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01_Modeling Species Transport Without Reactions Flipbook PDF
01_Modeling Species Transport Without Reactions
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Tutorial: Modeling Species Transport Without Reactions
Introduction This tutorial demonstrates the use of species transport model in ANSYS FLUENT to study the species diffusion and mixing characteristics in baffled reactors. This tutorial demonstrates how to do the following: • Set up the species transport problem. • Analyse residence time distribution (RTD) of the reactor. • Compare the mixing characteristics of the two reactors using RTD curves. Similar approach can also be applied for non-industrial applications such as spread of pollutant in atmospheric air.
Prerequisites This tutorial is written with the assumption that you have completed Tutorial 1 from ANSYS FLUENT 14.0 Tutorial Guide, and that you are familiar with the ANSYS FLUENT navigation pane and menu structure. Some steps in the setup and solution procedure will not be shown explicitly. For more information on species transport model, see Chapter 15, Modeling Species Transport and Finite-Rate Chemistry in the ANSYS FLUENT 14.0 User’s Guide.
Problem Description As a part of designing a steady state well mixed reactor, it is necessary to analyze the flow characteristics of two baffled reactors and compare the RTDs. For this a tracer is injected for 1 second into the reactor on a frozen flow field and the concentration variation of the tracer with time is monitored at the outlet. The schematics of two models are shown in Figures 1 and 2. The first model has 15 baffles, whereas, the second model has 5 baffles. All the other design parameters are the same in both the reactors. The flow is turbulent and the inlet fluid has a velocity of 0.5 m/s.
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Figure 1: Baffled Reactor—With 15 Baffles
Figure 2: Baffled Reactor—With 5 Baffles
Setup and Solution Preparation 1. Copy the mesh file (baffled reactor.msh.gz) to your working folder. 2. Use FLUENT Launcher to start the 2D version of ANSYS FLUENT. For more information about FLUENT Launcher see Section 1.1.2 Starting ANSYS FLUENT Using FLUENT Launcher in ANSYS FLUENT 14.0 User’s Guide. 3. Enable Double-Precision in the Options list. The Display Options are enabled by default. Therefore, after you read in the mesh, it will be displayed in the embedded graphics window. Step 1: Mesh 1. Read the mesh file (baffled reactor.msh.gz). File −→ Read −→Mesh... As the mesh file is read, ANSYS FLUENT will report the progress in the console.
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Step 2: General Settings 1. Retain the default solver settings. 2. Check the mesh (Figure 3). General −→ Check
Figure 3: Mesh Display ANSYS FLUENT will perform various checks on the mesh and will report the progress in the console. Make sure the minimum volume reported is a positive number. Step 3: Models 1. Enable the standard k-epsilon (2 eqn) turbulence model. Models −→
Viscous −→ Edit...
2. Enable Species transport model. Models −→
Species −→ Edit...
(a) Enable Species Transport from the list of Model. (b) Retain the default settings and click Apply. An Information dialog box will appear informing that the material properties are changed. Click OK. (c) Close the Species Model dialog box.
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Step 4: Materials Materials −→ Create/Edit... 1. Copy the water-liquid (h2o) from FLUENT Database.... (a) Select fluid from Material Type drop-down list. (b) Select water-liquid (h2o) from the FLUENT Fluid Materials list. (c) Click Copy and close the FLUENT Database Materials dialog box. (d) Click Change/Create. 2. Create a new fluid tracer. This fluid will have the same properties of water-liquid (h2o). (a) Select water-liquid (h2o) from the FLUENT Fluid Materials drop-down list. (b) Enter tracer as the Name and Chemical Formula. (c) Click Change/Create. A Question dialog box will appear asking change/create mixture and overwrite water-liquid (h2o). Click No. 3. Create a mixture of water-liquid (h2o) and tracer. (a) Select mixture from the Material Type drop-down list. (b) Select mixture-template from the FLUENT Mixture Materials drop-down list. (c) Enter water-tracer-mixture for the Name. (d) Click Edit... for the Mixture Species.
i. Add tracer and water-liquid (h2o) to the Selected Species list.
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ii. Remove all other species from Selected Species list. iii. Click OK to close the Species dialog box. iv. Click Yes to overwrite mixture-template.
(e) Select volume-weighted-mixing-law for Density. (f) Ensure that mixing-law is selected for Cp (Specific Heat). (g) Select mass-weighted-mixing-law for Thermal Conductivity and Viscosity. (h) Ensure that constant-dilute-appx is selected for Mass Diffusivity and enter 1e-9 m2 /s. (i) Click Change/Create and close the Create/Edit Materials dialog box.
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Step 5: Boundary Conditions Boundary Conditions 1. Set the boundary conditions for velocity inlet. Boundary Conditions −→
velocity inlet −→ Edit...
(a) Enter 0.5 m/s for Velocity Magnitude. (b) Select Intensity and Hydraulic Diameter from the Specification Method drop-down list in the Turbulence group box. (c) Enter 5% for Turbulent Intensity and 0.8 m for Hydraulic Diameter. (d) Click OK to close the Velocity Inlet dialog box. 2. Set the boundary conditions for the pressure outlet. Boundary Conditions −→
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pressure outlet −→ Edit...
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(a) Select Intensity and Hydraulic Diameter from the Specification Method drop-down list in the Turbulence group box. (b) Enter 3% for Turbulent Intensity and 0.8 m for Hydraulic Diameter. (c) Retain the default setting for all other parameters. (d) Click OK to close the Pressure Outlet dialog box. Step 6: Solution for Reactor with 15 Baffles 1. Select PRESTO! from Pressure drop-down list in the Spatial Discretization group box. Solution Methods 2. Deselect tracer equation for obtaining flow field solution. Solution Controls −→ Equations...
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3. Enable the plotting of residuals during the calculation. Monitors −→
Residuals −→ Edit...
(a) Set Convergence Criterion to none. (b) Click OK to close the Residual Monitors dialog box. 4. Define the surface monitor for flow. Monitors (Surface Monitors)−→ Create... (a) Enable Plot and Write. (b) Select Area-Weighted Average from the Report Type drop-down list. (c) Select Velocity... and Velocity Magnitude from the Field Variable drop-down lists. (d) Select pressure outlet from the Surfaces list. (e) Click OK to close the Surface Monitor dialog box. 5. Initialize the solution. Solution Initialization (a) Select Standard Initialization from the Initialization Methods group box. (b) Enter 0.1 m2 /s2 for Turbulent Kinetic Energy. (c) Enter 100 m2 /s3 for Turbulent Dissipation Rate. (d) Retain the default setting for all other parameters. (e) Click Initialize. 6. Run the calculation for 700 iterations (see Figure 4). Run Calculation
Figure 4: Scaled Residuals The convergence history of Velocity Magnitude on pressure outlet is shown in Figure 5.
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Figure 5: Surface Monitor of Average Velocity on Outlet
7. Save the case and data files (case-1.cas/dat.gz). File −→ Write −→Case & Data... 8. Display the velocity contours. Graphics and Animations −→
Contours −→ Set Up...
(a) Enable Filled in the Options group box. (b) Select Velocity... and Velocity Magnitude from the Contours of drop-down list. (c) Click Display (see Figure 6).
Figure 6: Contours of Velocity
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Step 7: Transient Simulation with Tracer 1. Select Transient from the Time list. General −→
Transient
2. Inject tracer through the velocity inlet. Boundary Condition −→
velocity inlet −→ Edit...
(a) Click Species tab. (b) Enter 1 for tracer in the Species Mass Fractions group box. (c) Retain the default setting for all other parameters. (d) Click OK to close the Velocity Inlet dialog box. 3. Enable frozen flow field so that the tracer should not affect the bulk fluid. Solution Controls −→ Equations... (a) Deselect Flow, Turbulence, and Energy and select tracer from the Equations list. (b) Click OK to close the Equations dialog box. 4. Set Convergence Criterion to absolute. Monitors −→
Residuals −→ Edit...
5. Define species concentration monitor at the outlet with time for calculating RTD. Monitors (Surface Monitors)−→ Edit...
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(a) Enter case-1-tracer.out for the File Name. (b) Select Flow Time from the X-Axis drop-down list. (c) Select Time Step from the Get Data Every drop-down list. (d) Select Mass-Weighted Average from the Report Type drop-down list. (e) Select Species... and Molar Concentration of tracer from the Field Variable dropdown lists. (f) Ensure that pressure outlet is selected from the Surfaces list. (g) Click OK to close the Surface Monitor dialog box. 6. Save the case and data files (case-1-tracer-init.cas/dat.gz). File −→ Write −→Case & Data... 7. Run the simulation for 1 second to inject the tracer. Run Calculation (a) Enter 0.1 second for Time Step Size. (b) Enter 10 for Number of Time Steps. (c) Retain 20 for Max Iterations/Time Step. (d) Click Calculate. 8. Save the case and data files (case-1-tracer-injection-complete.cas/dat.gz). File −→ Write −→Case & Data... 9. Display the tracer injection. Graphics and Animations −→
Contours −→ Set Up...
(a) Select Species... and Mass fraction of tracer from the Contours of drop-down list. (b) Click Display (see Figure 7).
Figure 7: Contours of Tracer Concentration After 1 Second of Injection
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Step 8: Transient Simulation Without Tracer Stop injecting tracer and run the simulation further to analyze RTD of the reactor. 1. Remove the injection of tracer from velocity inlet. Boundary Condition −→
velocity inlet −→ Edit...
(a) Click Species tab. (b) Enter 0 for tracer in the Species Mass Fractions group box. (c) Retain the default setting for all other parameters. (d) Click OK to close the Velocity Inlet dialog box. 2. Run the calculation for 2000 time steps. The mass weighted average of tracer concentration is negligibly small at the end of calculation. So the data should be sufficient to do the RTD analysis. 3. Save the case and data files (case-1-rtd-complete.cas/dat.gz). Step 9: Postprocessing and RTD Analysis 1. Display contours of Mass fraction of tracer (see Figure 8).
Figure 8: Contours of Mass fraction of tracer The concentration of tracer at outlet as a function of time is shown in Figure 9. Calculation of RTD of the reactor is explained in the Appendix.
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Figure 9: Concentration of Tracer with Time
Step 10: Solution for Reactor with 5 Baffles 1. Change the removable baffles from wall to interior. Boundary Conditions −→
removable baffles
(a) Select interior from the Type drop-down list. A Question dialog box will appear asking to change type of removable baffles from wall to interior. Click Yes. (b) Retain the default name and click OK to close the interior dialog box. 2. Display the mesh to see the modified reactor. Graphics and Animations −→
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Mesh −→ Set Up...
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Figure 10: Mesh for Reactor with 5 Baffles
3. Change the model from Transient to Steady to get the flow field. General −→
Steady
4. Enable the flow and turbulence equations to get the steady flow field. Solution Controls −→ Equations... (a) Select Flow, Turbulence, and Energy and deselect tracer in the Equations list. (b) Click OK to close the Equations dialog box. 5. Set Convergence Criterion to none. Monitors −→
Residuals −→ Edit...
6. Change the surface monitor to velocity monitor. Monitors (Surface Monitors)−→ Edit... (a) Deselect Write option. (b) Select Area-Weighted Average from the Report Type drop-down list. (c) Select Velocity... and Velocity Magnitude from the Field Variables drop-down list. (d) Ensure that pressure outlet is selected from the Surfaces list. (e) Click OK to close the Surface Monitor dialog box. 7. Initialize the solution. Solution Initialization −→ Initialize Ensure that the mass fraction for tracer is zero. 8. Run the calculation for 2000 iterations (see Figure 11). 14
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Figure 11: Scaled Residuals After 2000 Iterations
9. Display the velocity contours (see Figure 12).
Figure 12: Contours of Velocity for Reactor with 5 Baffles
10. Write the case and data files (case-2.cas/dat.gz).
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Step 11: Unsteady Solution for Reactor with 5 Baffles 1. Repeat Step 7 to Step 9 to get the unsteady solution for this case. 2. Display the contours of tracer concentration after 1 second of injection (see Figure 13).
Figure 13: Tracer Concentration Contours After 1 Second of Injection for Reactor with 5 Baffles 3. Display contours of Mass fraction of tracer (see Figure 14).
Figure 14: Contours of Mass fraction of tracer for Reactor with 5 Baffles The concentration of tracer at outlet as a function of time is shown in Figure 15. There is still finite concentration of the tracer at the outlet at the end of the 2000 time steps. Continue the unsteady run for 2500 more time steps. The concentration of tracer at outlet as a function of time after 4500 time steps is shown in Figure 16. 16
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Figure 15: Concentration of Tracer with Time for Reactor with 5 Baffles
Figure 16: Concentration of Tracer with Time After 4500 Time Steps
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The contours of Mass fraction of tracer are shown in Figure 17.
Figure 17: Contours of Mass fraction of tracer After 4500 Time Steps
Appendix For the calculation of RTD of the reactor (Levenspiel, O. 1999) perform the following: 1. Open an excel file. 2. Load the surface monitor output file (case-1-tracer.out) into the sheet. 3. Multiply all the concentration values with delta-t (in this case it is 0.1 seconds). 4. Add all the values of this column to get the denominator of the equation for external time distribution, E (t). 5. Take the ratio of concentration at each time step with the sum of the product of concentration with delta-t to get the RTD (E-curve). See Figure 18. 6. The area under this curve must be unity. Exit age distribution C (t) E (t) = R ∞ 0 C (t) dt Here C (t) is the concentration of tracer at the outlet as a function of time. Rt
0 E (t) dt represents the fraction of particles which spend a time less than t inside the reactor.
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Figure 18: E-curve for Reactor with 15 Baffles
7. The fraction of particle which spend a time more than t is
1−
Z
t
E (t) dt
0
8. You can calculate the minimum time for which 75% of the particles spend inside the reactor by solving the following equation for t75 .
1−
Z
t75
E (t) dt = 0.75
(1)
0
Using an excel sheet, if you solve for t75 , you will get the value as 97.3 seconds. 9. Using the same method, calculate the minimum time for which 50% and 25% of particles spend inside the reactor. They are 106.9 seconds and 117.6 seconds respectively. The E-curve for Reactor with 5 Baffles is shown in Figure 19.
Figure 19: E-curve for Reactor with 5 Baffles
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10. Once you obtain the E-curve, calculate the minimum time for which 75%, 50%, and 25% of the particles spend inside the reactor. Using the same method explained earlier, you can get the values as 62 seconds, 94.6 seconds, and 138 seconds respectively. 11. The following table shows the residence time comparison which is helpful for selecting the suitable design of the reactors based on the requirement. Particle % Inside Reactor 75 50 25
Time (s) for Reactor with 15 Baffles 97.3 106.9 117.6
Time (s) for Reactor with 5 Baffles 62 94.6 138
Summary This tutorial demonstrated that the species transport model without reaction can be used for the analysis of spread and residence time of tracer. This was helpful for RTD analysis and the selection of suitable design of reactor for the particular application. Similar procedure can be used to predict the spread of pollutant from the given point into the atmosphere.
Reference (Levenspiel, O. 1999), Chemical Reaction Engineering. 3rd Ed. John Wiley & Sons.
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