Modeling Evaporating Liquid Spray

Tutorial 16. Modeling Evaporating Liquid Spray Introduction In this tutorial, FLUENT s air-blast atomizer model is used to predict the behavior of an evaporating methanol spray. Initially, the air flow is modeled without droplets. To predict the behavior of the spray, several other discrete-phase models, including collision and breakup, are used. This tutorial demonstrates how to do the following: Create periodic zones. Define a spray injection for an air-blast atomizer. Calculate a solution using FLUENT s discrete phase model. Prerequisites This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have completed Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description The geometry to be considered in this tutorial is shown in Figure 16.1. Methanol is cooled to 10 C before being introduced into an air-blast atomizer. The atomizer contains an inner air stream surrounded by a swirling annular stream. (The species include the components of air as well as water vapor, so the model can be expanded to include combustion, if required.) To make use of the periodicity of the problem, only a 30 degree section of the atomizer will be modeled. c Fluent Inc. September 21, 2006 16-1

inner air stream swirling annular stream Z Y X Figure 16.1: Problem Specification Setup and Solution Preparation 1. Download evaporate_liquid.zip from the Fluent Inc. User Services Center or copy it from the FLUENT documentation CD to your working folder (as described in Tutorial 1). 2. Unzip evaporate_liquid.zip. The file, sector.msh can be found in the evaporate liquid folder created after unzipping the file. 3. Start the 3D (3d) version of FLUENT. 16-2 c Fluent Inc. September 21, 2006

Step 1: Grid 1. Read in the mesh file sector.msh. File Read Case... 2. Check the grid. Grid Check FLUENT will perform various checks on the mesh and report the progress in the console. Make sure that the minimum volume reported is a positive number. 3. Display the grid. Display Grid... (a) Enable Faces in the Options group box. (b) Select only atomizer-wall, central air, and swirling air from the Surfaces selection list. c Fluent Inc. September 21, 2006 16-3

(c) Click the Colors... button to open the Grid Colors panel. i. Select Color by ID in the Options list. ii. Close the Grid Colors panel. This will assign a different color to each zone in the domain, rather than to each type of zone. (d) Click Display and close the Grid Display panel. The graphics display will be updated to show the grid. 4. Change the display to an isometric view. Display Views... (a) Select isometric in the Views list and click Apply. (b) Close the Views panel. (c) Rotate and zoom in with the mouse to obtain the view shown in Figure 16.2. 16-4 c Fluent Inc. September 21, 2006

Z Y X Grid FLUENT 6.3 (3d, pbns, lam) Figure 16.2: Air-Blast Atomizer Mesh Display c Fluent Inc. September 21, 2006 16-5

> grid /grid> 5. Change zones periodic-a and periodic-b from wall zones to periodic zones using the text interface as follows: modify-zones /grid/modify-zones> list-zones id name type material kind ---- ---------------- ----------------- ------------------ ---- 1 fluid fluid air cell 2 atomizer-wall wall aluminum face 3 central_air mass-flow-inlet face 4 co-flow-air velocity-inlet face 5 outlet pressure-outlet face 6 swirling_air velocity-inlet face 7 periodic-a wall aluminum face 8 periodic-b wall aluminum face 9 outer-wall wall aluminum face 11 default-interior interior face /grid/modify-zones> make-periodic Periodic zone [()] 7 Shadow zone [()] 8 Rotational periodic? (if no, translational) [yes] Create periodic zones? [yes] yes yes all 1923 faces matched for zones 7 and 8. zone 8 deleted created periodic zones. 16-6 c Fluent Inc. September 21, 2006

6. Reorder the grid twice. To speed up the solution procedure, the mesh should be reordered, which will substantially reduce the bandwidth. Grid Reorder Domain FLUENT will report the progress in the console: >> Reordering domain using Reverse Cuthill-McKee method: zones, cells, faces, done. Bandwidth reduction = 3286/103 = 31.90 Done. >> Reordering domain using Reverse Cuthill-McKee method: zones, cells, faces, done. Bandwidth reduction = 103/103 = 1 Done. Step 2: Models 1. Retain the default solver settings. Define Models Solver... c Fluent Inc. September 21, 2006 16-7

2. Enable heat transfer by enabling the energy equation. Define Models Energy... 3. Enable the realizable k-ɛ turbulence model. Define Models Viscous... The realizable k-ɛ model gives a more accurate prediction of the spreading rate of both planar and round jets than the standard k-ɛ model. 16-8 c Fluent Inc. September 21, 2006

4. Enable chemical species transport and reaction. Define Models Species Transport & Reaction... (a) Select Species Transport in the Model list. (b) Select methyl-alcohol-air in the Mixture Material drop-down list. The Mixture Material list contains the set of chemical mixtures that exist in the FLUENT database. You can access a complete description of the reacting system by selecting one of the pre-defined mixtures. The chemical species in the system and their physical and thermodynamic properties are defined by the selection of the mixture material. You can alter the mixture material selection or modify the mixture material properties using the Materials panel. (c) Click OK to close the Species Model panel. When you click OK, FLUENT will list the properties that are required for the models you have enabled. An Information dialog box will open, reminding you to confirm the property values that have been extracted from the database. (d) Click OK in the Information dialog box to continue. c Fluent Inc. September 21, 2006 16-9

Step 3: Boundary Conditions Define Boundary Conditions... 1. Set the boundary conditions for the inner air stream (central air). 16-10 c Fluent Inc. September 21, 2006

(a) Enter 9.167e-5 kg/s for Mass Flow-Rate. (b) Enter 0 for X-Component of Flow Direction and Y-Component of Flow Direction. (c) Enter 1 for Z-Component of Flow Direction. (d) Select Intensity and Viscosity Ratio from the Specification Method drop-down list. (e) Retain the default values for Turbulent Intensity and Turbulent Viscosity Ratio. (f) Click the Thermal tab and enter 293 K for Total Temperature. (g) Click the Species tab and enter 0.23 for o2 in the Species Mass Fractions group box. (h) Click OK to close the Mass-Flow Inlet panel. c Fluent Inc. September 21, 2006 16-11

2. Set the boundary conditions for the air stream surrounding the atomizer (co-flowair). (a) Enter 1 m/s for Velocity Magnitude. (b) Select Intensity and Viscosity Ratio from the Specification Method drop-down list. (c) Enter 5 for Turbulence Intensity and Turbulent Viscosity Ratio. (d) Click the Thermal tab and enter 293 K for Total Temperature. (e) Click the Species tab and enter 0.23 for o2 in the Species Mass Fractions group box. (f) Click OK to close the Velocity Inlet panel. 16-12 c Fluent Inc. September 21, 2006

3. Set the boundary conditions for the exit boundary (outlet). (a) Select From Neighboring Cell from the Backflow Direction Specification Method drop-down list. (b) Select Intensity and Viscosity Ratio from the Specification Method drop-down list. (c) Enter 5 for Turbulence Intensity and Turbulent Viscosity Ratio. (d) Click the Thermal tab and enter 293 K for Total Temperature. (e) Click the Species tab and enter 0.23 for o2 in the Species Mass Fractions group box. (f) Click OK to close the Pressure Outlet panel. c Fluent Inc. September 21, 2006 16-13

4. Set the boundary conditions for the swirling annular stream (swirling air). (a) Select Magnitude and Direction from the Velocity Specification Method dropdown list. (b) Enter 19 m/s for Velocity Magnitude. (c) Select Cylindrical (Radial, Tangential, Axial) from the Coordinate System dropdown list. (d) Enter 0 for Radial-Component of Flow Direction. (e) Enter 0.7071 for Tangential-Component of Flow Direction and Axial-Component of Flow Direction. (f) Select Intensity and Viscosity Ratio from the Specification Method drop-down list. (g) Enter 5 for Turbulence Intensity and Turbulent Viscosity Ratio. (h) Click the Thermal tab and enter 293 K for Total Temperature. (i) Click the Species tab and enter 0.23 for o2 in the Species Mass Fractions group box. (j) Click OK to close the Velocity Inlet panel. 16-14 c Fluent Inc. September 21, 2006

5. Set the boundary conditions for the outer wall of the atomizer (outer-wall). (a) Select Specified Shear from the Shear Condition list. (b) Retain the default values for the remaining parameters. (c) Click OK to close the Wall panel. 6. Close the Boundary Conditions panel. c Fluent Inc. September 21, 2006 16-15

Step 4: Initial Solution Without Droplets The airflow will first be solved and analyzed without droplets. 1. Initialize the flow field. Solve Initialize Initialize... (a) Select co-flow-air from the Compute From drop-down list. (b) Click Init to initialize the variables, and close the Solution Initialization panel. 16-16 c Fluent Inc. September 21, 2006

2. Retain the default under-relaxation factors. Solve Controls Solution... c Fluent Inc. September 21, 2006 16-17

3. Enable residual plotting during the calculation. Solve Monitors Residual... (a) Enable Plot in the Options group box. (b) Click OK to close the Residual Monitors panel. 4. Save the case file (spray1.cas.gz). File Write Case... 5. Start the calculation by requesting 200 iterations. Solve Iterate... The solution will converge in approximately 160 iterations. 6. Save the case and data files (spray1.cas.gz and spray1.dat.gz). File Write Case & Data... Note: FLUENT will ask you to confirm that the previous case file is to be overwritten. 16-18 c Fluent Inc. September 21, 2006

7. Create a clip plane to examine the flow field at the midpoint of the atomizer section. Surface Iso-Surface... (a) Select Grid... and Angular Coordinate from the Surface of Constant drop-down lists. (b) Click Compute to update the minimum and maximum values. (c) Enter 15 for Iso-Values. (d) Enter angle=15 for the New Surface Name. (e) Click Create to create the isosurface and close the Iso-Surface panel. c Fluent Inc. September 21, 2006 16-19

8. Review the current state of the solution by examining contours of velocity magnitude (Figure 16.3). Display Contours... (a) Select Velocity... and Velocity Magnitude from the Contours of drop-down lists. (b) Enable Filled in the Options group box. (c) Enable the Draw Grid option. The Grid Display panel will open. 16-20 c Fluent Inc. September 21, 2006

i. Retain the current grid display settings. ii. Close the Grid Display panel. (d) Select angle=15 from the Surfaces selection list in the Contours panel. (e) Click Display and close the Contours panel. (f) Use the mouse to obtain the view shown in Figure 16.3. Figure 16.3: Velocity Magnitude at Mid-Point of Atomizer Section c Fluent Inc. September 21, 2006 16-21

9. Modify the view to include the entire atomizer. Display Views... (a) Click the Define... button to open the Graphics Periodicity panel. i. Select fluid from the Cell Zones list. ii. Retain the selection of Rotational in the Periodic Type list. iii. Increase the Number of Repeats to 12. iv. Click Set and close the Graphics Periodicity panel. The graphics display will be updated to show the entire atomizer. (b) Click Apply and close the Views panel. 16-22 c Fluent Inc. September 21, 2006

10. Display path lines of the air in the swirling annular stream (Figure 16.4). Display Pathlines... (a) Select swirling air from the Release from Surfaces selection list. You will need to scroll down the list to access this item. (b) Increase the Path Skip value to 5. (c) Enable Draw Grid in the Options group box. The Grid Display panel will open. i. Retain the current grid display settings. ii. Close the Grid Display panel. (d) Click Display and close the Pathlines panel. (e) Use the mouse to obtain the view shown in Figure 16.4. Hint: Click Reset in the Graphics Periodicity panel to revert to the original display. c Fluent Inc. September 21, 2006 16-23

4.90e+01 4.65e+01 4.41e+01 4.17e+01 3.92e+01 3.68e+01 3.43e+01 3.19e+01 2.94e+01 2.70e+01 2.45e+01 2.20e+01 1.96e+01 1.71e+01 1.47e+01 1.23e+01 9.80e+00 7.35e+00 4.90e+00 Y 2.45e+00 0.00e+00 X Z Pathlines Colored by Particle ID FLUENT 6.3 (3d, pbns, spe, rke) Figure 16.4: Path Lines of Air in the Swirling Annular Stream 16-24 c Fluent Inc. September 21, 2006

Step 5: Create a Spray Injection 1. Define the discrete phase modeling parameters. Define Models Discrete Phase... (a) Enable Interaction with Continuous Phase in the Interaction group box. This will include the effects of the discrete phase trajectories on the continuous phase. (b) Set Number of Continuous Phase Iterations per DPM Iteration to 2. (c) Click the Physical Models tab to enable the physical models. i. Enable Droplet Collision and Droplet Breakup in the Spray Model group box. ii. Retain the default selection of TAB in the Breakup Model list. iii. Retain the default value of 0 for y0 in the Breakup Constants group box. c Fluent Inc. September 21, 2006 16-25

iv. Enter 50 for Breakup Parcels. This parameter is the dimensionless droplet distortion at t = 0. (d) Click the Tracking tab to specify the Tracking Parameters. i. Retain the default value of 5 for Step Length Factor. 16-26 c Fluent Inc. September 21, 2006

ii. Select dynamic-drag in the Drag Law drop-down list in the Drag Parameters group box. The dynamic-drag law is available only when the Droplet Breakup model is used. (e) Retain the Unsteady Particle Tracking option in the Particle Treatment group box. (f) Enter 0.0001 for Particle Time Step Size. (g) Retain the default value of 1 for Number of Time Steps. (h) Click OK to close the Discrete Phase Model panel. An Information dialog box will open, reminding you to confirm the property values before continuing. (i) Click OK in the Information dialog box to proceed. 2. Create the spray injection. In this step, you will define the characteristics of the atomizer. Define Injections... c Fluent Inc. September 21, 2006 16-27

(a) Click the Create button to open the Set Injection Properties panel. (b) Select air-blast-atomizer from the Injection Type drop-down list. (c) Enter 60 for Number of Particle Streams. This option controls how many droplet parcels are introduced into the domain at every time step. (d) Select Droplet in the Particle Type group box. (e) Select methyl-alcohol-liquid from the Material drop-down list. (f) Enter 0, 0, and 0.0015 for X-Position, Y-Position, and Z-Position, respectively, in the Point Properties tab. Scroll down the list to see the remaining point properties. (g) Enter 0, 0, and 1 for X-Axis, Y-Axis, and Z-Axis, respectively. (h) Enter 263 K for Temperature. (i) Enter 1.7e-4 kg/s for Flow Rate. 16-28 c Fluent Inc. September 21, 2006

This is the methanol flow rate for a 30-degree section of the atomizer. The actual atomizer flow rate is 12 times this value. (j) Retain the default Start Time of 0 s and enter 100 s for the Stop Time. For this problem, the injection should begin at t = 0 and not stop until long after the time period of interest. A large value for the stop time (e.g., 100 s) will ensure that the injection will essentially never stop. (k) Enter 0.0035 m for the Injector Inner Diameter and 0.0045 m for the Injector Outer Diameter. (l) Enter -45 degrees for the Spray Half Angle. The spray angle is the angle between the liquid sheet trajectory and the injector centerline. In this case, the value is negative because the sheet is initially converging toward the centerline. (m) Enter 82.6 m/s for the Relative Velocity. The relative velocity is the expected relative velocity between the atomizing air and the liquid sheet. (n) Retain the default Azimuthal Start Angle of 0 degrees and enter 30 degrees for the Azimuthal Stop Angle. This will restrict the injection to the 30-degree section of the atomizer that is being modeled. (o) Define the turbulent dispersion. i. Click the Turbulent Dispersion tab. c Fluent Inc. September 21, 2006 16-29

The lower half of the panel will change to show options for the turbulent dispersion model. ii. Enable Discrete Random Walk Model and Random Eddy Lifetime in the Stochastic Tracking group box. These models will account for the turbulent dispersion of the droplets. (p) Click OK to close the Set Injection Properties panel. (q) Close the Injections panel. Note: In the case that the spray injection would be striking a wall, you would need to specify the wall boundary conditions for the droplets. Though this tutorial does have wall zones, they are a part of the atomizer apparatus. Because these walls are not in the path of the spray droplets, you do not need to change the wall boundary conditions any further. 16-30 c Fluent Inc. September 21, 2006

3. Set the droplet material properties. Because the secondary atomization models (breakup and coalescence) are used, the droplet properties must be set. Define Materials... (a) Select droplet-particle from the Material Type drop-down list. (b) Enter 0.0056 kg/m-s for Viscosity in the Properties list. (c) Select piecewise-linear from the Saturation Vapor Pressure drop-down list. Scroll down to find the Saturation Vapor Pressure drop-down list. The Piecewise-Linear Profile panel will open. i. Click OK to retain the default values and close the Piecewise-Linear Profile panel. (d) Scroll down and enter 0.0222 N/m for Droplet Surface Tension. (e) Click Change/Create to accept the change in properties for the methanol droplet material and close the Materials panel. c Fluent Inc. September 21, 2006 16-31

Step 6: Solution 1. Disable Check Convergence for all the residuals. Solve Monitors Residual... 2. Reduce the Under-Relaxation Factor for Discrete Phase Sources to 0.1. Solve Controls Solution... 3. Request 200 iterations. Solve Iterate... 4. Save the case and data files (spray2.cas.gz and spray2.dat.gz). File Write Case & Data... 5. Display the trajectories of the droplets in the spray injection (Figure 16.5). This will allow you to review the location of the droplets. Display Particle Tracks... (a) Retain the default selection of point in the Style drop-down list. 16-32 c Fluent Inc. September 21, 2006

(b) Enable Draw Grid in the Options group box. The Grid Display panel will open. i. Retain the current display settings. ii. Close the Grid Display panel. (c) Select Particle Variables... and Particle Diameter from the Color by drop-down lists in the Particle Tracks panel. This will display the location of the droplets colored by their diameters. (d) Select injection-0 from the Release from Injections selection list. (e) Click Display and close the Particle Tracks panel. (f) Use the mouse to obtain the view shown in Figure 16.5. The air-blast atomizer model assumes that a cylindrical liquid sheet exits the atomizer, which then disintegrates into ligaments and droplets. Appropriately, the model determines that the droplets should be input into the domain in a ring. The radius of this disk is determined from the inner and outer radii of the injector. Note: The maximum diameter of the droplets is about 10 4 m, or 0.1 mm. This is slightly smaller than the film height, which makes sense. Recall that the inner diameter and outer diameter of the injector are 3.5 mm and 4.5 mm, respectively. The film height is then 1 (4.5 3.5) = 0.5 mm. 2 The range in the droplet sizes is due to the fact that the air-blast atomizer automatically uses a distribution of droplet sizes. Also note that the droplets are placed a slight distance away from the injector. Once the droplets are injected into the domain, they can collide/coalesce with other droplets as determined by the secondary models c Fluent Inc. September 21, 2006 16-33

2.89e-04 2.75e-04 2.60e-04 2.46e-04 2.32e-04 2.18e-04 2.03e-04 1.89e-04 1.75e-04 1.61e-04 1.46e-04 1.32e-04 1.18e-04 1.04e-04 8.92e-05 7.50e-05 6.07e-05 4.65e-05 3.22e-05 Z 1.79e-05 3.67e-06 X Y Particle Traces Colored by Particle Diameter (m) FLUENT 6.3 (3d, pbns, spe, rke) Figure 16.5: Particle Tracks for the Spray Injection After 200 Iterations (breakup and collision). However, once a droplet has been introduced into the domain, the air-blast atomizer model no longer affects the droplet. 6. Request 200 more iterations. Solve Iterate... 7. Save the new case and data files (spray3.cas.gz and spray3.dat.gz). File Write Case & Data... Step 7: Postprocessing 1. Display the particle trajectories again, to examine the droplet dispersion. Display Particle Tracks... (a) Click Display and close the Particle Tracks panel. (b) Use the mouse to obtain the view shown in Figure 16.6. 16-34 c Fluent Inc. September 21, 2006

2.98e-04 2.83e-04 2.68e-04 2.54e-04 2.39e-04 2.24e-04 2.10e-04 1.95e-04 1.80e-04 1.65e-04 1.51e-04 1.36e-04 1.21e-04 1.07e-04 9.20e-05 7.74e-05 6.27e-05 4.80e-05 3.33e-05 Z 1.86e-05 3.92e-06 X Y Particle Traces Colored by Particle Diameter (m) FLUENT 6.3 (3d, pbns, spe, rke) Figure 16.6: Particle Tracks for the Spray Injection After 400 Iterations. 2. Create an isosurface of the methanol mass fraction. Surface Iso-Surface... (a) Select Species... and Mass fraction of ch3oh from the Surface of Constant dropdown lists. (b) Click Compute to update the minimum and maximum values. (c) Enter 0.0075 for Iso-Values. (d) Enter methanol-mf=0.0075 for the New Surface Name. (e) Click Create and the close the Iso-Surface panel. c Fluent Inc. September 21, 2006 16-35

3. Display the isosurface you just created (methanol-mf=0.0075). Display Grid... (a) Deselect atomizer-wall and select methanol-mf=0.0075 in the Surfaces selection list. (b) Click the Colors... button to open the Grid Colors panel. i. Select Color By Type from the Options list. ii. Select surface in the Types list and green in the Colors list. Scroll down the Types list to locate surface. The isosurface will now be displayed in green, which contrasts better with the rest of the grid. iii. Close the Grid Colors panel. 16-36 c Fluent Inc. September 21, 2006

(c) Click Display in the Grid Display panel. The graphics display will be updated to show the isosurface. 4. Modify the view to include the entire atomizer. Display Views... (a) Click Define... to open the Graphics Periodicity panel. i. Select fluid from the Cell Zones list. ii. Make sure Rotational is selected from the Periodic Type list. iii. Set the Number of Repeats to 12. c Fluent Inc. September 21, 2006 16-37

Z Y X Grid FLUENT 6.3 (3d, pbns, spe, rke) Figure 16.7: Full Atomizer Display with Surface of Constant Methanol Mass Fraction iv. Click Set and close the Graphics Periodicity panel. (b) Click Apply and close the Views panel. (c) Click Display and close the Grid Display panel. The graphics display will be updated to show the entire atomizer. (d) Use the mouse to obtain the view shown in Figure 16.7. Summary In this tutorial, a spray injection was defined for an air-blast atomizer and the solution was calculated using FLUENT s discrete-phase model. The location of methanol droplet particles after exiting the atomizer and an isosurface of the methanol mass fraction were examined. Further Improvements This tutorial guides you through the steps to reach an initial solution. You may be able to obtain a more accurate solution by using an appropriate higher-order discretization scheme and by adapting the grid. Grid adaption can also ensure that the solution is independent of the grid. These steps are demonstrated in Tutorial 1. 16-38 c Fluent Inc. September 21, 2006