature distribution in the reactor. The temperature affects both the flow velocity of the reacting gas as well as the reaction rates. Cross sections of the reactor temperature are shown in Figure 4.
Figure 4: Temperature distribution in cross sections of the reactor. Fluid flow from left to right.
The exothermic reactions increase the temperature in the central parts of the reactor, while the temperature in the outer parts is decreased through heat loss to the surroundings. The maximum temperature calculated for the 3D reactor is 544 K (see Modeling Instructions, Volume Maximum, page 25), which is about 10 K higher than for the single channel model. The effect of the relatively high thermal conductivity of the supporting walls is clearly visible.
A seen from the initial kinetic analysis in Analysis of NOx Reaction Kinetics, elevated temperatures have a detrimental effect on the selectivity, leading to ammonia getting oxidized rather than to be consumed in the desired NO reducing reaction. The connection between temperature and selectivity is clearly seen in the final plot in Figure 5, where both S and T are shown. Here, symmetry is used to visualize the full monolithic structure.
Figure 5: Selectivity and temperature in slices throughout the monolith reactor. Fluid flow from left to right..
Figure 5 shows that channels in the relatively cold region near the reactor outer surface display high selectivity throughout, whereas channels in the region close to the center see selectivity falling off comparatively fast. The fact that r1/r2 is greater than 1 throughout the whole reactor means that the desired reducing reaction is favored. The inclusion of Darcy’s velocity field aids in showing the flow direction through the reactor.
References
1. G. Schaub, D. Unruh, J. Wang, and T. Turek, “Kinetic analysis of selective catalytic NOx reduction (SCR) in a catalytic filter,” Chem.Eng. and Processing, vol. 42, no. 5, pp. 365–371, 2003.
Application Library path: Chemical_Reaction_Engineering_Module/Tutorials/monolith_3d
Modeling Instructions
Root
Open the Application Library file monolith_kinetics.mph in the following way:
1
From the File menu, choose Open.
2
From the Application Libraries root, browse to the folder Chemical_Reaction_Engineering_Module/Tutorials and double-click the file monolith_kinetics.mph.
Start by changing the molar NH3:NO ratio, X0, to the optimal value found in the investigation of the reaction kinetics. Continue by adding the model geometry settings to the table.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
X0
1.35
1.35
Ratio NH3 to NO at inlet
por
0.75
0.75
Gas phase volume fraction
d_N2_in
0.65[kg/m^3]
0.65 kg/m³
Density of nitrogen at T_in
A_in
3359.9 [mm^2]
0.0033599 m²
Inlet cross sectional area
M0_in
v_av*por*A_in*d_N2_in
4.9139E-4 kg/s
Mass flow inlet
Component 1 (comp1)
In the Model Builder window, expand the Component 1 (comp1) node.
Reaction Engineering (re)
To simplify the problem of calculating the transport properties, nitrogen is set to solvent from here on.
Species: N2
1
In the Model Builder window, expand the Component 1 (comp1)>Reaction Engineering (re) node, then click Species: N2.
2
In the Settings window for Species, locate the Species Type section.
3
From the list, choose Solvent.
In the next phase of the example you prepare to set up a 3D model of the monolithic reactor, including mass transport and reaction, heat transfer, and fluid flow.
Generate Space-Dependent Model 1
The Generate Space-Dependent Model feature creates a link between the plug flow channel model and the full 3D monolith model. It allows you to transfer reaction kinetics, thermodynamics, and transport properties set up in the Reaction Engineering feature to the physics interfaces describing space and time-dependent systems.
1
In the Reaction Engineering toolbar, click  Generate Space-Dependent Model.
2
In the Settings window for Generate Space-Dependent Model, locate the Physics Interfaces section.
3
Find the Chemical species transport subsection. From the list, choose Transport of Diluted Species in Porous Media: New.
4
Find the Fluid flow subsection. From the list, choose Darcy’s Law: New.
5
Find the Heat transfer subsection. From the list, choose Heat Transfer in Porous Media: New.
6
Locate the Space-Dependent Model Generation section. Click Create/Refresh.
3D Model
1
In the Model Builder window, click Component 2 (comp2).
2
In the Settings window for Component, type 3D Model in the Label text field.
Definitions (comp2)
Variables 2
1
In the Model Builder window, expand the 3D Model (comp2) node.
2
Right-click 3D Model (comp2)>Definitions and choose Variables.
3
In the Settings window for Variables, locate the Variables section.
4
In the table, enter the following settings:
Name
Expression
Unit
Description
S
chem.r_1/chem.r_2
 
Selectivity
a
a0*exp(-E0/(R_const*chem.T))
m³/mol
Concentration correction
Geometry 1(3D)
Now import a file with the reactor geometry. Symmetry reduces the modeling domain to one eighth of the full monolith.
1
In the Geometry toolbar, click  Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file monolith_3d_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
Global Definitions
Transport properties need to be calculated for the space-dependent 3D model. Assuming nitrogen as solvent, generate a material node from Thermodynamics.
Gas System 1 (pp1)
1
In the Model Builder window, expand the Global Definitions>Thermodynamics node.
2
Right-click Global Definitions>Thermodynamics>Gas System 1 (pp1) and choose Generate Material.
Select Phase
1
Go to the Select Phase window.
2
Click Next in the window toolbar.
Select Species
1
Go to the Select Species window.
2
Click  Add All.
3
Find the Material composition subsection. In the table, enter the following settings:
Species
Mole fraction
ammonia
0
nitrogen
1
nitrogen oxide
0
oxygen
0
water
0
4
Click the Mass fraction button.
5
Click Next in the window toolbar.
Select Properties
1
Go to the Select Properties window.
2
In the list, select Diffusion coefficient at infinite dilution (m^2/s).
3
Click  Add Selected.
4
Find the Select solvent subsection. From the Select solvent list, choose nitrogen.
5
Click Next in the window toolbar.
Define Material
1
Go to the Define Material window.
Add the material to the global Materials node. This is needed in order to use it in a Porous Material. Additionally, create interpolation functions for the material properties. This provides faster property evaluations.
2
From the Component list, choose Global.
3
From the Function type list, choose Interpolation.
4
In row Temperature, set High to 673.
5
Click Finish in the window toolbar.
Global Definitions
Gas: Nitrogen
1
In the Model Builder window, expand the Global Definitions>Materials node, then click Gas: ammonia(0)-nitrogen(1)-nitrogen oxide(0)-oxygen(0)-water(0) 1 (pp1mat1).
2
In the Settings window for Material, type Gas: Nitrogen in the Label text field.
Solid: Monolith Material
1
In the Model Builder window, right-click Materials and choose Blank Material.
2
In the Model Builder window, expand the Material 1 (mat1) node, then click Basic (def).
3
In the Settings window for Property Group, locate the Output Properties section.
4
Click  Select Quantity.
5
In the Physical Quantity dialog box, type density in the text field.
6
Click  Filter.
7
In the tree, select General>Density (kg/m^3).
8
Click OK.
9
In the Settings window for Property Group, locate the Output Properties section.
10
Click  Select Quantity.
11
In the Physical Quantity dialog box, type heatcapacity in the text field.
12
Click  Filter.
13
In the tree, select Transport>Heat capacity at constant pressure (J/(kg*K)).
14
Click OK.
15
In the Settings window for Property Group, locate the Output Properties section.
16
Click  Select Quantity.
17
In the Physical Quantity dialog box, type thermalconductivity in the text field.
18
Click  Filter.
19
In the tree, select Transport>Thermal conductivity (W/(m*K)).
20
Click OK.
21
In the Settings window for Property Group, locate the Output Properties section.
22
In the table, enter the following settings:
Property
Variable
Expression
Unit
Size
Density
rho
2970[kg/m^3]
kg/m³
1x1
Heat capacity at constant pressure
Cp
975[J/kg/K]
J/(kg·K)
1x1
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
35[W/m/K]
W/(m·K)
3x3
23
In the Model Builder window, right-click Material 1 (mat1) and choose Rename.
24
In the Rename Material dialog box, type Solid: Monolith Material in the New label text field.
25
Click OK.
Now add a Porous Material to be used in the monolith channels.
Materials
Porous Material 1 (poromat1)
1
In the Materials toolbar, click  More Materials and choose Local>Porous Material.
2
In the Settings window for Porous Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Channel blocks.
Fluid 1 (poromat1.fluid1)
Right-click Porous Material 1 (poromat1) and choose Fluid.
Note that the global nitrogen material is used by this node.
Solid 1 (poromat1.solid1)
1
In the Model Builder window, right-click Porous Material 1 (poromat1) and choose Solid.
2
In the Settings window for Solid, locate the Solid Properties section.
3
From the Material list, choose Solid: Monolith Material (mat1).
4
In the θs text field, type 1-por.
Add a material for the monolith walls by linking to the global monolith material.
Walls
1
In the Materials toolbar, click  More Materials and choose Local>Material Link.
2
In the Settings window for Material Link, locate the Geometric Entity Selection section.
3
From the Selection list, choose Supporting walls.
4
Locate the Link Settings section. From the Material list, choose Solid: Monolith Material (mat1).
5
In the Label text field, type Walls.
In the next stage of the modeling process you will set up the physics interfaces describing the mass transport, heat transfer, and fluid flow in the monolithic reactor.
Transport of Diluted Species in Porous Media (tds)
1
In the Model Builder window, under 3D Model (comp2) click Transport of Diluted Species in Porous Media (tds).
2
In the Settings window for Transport of Diluted Species in Porous Media, locate the Domain Selection section.
3
From the Selection list, choose Channel blocks.
Porous Medium 1
In the Model Builder window, expand the Transport of Diluted Species in Porous Media (tds) node.
Fluid 1
1
In the Model Builder window, expand the Porous Medium 1 node, then click Fluid 1.
2
In the Settings window for Fluid, locate the Convection section.
3
From the u list, choose Darcy’s velocity field (dl).
The mass transport model for the monolith channels assumes that there is only diffusive mass transport in the axial direction of the reactor, here along the x-axis. This can be accomplished by specifying the diffusivity only in the first element of the diagonal diffusion matrix. This is done in the following way:
4
Locate the Diffusion section. From the Source list, choose Material.
For each species, change from Isotropic to Diagonal, for the Fluid diffusion coefficient.
5
From the list, choose Diagonal.
6
In the DF,cH2O table, enter the following settings:
pp1mat1.df4.D11
0
0
0
0
0
0
0
0
7
From the list, choose Diagonal.
8
In the DF,cNH3 table, enter the following settings:
pp1mat1.df1.D11
0
0
0
0
0
0
0
0
9
From the list, choose Diagonal.
10
In the DF,cNO table, enter the following settings:
pp1mat1.df2.D11
0
0
0
0
0
0
0
0
11
From the list, choose Diagonal.
12
In the DF,cO2 table, enter the following settings:
pp1mat1.df3.D11
0
0
0
0
0
0
0
0
13
From the Effective diffusivity model list, choose No correction.
The entered expressions were set up by the Generate Material wizard and they can be found under the Global Definitions>Materials>Gas: Nitrogen (pp1mat1) node. D11 represents the xx-component in the diffusivity matrix.
Porous Matrix 1
The porosity is by default defined from the Porous Material.
This model is highly nonlinear due to the reaction kinetics. In this case, to solve all the physics simultaneously, starting from a non-reacting system leads to a more robust simulation. To achieve this set the initial concentration to zero.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the cH2O text field, type 0.
4
In the cNH3 text field, type 0.
5
In the cNO text field, type 0.
6
In the cO2 text field, type 0.
Features defining reaction rates and inlet concentrations have also been set up during the model generation procedure. Definitions correspond to the reactor conditions specified for the plug flow channel model. Make sure that the Inlet and Outlet features are assigned to the proper domains and boundaries in the 3D reactor.
Inflow 1
1
In the Model Builder window, click Inflow 1.
2
In the Settings window for Inflow, locate the Boundary Selection section.
3
From the Selection list, choose Inlet.
Outflow 1
1
In the Model Builder window, click Outflow 1.
2
In the Settings window for Outflow, locate the Boundary Selection section.
3
From the Selection list, choose Outlet.
Heat Transfer in Porous Media 1 (ht)
Next, set up the Heat Transfer interface.
Fluid 1
1
In the Model Builder window, expand the Porous Medium 1 node, then click Fluid 1.
2
In the Settings window for Fluid, locate the Heat Convection section.
3
From the u list, choose Darcy’s velocity field (dl).
4
Locate the Heat Conduction, Fluid section. From the kf list, choose From material.
5
Locate the Thermodynamics, Fluid section. From the ρf list, choose From material.
6
From the Cp,f list, choose From material.
7
From the γ list, choose From material.
Note that the fluid properties are now defined by the corresponding node of the Porous Material.
Porous Matrix 1
1
In the Model Builder window, click Porous Matrix 1.
2
In the Settings window for Porous Matrix, locate the Matrix Properties section.
3
From the Define list, choose Solid phase properties.
4
Locate the Heat Conduction, Porous Matrix section. From the ks list, choose User defined. From the list, choose Diagonal.
Specifying the diagonal thermal conductivity elements allows you to represent anisotropic conductive heat transfer in the channel blocks.
5
In the ks table, enter the following settings:
0.13[W/m/K]
0
0
0
0.25[W/m/K]
0
0
0
0.25[W/m/K]
Note that apart from the conductivity, the matrix properties are now defined by the Solid node added to the Porous Material.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T_in.
Heat Source 1
Associate the Heat Source to the exothermic chemistry within the channel blocks. Note that the feature and the expressions describing the heat source are generated by the Generate Space-Dependent Model feature, linking the 3D monolith model to the plug flow model.
1
In the Model Builder window, click Heat Source 1.
2
In the Settings window for Heat Source, locate the Domain Selection section.
3
From the Selection list, choose Channel blocks.
Temperature 1
1
In the Model Builder window, click Temperature 1.
2
In the Settings window for Temperature, locate the Boundary Selection section.
3
From the Selection list, choose Inlet walls.
Outflow 1
1
In the Model Builder window, click Outflow 1.
2
In the Settings window for Outflow, locate the Boundary Selection section.
3
From the Selection list, choose Outlet.
Solid 1
1
In the Physics toolbar, click  Domains and choose Solid.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Supporting walls.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Reactor surface.
4
Locate the Heat Flux section. Click the Convective heat flux button.
5
In the h text field, type 10[W/(m^2*K)].
6
In the Text text field, type T_amb.
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Outlet walls.
4
Locate the Heat Flux section. Click the Convective heat flux button.
5
In the h text field, type 1.
6
In the Text text field, type T_amb.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, locate the Boundary Selection section.
3
From the Selection list, choose Symmetry.
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Upstream Properties section.
3
In the Tustr text field, type T_in.
4
Locate the Boundary Selection section. From the Selection list, choose Inlet.
Darcy’s Law 1 (dl)
1
In the Model Builder window, under 3D Model (comp2) click Darcy’s Law 1 (dl).
2
In the Settings window for Darcy’s Law, locate the Domain Selection section.
3
From the Selection list, choose Channel blocks.
Fluid and Matrix Properties 1
1
In the Model Builder window, expand the Darcy’s Law 1 (dl) node, then click Fluid and Matrix Properties 1.
2
In the Settings window for Fluid and Matrix Properties, locate the Fluid Properties section.
3
From the Fluid material list, choose Gas: Nitrogen (pp1mat1).
4
From the ρ list, choose From material.
5
From the μ list, choose From material.
6
Locate the Matrix Properties section. From the Porous material list, choose Solid: Monolith Material (mat1).
7
From the εp list, choose User defined. In the associated text field, type 1-por.
8
From the κ list, choose User defined. From the list, choose Diagonal.
9
In the κ table, enter the following settings:
3.3e-7[m^2]
0
0
0
0
0
0
0
0
Inlet 1
1
In the Model Builder window, click Inlet 1.
2
In the Settings window for Inlet, locate the Boundary Selection section.
3
From the Selection list, choose Inlet.
4
Locate the Boundary Condition section. From the list, choose Mass flow.
5
Locate the Mass Flow section. In the M0 text field, type M0_in.
Outlet 1
1
In the Model Builder window, click Outlet 1.
2
In the Settings window for Outlet, locate the Boundary Selection section.
3
From the Selection list, choose Outlet.
4
Locate the Boundary Condition section. From the list, choose Pressure.
This completes the setup of the model equations describing the reacting flow and heat transfer in the monolith. Before solving the problem, the geometry needs to be meshed.
Mesh 1
First create a Free Triangular mesh at the reactor inlet and then, complete the mesh by sweeping in the axial direction of the reactor.
Free Triangular 1
1
In the Mesh toolbar, click  Boundary and choose Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose Inlet end.
Size 1
1
Right-click Free Triangular 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Selection list, choose Inlet walls.
4
Locate the Element Size section. Click the Custom button.
5
Locate the Element Size Parameters section. Select the Maximum element size check box.
6
In the associated text field, type 2.2.
7
Select the Resolution of narrow regions check box.
8
In the associated text field, type 0.85.
9
Click  Build All.
Size 2
1
In the Model Builder window, right-click Free Triangular 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Edge.
4
Select Edges 5 and 17 only.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section. Select the Maximum element size check box.
7
In the associated text field, type 5.
8
Click  Build All.
Swept 1
In the Mesh toolbar, click  Swept.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
In the Number of elements text field, type 50.
4
Click  Build All.
Study 2
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, locate the Study Settings section.
3
Clear the Generate default plots check box.
4
In the Home toolbar, click  Compute.
Follow these instruction to generate Figure 3 through Figure 5.
Results
Follow these instruction to generate Figure 3.
Conversion 3D Model
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Conversion 3D Model in the Label text field.
3
Locate the Color Legend section. From the Position list, choose Left.
Isosurface 1
1
Right-click Conversion 3D Model and choose Isosurface.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type (F_NO_in/vrate-cNO)/(F_NO_in/vrate).
4
Locate the Levels section. In the Total levels text field, type 20.
5
Click the  Zoom Extents button in the Graphics toolbar.
6
In the Conversion 3D Model toolbar, click  Plot.
Follow these instruction to generate Figure 4.
Temperature 3D Model
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Temperature 3D Model in the Label text field.
3
Locate the Color Legend section. From the Position list, choose Left.
Slice 1
1
Right-click Temperature 3D Model and choose Slice.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type T.
4
Locate the Plane Data section. In the Planes text field, type 10.
5
Click the  Zoom Extents button in the Graphics toolbar.
6
In the Temperature 3D Model toolbar, click  Plot.
To plot the full monolithic structure seen in Figure 5, complete the following steps.
Monolith
1
In the Results toolbar, click  More Datasets and choose Sector 3D.
2
In the Settings window for Sector 3D, type Monolith in the Label text field.
3
Locate the Axis Data section. In row Point 2, set X to 1.
4
In row Point 2, set Z to 0.
5
Locate the Symmetry section. In the Number of sectors text field, type 8.
6
From the Sectors to include list, choose Manual.
7
From the Transformation list, choose Rotation and reflection.
8
Find the Radial direction of reflection plane subsection. In the X text field, type 0.
9
In the Z text field, type 1.
10
Click to expand the Advanced section. Select the Define variables check box.
Temperature sector
1
Right-click Monolith and choose Duplicate.
2
In the Settings window for Sector 3D, type Temperature sector in the Label text field.
3
Locate the Symmetry section. In the Start sector text field, type 2.
4
In the Number of sectors to include text field, type 1.
Monolith view
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Monolith view in the Label text field.
3
Locate the Data section. From the Dataset list, choose Monolith.
4
Locate the Plot Settings section. Clear the Plot dataset edges check box.
5
Locate the Color Legend section. Select the Show units check box.
Selectivity
1
Right-click Monolith view and choose Slice.
2
In the Settings window for Slice, type Selectivity in the Label text field.
3
Locate the Expression section. In the Expression text field, type S.
4
Select the Description check box.
5
Locate the Plane Data section. From the Entry method list, choose Coordinates.
6
Click  Range.
7
In the Range dialog box, choose Number of values from the Entry method list.
8
In the Start text field, type 0.
9
In the Stop text field, type L.
10
In the Number of values text field, type 5.
11
Click Replace.
12
In the Monolith view toolbar, click  Plot.
Temperature
1
Right-click Selectivity and choose Duplicate.
2
In the Settings window for Slice, type Temperature in the Label text field.
3
Locate the Data section. From the Dataset list, choose Temperature sector.
4
Locate the Expression section. In the Expression text field, type T.
5
In the Description text field, type Temperature.
6
Locate the Coloring and Style section. From the Color table list, choose HeatCameraLight.
Selectivity
1
In the Model Builder window, click Selectivity.
2
In the Settings window for Slice, click to expand the Quality section.
3
From the Smoothing list, choose None.
Filter 1
1
Right-click Selectivity and choose Filter.
2
In the Settings window for Filter, locate the Element Selection section.
3
In the Logical expression for inclusion text field, type sec1number!=2.
4
In the Monolith view toolbar, click  Plot.
Cut Plane 1
1
In the Results toolbar, click  Cut Plane.
2
In the Settings window for Cut Plane, locate the Data section.
3
From the Dataset list, choose Monolith.
4
Locate the Plane Data section. From the Plane list, choose YX-planes.
5
In the Z-coordinate text field, type 2.
6
Click  Plot.
Arrow Surface 1
1
In the Model Builder window, right-click Monolith view and choose Arrow Surface.
2
In the Settings window for Arrow Surface, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose 3D Model (comp2)>Darcy’s Law 1>Velocity and pressure>dl.u,dl.v,dl.w - Darcy’s velocity field.
5
Locate the Coloring and Style section. From the Arrow type list, choose Cone.
6
Select the Scale factor check box.
7
In the associated text field, type 80.
8
In the Monolith view toolbar, click  Plot.
Monolith view
Click the  Go to Default View button in the Graphics toolbar.
The final step is to derive values for the outlet average conversion, as well as the highest temperature reached in the reactor.
Surface Average 1
1
In the Results toolbar, click  More Derived Values and choose Average>Surface Average.
2
In the Settings window for Surface Average, locate the Selection section.
3
From the Selection list, choose Outlet.
4
Locate the Expressions section. Click  Clear Table.
5
In the table, enter the following settings:
Expression
Unit
Description
(F_NO_in/vrate-chem.c_NO)/(F_NO_in/vrate)
1
Conversion
6
Click  Evaluate.
Volume Maximum 1
1
In the Results toolbar, click  More Derived Values and choose Maximum>Volume Maximum.
2
In the Settings window for Volume Maximum, locate the Selection section.
3
From the Selection list, choose All domains.
4
Click  Evaluate.