tutorial vof

Tutorial 16. Using the VOF Model

Introduction

This tutorial illustrates the setup and solution of the two-dimensional turbulent fluidflow 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 toread about VOF multiphase flow modeling in the FLUENT by reading Section 24.2 of theUsers Guide for more information. Otherwise, no previous experience with multiphasemodeling is required.

Problem Description

The information relevant to this problem is shown in Figure 16.1. A large bowl, 1 m inradius, is one-third filled with water and is open to the atmosphere. The bowl spins withan angular velocity of 3 rad/sec. Based on the rotating water, the Reynolds number isabout 106, so the flow is modeled as turbulent.

c Fluent Inc. January 11, 2005 16-1

Using the VOF Model

2 m

1 m

=Bowl: 3 rad/s3

-5

-3

Air: = 1.225 kg/m = 1.7894 x 10

Water: = 998.2 kg/m3

= 1 x 10

kg/m-s

kg/m-s

Figure 16.1: Water and Air in a Spinning Bowl

Setup and Solution

Preparation

1. Download vof.zip from the Fluent Inc. User Services Center or copy it from theFLUENT documentation CD to your working directory (as described in Tutorial 1).

2. Unzip vof.zip.

bowl.msh can be found in the /vof folder created after unzipping the file.

The mesh file bowl.msh is a quadrilateral mesh describing the system geometryshown in Figure 16.1.

3. Start the 2D version of FLUENT.

16-2 c Fluent Inc. January 11, 2005

Using the VOF Model

Step 1: Grid

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

File Read Case...2. Display the grid (Figure 16.2).

Display Grid...

As shown in Figure 16.2, half of the bowl is modeled, with a symmetry boundary atthe centerline. The bowl is shown lying on its side, with the region to be modeledextending from the centerline to the outer wall. When you begin to display datagraphically, you will need to rotate the view and mirror it across the centerline toobtain a more realistic view of the model. This step will be performed later in thetutorial.


Using the VOF Model

Grid FLUENT 6.2 (2d, segregated, lam)

Figure 16.2: Grid Display


Using the VOF Model

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.


Using the VOF Model

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 formost transient VOF calculations.

When you click OK, FLUENT will report that one of the zone types will needto be changed before proceeding with the calculation. You will take care of thisstep when you input boundary conditions for the problem.


Using the VOF Model

3. Turn on the standard k- turbulence model.

Define Models Viscous...

(a) Select k-epsilon as the Model, and retain the default setting of Standard underk-epsilon Model.


Using the VOF Model

Step 3: Materials

1. Copy water from the FLUENT database materials so that it can be used for thesecondary phase.

Define Materials...(a) Click on the Fluent Database... button to open the Fluent Database Materials

panel.

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

(c) Click Copy and close the Fluent Database Materials and Materials panels.


Using the VOF Model

Step 4: Phases

Here, water is defined as the secondary phase mainly for convenience in setting up theproblem. When you define the initial solution, you will be patching an initial swirl velocityin the bottom third of the bowl, where the water is. It is more convenient to patch a watervolume fraction of 1 there than to patch an air volume fraction of 1 in the rest of thedomain. Also, the default volume fraction at the pressure inlet is 0, which is the correctvalue 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 choicewill affect the ease of problem setup.

1. Define the air and water phases within the bowl.

Define Phases...

(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.


Using the VOF Model

(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.


Using the VOF Model

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/s2.

Since the centerline of the bowl is the x axis, gravity points in the positive xdirection.

2. Set the operating density.

(a) Under Variable-Density Parameters, turn on the Specified Operating Density op-tion and accept the Operating Density of 1.225.

It is a good idea to set the operating density to be the density of the lighterphase. This excludes the buildup of hydrostatic pressure within the lighterphase, improving the round-off accuracy for the momentum balance.

Note: The Reference Pressure Location (0,0) is situated in a region where the fluidwill always be 100% of one of the phases (air), a condition that is essentialfor smooth and rapid convergence. If it were not, you would need to change itto a more appropriate location.


Using the VOF Model

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.

2. Set the conditions at the top of the bowl (pressure-inlet-4).

For the VOF model, you will specify conditions for the mixture (i.e., conditions thatapply 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 inthe Phase drop-down list and click Set....


Using the VOF Model

ii. Set the Turb. Kinetic Energy to 2.25e-2 and the Turb. Dissipation Rate to7.92e-3.

Since there is initially no flow passing through the pressure inlet, you needto specify k and explicitly rather than using one of the other turbulencespecification methods. All of the other methods require you to specify theturbulence intensity, which is 0 in this case.

The values for k and are computed as follows:

k = (Iwwall)2

=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 multiplying 0.07 by the maximum radius of thebowl, which is 1).

See Section 7.2.2 of the Users 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 the Phase drop-downlist and click Set....


Using the VOF Model

ii. Retain the default Volume Fraction of 0.

A water volume fraction of 0 indicates that only air is present at thepressure inlet.

3. Set the conditions for the spinning bowl (wall-1).

For a wall boundary, all conditions are specified for the mixture. There are noconditions to be specified for the individual phases.

(a) In the Boundary Conditions panel, select mixture in the Phase drop-down listand click Set....


Using the VOF Model

(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 rotational Speed (rad/s) to3.


Using the VOF Model

Step 7: Solution

In simple flows, the under-relaxation factors can usually be increased at the start of thecalculation. 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 areinitially out of view.

(b) Under Discretization, choose the PRESTO! scheme in the drop-down list nextto Pressure.

(c) Under Pressure-Velocity Coupling, select PISO.

PISO is recommended for transient flow calculations.


Using the VOF Model

2. Enable the display of residuals during the solution process.

Solve Monitors Residual...

(a) Under Options, select Plot.

(b) Click OK button to close the panel.

3. Enable the plotting of the axial velocity of water near the outer edge of the bowlduring the calculation.

For transient calculations, it is often useful to monitor the value of a particularvariable to see how it changes over time. Here you will first specify the point atwhich 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...


Using the VOF Model

i. Set the x0 and y0 coordinates to 0.75 and 0.65.

ii. Enter point for the New Surface Name.

iii. Click Create.

(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, thevelocity history will be written to a file. If you do not select the Writeoption, the history information will be lost when you exit FLUENT.

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


Using the VOF Model

iv. Click on Define... to specify the surface monitor parameters in the DefineSurface Monitor panel.

v. Select Vertex Average from the Report Type drop-down list.

This is the recommended choice when you are monitoring the value at asingle 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 in the SurfaceMonitors panel.


Using the VOF Model

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.

5. Patch the initial distribution of water (i.e., water volume fraction of 1.0) and aswirl 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 definea cell register for that region. You will use the same tool that is used to mark aregion of cells for adaption. Also, you will need to define a custom function for theswirl velocity.

(a) Define a register for the bottom third of the domain.

Adapt Region...


Using the VOF Model

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

ii. Click the Mark button.

This creates a register containing the cells in this region.

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

Adapt Manage...

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

The graphics display will show the bottom third of the bowl in red.


Using the VOF Model

6. Define a custom field function for the swirl velocity w = 3r.

Define Custom Field Functions...

(a) Click the 3 button on the calculator pad.

The 3 will appear in the Definition field. If you make a mistake, click the DELbutton to delete the last item you added to the function definition.

(b) Click the X button on the calculator pad.

(c) In the Field Functions drop-down list, select Grid... and Radial Coordinate.

(d) Click the Select button.

radial-coordinate will appear in the Definition.

(e) Enter a New Function Name of swirl-init.

(f) Click Define.

Note: If you wish to check the function definition, click on the Manage...button and select swirl-init.


Using the VOF Model

7. Patch the water volume fraction in the bottom third of the bowl.

Solve Initialize Patch...

(a) In the Phase drop-down list, select water.

(b) Select Volume Fraction in the Variable list.

(c) Select hexahedron-r0 in the Registers to Patch list.

(d) Set the Value to 1.

(e) Click Patch.

This sets the water volume fraction to 1 in the lower third of the bowl. Thatis, you have defined the lower third of the bowl to be filled with water.


Using the VOF Model

(f) Patch the swirl velocity in the bottom third of the bowl.

i. In the Phase drop-down list, select mixture.

ii. Choose Swirl Velocity in the Variable list.

iii. Enable the Use Field Function option and select swirl-init in the Field Func-tion list.

iv. Click Patch.

Its a good idea to check your patch by displaying contours of the patched fields.


Using the VOF Model

8. Display contours of swirl velocity.

Display Contours...

(a) Select Velocity... and Swirl Velocity in the Contours of lists.

(b) 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 cor-rectly. (FLUENT computes the node values by averaging the cell values.)

(c) Click Display.

To make the view more realistic, you will need to rotate the display and mirror itacross the centerline.


Using the VOF Model

9. Rotate the view and mirror it across the centerline.

Display Views...

(a) Select axis-2 in the Mirror Planes list and click Apply.

(b) Use your middle and left mouse buttons to zoom and translate the view sothat the entire bowl is visible in the graphics display.

(c) Click on the Camera... button to open the Camera Parameters panel.

(d) Using your left mouse button, rotate the dial clockwise until the bowl appearsupright in the graphics window (90).

(e) Close the Camera Parameters panel.

(f) 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 16.3 correctly shows that w = 3r in theregion of the bowl that is filled with water.


Using the VOF Model

Contours of Swirl Velocity (mixture) (m/s) (Time=0.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

2.35e+002.23e+002.12e+002.00e+001.88e+001.76e+001.65e+001.53e+001.41e+001.29e+001.18e+001.06e+009.41e-018.23e-017.06e-015.88e-014.70e-013.53e-012.35e-011.18e-010.00e+00

Figure 16.3: Contours of Initial Swirl Velocity


Using the VOF Model

10. Display contours of water volume fraction.

(a) Select Phases... and Volume fraction of water in the Contours of lists.

(b) Select water in the Phase drop-down list.

(c) 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 or1.


Using the VOF Model

Contours of Volume fraction (water) (Time=0.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

5.00e-01

0.00e+00

Figure 16.4: Contours of Initial Water Volume Fraction

Figure 16.4 correctly shows that the bottom third of the bowl contains water.

11. Set the time-step parameters for the calculation.

Solve Iterate...(a) Under Time, specify a value of 0.002 for Time Step Size and a value of 1000

for Number of Time Steps.

(b) Under Time Stepping Method, select Variable.

(c) Under Variable Time Step Parameters, specify a value of 0.002 for MinimumTime Step Size and a value of 0.01 for Maximum Time Step Size.

(d) Retain the other default parameters.

(e) Click Apply.

This will save the time step size to the case file (the next time a case file issaved).

(f) Save the initial case and data files (bowl.cas and bowl.dat).

File Write Case & Data...(g) Specify a value of 0.4 for Ending Time.

As iterations will begin with variable time step method, a value of 0.4 forEnding Time will stop the calculations after t = 0.4sec. Save the data file atthis moment and proceed the calculations for Ending Time of 0.6, 0.8, 1.0, and2.0. You may have to reset the value of Time Step Size to a value of 0.002after saving each data file.


Using the VOF Model

Figure 16.5 shows the time history for the axial velocity. The velocity is clearlyoscillating, and the oscillations appear to be decaying over time (as the peaksbecome smaller). This periodic oscillation has a cycle of 1 second. The switchfrom a positive to a negative axial velocity indicates that the water is sloshingup and down the sides of the bowl in an attempt to reach an equilibrium po-sition. The fact that the amplitude is decaying suggests that equilibrium willbe reached at some point. The periodic behavior in evidence will therefore bepresent only during the initial startup phase of the bowl rotation.

Convergence history of Axial Velocity on point (in SI units) (Time=2.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

Flow Time

VelocityAxial

AverageVertex

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 16.5: Time History of Axial Velocity


Using the VOF Model

Step 8: Postprocessing

As indicated by changes in axial velocity in Figure 16.5, the flow field is oscillating peri-odically. In this step, you will examine the flow field at several different times. (Recallthat you have saved the data files for t = 0.4, 0.6, 0.8, and, 1.0.)

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 16-28),

but turn Node Values back on.

Figures 16.616.9 show that the water level decreases from t = 0.4 to t = 0.6, thenincreases from t = 0.6 to t = 1. At t = 1, the water level in the center of thebowl has risen above the initial level, so you can expect the cycle to repeat as thewater level begins to decrease again in an attempt to return to equilibrium. (Youcan read in the data files between t = 1 and t = 2 to confirm that this is in factwhat happens.

Since the time history of axial velocity (Figure 16.5) shows that the velocity os-cillation is decaying over time, you can expect that if you were to continue thecalculation, the water level would eventually reach some point where the gravita-tional and centrifugal forces balance and the water level reaches a new equilibriumpoint.

Extra: Try continuing the calculation to determine how long it takes for the axialvelocity oscillations in Figure 16.5 to disappear.


Using the VOF Model

Contours of Volume fraction (water) (Time=4.0000e-01)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

5.00e-01

0.00e+00

Figure 16.6: Shape of the Free Surface at t = 0.4


1.00e+00

5.00e-01

0.00e+00



Using the VOF Model


1.00e+00

5.00e-01

0.00e+00


Contours of Volume fraction (water) (Time=1.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

5.00e-01

0.00e+00

Figure 16.9: Shape of the Free Surface at t = 1


Using the VOF Model

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 16.1016.13, you can see a recirculation region that falls and rises asthe water level changes. To get a better sense of these recirculating patterns, youwill next look at velocity vectors.


Using the VOF Model

Contours of Stream Function (mixture) (kg/s) (Time=4.0000e-01)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

2.77e+01

2.59e+01

2.40e+01

2.22e+01

2.03e+01

1.85e+01

1.66e+01

1.48e+01

1.29e+01

1.11e+01

9.25e+00

7.40e+00

5.55e+00

3.70e+00

1.85e+00

0.00e+00

Figure 16.10: Contours of Stream Function at t = 0.4


2.47e+01

2.30e+01

2.14e+01

1.97e+01

1.81e+01

1.64e+01

1.48e+01

1.31e+01

1.15e+01

9.86e+00

8.22e+00

6.57e+00

4.93e+00

3.29e+00

1.64e+00

0.00e+00



Using the VOF Model


4.68e+01

4.37e+01

4.06e+01

3.74e+01

3.43e+01

3.12e+01

2.81e+01

2.50e+01

2.18e+01

1.87e+01

1.56e+01

1.25e+01

9.36e+00

6.24e+00

3.12e+00

0.00e+00


Contours of Stream Function (mixture) (kg/s) (Time=1.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

7.02e+00

6.55e+00

6.08e+00

5.61e+00

5.14e+00

4.68e+00

4.21e+00

3.74e+00

3.27e+00

2.81e+00

2.34e+00

1.87e+00

1.40e+00

9.35e-01

4.68e-01

0.00e+00

Figure 16.13: Contours of Stream Function at t = 1


Using the VOF Model

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.


Using the VOF Model

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 16.1416.17 show the changes in water and air flow patterns between t = 0.4and t = 1. In Figure 16.14, you can see that the flow in the middle of the bowl isbeing pulled down by gravitational forces, and pushed out and up along the sides ofthe bowl by centrifugal forces. This causes the water level to decrease in the centerof the bowl, as shown in the volume fraction contour plots, and also results in theformation of a recirculation region in the air above the water surface.

In Figure 16.15, the flow has reversed direction, and is slowly rising up in the mid-dle of the bowl and being pulled down along the sides of the bowl. This reversaloccurs because the earlier flow pattern caused the water to overshoot the equilib-rium position. The gravity and centrifugal forces now act to compensate for thisovershoot.


Using the VOF Model

Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=4.0000e-01)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

1.91e+001.82e+001.72e+001.63e+001.53e+001.44e+001.34e+001.25e+001.15e+001.06e+009.61e-018.66e-017.71e-016.75e-015.80e-014.85e-013.89e-012.94e-011.99e-011.03e-017.98e-03

Figure 16.14: Velocity Vectors for the Air and Water at t = 0.4


1.96e+001.87e+001.77e+001.67e+001.57e+001.47e+001.37e+001.28e+001.18e+001.08e+009.82e-018.84e-017.86e-016.88e-015.90e-014.91e-013.93e-012.95e-011.97e-019.88e-026.55e-04



Using the VOF Model


2.12e+002.01e+001.91e+001.80e+001.70e+001.59e+001.48e+001.38e+001.27e+001.17e+001.06e+009.56e-018.51e-017.45e-016.39e-015.34e-014.28e-013.22e-012.17e-011.11e-015.18e-03


Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=1.0000e+00)FLUENT 6.2 (axi, swirl, segregated, vof, ske, unsteady)

2.12e+002.01e+001.91e+001.80e+001.70e+001.59e+001.48e+001.38e+001.27e+001.17e+001.06e+009.55e-018.49e-017.44e-016.38e-015.32e-014.26e-013.20e-012.14e-011.08e-012.22e-03

Figure 16.17: Velocity Vectors for the Air and Water at t = 1


Using the VOF Model

In Figure 16.16 you can see that the flow is rising up more quickly in the middle ofthe bowl, and in Figure 16.17 you can see that the flow is still moving upward, butmore 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 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 free surface model to solve aproblem involving a spinning bowl of water. The time-dependent VOF formulation isused in this problem to 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 bowl by displaying volumefraction contours, stream function contours, and velocity vectors at t = 0.4, t = 0.6,t = 0.8, and t = 1 second.


Using the VOF Model


16 Using the VOF ModelIntroductionPrerequisitesProblem DescriptionSetup and SolutionPreparationStep 1: GridStep 2: ModelsStep 3: MaterialsStep 4: PhasesStep 5: Operating ConditionsStep 6: Boundary ConditionsStep 7: SolutionStep 8: Postprocessing

Summary

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