models.chem.monolith thermal stress

7/28/2019 Models.chem.Monolith Thermal Stress

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Solved with COMSOL Multiphysics 4.3b

2 0 1 3 C O M S O L 1 | T H E R M A L S T R E S S E S I N A M O N O L I T H I C R E A C T O R

Th e rma l S t r e s s e s i n a Mono l i t h i c

R e a c t o r

Introduction

The removal of pollutants from high-temperature gases is often required in

combustion processes. In this example, the selective reduction of NOx by ammonia

occurs as flue gas passes through the channels of a monolithic reactor. The chemicalreactions take place on a V2O5/TiO2 catalyst. The full reactor is a modular structure

made up of blocks of reactive channels and supporting solid walls.

Channel block

Inlet

Outlet

Supporting wall

Reactive channel

Figure 1: NOx reduction chemistry takes place in the channel blocks. Supporting walls holdtogether the full reactor geometry. Symmetry reduces the modeling domain to one eighth of

the full reactor geometry.

Thermal gradients occur in the unit as heat is released by the chemical reactions while

at the same time, heat is lost to the surroundings. This model investigates the thermal

stresses in the reactor induced by the varying temperature field and the different

material properties in the modular structure.


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2 | T H E R M A L S T R E S S E S I N A M O N O L I T H I C R E A C T O R 2 0 1 3 C O M S O L

Note: This model requires the Chemical Reaction Engineering Module and the

Structural Mechanics Module.

Model Definition

A separate model, NOx Reduction in a Monolithic Reactor, solves the coupled mass

transport, heat transfer, and fluid flow equations representing the NOx reduction

process in the reactor. Load this model from the Model Library of the Chemical

Reaction Engineering Module and extend it by coupling the temperature field to a

structural mechanics analysis to evaluate the thermal stresses in the reactor.

S U M M A R Y O F T H E R E A C T I V E T R A N S P O R T M O D E L

A pseudo homogeneous approach is used to model the reactive transport in the

hundreds of channels present in the monolith reactor. As no mass is exchanged

between channels, each channel is described by 1D mass transport equations.Furthermore, fully developed laminar flow is assumed 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 monolith structure and the supporting walls. As the temperature

affects not only 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.

The following reactions summarize the NO chemistry in the reactor (Ref. 1):

(1)

(2)

Both reactions are exothermic and produce heat according to:

(3)

where r1 and r2 are the temperature dependent reaction rates (mol/(m3s)). The heats

of reaction areH2 = -1.63106 J/mol andH2 = -1.2610

6 J/mol.

4NO 4N2O2+ 6H2O+4NH3+

+ 3O2 2N2 6H2O+4NH3

Q r1H1 r2H2=
http://models_chem.pdf/http://models_chem.pdf/


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Figure 2 shows the conversion of NO in the monolith channel blocks. The average

conversion at the outlet is 97.5 %. The isosurfaces in the plot show how a channels

performance depends on its position in the reactor, clearly pointing to the 3D natureof the problem.

Figure 2: Isosurfaces showing the conversion of NO in the reactor.


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Cross sections of the reactor temperature are shown in Figure 3.

Figure 3: Temperature distribution in cross sections of the reactor.

The exothermic reactions increase the temperature in the central parts of the reactor,

while the temperature is decreased through heat loss to the surroundings. The effect

of the relatively high thermal conductivity of the supporting walls is clearly visible.

T H E R M A L E X P A N S I O N

The Solid Mechanics interface has the equations and features required for stress

analysis and general linear and nonlinear solid mechanics, solving for the structural

displacements. Thermal loads are introduced into the constitutive equations according

to:

(4)

whereis the stress,D is the elasticity matrix, and represents the strain. The equation

for the thermal strain is given by:

(5)

where is the coefficient of thermal expansion, Tis the temperature (K), and Trefis

the strain-free reference temperature (K).

Del 0+ D th 0( ) 0+= =

th T T ref( )=


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Reactor Materials

As mentioned above, the reactor treated in this example has a modular structure and

is made up of blocks of reactive channels and supporting solid walls. Both materials aretreated as being linear elastic. The wall material is isotropic while the channel block

material is othotropic. Their properties are summarized in the tables below:

SUPPORTING WALLS

Youngs modulus 1.5 GPa

Poissons ratio 0.2

Thermal expansion coefficient 2.7e-6 1/K

CHANNEL BLOCKS

Youngs modulus Ex = 85 GPa

Ey =47 GPa

Ez = 47 GPa

Poissons ratio x = 0.19

y = 0.021

z = 0.021

Shear modulus Gxy = 35 GPa

Gxz =35 GPa

Gyz = 13 GPa

Thermal expansion coefficient 4e-6 1/K

Results and Discussion

Figure 4 shows thex-component of the stress tensor plotted in a number of cross

sections. The highest negative values are found in the channel blocks closest to the

center, signaling compressive stresses in this part of the reactor. This is a direct result

of the temperature field in the reactor; the material in regions with high temperatures

expand more than material at lower temperatures. The opposite effect is observed in

channel blocks located near the outer surface of the reactor. In this relatively cool

region the monolith structure experiences tensile stresses. The compressive stress is

evaluated to approximately 5.0 MPa and the tensile stress to be 7.2 MPa. This

indicates moderate stress levels in the monolith working under the stationary

TABLE 1: WALL MATERIAL PROPERTIES

TABLE 2: CHANNEL BLOCK MATERIAL PROPERTIES


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conditions presented in this example. More pronounced stress levels are expected as

thermal gradients increase, for instance, during system startup.

Figure 4: The stress tensor component in the x direction. Compressive stress is indicated bynegative values, and tensile stress by positive values.

Reference

1. G. Shaub, D. Unruh, J. Wang, and T. Turek, Chemical Engineering and

Processing, vol. 42, p. 365, 2003.

Model Library path: Chemical_Reaction_Engineering_Module/

Heterogeneous_Catalysis/monolith_thermal_stress

Modeling Instructions

Start by opening the model library file monolith_3d.mph.

1 From the View menu, choose Model Library.

2 Go to the Model Library window.


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3 In the Model Library tree, select Chemical Reaction Engineering Module>Heterogeneous

Catalysis>monolith 3d.

4 ClickOpen.

First review the temperature distribution of the solved reactor model, available in 3D

Plot Group 11.

R E S U L T S

3D Plot Group 11

1 Click the Zoom Extents button on the Graphics toolbar.

The exothermic reactions increase the temperature in the central parts of the reactor,

while the temperature is decreased through heat loss to the surroundings.

Now, add a Solid Mechanics interface to extend the model with an analysis of the

thermal stresses in the reactor materials.

3 D M O D E L

In the Model Builderwindow, right-click3D Model and choose Add Physics.

M O D E L W I Z A R D

1 Go to the Model Wizard window.


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2 In the Add physics tree, select Structural Mechanics>Solid Mechanics (solid).

3 ClickAdd Selected.

4 ClickNext.

5 Find the Studies subsection. In the tree, select Custom Studies>Preset Studies for

Some Physics>Stationary.

6 ClickFinish.

S O L I D M E C H A N I C S

Two Linear Elastic Material Models are needed for the analysis, one for the supporting

wall material and one for the channel blocks. Note that the wall material is isotropic

while the block material is orthotropic

Linear Elastic Material 2

1 In the Model Builderwindow, under 3D Model right-clickSolid Mechanics and choose

Linear Elastic Material.

2 In the Linear Elastic Material settings window, locate the Domain Selection section.

3 From the Selection list, choose supporting walls.

4 Locate the Linear Elastic Material section. From theE list, choose User defined. In

the associated edit field, type 1.5e9.

5 From the list, choose User defined. In the associated edit field, type 0.2.

Add a Thermal Expansion feature to each Linear Elastic node. Make sure the features

take the temperature field solved by the Heat Transfer interface as Model Input.

Thermal Expansion 11 Right-click3D Model>Solid Mechanics>Linear Elastic Material 2 and choose Thermal

Expansion.

2 In the Thermal Expansion settings window, locate the Model Inputs section.

3 From the Tlist, choose Temperature (ht).

4 Locate the Thermal Expansion section. From the list, choose User defined. In the

associated edit field, type 2.7e-6.

Linear Elastic Material 1

1 In the Model Builderwindow, under 3D Model>Solid Mechanics clickLinear Elastic

Material 1.

2 In the Linear Elastic Material settings window, locate the Linear Elastic Material

section.

3 From the Solid model list, choose Orthotropic.


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4 From the E list, choose User defined. In the associated table, enter the following

settings:

5 From the list, choose User defined. In the associated table, enter the following

settings:

6 From the G list, choose User defined. In the associated table, enter the following

settings:

Thermal Expansion 1

1 Right-click3D Model>Solid Mechanics>Linear Elastic Material 1 and choose Thermal

Expansion.

2 In the Thermal Expansion settings window, locate the Model Inputs section.

3 From the Tlist, choose Temperature (ht).

4 Locate the Thermal Expansion section. From the list, choose User defined. In the

associated edit field, type 4e-6.

Complete the setup of the structural mechanics problem by defining the following

boundary conditions.

Roller 1

1 In the Model Builderwindow, right-clickSolid Mechanics and choose Roller.

2 Select Boundaries 1, 4, 9, 13, 19, and 23 only. You can use the Selection List from

the View menu.

Symmetry 1

1 Right-clickSolid Mechanics and choose Symmetry.

2 In the Symmetry settings window, locate the Boundary Selection section.

8.5e10 X

4.7e10 Y

4.7e10 Z

0.19 XY

0.021 YZ

0.021 XZ

3.5E10 XY

1.3e10 YZ

3.5E10 XZ


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3 From the Selection list, choose symmetry.

Follow the steps below to solve only the structural mechanics problem, using the

temperature field from the solved reactor model as input to the calculations.

S T U D Y 3

1 In the Model Builderwindow, clickStudy 3.

2 In the Study settings window, locate the Study Settings section.

3 Clear the Generate default plots check box. This selection turns off the plots set up

by default for each of the physics interfaces.

Step 1: Stationary

Clear all physics interfaces except Solid Mechanics to solve only for the displacement

field.

1 In the Model Builderwindow, expand the Study 3 node, then clickStep 1: Stationary.

2 In the Stationary settings window, locate the Physics and Variables Selection section.

3 In the table, enter the following settings:

Now, instruct the solver to use the results from the reactor model for the variablesnot solved for.

4 Click to expand the Values of Dependent Variables section. Select the Values of

variables not solved forcheck box.

5 From the Method list, choose Solution.

6 From the Study list, choose Study 2, Stationary.

The reactor model results are stored under Study 2.To conserve computer memory, change the default Direct solver to an Iterative solver.

Solver 3

1 In the Model Builderwindow, right-clickStudy 3 and choose Show Default Solver.

2 Expand the Solver 3 node.

3 Right-clickStationary Solver 1 and choose Iterative.

Physics Solve for

Reaction Engineering

Transport of Diluted Species 1

Heat Transfer in Fluids 1

Darcy's Law


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4 In the Iterative settings window, locate the General section.

5 From the Solverlist, choose Conjugate gradients.

6 Right-clickStudy 3>Solver Configurations>Solver 3>Stationary Solver 1>Iterative 1

and choose SOR Vector.

Remove all dependent variables except the displacement field u.

7 In the SOR Vectorsettings window, locate the Main section.

8 In the Variables list, select Pressure (mod2.p).

9 Under Variables, clickDelete.

10 In the Variables list, select Concentration (mod2.cNO).


12 In the Variables list, select Concentration (mod2.cO2).


14 In the Model Builderwindow, right-clickStudy 3 and choose Compute.

R E S U L T S

Data Sets

The Data Sets node allows you great freedom to define tailored sets of plot data to be

used by the plot nodes. Here, use the Mirror 3D feature to reflect the results in the

symmetry planes of the model.

Mirror the data in the symmetry plane that is at a 45 degree angle to the xy-plane.

1 In the Model Builderwindow, under Results right-clickData Sets and choose MoreData Sets>Mirror 3D.

2 In the Mirror 3D settings window, locate the Data section.

3 From the Data set list, choose Solution 3.

4 Locate the Plane Data section. From the Plane type list, choose General.

5 In rowPoint 2, set X to 0.1.

6 In rowPoint 3, set Y to 3.575e-3.7 In rowPoint 3, set Z to 3.575e-3.

Create the plot in Figure 4 by following these steps.

3D Plot Group 13

1 In the Model Builderwindow, right-clickResults and choose 3D Plot Group.

2 In the 3D Plot Group settings window, locate the Data section.


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3 From the Data set list, choose Mirror 3D 1.

4 Right-clickResults>3D Plot Group 13 and choose Slice.

5 In the Slice settings window, clickReplace Expression in the upper-right corner of the

Expression section. From the menu, choose Solid Mechanics>Stress>Stress tensor

(Spatial)>Stress tensor, x component (solid.sx).

6 Locate the Plane Data section. In the Planes edit field, type 8.

7 Click the Plot button.

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