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 veloc- ity 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 ﬁlled with water and is open to the atmosphere. The bowl spins with an angular velocity of 3 rad/sec. Based on the rotating wa- ter, the Reynolds number is about 10 6 , so the ﬂow is modeled as turbulent. c Fluent Inc. November 27, 2001 15-1
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Tutorial 15. Using the VOF Model

Introduction: This tutorial illustrates the setup and solution of thetwo-dimensional turbulent fluid flow in a partially filled spinningbowl.

In this tutorial you will learn how to:

• Set up and solve a transient free-surface problem using thesegregated 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 veloc-ity 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 flowmodeling in the FLUENT User’s Guide. Otherwise, no previousexperience with multiphase modeling is required.

Problem Description: The information relevant to this problem isshown in Figure 15.1. A large bowl, 1 m in radius, is one-thirdfilled with water and is open to the atmosphere. The bowl spinswith an angular velocity of 3 rad/sec. Based on the rotating wa-ter, the Reynolds number is about 106, so the flow is modeled asturbulent.

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2 m

1 m

-5

-3

Air: ρ = 1.225 kg/m

µ = 1.7894 x 10 kg/m-sWater: ρ = 998.2 kg/m 3

µ = 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 CDto your working directory (as described in Tutorial 1).

The mesh file bowl.msh is a quadrilateral mesh describing the sys-tem geometry shown in Figure 15.1.

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the 2D grid file, bowl.msh.

2. Display the grid (Figure 15.2).

Display −→Grid...

As shown in Figure 15.2, half of the bowl is modeled, with a sym-metry boundary at the centerline. The bowl is shown lying on itsside, with the region to be modeled extending from the centerline tothe outer wall. When you begin to display data graphically, you willneed to rotate the view and mirror it across the centerline to obtaina more realistic view of the model. This step will be performed laterin the tutorial.

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GridFLUENT 6.0 (2d, segregated, lam)

Jun 12, 2001

Figure 15.2: Grid Display

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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.

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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 isrecommended for most transient VOF calculations.

When you click OK, FLUENT will report that one of the zonetypes will need to be changed before proceeding with the calcu-

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lation. You will take care of this step when you input boundaryconditions for the problem.

3. Turn on the standard k-ε turbulence model.

Define −→ Models −→Viscous...

(a) Select k-epsilon as the Model, and retain the default setting ofStandard under k-epsilon Model.

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Step 3: Materials

1. Copy water from the materials database so that it can be used forthe secondary phase.

Define −→Materials...

(a) Click on the Database... button to open the Database Materialspanel.

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(b) In the Fluid Materials list (near the bottom), select water-liquid.

(c) Click on Copy and close the Database Materials and Materialspanels.

Step 4: Phases

Here, water is defined as the secondary phase mainly for convenience insetting up the problem. When you define the initial solution, you will bepatching an initial swirl velocity in the bottom third of the bowl, wherethe water is. It is more convenient to patch a water volume fraction of 1there 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 thecorrect value if water is the secondary phase.

In general, you can specify the primary and secondary phases whicheverway 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...

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(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.

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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 9.81m/s2.

Since the centerline of the bowl is the x axis, gravity points inthe positive x direction.

2. Set the operating density.

(a) Under Variable-Density Parameters, turn on the Specified Op-erating Density option and accept the Operating Density of1.225.

It is a good idea to set the operating density to be the densityof the lighter phase. This excludes the buildup of hydrostaticpressure within the lighter phase, improving the round-off ac-curacy for the momentum balance.

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Note: The Reference Pressure Location (0,0) is situated in a re-gion where the fluid will always be 100% of one of the phases(air), a condition that is essential for smooth and rapid con-vergence. If it were not, you would need to change it to amore appropriate location.

Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Change the bowl centerline from a symmetry boundary to an axisboundary.

For axisymmetric models, the axis of symmetry must be an axiszone.

(a) Select symmetry-2 in the Zone list in the Boundary Conditionspanel.

(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.

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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 thatare specific to the secondary phase. There are no conditions to bespecified for the primary phase.

(a) Set the conditions for the mixture.

i. In the Boundary Conditions panel, keep the default se-lection of mixture in the Phase drop-down list and clickSet....

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 pres-sure inlet, you need to specify k and ε explicitly ratherthan using one of the other turbulence specification meth-ods. All of the other methods require you to specify theturbulence intensity, which is 0 in this case.

The values for k and ε are computed as follows:

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k = (Iwwall)2

ε =0.093/4k3/2

`

where the turbulence intensity I is 0.05 (close to zero),wwall is 3 m/s, and ` is 0.07 (obtained by multiplying0.07 by the maximum radius of the bowl, which is 1).See the User’s Guide for details about the specification ofturbulence 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 thePhase drop-down list and click Set....

ii. Retain the default Volume Fraction of 0.

A water volume fraction of 0 indicates that only air ispresent at the pressure inlet.

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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 Phasedrop-down list and click Set....

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(b) Select Moving Wall under Wall Motion.

The panel will expand to show inputs for the wall motion.

(c) Under Motion, choose Rotational and then set the rotationalSpeed (Ω) to 3 rad/s.

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Step 7: Solution

In simple flows, the under-relaxation factors can usually be increased atthe start of the calculation. This is particularly true when the VOF modelis used, where high under-relaxation on all variables can greatly improvethe 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-relaxationfactors that are initially out of view.

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(b) Under Discretization, choose the Body Force Weighted schemein the drop-down list next to Pressure.

The body-force-weighted pressure discretization scheme is rec-ommended when you solve a VOF problem involving gravity.

(c) Also under Discretization, select PISO as the Pressure-VelocityCoupling 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.

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3. Enable the plotting of the axial velocity of water near the outeredge of the bowl during the calculation.

For transient calculations, it is often useful to monitor the valueof a particular variable to see how it changes over time. Here youwill 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.

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(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 SurfaceMonitors panel, the velocity history will be written to afile. If you do not select the Write option, the historyinformation will be lost when you exit FLUENT.

iii. In the drop-down list under Every, choose Time Step.

iv. Click on Define... to specify the surface monitor parame-ters in the Define Surface Monitor panel.

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v. Select Vertex Average from the Report Type drop-downlist.

This is the recommended choice when you are monitoringthe value at a single point using a point surface.

vi. Select Flow Time in the X Axis drop-down list.

vii. Select Velocity... and Axial Velocity in the Report Of drop-down 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 inthe Surface Monitors panel.

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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 turbulencequantities.

(b) Click Init and close the panel.

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5. Patch the initial distribution of water (i.e., water volume fractionof 1.0) and a swirl velocity of 3 rad/s in the bottom third of thebowl (where the water is).

In order to patch a value in just a portion of the domain, you willneed to define a cell “register” for that region. You will use thesame 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.

i. Set the (Xminimum,Yminimum) coordinate to (0.66,0),and the (Xmaximum,Ymaximum) coordinate to (1,1).

ii. Click the Mark button.

This creates a register containing the cells in this region.

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(b) Check the register to be sure it is correct.

i. Select the register (hexahedron-r0) in the Registers list andclick Display.

The graphics display will show the bottom third of the bowlin red.

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(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 amistake, click the DEL button to delete the last item youadded to the function definition.

ii. Click the X button on the calculator pad.

iii. In the Field Functions drop-down list, select Grid... andRadial 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, clickon the Manage... button and select swirl-init.

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(d) Patch the water volume fraction in the bottom third of thebowl.

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 ofthe bowl. That is, you have defined the lower third of the bowlto be filled with water.

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(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-initin the Field Function list.

iii. Click Patch.

It’s a good idea to check your patch by displaying contours ofthe patched fields.

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(f) Display contours of swirl velocity.

Display −→Contours...

i. Select Velocity... and Swirl Velocity in the Contours Oflists.

ii. Enable the Filled option and turn off the Node Valuesoption.

Since the values you patched are cell values, you shouldview the cell values, rather than the node values, to checkthat the patch has been performed correctly. (FLUENTcomputes the node values by averaging the cell values.)

iii. Click Display.

To make the view more realistic, you will need to rotate thedisplay and mirror it across the centerline.

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(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 andtranslate the view so that the entire bowl is visible in thegraphics display.

iii. Click on the Camera... button to open the Camera Param-eters panel.

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iv. Using your left mouse button, rotate the dial clockwiseuntil 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 Actionsto save the mirrored, upright view, and then close thepanel.

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 showsthat w = 3r in the region of the bowl that is filled with water.

Contours of Swirl Velocity (m/s) (Time=0.0000e+00)FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

Jun 12, 2001

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

Figure 15.3: Contours of Initial Swirl Velocity

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(h) Display contours of water volume fraction.

i. Select Phases... and Volume fraction of water in the Con-tours Of lists.

ii. Set the number of contour Levels to 2 and click Display.

There are only two possible values for the volume fractionat this point: 0 or 1.

Figure 15.4 correctly shows that the bottom third of the bowlcontains water.

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Using the VOF Model

Contours of Volume fraction of water (Time=0.0000e+00) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.4: Contours of Initial Water Volume Fraction

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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 timea 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 AutosaveData File Frequency to 100.

(b) Enter the Filename bowl and then click OK.

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, where 100is 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...

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Since the time step is 0.002 seconds, you will be calculating up tot= 2 seconds. FLUENT will automatically save a data file afterevery 0.2 seconds, so you will have 10 data files for postprocessing.

Figure 15.5 shows the time history for the axial velocity. The veloc-ity is clearly oscillating, and the oscillations appear to be decayingover time (as the peaks become smaller). This periodic oscillationhas a cycle of 1 second. The switch from a positive to a negativeaxial velocity indicates that the water is sloshing up and down thesides of the bowl in an attempt to reach an equilibrium position.The fact that the amplitude is decaying suggests that equilibriumwill be reached at some point. The periodic behavior in evidencewill therefore be present only during the initial startup phase of thebowl rotation.

Convergence history of Axial Velocity on point (Time=2.0000e+00)FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

Jun 13, 2001

Flow Time

(m/s)ValuesVertex

Surfaceof

Average

2.00001.80001.60001.40001.20001.00000.80000.60000.40000.20000.0000

0.3000

0.2000

0.1000

0.0000

-0.1000

-0.2000

-0.3000

Figure 15.5: Time History of Axial Velocity

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Step 8: Postprocessing

As indicated by changes in axial velocity in Figure 15.5, the flow field isoscillating periodically. In this step, you will examine the flow field atseveral different times. (Recall that FLUENT saved 10 data files for youduring the calculation.)

1. Read in the data file of interest.

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 = 0.4to t = 0.6, then increases from t = 0.6 to t = 1. At t = 1, thewater level in the center of the bowl has risen above the initiallevel, so you can expect the cycle to repeat as the water level beginsto decrease again in an attempt to return to equilibrium. (You canread in the data files between t = 1 and t = 2 to confirm that thisis in fact what happens.

Since the time history of axial velocity (Figure 15.5) shows thatthe velocity oscillation is decaying over time, you can expect that ifyou were to continue the calculation, the water level would eventu-ally reach some point where the gravitational and centrifugal forcesbalance and the water level reaches a new equilibrium point.

Extra: Try continuing the calculation to determine how long ittakes for the axial velocity oscillations in Figure 15.5 to dis-appear.

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Contours of Volume fraction of water (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.6: Shape of the Free Surface at t = 0.4

Contours of Volume fraction of water (Time=6.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.7: Shape of the Free Surface at t = 0.6

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Contours of Volume fraction of water (Time=8.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.8: Shape of the Free Surface at t = 0.8

Contours of Volume fraction of water (Time=9.9999e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.9: Shape of the Free Surface at t = 1

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3. Plot contours of stream function.

(a) Select Stream Function (in the Velocity... category) in the Con-tours Of drop-down list.

(b) Turn off the Filled option and increase the number of contourLevels to 30.

(c) Click on Display.

In Figures 15.10–15.13, you can see a recirculation region that fallsand rises as the water level changes. To get a better sense of theserecirculating patterns, you will next look at velocity vectors.

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Contours of Stream Function (kg/s) (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

2.58e+01

0.00e+00

1.72e+00

3.44e+00

5.16e+00

6.88e+00

8.60e+00

1.03e+01

1.20e+01

1.38e+01

1.55e+01

1.72e+01

1.89e+01

2.06e+01

2.24e+01

2.41e+01

Figure 15.10: Contours of Stream Function at t = 0.4

Contours of Stream Function (kg/s) (Time=6.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

2.65e+01

0.00e+00

1.76e+00

3.53e+00

5.29e+00

7.06e+00

8.82e+00

1.06e+01

1.24e+01

1.41e+01

1.59e+01

1.76e+01

1.94e+01

2.12e+01

2.29e+01

2.47e+01

Figure 15.11: Contours of Stream Function at t = 0.6

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Contours of Stream Function (kg/s) (Time=8.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

4.73e+01

0.00e+00

3.15e+00

6.31e+00

9.46e+00

1.26e+01

1.58e+01

1.89e+01

2.21e+01

2.52e+01

2.84e+01

3.15e+01

3.47e+01

3.78e+01

4.10e+01

4.41e+01

Figure 15.12: Contours of Stream Function at t = 0.8

Contours of Stream Function (kg/s) (Time=9.9999e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

8.84e+00

0.00e+00

5.89e-01

1.18e+00

1.77e+00

2.36e+00

2.95e+00

3.54e+00

4.13e+00

4.71e+00

5.30e+00

5.89e+00

6.48e+00

7.07e+00

7.66e+00

8.25e+00

Figure 15.13: Contours of Stream Function at t = 1

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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 to1.

(c) Click on Vector Options... to open the Vector Options panel.

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i. Turn off the Z Component.

This allows you to examine the non-swirling componentsonly.

ii. Click Apply and close the panel.

(d) Click on Display.

Figures 15.14–15.17 show the changes in water and air flow pat-terns between t = 0.4 and t = 1. In Figure 15.14, you can see thatthe flow in the middle of the bowl is being pulled down by gravi-tational forces, and pushed out and up along the sides of the bowlby centrifugal forces. This causes the water level to decrease in thecenter of the bowl, as shown in the volume fraction contour plots,and also results in the formation of a recirculation region in theair above the water surface.

In Figure 15.15, the flow has reversed direction, and is slowly risingup in the middle of the bowl and being pulled down along the sidesof the bowl. This reversal occurs because the earlier flow patterncaused the water to overshoot the equilibrium position. The gravityand centrifugal forces now act to compensate for this overshoot.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.92e+00

8.63e-03

1.36e-01

2.63e-01

3.91e-01

5.18e-01

6.46e-01

7.73e-01

9.00e-01

1.03e+00

1.16e+00

1.28e+00

1.41e+00

1.54e+00

1.66e+00

1.79e+00

Figure 15.14: Velocity Vectors for the Air and Water at t = 0.4

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=6.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.94e+00

4.88e-04

1.30e-01

2.59e-01

3.89e-01

5.18e-01

6.48e-01

7.77e-01

9.07e-01

1.04e+00

1.17e+00

1.30e+00

1.42e+00

1.55e+00

1.68e+00

1.81e+00

Figure 15.15: Velocity Vectors for the Air and Water at t = 0.6

c© Fluent Inc. November 27, 2001 15-43

Using the VOF Model

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=8.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

2.13e+00

5.04e-03

1.47e-01

2.89e-01

4.31e-01

5.73e-01

7.15e-01

8.56e-01

9.98e-01

1.14e+00

1.28e+00

1.42e+00

1.57e+00

1.71e+00

1.85e+00

1.99e+00

Figure 15.16: Velocity Vectors for the Air and Water at t = 0.8

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=9.9999e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

2.12e+00

3.06e-03

1.44e-01

2.85e-01

4.27e-01

5.68e-01

7.09e-01

8.50e-01

9.91e-01

1.13e+00

1.27e+00

1.41e+00

1.56e+00

1.70e+00

1.84e+00

1.98e+00

Figure 15.17: Velocity Vectors for the Air and Water at t = 1

15-44 c© Fluent Inc. November 27, 2001

Using the VOF Model

In Figure 15.16 you can see that the flow is rising up more quicklyin the middle of the bowl, and in Figure 15.17 you can see that theflow is still moving upward, but more slowly. These patterns cor-respond to the volume fraction plots at these times. As the upwardmotion in the center of the bowl decreases, you can expect the flowto reverse as the water again seeks to reach a state of equilibrium.

Summary: In this tutorial, you have learned how to use the VOF freesurface model to solve a problem involving a spinning bowl of wa-ter. The time-dependent VOF formulation is used in this problemto track the shape of the free surface and the flow field inside thespinning bowl.

You observed the changing pattern of the water and air in the bowlby 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

Using the VOF Model

15-46 c© Fluent Inc. November 27, 2001