c Fluent Inc. November 27,

Tutorial 15. Using the VOF Model Introduction: This tutorial illustrates the setup and solution of the two-dimensional turbulent fluid flow in a partially filled spinning bowl. In this tutorial you will learn how to: Set up and solve a transient free-surface problem using the segregated solver Model the effect of gravity Copy a material from the property database Patch initial conditions in a subset of the domain Define a custom field function Mirror and rotate the view in the graphics window Examine the fluid flow and the free-surface shape using velocity vectors and volume fraction contours Prerequisites: This tutorial requires a basic familiarity with FLUENT. You may also find it helpful to read about VOF multiphase flow modeling in the FLUENT User s Guide. Otherwise, no previous experience with multiphase modeling is required. Problem Description: The information relevant to this problem is shown in Figure 15.1. A large bowl, 1 m in radius, is one-third filledwithwaterandisopentotheatmosphere. Thebowlspins with an angular velocity of 3 rad/sec. Based on the rotating water, the Reynolds number is about 10 6, so the flow is modeled as turbulent. c Fluent Inc. November 27, 2001 15-1

2 m 1 m Bowl: Ω = 3 rad/s Air: ρ = µ = 3 1.225 kg/m -5 1.7894 x 10 kg/m-s Water: ρ = 998.2 kg/m 3 µ -3 = 1 x 10 kg/m-s Figure 15.1: Water and Air in a Spinning Bowl Preparation 1. Copy the file vof/bowl.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). The mesh file bowl.msh is a quadrilateral mesh describing the system geometry shown in Figure 15.1. 2. Start the 2D version of FLUENT. 15-2 c Fluent Inc. November 27, 2001

Step 1: Grid 1. Read the 2D grid file, bowl.msh. File Read Case... 2. Display the grid (Figure 15.2). Display Grid... As shown in Figure 15.2, half of the bowl is modeled, with a symmetry boundary at the centerline. The bowl is shown lying on its side, with the region to be modeled extending from the centerline to the outer wall. When you begin to display data graphically, you will need to rotate the view and mirror it across the centerline to obtain a more realistic view of the model. This step will be performed later in the tutorial. c Fluent Inc. November 27, 2001 15-3

Grid Jun 12, 2001 FLUENT 6.0 (2d, segregated, lam) Figure 15.2: Grid Display 15-4 c Fluent Inc. November 27, 2001

Step 2: Models 1. Specify a transient model with axisymmetric swirl. Define Models Solver... (a) Retain the default Segregated solver. The segregated solver must be used for multiphase calculations. (b) Under Space, select Axisymmetric Swirl. (c) Under Time, select Unsteady. c Fluent Inc. November 27, 2001 15-5

2. Turn on the VOF model. Define Models Multiphase... (a) Select Volume of Fluid as the Model. The panel will expand to show inputs for the VOF model. (b) Under VOF Parameters, select Geo-Reconstruct (the default) as the VOF Scheme. This is the most accurate interface-tracking scheme, and is recommended for most transient VOF calculations. When you click OK, FLUENT will report that one of the zone types will need to be changed before proceeding with the calcu- 15-6 c Fluent Inc. November 27, 2001

lation. You will take care of this step when you input boundary conditions for the problem. 3. Turn on the standard k-ɛ turbulence model. Define Models Viscous... (a) Select k-epsilon as the Model, and retain the default setting of Standard under k-epsilon Model. c Fluent Inc. November 27, 2001 15-7

Step 3: Materials 1. Copy water from the materials database so that it can be used for the secondary phase. Define Materials... (a) Click on the Database... button toopen thedatabase Materials panel. 15-8 c Fluent Inc. November 27, 2001

(b) In the Fluid Materials list (near the bottom), select waterliquid. (c) Click on Copy and close the Database Materials and Materials panels. Step 4: Phases Here, water is defined as the secondary phase mainly for convenience in setting up the problem. When you define the initial solution, you will be patching an initial swirl velocity in the bottom third of the bowl, where the water is. It is more convenient to patch a water volume fraction of 1 there than to patch an air volume fraction of 1 in the rest of the domain. Also, the default volume fraction at the pressure inlet is 0, which is the correct value if water is the secondary phase. In general, you can specify the primary and secondary phases whichever way you prefer. It is a good idea, especially in more complicated problems, to consider how your choice will affect the ease of problem setup. 1. Define the air and water phases within the bowl. Define Phases... c Fluent Inc. November 27, 2001 15-9

(a) Specify air as the primary phase. i. Select phase-1 and click the Set... button. ii. In the Primary Phase panel, enter air for the Name. iii. Keep the default selection of air for the Phase Material. (b) Specify water as the secondary phase. i. Select phase-2 and click the Set... button. ii. In the Secondary Phase panel, enter water for the Name. iii. Select water-liquid from the Phase Material drop-down list. 15-10 c Fluent Inc. November 27, 2001

Step 5: Operating Conditions 1. Set the gravitational acceleration. Define Operating Conditions... (a) Turn on Gravity. The panel will expand to show additional inputs. (b) Set the Gravitational Acceleration in the X direction to 9.81 m/s 2. Since the centerline of the bowl is the x axis, gravity points in the positive x direction. 2. Set the operating density. (a) Under Variable-Density Parameters, turnonthespecified Operating Density option and accept the Operating Density of 1.225. It is a good idea to set the operating density to be the density of the lighter phase. This excludes the buildup of hydrostatic pressure within the lighter phase, improving the round-off accuracy for the momentum balance. c Fluent Inc. November 27, 2001 15-11

Note: The Reference Pressure Location (0,0)issituatedinare- gion where the fluid will always be 100% of one of the phases (air), a condition that is essential for smooth and rapid convergence. If it were not, you would need to change it to a more appropriate location. Step 6: Boundary Conditions Define Boundary Conditions... 1. Change the bowl centerline from a symmetry boundary to an axis boundary. For axisymmetric models, the axis of symmetry must be an axis zone. (a) Select symmetry-2 in the Zone list in the Boundary Conditions panel. (b) In the Type list, choose axis. You will have to scroll to the top of the list. (c) Click Yes in the Question dialog box that appears. (d) Click OK in the Axis panel to accept the default Zone Name. 15-12 c Fluent Inc. November 27, 2001

2. Set the conditions at the top of the bowl (the pressure inlet). For the VOF model, you will specify conditions for the mixture (i.e., conditions that apply to all phases) and also conditions that are specific to the secondary phase. There are no conditions to be specified for the primary phase. (a) Set the conditions for the mixture. i. In the Boundary Conditions panel, keep the default selection of mixture in the Phase drop-down list and click Set... ii. Set the Turb. Kinetic Energy to 2.25e-2 and the Turb. Dissipation Rate to 7.92e-3. Since there is initially no flow passing through the pressure inlet, you need to specify k and ɛ explicitly rather than using one of the other turbulence specification methods. All of the other methods require you to specify the turbulence intensity, which is 0 in this case. The values for k and ɛ are computed as follows: c Fluent Inc. November 27, 2001 15-13

k =(Iw wall ) 2 ɛ = 0.093/4 k 3/2 l where the turbulence intensity I is 0.05 (close to zero), w wall is 3 m/s, and l is 0.07 (obtained by multiplying 0.07 by the maximum radius of the bowl, which is 1). See the User s Guide for details about the specification of turbulence boundary conditions at flow inlets and exits. (b) Check the volume fraction of the secondary phase. i. In the Boundary Conditions panel, select water from the Phase drop-down list and click Set... ii. Retain the default Volume Fraction of 0. A water volume fraction of 0 indicates that only air is present at the pressure inlet. 15-14 c Fluent Inc. November 27, 2001

3. Set the conditions for the spinning bowl (the wall boundary). For a wall boundary, all conditions are specified for the mixture. There are no conditions to be specified for the individual phases. (a) In the Boundary Conditions panel, select mixture in the Phase drop-down list and click Set... c Fluent Inc. November 27, 2001 15-15

(b) Select Moving Wall under Wall Motion. The panel will expand to show inputs for the wall motion. (c) Under Motion, chooserotational and then set the rotational Speed (Ω) to 3 rad/s. 15-16 c Fluent Inc. November 27, 2001

Step 7: Solution In simple flows, the under-relaxation factors can usually be increased at the start of the calculation. This is particularly true when the VOF model is used, where high under-relaxation on all variables can greatly improve the performance of the solver. 1. Set the solution parameters. Solve Controls Solution... (a) Set all Under-Relaxation factors to 1.! Be sure to use the scroll bar to access the under-relaxation factors that are initially out of view. c Fluent Inc. November 27, 2001 15-17

(b) Under Discretization, choose the Body Force Weighted scheme in the drop-down list next to Pressure. The body-force-weighted pressure discretization scheme is recommended when you solve a VOF problem involving gravity. (c) Also under Discretization, select PISO as the Pressure-Velocity Coupling method. PISO is recommended for transient flow calculations. 2. Enable the display of residuals during the solution process. Solve Monitors Residual... (a) Under Options, select Plot. (b) Click the OK button. 15-18 c Fluent Inc. November 27, 2001

3. Enable the plotting of the axial velocity of water near the outer edge of the bowl during the calculation. For transient calculations, it is often useful to monitor the value of a particular variable to see how it changes over time. Here you will first specify the point at which you want to track the velocity, and then define the monitoring parameters. (a) Define a point surface near the outer edge of the bowl. Surface Point... i. Set the x0 and y0 coordinates to 0.75 and 0.65. ii. Enter point for the New Surface Name. iii. Click Create. c Fluent Inc. November 27, 2001 15-19

(b) Define the monitoring parameters. Solve Monitors Surface... i. Increase the Surface Monitors value to 1. ii. Turn on the Plot and Write options for monitor-1. Note: When the Write option is selected in the Surface Monitors panel, the velocity history will be written to a file. If you do not select the Write option, the history information will be lost when you exit FLUENT. iii. In the drop-down list under Every, choosetime Step. iv. Click on Define... to specify the surface monitor parameters in the Define Surface Monitor panel. 15-20 c Fluent Inc. November 27, 2001

v. Select Vertex Average from the Report Type drop-down list. This is the recommended choice when you are monitoring the value at a single point using a point surface. vi. Select Flow Time in the XAxisdrop-down list. vii. Select Velocity... and Axial Velocity in the Report Of dropdown lists. viii. Select point in the Surfaces list. ix. Enter axial-velocity.out for the File Name. x. Click OK in the Define Surface Monitor panel and then in the Surface Monitors panel. c Fluent Inc. November 27, 2001 15-21

4. Initialize the solution. Solve Initialize Initialize... (a) Select pressure-inlet-4 in the Compute From drop-down list. All initial values will be set to zero, except for the turbulence quantities. (b) Click Init and close the panel. 15-22 c Fluent Inc. November 27, 2001

5. Patch the initial distribution of water (i.e., water volume fraction of 1.0) and a swirl velocity of 3 rad/s in the bottom third of the bowl (where the water is). In order to patch a value in just a portion of the domain, you will need to define a cell register for that region. You will use the same tool that is used to mark a region of cells for adaption. Also, you will need to define a custom function for the swirl velocity. (a) Define a register for the bottom third of the domain. Adapt Region... i. Set the (Xminimum,Yminimum) coordinateto(0.66,0), and the (Xmaximum,Ymaximum) coordinateto(1,1). ii. Click the Mark button. This creates a register containing the cells in this region. c Fluent Inc. November 27, 2001 15-23

(b) Check the register to be sure it is correct. Adapt Manage... i. Select the register (hexahedron-r0) intheregisters list and click Display. The graphics display will show the bottom third of the bowl in red. 15-24 c Fluent Inc. November 27, 2001

(c) Define a custom field function for the swirl velocity w =3r. Define Custom Field Functions... i. Click the 3 button on the calculator pad. The 3 will appear in the Definition field. If you make a mistake, click the DEL button to delete the last item you added to the function definition. ii. Click the X button on the calculator pad. iii. In the Field Functions drop-down list, select Grid... and Radial Coordinate. iv. Click the Select button. radial-coordinate will appear in the Definition. v. Enter a New Function Name of swirl-init. vi. Click Define. Note: If you wish to check the function definition, click on the Manage... button and select swirl-init. c Fluent Inc. November 27, 2001 15-25

(d) Patch the water volume fraction in the bottom third of the bowl. Solve Initialize Patch... i. Choose water Volume Fraction in the Variable list. ii. Select hexahedron-r0 in the Registers To Patch list. iii. Set the Value to 1. iv. Click Patch. This sets the water volume fraction to 1 in the lower third of the bowl. That is, you have defined the lower third of the bowl to be filled with water. 15-26 c Fluent Inc. November 27, 2001

(e) Patch the swirl velocity in the bottom third of the bowl. i. Choose Swirl Velocity in the Variable list. ii. Enable the Use Field Function option and select swirl-init in the Field Function list. iii. Click Patch. It s a good idea to check your patch by displaying contours of the patched fields. c Fluent Inc. November 27, 2001 15-27

(f) Display contours of swirl velocity. Display Contours... i. Select Velocity... and Swirl Velocity in the Contours Of lists. ii. Enable the Filled option and turn off the Node Values option. Since the values you patched are cell values, you should view the cell values, rather than the node values, to check that the patch has been performed correctly. (FLUENT computes the node values by averaging the cell values.) iii. Click Display. To make the view more realistic, you will need to rotate the display and mirror it across the centerline. 15-28 c Fluent Inc. November 27, 2001

(g) Rotate the view and mirror it across the centerline. Display Views... i. Select axis-2 in the Mirror Planes list and click Apply. ii. Use your middle and left mouse buttons to zoom and translate the view so that the entire bowl is visible in the graphics display. iii. Click on the Camera... button to open the Camera Parameters panel. c Fluent Inc. November 27, 2001 15-29

iv. Using your left mouse button, rotate the dial clockwise until the bowl appears upright in the graphics window (90 ). v. Close the Camera Parameters panel. vi. In the Views panel, click on the Save button under Actions to save the mirrored, upright view, and then close the panel. When you do this, view-0 will be added to the list of Views. The upright view of the bowl in Figure 15.3 correctly shows that w =3r in the region of the bowl that is filled with water. 2.35e+00 2.12e+00 1.88e+00 1.65e+00 1.41e+00 1.18e+00 9.41e-01 7.06e-01 4.70e-01 2.35e-01 0.00e+00 Contours of Swirl Velocity (m/s) (Time=0.0000e+00) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.3: Contours of Initial Swirl Velocity 15-30 c Fluent Inc. November 27, 2001

(h) Display contours of water volume fraction. i. Select Phases... and Volume fraction of water in the Contours Of lists. ii. Set the number of contour Levels to 2 and click Display. There are only two possible values for the volume fraction at this point: 0 or 1. Figure 15.4 correctly shows that the bottom third of the bowl contains water. c Fluent Inc. November 27, 2001 15-31

1.00e+00 0.00e+00 Contours of Volume fraction of water (Time=0.0000e+00) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.4: Contours of Initial Water Volume Fraction 15-32 c Fluent Inc. November 27, 2001

6. Set the time-step parameters for the calculation. Solve Iterate... (a) Set the Time Step Size to 0.002 seconds. (b) Click Apply. This will save the time step size to the case file (the next time a case file is saved). 7. Request saving of data files every 100 time steps. File Write Autosave... (a) Set the Autosave Case File Frequency to 0 and the Autosave Data File Frequency to 100. (b) Enter the Filename bowl andthenclickok. FLUENT will append the time step value to the file name prefix (bowl). The standard.dat extension will also be appended. This will yield file names of the form bowl100.dat, where100 is the time step number. 8. Save the initial case and data files (bowl.cas and bowl.dat). File Write Case & Data... 9. Request 1000 time steps. Solve Iterate... c Fluent Inc. November 27, 2001 15-33

Since the time step is 0.002 seconds, you will be calculating up to t= 2 seconds. FLUENT will automatically save a data file after every 0.2 seconds, so you will have 10 data files for postprocessing. Figure 15.5 shows the time history for the axial velocity. The velocity is clearly oscillating, and the oscillations appear to be decaying over time (as the peaks become smaller). This periodic oscillation has a cycle of 1 second. The switch from a positive to a negative axial velocity indicates that the water is sloshing up and down the sides of the bowl in an attempt to reach an equilibrium position. The fact that the amplitude is decaying suggests that equilibrium will be reached at some point. The periodic behavior in evidence will therefore be present only during the initial startup phase of the bowl rotation. 0.3000 0.2000 0.1000 Average Surface of Vertex Values (m/s) 0.0000-0.1000-0.2000-0.3000 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 Flow Time Convergence history of Axial Velocity on point (Time=2.0000e+00) Jun 13, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.5: Time History of Axial Velocity 15-34 c Fluent Inc. November 27, 2001

Step 8: Postprocessing As indicated by changes in axial velocity in Figure 15.5, the flow field is oscillating periodically. In this step, you will examine the flow field at several different times. (Recall that FLUENT saved 10 data files for you during the calculation.) 1. Read in the data file of interest. File Read Data... 2. Display filled contours of water volume fraction. Display Contours... Hint: Follow the instructions in substep 5h of Step 7: Solution (on page 15-31), but turn Node Values back on. Figures 15.6 15.9 show that the water level decreases from t =0.4 to t =0.6, then increases from t =0.6 to t =1. At t =1,the water level in the center of the bowl has risen above the initial level, so you can expect the cycle to repeat as the water level begins to decrease again in an attempt to return to equilibrium. (You can read in the data files between t =1and t =2to confirm that this is in fact what happens. Since the time history of axial velocity (Figure 15.5) shows that the velocity oscillation is decaying over time, you can expect that if you were to continue the calculation, the water level would eventually reach some point where the gravitational and centrifugal forces balance and the water level reaches a new equilibrium point. Extra: Try continuing the calculation to determine how long it takes for the axial velocity oscillations in Figure 15.5 to disappear. c Fluent Inc. November 27, 2001 15-35

1.00e+00 0.00e+00 Contours of Volume fraction of water (Time=4.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.6: Shape of the Free Surface at t =0.4 1.00e+00 0.00e+00 Contours of Volume fraction of water (Time=6.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.7: Shape of the Free Surface at t =0.6 15-36 c Fluent Inc. November 27, 2001

1.00e+00 0.00e+00 Contours of Volume fraction of water (Time=8.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.8: Shape of the Free Surface at t =0.8 1.00e+00 0.00e+00 Contours of Volume fraction of water (Time=9.9999e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.9: Shape of the Free Surface at t =1 c Fluent Inc. November 27, 2001 15-37

3. Plot contours of stream function. (a) Select Stream Function (in the Velocity... category) in the Contours Of drop-down list. (b) Turn off the Filled option and increase the number of contour Levels to 30. (c) Click on Display. In Figures 15.10 15.13, you can see a recirculation region that falls and rises as the water level changes. To get a better sense of these recirculating patterns, you will next look at velocity vectors. 15-38 c Fluent Inc. November 27, 2001

2.58e+01 2.41e+01 2.24e+01 2.06e+01 1.89e+01 1.72e+01 1.55e+01 1.38e+01 1.20e+01 1.03e+01 8.60e+00 6.88e+00 5.16e+00 3.44e+00 1.72e+00 0.00e+00 Contours of Stream Function (kg/s) (Time=4.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.10: Contours of Stream Function at t = 0.4 2.65e+01 2.47e+01 2.29e+01 2.12e+01 1.94e+01 1.76e+01 1.59e+01 1.41e+01 1.24e+01 1.06e+01 8.82e+00 7.06e+00 5.29e+00 3.53e+00 1.76e+00 0.00e+00 Contours of Stream Function (kg/s) (Time=6.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.11: Contours of Stream Function at t = 0.6 c Fluent Inc. November 27, 2001 15-39

4.73e+01 4.41e+01 4.10e+01 3.78e+01 3.47e+01 3.15e+01 2.84e+01 2.52e+01 2.21e+01 1.89e+01 1.58e+01 1.26e+01 9.46e+00 6.31e+00 3.15e+00 0.00e+00 Contours of Stream Function (kg/s) (Time=8.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.12: Contours of Stream Function at t = 0.8 8.84e+00 8.25e+00 7.66e+00 7.07e+00 6.48e+00 5.89e+00 5.30e+00 4.71e+00 4.13e+00 3.54e+00 2.95e+00 2.36e+00 1.77e+00 1.18e+00 5.89e-01 0.00e+00 Contours of Stream Function (kg/s) (Time=9.9999e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.13: Contours of Stream Function at t =1 15-40 c Fluent Inc. November 27, 2001

4. Plot velocity vectors in the bowl. Display Vectors... (a) In the Style drop-down list, select arrow. This will make the velocity direction easier to see. (b) Increase the Scale factor to 6 and increase the Skip value to 1. (c) Click on Vector Options... to open the Vector Options panel. c Fluent Inc. November 27, 2001 15-41

i. Turn off the Z Component. This allows you to examine the non-swirling components only. ii. Click Apply and close the panel. (d) Click on Display. Figures 15.14 15.17 show the changes in water and air flow patterns between t =0.4 and t =1. In Figure 15.14, you can see that the flow in the middle of the bowl is being pulled down by gravitational forces, and pushed out and up along the sides of the bowl by centrifugal forces. This causes the water level to decrease in the center of the bowl, as shown in the volume fraction contour plots, and also results in the formation of a recirculation region in the air above the water surface. In Figure 15.15, the flow has reversed direction, and is slowly rising up in the middle of the bowl and being pulled down along the sides of the bowl. This reversal occurs because the earlier flow pattern caused the water to overshoot the equilibrium position. The gravity and centrifugal forces now act to compensate for this overshoot. 15-42 c Fluent Inc. November 27, 2001

1.92e+00 1.79e+00 1.66e+00 1.54e+00 1.41e+00 1.28e+00 1.16e+00 1.03e+00 9.00e-01 7.73e-01 6.46e-01 5.18e-01 3.91e-01 2.63e-01 1.36e-01 8.63e-03 Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=4.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.14: Velocity Vectors for the Air and Water at t =0.4 1.94e+00 1.81e+00 1.68e+00 1.55e+00 1.42e+00 1.30e+00 1.17e+00 1.04e+00 9.07e-01 7.77e-01 6.48e-01 5.18e-01 3.89e-01 2.59e-01 1.30e-01 4.88e-04 Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=6.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.15: Velocity Vectors for the Air and Water at t =0.6 c Fluent Inc. November 27, 2001 15-43

2.13e+00 1.99e+00 1.85e+00 1.71e+00 1.57e+00 1.42e+00 1.28e+00 1.14e+00 9.98e-01 8.56e-01 7.15e-01 5.73e-01 4.31e-01 2.89e-01 1.47e-01 5.04e-03 Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=8.0000e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.16: Velocity Vectors for the Air and Water at t =0.8 2.12e+00 1.98e+00 1.84e+00 1.70e+00 1.56e+00 1.41e+00 1.27e+00 1.13e+00 9.91e-01 8.50e-01 7.09e-01 5.68e-01 4.27e-01 2.85e-01 1.44e-01 3.06e-03 Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=9.9999e-01) Jun 12, 2001 FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady) Figure 15.17: Velocity Vectors for the Air and Water at t =1 15-44 c Fluent Inc. November 27, 2001

In Figure 15.16 you can see that the flow is rising up more quickly in the middle of the bowl, and in Figure 15.17 you can see that the flow is still moving upward, but more slowly. These patterns correspond to the volume fraction plots at these times. As the upward motion in the center of the bowl decreases, you can expect the flow to reverse as the water again seeks to reach a state of equilibrium. Summary: In this tutorial, you have learned how to use the VOF free surface model to solve a problem involving a spinning bowl of water. The time-dependent VOF formulation is used in this problem to track the shape of the free surface and the flow field inside the spinning bowl. You observed the changing pattern of the water and air in the bowl by displaying volume fraction contours, stream function contours, and velocity vectors at t =0.4, t =0.6, t =0.8, and t = 1 second. c Fluent Inc. November 27, 2001 15-45

15-46 c Fluent Inc. November 27, 2001