tutorial: modeling liquid reactions in cijr using the...

Tutorial: Modeling Liquid Reactions in CIJR Using the

Eulerian PDF transport (DQMOM-IEM) Model

Introduction

The purpose of this tutorial is to demonstrate setup and solution procedure of liquid chem-ical reactions using the Eulerian Composition PDF transport model with Discrete Quadra-ture Method of Moments (DQMOM) in ANSYS FLUENT.

For reactions involving liquids, mixing at molecular level- termed as micromixing, plays asignificant role in determining the conversion of products. In cases where there are parallelcompeting reactions, the micromixing can singularly affect the yield of the desired product.Fast chemistry models in ANSYS FLUENT like Non-premixed equilibrium model, steadylaminar flamelet and eddy dissipation model cannot capture the physics of micromixingand thus may not predict conversion, selectivity and scale-up accurately. While the Fullcomposition PDF transport is well equipped to solve liquid reactions, the computation costinvolved with the lagrangian approach is very high since kinetic calculations are performedusing particle based methods (Monte-carlo methods) which are computationally intensive.The DQMOM-IEM model solves for the PDF transport in Eulerian framework, this sig-nificantly reduces the computational cost involved while preserving the accuracy of thecalculations.

This tutorial demonstrates how to do the following:

• Set up liquid chemical reactions in a confined impinging jet reactor.

• Set up DQMOM-IEM PDF Transport model with liquid micro-mixing extension.

• Calculate the solution..

• Examine results using graphics.

Prerequisites

This tutorial is written with the assumption that you have completed Tutorial 1 from theANSYS FLUENT 14.5 Tutorial Guide, and that you are familiar with the ANSYS FLUENTnavigation pane and menu structure. Some steps in the setup and solution procedure willnot be shown explicitly. A good understanding of turbulence and species mixing/reaction,as well as their modeling is desirable.

c© ANSYS, Inc. December 4, 2012 1

Modeling Liquid Reactions in CIJR Using the Eulerian PDF transport (DQMOM-IEM) Model

Problem Description

A confined impinging-jets reactor (CIJR) consists of two high-velocity, coaxial liquid jetsthat collide and produce mixing times on the order of milliseconds. In this tutorial, thefollowing pair of second- order parallel reactions is employed to evaluate the extent ofmixing.

H+(A) + (OH)−(B) K1−−−→H2O(P1)

H+(A) + CH3C(OCH3)2(D) K2−−−→ H+(A) + CH3COCH3(P2) = 2CH3OH(P3)

The first reaction is very fast (K1 = 1.4E8m3/mol.s), and the second is very slow (K2 =643E − 3m3/mol.s). When the liquid micro-mixing model is enabled, ANSYS FLUENTinterpolates the mixing constant used in IEM model from model turbulence and scalarspectra. A diagram of the CIJR with two reactants impinging at the center of the reactoris shown in Figure 1.

The solution will be performed in two stages:

Figure 1: Problem Schematic

Preparation

1. Copy the mesh file, dqmom.msh.gz to the working folder.

2. Use FLUENT Launcher to start the (3D) version of ANSYS FLUENT.

3. Enable Double-Precision in the Options list.

2 c© ANSYS, Inc. December 4, 2012


Setup and Solution

Step 1: Mesh

1. Read the mesh file, dqmom.msh.gz.

File −→ Read −→Mesh...

As the mesh file is read, ANSYS FLUENT reports the progress in the console.

Figure 2: Mesh Display

Step 2: General Settings

1. Retain the default settings.

General

2. Check the mesh.

General −→ Check

ANSYS FLUENT performs various checks on the mesh and reports the progress inthe console. Pay attention to the minimum volume reported and make sure this is apositive number. Scaling is not required for this case.

3. Scale the mesh.

General −→ Scale...



(a) Select mm from the Mesh Was Created In drop-down list.

(b) Select mm from the View Length Unit In drop-down list.

(c) Close the Scale Mesh dialog box.

All dimensions will now be shown in millimeters

Step 3: Models

1. Select the standard k-turbulence model.

Models −→ Viscous −→ Edit...

(a) Select k-epsilon(2 eqn) from the Model list to open the Viscous Model dialog box.

The dialog box will expand after the selection.

(b) Select Enhanced Wall Treatment from the Near-Wall Treatment group box.

(c) Click OK to close the Viscous Model dialog box.



2. Define species model.

Models −→ Species −→ Edit...

(a) Select Composition PDF Transport from the Model list.

The dialog box will expand after the selection.

(b) Select Eulerian in the PDF Transport Options group box.

(c) Enable Volumetric in the Reactions group box.

(d) Enable Liquid Micro-Mixing in the Options group box.

(e) Click OK and close the Species Model dialog box.

At this stage, ANSYS FLUENTrequires the chemical mechanism which containsthe species, their properties, and kinetics. Since these have not been provided anError dialog box is displayed.

(f) Click OK to close the Error dialog box.

An information dialog box will open reminding you to confirm the property val-uesthat have been extracted from the database.



(g) Click OK to close the Information dialog box.

Step 4: Materials

The DQMOM model requires the mixture materials to be setup. This is done by creatingthe species participating in the reactions and then by adding them to the mixture specieslist.

Materials −→ Create/Edit...

1. Add water to the material list.

(a) Click Fluent Database to open the Fluent Database Materials dialog box.

(b) Select fluid under Material Type drop-down list.

(c) Select water-liquid (h2o<l>) from the Fluent Fluid Materials list and click Copy.

(d) Close the Fluent Database Materials dialog box.

2. Create a new material.



(a) Enter the name as a in the Name text field.

(b) Delete the entry for Chemical Formula.

(c) Enter 962 for Density.

(d) Enter 1 for Molecular Weight.

(e) Click Change/Create.

(f) Click Yes to overwrite water-liquid material.

3. Similarly create other species materials b,d,p1,p2,p3 and bulk with the propertiesgiven in the following table.

Species Molecular Weightb 17d 104p1 18p2 58p3 32bulk 18

4. Add the created species to the mixture list



(a) Select Mixture from Material Type drop-down list.

(b) Click Edit... next to Mixture Species and add the species in the order a,b,d,p1,p2,p3and bulk being the last species.

(c) Click OK to close the Species dialog box.

5. Add the reactions.

(a) Click Edit... next to Reaction.

(b) Enter 2 for Total Number of Reactions.

i. For the first reaction, (a+ b −→ p1), set Number of Reactants to 2.

ii. Select a and b from the Species drop-down lists.

iii. Enter 1 for Stoich. Coefficient and Rate Exponent for a.

iv. Enter 1.4e+11 for Pre-Exponential Factor.

v. Enter 0 for Activation Energy.

vi. Select p1 from the Species drop-down list for product.

vii. Enter 1 for Stoich. Coefficient for p1.



(c) Similarly set the second reaction, (a + d + bulk −→ a + p2 + 2p3), by changingID to 2.

i. Enter 3 for Number of Reactants and Number of Products.

ii. Enter 2 for Stoich. Coefficient of p3.

iii. Enter 673.13 for Pre-Exponential Factor.

iv. Enter 0 for Activation Energy.

v. Click OK in the Reactions dialog box.

6. Change the mixture properties.

(a) Select volume-weighted-mixing-law from the Density drop down list, as this is moreapplicable for liquid reactions.

(b) Enter 0.001995 for Viscosity.

(c) Enter 2e-9 for Mass Diffusivity.

Note: This is to account for the high Schmidt number for liquids due to whichthe diffusivity is low.

(d) Click Change/Create and close the Create/Edit Materials dialog box.



Step 5: Boundary Conditions

1. Define the species properties in species model.

Models −→ Species −→ Edit...

(a) Click Boundary tab in the Species Model dialog box.

i. Enter 0.00064 for a and 0.99936 for bulk for Fuel.

ii. Enter 0.01149 for b, 0.06692 for d, and 0.9216 for bulk corresponding toOxidizer stream.

iii. Click Apply and close the Species Model dialog box



2. Set the boundary conditions for the leftinlet zone.

Boundary Conditions −→ leftinlet −→ Edit...

(a) Enter 1.666 m/s for Velocity Magnitude.

(b) Retain the selection of Intensity and Viscosity Ratio from the Specification Methoddrop-down list in the Turbulence group box.

(c) Retain 5% for Turbulent Intensity and enter 5 for Turbulent Viscosity Ratio.



(d) Click the Species tab and enter 1 for Mixture Fraction.

This is the fuel reactant inlet, so the Mixture Fraction is 1.

(e) Click OK to close the Velocity Inlet dialog box.

3. Set the boundary conditions for the rightinlet zone.

Boundary Conditions −→ rightinlet −→ Edit...

(a) Enter 1.666 m/s for Velocity Magnitude.

(b) Retain the selection of Intensity and Viscosity Ratio from the Specification Methoddrop-down list in the Turbulence group box.

(c) Retain 5% for Turbulent Intensity and enter 5 for Turbulent Viscosity Ratio.

(d) Click the Species tab and retain 0 for Mixture Fraction.

(e) Click OK to close the Velocity Inlet dialog box.

4. Set the boundary conditions for the pressure outlet zone.

Boundary Conditions −→ outlet −→ Edit...

(a) Retain the selection of Intensity and Viscosity Ratio from the Specification Methoddrop-down list in the Turbulence group box.

(b) Retain 5% for Backflow Turbulent Intensity

(c) Retain 10 for Backflow Turbulent Viscosity Ratio.

(d) Click OK to close the Pressure Outlet dialog box.



Step 6: Solution

1. Set the solution parameters.

Solution Methods

(a) Select Green-Gauss Node Based from the Gradient drop-down list.

(b) Select PRESTO! from the Pressure drop-down list.



2. Set the solution controls.

Solution Controls

(a) Enter 0.8 for Eulerian PDF in the Under-Relaxation Factors group box.

(b) Click Equations... and de-select Energy from the equations list.

(c) Click OK to close the Equations dialog box

Note: Energy equation is enabled by default for species model with reactions. Howeverfor your case the flow is isothermal. The densities are also constant. Thereforesolving for energy is not necessary.



3. Set the convergence limits.

Monitors −→ Residuals −→ Edit...

(a) Enter 1e-4 for fmean, a, b, d, and p3.

(b) Enter 5e-4 for p1 and p2.

(c) Click OK and close the Residual Monitors dialog box.

4. Initialize the solution.

Solution Initialization −→ Initialize

Hybrid Initialization is the default Initialization Method in ANSYS FLUENT 14.5. Referto the section 28.11 Hybrid Initialization, in the ANSYS FLUENT 14.5 User’s Guide.

5. Save the case file (dqmom.cas.gz).

File −→ Write −→Case...



6. Run the calculation for 100 iterations.

Run Calculation −→ Calculate

7. Change under relaxation factor for Eulerian PDF to 1.



9. Select Second Order Upwind for all the rest of the parameters in the Spatial Discretiza-tion group box.

Solution Methods



The solution converges in approximately 36 more iterations. See Figure 3.

Figure 3: Residual History

11. Save the data file (dqmom.dat.gz).

File −→ Write −→Data...



Step 7: Postprocessing

1. Display contours of velocity magnitude.

Graphics and Animations −→ Contours −→ Set Up...

(a) Enable Filled from the Options group box.

(b) Select Velocity... and Velocity Magnitude from the Contours of drop-down lists.

(c) Select symmetry from the Surfaces selection list.

(d) Click Display (Figure 4).

Figure 4: Contours of Velocity Magnitude

2. Display contours of mixture fraction.

(a) Select Eulerian PDF Transport... and Mixture Fraction from the Contours of drop-down lists.

(b) Click Display (Figure 5).



Figure 5: Contours of Mixture Fraction

3. Display contours of mass fraction of a.

(a) Select Species... and Mass Fraction of a from the Contours of drop-down lists.

(b) Click Display (Figure 6).

Figure 6: Contours of Mass Fraction of a



4. Similarly display the contours of mass fraction of b and d species. Refer to Figures 7and 8

Figure 7: Contours of Mass Fraction of b

Figure 8: Contours of Mass Fraction of d

Summary

This tutorial has demonstrated that the DQMOM model can simulate reactions in liquidswith slow chemistry and low diffusivity.


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