chapter 10. vof free surface model

Chapter 10. VOF Free Surface Model

Information about the VOF model is divided into the followingsections:

� Section 10.1: Introduction

� Section 10.2: Theory

� Section 10.3: Using the VOF Model

10.1 Introduction

Two models are available in FLUENT for simulations where two ormore uids are present. The Volume of Fluid (VOF) model (Hirtand Nichols, 1981 [49]) is designed for two or more immiscible uids,where the position of the interface between the uids is of interest.The Eulerian model, described in Chapter 9, is designed for two ormore interpenetrating uids. Whereas the Eulerian model makesuse of multiple momentum equations to describe the individual u-ids, the VOF model does not. In the VOF model, a single setof momentum equations is shared by the uids, and the volumefraction of each of the uids is tracked throughout the domain. Ap-plications of the VOF model include the prediction of jet break-up,the motion of large bubbles in a liquid, the motion of liquid after adam break, or the steady or transient tracking of any liquid-gas in-terface. The Eulerian multiphase model, on the other hand, is bestsuited for applications involving slurries or liquid-liquid and liquid-gas mixtures involving small bubbles. The distinction between largeand small bubbles in these examples is based on the size of a typicalcontrol volume. If a bubble is much smaller than a control volume,many such bubbles can be treated as a separate uid in the Eu-lerian multiphase model. If the bubble is so large that it extendsacross several control volumes, the VOF formulation is appropriateto track its boundary.

To illustrate the capabilities of the VOF model, consider a rectan-Example of a DamBreak gular domain, 4 m long and 2.2 m high, in which water is initially

con�ned to a region on the left side by the presence of a dam. Attime t=0, the dam breaks, and the water starts to ow to the right.

10-2 Chapter 10 | VOF Free Surface Model

Figures 10.1.1 and 10.1.2 illustrate the spread of the water duringthe �rst 0.7 seconds.

By 0.9 and 1.1 seconds, the water has reached the opposite side ofthe container and is moving up the wall (Figure 10.1.3).

If the grid is su�ciently �ne, FLUENT can predict the formation oflarge water \drops" that separate from the water stream as it hitsthe upper boundary of the domain. These drops will then fall tothe bottom of the container, where they will reattach to the waterthere.

Most FLUENT models are available in combination with the VOFAuxiliary Modelsand Limitations model. For example, the sliding-mesh model can be used to pre-

dict the shape of the surface of a liquid in a mixing tank. Thedeforming mesh capability is also compatible with the VOF model.The porous media model can be used to track the motion of theinterface between two uids through a packed bed or other porousregion. The e�ects of surface tension may be included (for onespeci�ed phase only), and in combination with this model, you canspecify the wall adhesion angle. Heat transfer from walls to eachof the phases can be modeled, as can heat transfer between phases.Turbulence modeling is available through the standard or the RNGk-�-model. Turbulence modeling with the Reynolds Stress modelis not available, however. For any of these applications, note thatall control volumes must be �lled with either a single uid phaseor a combination of phases, since the model does not allow for voidregions where no uid of any type is present.

Some models are available for only one of the phases. Only onephase's density can be calculated using the gas law. Species mix-ing and reacting ow can be modeled in one of the phases, butmass transfer between phases cannot be modeled without User-De�ned Subroutines. While temperature-dependent properties areavailable for both phases, the kinetic theory option is only avail-able for one of the phases, as is property de�nition through User-De�ned-Subroutines. Only one of the phases can be modeled witha non-Newtonian viscosity law.

If you model solidi�cation (using the phase change model describedin Chapter 8), the solidi�cation can occur in only one phase. Bydefault, this solidifying phase is the �rst secondary phase. You willhave the opportunity to specify a di�erent phase for solidi�cationwhen you specify the phase change properties (see Section 8.3).Note also that solidi�cation cannot take place in the vicinity of theinterface between two phases.

c Fluent Inc. May 10, 1997

10.1 Introduction 10-3

0.00E+00

5.00E-01

1.00E+00

Lmax = 1.000E+00 Lmin = 0.000E+00 Time = 2.000E-01

Water Volume Fraction (Dim)

Transient Simulation of a Dam Break

Fluent Inc.

Fluent 4.30

Oct 20 1994Y

XZ

Figure 10.1.1: Transient Simulation of a Dam Break During theFirst 0.2 Seconds

0.00E+00

5.00E-01

1.00E+00




Fluent Inc.

Fluent 4.30

Oct 20 1994Y

XZ

Figure 10.1.2: Transient Simulation of a Dam Break at 0.5 and 0.7Seconds



0.00E+00

5.00E-01

1.00E+00

Lmax = 1.000E+00 Lmin = 0.000E+00 Time = 1.100E+00



Fluent Inc.

Fluent 4.30

Oct 24 1994Y

XZ

Figure 10.1.3: Transient Simulation of a Dam Break at 0.9 and 1.1Seconds

The VOF formulation in FLUENT is, by default, time-dependent,Steady State vs.Time Dependence but for problems in which you are concerned only with a steady-

state solution, it is possible to perform a steady-state calculation.A steady-state VOF calculation is sensible only when your solutionis independent of the initial conditions and there are distinct in owboundaries for the individual phases. For example, since the shapeof the free surface inside a rotating cup depends on the initial level ofthe uid, such a problem must be solved using the time-dependentformulation. On the other hand, the ow of water in a channel witha region of air on top and a separate air inlet can be solved withthe steady-state formulation.


10.2 Theory 10-5

10.2 Theory

The VOF formulation relies on the fact that two or more uids(or phases) are not interpenetrating. For each additional phasethat you add to your model, a variable is introduced, which is thevolume fraction of that phase. In each control volume, the volumefractions of all phases add to unity. The �elds for all variables andproperties are shared by the phases, as long as the volume fractionof each of the phases is known at each location. Thus the variablesand properties in any given cell are either purely representative ofone of the phases, or are representative of a mixture of the phases,depending upon the volume fraction values. In other words, if thevolume fraction of the kth uid in a multi- uid system is denoted�k, then the following three conditions are possible:

�k = 0 the cell is empty (of the kth uid)�k = 1 the cell is full (of the kth uid)0 < �k < 1 the cell contains the interface between the uids

Based on the local value of �k, the appropriate properties and vari-ables will be assigned to each control volume within the domain.

The tracking of the interface(s) between the phases is accomplishedThe VolumeFraction Equation by the solution of a continuity equation for the volume fraction of

one (or more) of the phases. For the kth phase, this equation hasthe form:

@�k@t

+ uj

@�k@xi

= S�k (10.2-1)

The source term on the right hand side of Equation 10.2-1 is nor-mally zero, but can be constructed with a User-De�ned Subroutineto generate a source of the kth phase in one or more regions of thesolution domain to simulate mass transfer between phases. (Thistask requires the additional speci�cation of a mass source.)

The properties appearing in the transport equations are determinedPropertiesby the presence of the component phases in each control volume.In a two-phase system, for example, if the phases are representedby the subscripts 1 and 2, and if the volume fraction of the secondof these is being tracked, the density in each cell is given by:

� = �2�2 + (1� �2)�1 (10.2-2)

In general, for an N-phase system, the volume-fraction averageddensity takes on the form:



� =X

�k�k (10.2-3)

All other properties are computed in this manner (viscosity andthermal conductivity, for example) with the exception of the speci�cheat, which is mass fraction averaged:

cp =

P�k�kcpkP�k�k

(10.2-4)

The basis for the mass-weighted averaging done for the speci�c heatlies in the manner in which the enthalpy is calculated at cells nearthe interface. The enthalpy in general is dependent upon the ther-mal mass of the uid. It follows, therefore, that a mass-averagedenthalpy be computed at (and near) interface cells. For cells in thisregion, the enthalpy at the node P is computed as follows:

hP =

P�k�khkP�k�k

(10.2-5)

A single momentum equation is solved throughout the domain, andThe MomentumEquation the resulting velocity �eld is shared among the phases. The momen-

tum equation, shown below, is dependent on the volume fraction ofthe kth phase through the properties � and �.

@

@t�uj +

@

@xi�uiuj

= �@P

@xj+

@

@xi�

@ui

@xj+

@uj

@xi

!+ �gj + Fj (10.2-6)

One limitation of the shared-�elds approximation is that in caseswhere large velocity di�erences exist between the phases, the accu-racy of the velocities computed near the interface can be adverselya�ected.

The enthalpy equation, also shared between the phases, is shownThe EnthalpyEquation below.

@

@t�h+

@

@xi�uih =

@

@xi

k@T

@xi

!+ Sh (10.2-7)

The properties � and k are shared by the phases, as discussed earlier.The source term, Sh, contains contributions from radiation, and the


10.2 Theory 10-7

heat of reaction in the primary phase if reactions are a part of themodel.

As with the velocity �eld, the accuracy of the enthalpy and conse-quently the temperature near the interface is limited in cases wherelarge temperature di�erences exist between the phases. Such prob-lems also arise in cases where the properties vary by several ordersof magnitude. For example, if a model includes liquid metal incombination with air, the conductivities of the materials can di�erby as much as 4 orders of magnitude. Such large discrepancies inproperties lead to equation sets with anisotropic coe�cients, whichin turn lead to convergence and precision limitations.

Depending upon your problem de�nition, additional scalar equa-Additional ScalarEquations tions may be involved in your solution. In the case of turbulence

quantities, a single set of transport equations is solved, and the vari-ables k and � are shared by the phases throughout the �eld. In thecase of species mixing, the species conservation equations are solvedthroughout the �eld, but only pertain to one of the phases. If a cellis completely devoid of that phase, the mass fractions of the �rstN-1 species that you name will all take a value of zero in that cell.

The control volume formulation requires that convection and dif-Interpolation Nearthe Interface fusion uxes through the control volume faces be computed and

balanced with source terms within the control volume itself. Thereare two options in FLUENT for the calculation of face uxes for theVOF model.

In the default method, which is an explicit approach, the standardinterpolation schemes that are used in FLUENT are used to obtainthe face uxes whenever a cell is completely �lled with one phase oranother. When the cell is near the interface between two phases, a\donor-acceptor" scheme is used to determine the amount of uidadvected through the face [49]. This scheme identi�es one cell as adonor of an amount of uid from one phase and another (neighbor)cell as the acceptor of that same amount of uid, and is used toprevent numerical di�usion at the interface. The amount of uidfrom one phase that can be convected across a cell boundary islimited by the minimum of two values: the �lled volume in thedonor cell or the free volume in the acceptor cell.

The orientation of the interface is also used in determining the face uxes. It is determined by the direction of the gradient of thevolume fraction of the ith phase within the cell, and that of theneighbor cell which shares the face in question. Depending uponthis as well as the motion of the interface, ux values are obtained by



pure upwinding, pure downwinding, or some combination of these.

In the alternative (implicit) interpolation method, FLUENT's stan-dard interpolation schemes are used to obtain the face uxes for allcells, including those near the interface. Thus, a standard scalartransport equation is solved for each of the secondary-phase volumefractions. The implicit formulation is valid for both steady-stateand time-dependent calculations. See Sections 10.1 and 10.3.2 formore information.

The default VOF formulation in FLUENT is time-dependent, soTime DependenceEquation 10.2-1 is solved using an explicit time-marching scheme.Time dependence is automatically enabled as soon as you activatethe VOF model. A number of options are available for the controlof the time-dependent solution. You may use a single time stepfor the calculation of all of the transport equations, or you canuse an automatic re�nement of the time step for the multi-stepintegration of the volume fraction equation. You may update thevolume fraction once for each time step, or once for each iterationwithin each time step. These options are discussed in more detailin the next section of this chapter.

If the explicit donor-acceptor interpolation method is disabled, itis possible to turn o� time dependence and perform a steady-statecalculation.

10.3 Using the VOF Model

10.3.1 Enabling VOF

The VOF model can be enabled in one of two ways. Either youcan enter the SETUP1 menu and use the DEFINE-MODELS commandfrom the text interface, or you can open the Models panel using thegraphical user interface.

When you use the panel, the VOF Free Surface model can be chosenUsing theGraphical Interface from among the options in the Model drop-down list under Multi-

phase on the right-hand side of the panel.


10.3 Using the VOF Model 10-9

Note that when you select the VOF model with the default donor-acceptor scheme, the Time Dependent Flow model is activated au-tomatically. If you wish to disable time dependence and performa steady-state calculation, you will need to �rst disable the donor-acceptor scheme, as described in Section 10.3.2.

When you click Apply in the Models panel, if you are just beginningthe problem setup, you may see the following question, which isneeded for the allocation of memory needed for the additional phase.



Once you have selected one of the multiphase models, the Multi-

phase Parameters... button becomes active, allowing you to specifyadditional model parameters. In the case of the VOF model, thispanel allows you to select the optional Surface Tension and Wall Ad-

hesion models, disable the Donor-Acceptor Model, and set some ofthe time-dependent solution control parameters.



The surface tension and wall-adhesion models and the time-dependenceparameters that are relevant to the VOF model are discussed laterin this chapter. The use of the implicit interpolation scheme ratherthan the default donor-acceptor scheme is also discussed later.

From the text interface, the VOF model can be enabled with theUsing the TextInterface DEFINE-MODELS command in the SETUP1 menu. This command re-

sults in a menu where you can choose from among many modelsthat are available in FLUENT.

SETUP1 �! DEFINE-MODELS



(SETUP1)-

DM

COMMANDS AVAILABLE FROM DEFINE-MODELS:

CYLINDRICAL-VELOCITIES HEAT-TRANSFER

TURBULENCE RADIATION

SPECIES-AND-CHEMISTRY MULTIPLE-PHASES

QUIT HELP

ENTER HELP (COMMAND) FOR MORE INFORMATION.

(DEFINE-MODELS)-

The option to perform either a VOF or an Eulerian multiphasecalculation is enabled with the MULTIPLE-PHASES command.

DEFINE-MODELS �! MULTIPLE-PHASES

(DEFINE-MODELS)-

MP

(MULTIPHASE MODELS (SELECT ONLY ONE))

NO EULERIAN-EULERIAN MULTIPHASE FLOW MODEL

NO EULERIAN-EULERIAN GRANULAR FLOW MODEL

YES VOF FREE SURFACE MODEL

D ACTION (TOP,DONE,QUIT,REFRESH)

After you select one of the multiphase models, a new menu appearsin which you can continue the model de�nition. If you are justbeginning the problem setup, you may �rst see the following ques-tion, which is needed for the allocation of memory needed for theadditional phase.

(MULTIPHASE MODEL (SELECT ONLY ONE))

(*)- ** MEMORY ALLOCATION **

(I)- NUMBER OF ADDITIONAL PHASES TO BE CONSIDERED

(I)- ++(DEFAULT 1)++

1

(I)- DEFAULT ASSUMED

COMMANDS AVAILABLE FROM MULTIPHASE:

DEFINE-PHASES MULTIPHASE-OPTIONS QUIT

HELP


(MULTIPHASE)-



The DEFINE-PHASES command is used to specify the number ofphases and their names, as described in Section 10.3.3. TheMULTIPHASE-OPTIONS command is used to enable the surface ten-sion and wall adhesion models that may be used in conjunction withthe VOF calculation, or to disable the donor-acceptor scheme.

MULTIPHASE �! MULTIPHASE-OPTIONS

(MULTIPHASE)-

MO

(VOF OPTIONS)

YES ENABLE DONOR-ACCEPTOR VOF MODEL

NO SURFACE TENSION

NO WALL ADHESION


These options are discussed in Section 10.3.2 and 10.3.9.

10.3.2 Choosing the VOF Formulation

The VOF formulations that are available in FLUENT are as follows:

� time-dependent with the donor-acceptor interpolation scheme(default)

� time-dependent with the implicit interpolation scheme

� steady-state with the implicit interpolation scheme

The time-dependent formulation with the donor-acceptor scheme isthe default scheme, and it should be used whenever you are inter-ested in the time-accurate transient behavior of the VOF solution.This formulation is activated automatically when you �rst enablethe VOF model as described in Section 10.3.1.

The time-dependent formulation with the implicit interpolation schemecan be used if you are looking for a steady-state solution and youare not interested in the intermediate transient ow behavior, butthe �nal steady-state solution is dependent on the initial ow con-ditions and/or you do not have a distinct in ow boundary for eachphase. To use this formulation, turn o� the donor-acceptor modelas described below. While the implicit time-dependent formulation



may converge faster than the donor-acceptor formulation, the in-terface between phases will not be as sharp as that predicted withthe donor-acceptor scheme. To reduce this di�usivity, it is rec-ommended that you use the QUICK discretization scheme for thevolume fraction equations. In addition, you may want to considerturning the donor-acceptor scheme back on after calculating a solu-tion with the implicit scheme, in order to obtain a sharper interface.

The steady-state formulation can be used if you are looking fora steady-state solution, you are not interested in the intermedi-ate transient ow behavior, and the �nal steady-state solution isnot a�ected by the initial ow conditions and there is a distinctin ow boundary for each phase. To use this formulation, turno� the donor-acceptor model as described below, and then disablethe time-dependent ow model in the Models panel or the EXPERT

TIME-DEPENDENCE table. As mentioned above, it is recommendedthat you use the QUICK discretization scheme for the volume frac-tion equations when you use the implicit interpolation scheme.

To help you determine the best formulation to use for your problem,Examplesexamples which use each of the three formulations are listed below:

� time-dependent with the donor-acceptor scheme: jet breakup

� time-dependent with the implicit interpolation scheme: shapeof the liquid interface in a centrifuge

� steady-state with the implicit interpolation scheme: ow arounda ship's hull

In the GUI, you can turn o� the donor-acceptor scheme in the Mul-Disabling theDonor-Acceptor

Schemetiphase Parameters panel. Click on the Multiphase Parameters... but-ton in the Models panel, and then turn o� the Donor-Acceptor Model

under VOF Free Surface Options:



If a steady-state formulation is desired, you can now turn o� theTime Dependent Flow option in the Models panel. (When the Donor-Acceptor Model is active, it is not possible to disable time depen-dence.)

When the donor-acceptor model is not active, FLUENT will solvestandard scalar transport equations for the secondary volume frac-tions.



In the text interface, you can deactivate the donor-acceptor schemein the VOF OPTIONS table (accessed when you use the MULTIPLE-

PHASES command in the DEFINE-MODELS menu to enable the VOFmodel, as described in Section 10.3.1):

(VOF OPTIONS)

NO ENABLE DONOR-ACCEPTOR VOF MODEL

NO SURFACE TENSION

NO WALL ADHESION

ACTION (TOP,DONE,QUIT,REFRESH)

If a steady-state formulation is desired, you can now turn o� TIME-

DEPENDENCE in the EXPERT menu. (When the DONOR-ACCEPTOR VOF

MODEL is active, it is not possible to disable time dependence.)

10.3.3 De�ning the Phases

The next step in the problem setup is the naming of the phases.Note that while this step is optional, it can facilitate the subse-quent setup process in that the phases will be identi�ed by namerather than by number. To de�ne the phases, you can use eitherthe DEFINE-PHASES text command in the SETUP1 menu, or theDEFINE-PHASES command in the MULTIPHASE menu that appearsafter you use the DEFINE-MODELS MULTIPLE-PHASES text commandto enable the VOF model.

You will be asked �rst for the number of secondary phases in theproblem (whether or not you were prompted for the number ofadditional phases to be considered earlier, for memory allocationpurposes). You will only be allowed to input the same value asbefore or a smaller value. A greater number of phases cannot beenabled at this point. If you respond that there is 1 secondaryphase, a table will result in which you can input the name of thePRIMARY PHASE and the secondary phase, PHASE 2.

SETUP1 �! DEFINE-PHASES



(SETUP1)-

DP

(I)- NUMBER OF SECONDARY PHASES


1

(PHASE NAMES)

NOTE : PHASE NAMES CANNOT CONSIST OF

A SINGLE CHARACTER C OR X

PHASE 1 PRIMARY PHASE

PHASE 2 PHASE 2


Before you name the phases, it is important to give some thoughtto which of the uids to identify as the PRIMARY PHASE. If you planto use the gas law, this model is only available for the primaryphase. In the same manner, any species mixing or chemical reac-tions will take place only within the primary phase. It is only thisphase that allows for the complete spectrum of property model-ing, including the use of kinetic theory, User-De�ned Subroutines,non-Newtonian ow, and composition-dependence. Temperaturedependence through polynomial or piecewise-linear pro�les, on theother hand, is available for all phases.

If your problem de�nition does not require the gas law, speciesmixing, or special property de�nitions, you should identify the lessdense of the uids as the primary phase. This means that the vol-ume fraction equation(s) will be solved for the denser uid(s). Themotivation for this choice has to do with numerics. If, during thecourse of the solution, small perturbations in the pressure �eld occurnear the interface, these will translate into perturbations in the ve-locity �eld. Because of the increased inertia, velocity perturbationsare smaller and much less destabilizing in the denser uid than inthe lighter uid. If the volume fraction is computed for the denser uid, the increased stability of the velocity �eld leads to increasedstability in the volume fraction calculation.

Once you have determined which uid should be assigned to whichphase, the phases can be named, as shown below for a two-phasesystem involving AIR and WATER.



(PHASE NAMES)



AIR PRIMARY PHASE

WATER PHASE 2


If you request 2 secondary phases, the table will ask for the namesof the primary and the two secondary phases.

(SETUP1)-

DP



2

(PHASE NAMES)



AIR PRIMARY PHASE

WATER PHASE 2

OIL PHASE 3


10.3.4 Time-Dependent Modeling Parameters

If you are using the time-dependent VOF formulation in FLUENT,an explicit solution for the volume fraction is obtained either onceeach time step or once each iteration, depending upon your inputsto the model. You also have control over the time step used for thevolume fraction calculation. It can be either the same as that usedfor the solution of the other transport equations in the model, orit can be adjusted automatically by FLUENT, again based on yourinputs.

From the text interface, the time-dependent solution controls areaccessed from the EXPERT menu using the TIME-DEPENDENCE com-mand.

EXPERT �! TIME-DEPENDENCE



(EXPERT)-

TD

(TIME DEPENDENT FLOW SOLUTION PARAMETERS)

100 MAX. NO. ITNS PER TIME STEP

1.0000E-03 MIN. RESIDUAL SUM (DIM)

1.0000E-03 SET TIME STEP (S)

YES SOLVE VOF EVERY ITERATION

NO AUTOMATIC TIME STEP REFINEMENT FOR VOF

2.5000E-01 MAXIMUM COURANT NUMBER FOR VOF (DIM)

NO AUTOMATIC SAVING

NO ENABLE TIME VARYING GRAVITY VECTOR


The input lines in this table are the same as those appearing inthe table when the VOF model is not active, with the exception ofthree. These are discussed below.

� SOLVE VOF EVERY ITERATION: A response of yes or no to thisquestion allows you to request that FLUENT solve the vol-ume fraction equation(s) every iteration within a time stepor simply once a time step. If you solve these equations ev-ery iteration, the convective ux coe�cients appearing in theother transport equations will be updated based on the up-dated volume fraction each iteration. If you solve the VOFequations once a time step, these coe�cients will not be com-pletely updated each iteration, since the volume fraction �eldwill not change from iteration to iteration.

In general, if you anticipate that the location of the inter-face will change as the other ow variables converge duringthe time step, you should use a response of YES. This situa-tion arises when large time steps are being used in hopes ofreaching a steady-state solution, for example. If small timesteps are being used, however, it is not necessary to performthe additional work of solving for the volume fraction everyiteration, so an input of NO can be used. This choice is themore stable of the two, and requires less computational e�ortper iteration than the �rst choice, but the overall result is lessaccurate in time.

� AUTOMATIC TIME STEP REFINEMENT FOR VOF: Two options areavailable for the choice of time step to be used for the volumefraction calculation. If you respond NO to this option, FLU-ENT will solve the VOF equation(s) using the time step that



is set in this table on the SET TIME STEP (S) line. If you re-spond YES, the time step will be re�ned automatically, basedon your input for the maximum Courant Number allowed nearthe free surface, discussed below.

� MAXIMUM COURANT NUMBER FOR VOF (DIM): The Courant Num-ber is a dimensionless number that compares the time step ina calculation to the characteristic time of transit of a uidelement across a control volume:

�t

�xcell=v uid(10.3-1)

In the region near the uid interface, FLUENT divides thevolume of each cell by the sum of the outgoing uxes. Theresulting time represents the time it would take for the uidto empty out of the cell. The smallest such time is used asthe characteristic time of transit for a uid element across acontrol volume, as described above. Based upon this timeand your input for the maximum allowed Courant Number,a time step is computed for use in the VOF calculation. Forexample, if the maximum allowed Courant Number is 0.25,the time step will be chosen to be at most one-fourth theminimum transit time for any cell near the interface.

You can access the time-dependent ow parameters from the graph-ical interface, as well. Recall that as soon as the VOF model isenabled in the Models panel, the Time Dependent Flow option is en-abled as well. If you open the Time Dependent Flow Parameters panelfrom the Models panel, you can set the standard time-dependent ow variables.



To set the time dependent ow parameters that are used in theVOF model, you can use the Multiphase Parameters panel that canbe accessed once one of the multiphase models is enabled.



In this panel, you can choose whether or not to solve the VOFequations every iteration, whether or not to use the automatic re-�nement of the time step, as described above, and set the limitingCourant Number.

10.3.5 De�ning the Properties

The uid properties are set up using the PHYSICAL-CONSTANTS com-mand in the SETUP1 menu. The items appearing in the PHYSICAL-CONSTANTS menu depend upon the scope of your problem de�nition.



At the very least, options for setting the DENSITY and VISCOSITY

will appear. Thermal properties appear when temperature is beingcalculated. Species-related properties appear when the calculationinvolves two or more species. Kinetic theory parameters appearwhen kinetic theory is active, and so forth. When the VOF modelis active, the same items appear in the menu, but the dialogue thatfollows when you set the properties changes. This dialogue is de-signed to allow you to set the properties for each of the active phasesin your problem. It is illustrated through a number of examples thatfollow.

When the VOF model is active, the gas law can be used for theSetting the Densitydensity calculation for the primary phase only. Alternatively, thephases can have temperature dependent densities. In the simplestcase, the phases have constant, but di�erent densities. If such asystem consists of two phases, the following dialogue illustrates thesetup of constant densities.

SETUP1 �! PHYSICAL-CONSTANTS �! DENSITY



(SETUP1)-

PC

COMMANDS AVAILABLE FROM PHYSICAL-CONSTANTS:

DENSITY VISCOSITY OPERATING-PRESSURE

QUIT HELP


(PHYSICAL-CONSTANTS)-

DE

COMMANDS AVAILABLE FROM PHASE-SELECTION:

AIR WATER QUIT HELP


(PHASE-SELECTION)-

AIR

(L)- USE GAS LAW FOR AIR?

(L)- Y OR N ++(DEFAULT-NO)++

N

(R)- DENSITY OF AIR

(R)- UNITS= KG/M3 ++(DEFAULT 1.0000E+03)++

1.0


AIR WATER QUIT HELP


(PHASE-SELECTION)-

WAT

(R)- DENSITY OF WATER


1000

(PHASE-SELECTION)-

Q

In the next example, consider a 3-phase system where the gas law isto be used for the primary phase. As with any single phase systeminvolving a single species, FLUENT will ask for the molecular weightfor the material being modeled with the gas law.




DE


AIR WATER QUIT HELP


(PHASE-SELECTION)-

AIR



Y

(R)- OPERATING PRESSURE

(R)- UNITS= PA ++(DEFAULT 1.0132E+05)++

X

(R)- DEFAULT ASSUMED

(R)- ENTER THE MOLECULAR WEIGHT FOR AIR

(R)- UNITS= DIM ++(DEFAULT 2.8970E+01)++

X


(PHASE-SELECTION)-

WAT

(R)- DENSITY OF WATER


1000

(PHASE-SELECTION)-

Q

If you are modeling multiple species in the primary phase, youwill not be asked to input the molecular weight, but will be re-minded to input molecular weights for all of the species using theMOLECULAR-WEIGHTS command.

When you are solving for temperature, FLUENT asks for the tem-perature dependence for all of the properties for all of the phases.For example, for a 3-phase system, the dialogue for setting up thedensities would be similar to that shown below.




DE


AIR OIL WATER QUIT HELP


(PHASE-SELECTION)-

AIR



Y

(R)- OPERATING PRESSURE

(R)- UNITS= PA ++(DEFAULT 1.0132E+05)++

X


(R)- ENTER THE MOLECULAR WEIGHT FOR AIR


X


(PHASE-SELECTION)-

WAT

(*)- DEFINE DENSITY OF WATER (KG/M3)

(*)- AS A FUNCTION OF TEMPERATURE (K)

(*)-

(I)- NUMBER OF COEFFICIENTS (+VE = POLYNOM., -VE = P.W.LINEAR)


1

(R)- DENSITY OF WATER (KG/M3)


X




(PHASE-SELECTION)-

OIL

(*)- DEFINE DENSITY OF OIL (KG/M3)


(*)-



2

(POLYNOMIAL FIT FOR DENSITY OF OIL)

8.0000E+02 ENTER COEFFICIENT - A1 (KG/M3)

-1.0000E-02 ENTER COEFFICIENT - A2 (-)


The viscosities for the phases are input in the same manner. In anSetting theViscosity isothermal, 3-phase system, the viscosities would be input in the

manner shown below.

PHYSICAL-CONSTANTS �! VISCOSITY


VI

(PHASE-SELECTION)-

AIR

(R)- VISCOSITY OF AIR

(R)- UNITS= KG/M-S ++(DEFAULT 2.0000E-05)++

1.7e-5

(PHASE-SELECTION)-

WAT

(R)- VISCOSITY OF WATER


X


(PHASE-SELECTION)-

OIL

(R)- VISCOSITY OF OIL


.01

If you are calculating temperature, FLUENT will ask for the tem-perature dependence of the viscosity for each phase, in the mannershown above for the density.



In the event that one of the phases is to be modeled as a non-Modeling aNon-Newtonian

ViscosityNewtonian uid, you must de�ne this uid as the primary phase.Once the non-Newtonian model has been enabled in the EXPERT

OPTIONS table or the Models panel, the VISCOSITY command in thePHYSICAL-CONSTANTS menu can be used to set the non-Newtonianviscosity constants as well as the viscosity for the additional phases.

(SETUP1)-

PC


DENSITY VISCOSITY PROPERTY-OPTIONS

OPERATING-PRESSURE QUIT HELP



VIS

(PHASE-SELECTION)-

AIR

(NON-NEWTONIAN FLOW PARAMETERS (POWER LAW) FOR AIR)

1.5 PARAMETER N (DIM)

1.0000E+00 PARAMETER K (PA*(S**N))


(PHASE-SELECTION)-

WAT

(R)- VISCOSITY OF WATER


9E-4

If you are using the gas law to model the primary phase, you willUsing KineticTheory for

Property De�nitionhave the option of using kinetic theory to model one or more ofthe other properties for that phase. The kinetic theory option isenabled in the usual way, using the PROPERTY-OPTIONS table in thePHYSICAL-CONSTANTS menu. Once enabled, you will be asked ifyou want to use kinetic theory when you set the various properties.For example, to use kinetic theory for the speci�c heat, the dia-logue would proceed as shown below. After setting the REFERENCE

TEMPERATURE FOR ENTHALPY and selecting the primary phase (AIRin the example below), you will be asked if you want to use kinetictheory for the primary phase:




CP

(R)- REFERENCE TEMPERATURE FOR ENTHALPY

(R)- UNITS= K ++(DEFAULT 2.7300E+02)++

X


(PHASE-SELECTION)-

AIR

(L)- COMPUTE SPECIFIC HEAT FROM KINETIC THEORY?

(L)- Y OR N ++(DEFAULT-YES)++

Y

You can then de�ne the (optionally temperature-dependent) speci�cheat for the remaining phase(s).

(PHASE-SELECTION)-

WAT

(*)- DEFINE SPECIFIC HEAT OF WATER (J/KG-K)


(*)-



X

(I)- DEFAULT ASSUMED

(R)- SPECIFIC HEAT OF WATER (J/KG-K)

(R)- UNITS= J/KG-K ++(DEFAULT 1.0000E+03)++

4136

Before kinetic theory can be used, you will need to set the kinetictheory parameters, appearing in the KINETIC-THEORY-PARMS. ta-ble. The setting of these parameters is described in Chapter 15.

10.3.6 Including Body Forces in the VOF Calculation

In many instances, the motion of the uids you are tracking with theVOF model is due, in part, to gravitational e�ects. When you ac-tivate a gravitational force in the BODY-FORCES table in the EXPERTmenu, you will be given a choice of whether to set the site of thereference density or to set the reference density itself.

EXPERT �! BODY-FORCES



(SETUP1)-

EX BF

(BODY FORCES)

YES IMPROVED TREATMENT OF BODY FORCE IN DISCRETE EQNS.

YES INCLUDE BODY FORCE TERMS IN VELOCITY INTERPOLATION

9.8000E+00 GRAVITY ACCELERATION IN X-DIRN - (M/S2)

0.0000E+00 GRAVITY ACCELERATION IN Y-DIRN - (M/S2)

YES USER DEFINED REFERENCE DENSITY


If you respond YES to the option to input a USER DEFINED REFERENCE

DENSITY, a second table will appear, where you will be able to inputthe value of this density.

(USER DEFINED REFERENCE DENSITY)

1.0000E+00 REFERENCE DENSITY (KG/M3)


If you respond NO to the input of a USER DEFINED REFERENCE DENSITY,a second table will appear asking you to input the location of thecell from which the reference density will be taken.

(REFERENCE DENSITY LOCATION)

2 REFERENCE DENSITY : I - LOCATION

2 REFERENCE DENSITY : J - LOCATION


While either selection works well for most single phase applications,the option to set the reference density rather than the site of thereference density is preferred when the VOF model is in use. Theaim is to have a reference density value that is stable throughoutthe calculation. Since many VOF applications involve a changefrom one phase to another in any given control volume throughoutthe course of the calculation, it is better to set the density valueitself, rather than assume that one cell in particular will always be�lled with one particular phase.

In terms of selecting the appropriate reference density value, thebest strategy is to use the density of the predominant uid. If,in a two-phase system, for example, water occupies over 50% of



the volume, the density of water should be used. This strategyminimizes the round-o� in the density uctuations that are thesource of the buoyancy forces in the domain.

If your model has in ow/out ow boundaries and you prefer to setthe reference density site, you should do so at an in ow boundarywhere the predominant uid enters the domain. This is becausethe density will be constant throughout the calculation at this site.If you choose an interior site, convergence problems will arise if uctuations of the density occur at the site that you choose.

10.3.7 Setting Boundary Conditions

Boundary conditions may be input using either the text interfacecommand for BOUNDARY-CONDITIONS in the SETUP1 menu, or theBoundary Conditions panel through the graphical user interface. Atinlets, one additional scalar, the volume fraction, must be set whenthe VOF model is active. Note that this scalar can only be set forthe non-primary phase(s).

In a 2-phase system, for example, where the primary phase is air andthe second phase is water, the steps for setting the inlet boundaryconditions from the graphical user interface are as follows. From theBoundary Conditions panel, choose an INLET cell type and select theappropriate zone ID. When you press the Set... button the Velocity(or Pressure) Inlet Boundary Conditions panel appears.



In the Inlet Boundary Conditions panel, the �rst Phase that younamed appears in the upper left corner, and the �elds for the rel-evant velocities and scalars are active. The Volume Fraction �eldunder Multiphase is not active at this time.

The speci�cation of the boundary conditions requires two steps.First, enter the velocity and other scalar values in the appropriate�elds and click on Apply. Second, choose one of the secondary phasesfrom the Phase drop-down list. When you do this, the velocity and



scalar �elds become inactive, and the Volume Fraction �eld becomesactive. Set the appropriate Volume Fraction and click on Apply. If,in a two-phase system, the inlet is to have a volume fraction of 1for the �rst phase, you will need to choose the second phase and seta volume fraction of 0.

Note that with the VOF Model, only values of 0 or 1 are meaningfulat any given inlet. If an inlet is to introduce a strati�ed layer oftwo uids into a domain, it should be replaced by two inlets, eachcarrying a single uid.



From the text interface, the VOLUME-FRACTION appears in the inletzone boundary conditions menu as shown below.

SETUP1 �! BOUNDARY-CONDITIONS

(SETUP1)-

BC

COMMANDS AVAILABLE FROM BOUNDS:

W-WALL Z-WALL SYMMETRY .(LIVE)

CYCLIC OUTLET INLET AXIS

QUIT HELP


(BOUNDS)-

I 1

COMMANDS AVAILABLE FROM I1-ZONE-BOUNDARY-CONDITIONS:

NORMAL-VELOCITY U-VELOCITY V-VELOCITY

VOLUME-FRACTION QUIT HELP


(I1-ZONE-BOUNDARY-CONDITIONS)-

As with the graphical interface, the VOLUME-FRACTION commandwill prompt you for the volume fraction of the secondary phase(s)only. Thus, if you are solving a problem in which there is one sec-ondary phase, FLUENT will ask for the volume fraction of only thatphase. Volume fractions of either 0 or 1.0 are the only meaningfulchoices for the VOF model, even though any value between thesetwo will be accepted.

BOUNDARY-CONDITIONS �! VOLUME-FRACTION


VF

(R)- VOLUME FRACTION OF WATER


1.0

Because the velocity (and turbulence and enthalpy) �elds are shared,there is no need to specify a separate velocity boundary conditionfor the various phases. (This is in contrast to the setting of bound-ary conditions in the Eulerian multiphase model, where each phase



carries its own velocity �eld.) Wall boundary condition optionsare not expanded by the presence of multiple phases within thedomain. A zero normal gradient boundary condition is imposed forthe volume fraction.

10.3.8 Solution Strategies

In addition to the appropriate choice for the primary phase uidand the time stepping technique to use, other steps can be taken toimprove the accuracy of the VOF calculation.

The site of the reference pressure can be moved to a location thatSetting theReference Pressure

Locationwill result in less round-o� in the pressure calculation. The optionto set the reference pressure location is in the EXPERT SOLUTION-

PARAMETERS table. If you respond YES, as shown below, a secondtable appears in which the location of the reference pressure can bechosen.

EXPERT �! SOLUTION-PARAMETERS

(SOLUTION PARAMETERS)

NO MONITOR SOLVER

NO ALLOW PATCHING OF BOUNDARY VALUES

YES CONVERGENCE-DIVERGENCE CHECK ON

1.0000E-03 SET MINIMUM RESIDUAL SUM (DIM)

YES NORMALIZE RESIDUALS

YES CONTINUITY CHECK

NO ENABLE HIGHER ORDER SCHEME

NO ENABLE LINEAR INTERPOLATION FOR PRESSURE

NO VISCOSITY WEIGHTED VELOCITY INTERPOLATION

NO ENABLE SIMPLEC METHOD (DEFAULT IS SIMPLE)

NO ENABLE FIX VARIABLE OPTION

YES SET PRESSURE REFERENCE LOCATION


(REFERENCE PRESSURE LOCATION)

2 I-VALUE

10 J-VALUE


The cell that you choose should be in a region that will alwayscontain the less dense of the two uids. This is because variationsin the static pressure are larger in a more dense uid than in a lessdense uid, given the same velocity distribution. If the zero of therelative pressure �eld is in a region where the pressure variations are



small, less round-o� will occur than if the variations occur in a �eldof large non-zero values. Thus in systems containing air and water,for example, it is important that the reference pressure location bein the portion of the domain �lled with air rather than that �lledwith water.

The calculation of pressure is perhaps the most important among allSetting theMultigrid

Parametersof the variables in a VOF simulation in terms of having an in uenceon the prediction of volume fraction. Whenever possible, the multi-grid solver should be enabled for pressure. To extract the most workfrom the multigrid solver each iteration, you should decrease theTERMINATION-CRITERIA to its minimum value, 1 � 10�3, at leastduring the �rst few time steps, using the TERMINATION-CRITERIA

command in the MULTIGRID-PARAMETERS menu or the TerminationCriterion �eld in the Multigrid Parameters panel.

EXPERT �! LINEAR-EQN.-SOLVERS �! MULTIGRID-PARAMETERS

Solve �! Controls �!Multigrid...

Reduction of this value leads to the maximum volume conservationcondition that can be imposed during each iteration, leading to themost accurate prediction of the volume fraction.

A third change that you may want to make to the solver settings isUnderrelaxationfor the

Time-DependentDonor-Acceptor

Formulation

in the underrelaxation factors that you use. Typically, the defaulttime-dependent VOF formulation allows for increased values on allunderrelaxation factors, provided a small time step is used, withouta loss of solution stability. In simple geometries with little gridskew, you can generally increase the underrelaxation factors for allvariables to 1.0 and expect stability and a rapid rate of convergence(in the form of few iterations required per time step). The defaultunderrelaxation factor of 1.0 on the body forces need not be reducedexcept in cases where gravity and strong swirl (or other user-de�nedmomentum sources) are involved.

EXPERT �! UNDERRELAX1

Solve �! Controls �!Underrelaxation...

As with any FLUENT simulation, the underrelaxation factors can(and should) be increased as the solution exhibits stable, convergentbehavior. You should always save a Data File beforehand, however,in case the increase you specify destabilizes the solution process.

If you have deactivated the donor-acceptor model (as described inUnderrelaxationfor the ImplicitFormulations

Section 10.3.2), you will be able to set underrelaxation parame-ters for each secondary-phase volume-fraction transport equation.



(This is true for both the time-dependent and steady-state implicitformulations.) By default, these underrelaxation factors are set to0.2. For improved convergence, you can set these as well as theunderrelaxation factors for all other equations to 0.5.

As mentioned earlier, if you have deactivated the donor-acceptorLinear SolverParameters for the

ImplicitFormulations

model (as described in Section 10.3.2), FLUENT will solve trans-port equations for the secondary-phase volume fractions. It is notpossible to use the multigrid solver for these volume fraction equa-tions, so you must always use the linear (LGS) solver.

When the implicit scheme is used instead of the donor-acceptorDiscretizationScheme Selectionfor the ImplicitFormulations

scheme, you should use the QUICK discretization scheme for thevolume fraction equations in order to improve the sharpness of theinterface between phases.

10.3.9 The Surface Tension Model

It is possible to include the e�ects of surface tension along the in-terface between two uids. The model can be augmented by theadditional speci�cation of a contact angle that one of the uidsmakes with the container wall.

Surface tension arises as a result of attractive forces between moleculesin a uid. Consider an air bubble in water, for example. Withinthe bubble, the net force on a molecule due to its neighbors is zero.At the surface, however, the net force is radially inward, and thecombined e�ect of the radial components of force across the entirespherical surface is to make the surface contract, thereby increasingthe pressure on the concave side of the surface. The surface tensionis a force, acting only at the surface, that is required to maintainequilibrium in such instances. It acts to balance the radially inwardinter-molecular attractive force with the radially outward pressuregradient force across the surface. In regions where two uids areseparated, but one of them is not in the form of spherical bubbles,the surface tension acts to decrease the area of the interface.

The surface tension model in FLUENT is the Continuum SurfaceForce (CSF) model proposed by Brackbill et al. [14]. With thismodel, the addition of surface tension to the VOF calculation resultsin a source term to the momentum equation. To understand theorigin of the source term, consider the special case where the surfacetension is constant along the surface, and where only the forcesnormal to the interface are considered. It can be shown that thepressure drop across the surface depends upon the surface tensioncoe�cient, �, and the surface curvature as measured by two radii



in orthogonal directions, R1 and R2:

p2 � p1 = ��1

R1

+1

R2

�(10.3-2)

where p1 and p2 are the pressures in the two uids on either side ofthe interface.

In FLUENT, a more general formulation is used, where the surfacecurvature is computed from local gradients in the surface normal atthe interface. Let n be the surface normal, de�ned as the gradientin �2, the secondary phase volume fraction.

n = r�2 (10.3-3)

The curvature, �, is de�ned in terms of the divergence of the unitnormal, n̂:

� = r � n̂ =1

jnj

" n

jnj� r

!jnj � (r � n)

#(10.3-4)

where

n̂ =n

jnj(10.3-5)

The surface tension can be written in terms of the pressure jumpacross the surface. The force at the surface can be expressed as avolume force using the divergence theorem. It is this volume forcethat is the source term which is added to the momentum equation.It has the following form:

Fvol(x) = 2��(x)�2r�2 (10.3-6)

Note that the source term is only added on one side of the inter-face: the side on which the volume fraction calculation is beingperformed. In the FLUENT VOF model, this corresponds to thesecondary phase.

As an example of the surface tension model, consider a section of aExample:Prediction of aCapillary Jet

Breakup

stationary cylinder of water in a zero gravitational �eld. The sec-tion is 5.236 cm in length, and roughly 1 cm in diameter, followingan example proposed in Reference [65]. A region of air, 3 cm indiameter, surrounds the cylinder of water. A 41 � 31 grid is used



in the axisymmetric model, which employs a symmetry boundarycondition on the axis and both ends, and a pressure boundary tomodel the plenum of air surrounding the water.

The liquid surface is initially perturbed at t=0 so that the diameterat the left side is 5% larger than that at the right (Figure 10.3.1),with the transition modeled using a cosine function.

0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 5.000E-04


Initial Conditions for Capillary Jet Breakup

Fluent Inc.

Fluent 4.30

Nov 03 1994Y

XZ

Figure 10.3.1: Initial Conditions for Capillary Jet Breakup Problem

As time evolves, the perturbation in the surface grows, as can beseen in Figure 10.3.2.

The reason that the perturbation grows in this manner is that thecurvature in the surface gives rise to di�erent pressure gradientsacross the surface in di�erent regions. Where the surface is concave(as seen from the water side), the pressure is higher on the water sidethan on the air side, forcing the boundary to move outward. Wherethe surface is convex, the opposite is true, so that the boundarymoves inward. At t = 0.75 seconds (Figure 10.3.3), the perturbationhas advanced to the point where the jet is about to break. Withinthe next 15 ms, the break up has occurred.

The surface tension model can be enabled three di�erent ways.Enabling theSurface Tension

ModelFirst, you can open the Multiphase Parameters panel and turn onthe Surface Tension check button.



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 7.000E-01


Capillary Jet Breakup at t = 0.5 / 0.7 sec

Fluent Inc.

Fluent 4.30

Nov 03 1994Y

XZ

Figure 10.3.2: Capillary Jet Breakup at T = 0.5 (top) and 0.7(bottom) sec



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 7.650E-01


Capillary Jet Breakup at t = 0.75 / 0.765 sec

Fluent Inc.

Fluent 4.30

Nov 03 1994Y

XZ

Figure 10.3.3: Capillary Jet Breakup at T = 0.75 (top) and 0.765(bottom) sec



Alternatively, you can use the text interface. In the SETUP1 menu,you can start with the DEFINE-MODELS command and select theMULTIPLE-PHASES option to turn on the VOF FREE SURFACE MODEL.

(DEFINE-MODELS)-

MP

(MULTIPHASE MODELS (SELECT ONLY ONE))

NO EULERIAN-EULERIAN MULTIPHASE FLOW MODEL

NO EULERIAN-EULERIAN GRANULAR FLOW MODEL

YES VOF FREE SURFACE MODEL


After you select one of the multiphase models, a new menu ap-pears in which you can name the phases, as described earlier, orchoose MULTIPHASE-OPTIONS that are relevant to the VOF model:the SURFACE TENSION model with the optional addition of WALLADHESION (described later in this section).

COMMANDS AVAILABLE FROM MULTIPHASE:

DEFINE-PHASES MULTIPHASE-OPTIONS QUIT

HELP


(MULTIPHASE)-

MO

(VOF OPTIONS)


YES SURFACE TENSION

NO WALL ADHESION


Finally, you can use the OPTIONS command in the EXPERT menu.

EXPERT �! OPTIONS



(EXPERT)-

OP

(MODELING OPTIONS)

NO ALLOW LINK SETTING

NO ALLOW PROFILE SETTING

NO ENABLE NON-NEWTONIAN FLOW MODEL

NO ENABLE POROUS FLOW MODEL

NO ENABLE FAN/RADIATOR MODEL

NO ALLOW FIXED PRESSURE BOUNDARIES

NO ALLOW SETTING FLOW ANGLES FOR PRESSURE-INLETS

NO ENABLE STEADY CORIOLIS FORCE

NO ENABLE TIME-DEPENDENT CORIOLIS FORCE

NO ENABLE MULTIPLE ROTATING REFERENCE FRAMES


YES SURFACE TENSION

NO WALL ADHESION

NO ENABLE SLIDING MESH CALCULATION

NO ACTIVATE PHASE CHANGE MODELING

NO ENABLE DEFORMING MESH CALCULATION


The setting of the surface tension coe�cient is illustrated along withthe setting of the contact angle that the uid makes with the wall.This so-called wall adhesion angle is discussed below.

An option to specify a wall adhesion angle in conjunction with theWall Adhesionsurface tension model is also available in the VOF model. Themodel is taken from work done by Brackbill et al. [14]. Rather thanimpose this boundary condition at the wall itself, the contact anglethat the uid is assumed to make with the wall is used to adjustthe surface normal in cells near the wall. This so-called dynamicboundary condition results in the adjustment of the curvature ofthe surface near the wall.

If �w is the contact angle at the wall, then the surface normal at thelive cell next to the wall is

n̂ = n̂w cos �w + t̂w sin �w (10.3-7)

where n̂w and t̂w are the unit vectors normal and tangential tothe wall, respectively. The combination of this contact angle withthe normally calculated surface normal one cell away from the walldetermine the local curvature of the surface, and this curvature isused to adjust the body force term in the surface tension calculation.



The ability to set the contact angle that the uid makes with theEnabling the WallAdhesion Model wall is set using one of the three methods discussed earlier for en-

abling surface tension. You can use theMultiphase Parameters panel,the MULTIPHASE-OPTIONS menu command, or the EXPERT OPTIONS

table.

As an example, consider a cylindrical container, partially �lled withExample:Formation of aWater Bubble

water, in a zero gravity �eld. The container is 10 cm tall and 10cm in diameter. An axisymmetric model is solved using a 51 � 31grid.

At time t=0, the water �lls the bottom 2 cm of the container, withair above it (Figure 10.3.4, left frame). The air is modeled as theprimary phase, which means that the surface tension value (0.07N/m) will be applied to the second phase, water. A contact angleof 175� is used. This contact angle is applied to the water, whichmeans that an obtuse angle, as measured in the water, will form atthe walls. For this condition to be met, the water level must rise inthe middle of the container and drop at the edges. The start of thisprocess is shown in Figure 10.3.4 (right frame), where the boundarycondition at the wall acts to change the water level nearby. Notethat the water level at the center of the vessel is not yet a�ected atthis time.

After 0.7 sec have passed Figure 10.3.5 (left frame), the uid in thecenter of the container has responded, and the water at the edgescontinues to try to satisfy the contact angle boundary condition. By1.3 sec Figure 10.3.5 (right frame), the water has become detachedfrom the bottom of the vessel and is moving slowly upward.

The surface tension coe�cient and contact angle at the wall are setSetting the SurfaceTension and Wall

AdhesionProperties

in the PHYSICAL-CONSTANTS menu, using the VOF-SURFACE-TENSIONcommand. Note that you can specify the surface tension coe�cientfor only one phase. The contact angle is that between the inter-face and the wall as measured inside the speci�ed phase uid. Inthe example below, a contact angle of 45�corresponds to the watercreeping up the side of its container, as is common with water in aglass.

SETUP1 �! PHYSICAL-CONSTANTS �! VOF-SURFACE-TENSION



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 2.000E-01


Formation of a Bubble in a Zero Gravity Field

Fluent Inc.

Fluent 4.30

Oct 21 1994

Y

X

Z

Figure 10.3.4: Initial Water Level in a Container (Left) and AlteredWater Level After 0.2 sec (Right)



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 1.300E+00


Formation of a Bubble in a Zero Gravity Field

Fluent Inc.

Fluent 4.30

Oct 21 1994

Y

X

Z

Figure 10.3.5: Formation of a Water Bubble Before (Left) and After(Right) it Separates from the Wall



(SETUP1)-

PC


DENSITY VISCOSITY

PROPERTY-OPTIONS OPERATING-PRESSURE

VOF-SURFACE-TENSION QUIT

HELP



VOF

(*)- SELECT PHASE FOR SURFACE TENSION

(*)- DEFAULT PHASE - WATER


AIR WATER QUIT HELP


(PHASE-SELECTION)-

WAT

(R)- ENTER SURFACE TENSION COEFFICIENT FOR WATER

(R)- UNITS= N/M ++(DEFAULT 7.3050E-02)++

X


(R)- ENTER CONTACT ANGLE IN DEGREES


45


The default setting for surface tension coe�cient corresponds towater at room temperature and atmospheric pressure. The contactangle is the angle between each boundary wall and the uid interfaceas measured in the speci�ed phase (here, water). The default value(90�) corresponds to a surface which is at all times normal to thesurrounding walls.

10.3.10 Using the VOF Model with Porous Media

The VOF model is compatible with the porous media model inFLUENT. If you have a region that needs to be described as a porousmedia, the setup begins in the normal way. First, you need to enablethe porous media model in the EXPERT OPTIONS table in the text



interface. The next step is to set the cell types appropriately so asto belong to one or more porous zones.

When you set the porous media constants from the PHYSICAL-CONSTANTSmenu, FLUENT will prompt you for the PERMEABILITY and INERTIAL-RESISTANCE-FACTOR for each of the phases separately.

PHYSICAL-CONSTANTS �! POROUS-MEDIA


PM

(*)- POROUS MEDIA INPUTS...

(*)- (ENTER QUIT WHEN FINISHED)

(SELECT-ZONE)-

1

COMMANDS AVAILABLE FROM * POROUS MEDIA INPUTS FOR ZONE 1 *:

PERMEABILITY INERTIAL-RESISTANCE-FACTOR

POROSITY QUIT

HELP


( * POROUS MEDIA INPUTS FOR ZONE 1 *)-

PER

(PERMEABILITY FOR ZONE 1)

1.0000E-08 PERMEABILITY IN THE I-DIRN. FOR PHASE 1 (M2)

1.0000E-08 PERMEABILITY IN THE J-DIRN. FOR PHASE 1 (M2)

5.0000E-09 PERMEABILITY IN THE I-DIRN. FOR PHASE 2 (M2)

5.0000E-09 PERMEABILITY IN THE J-DIRN. FOR PHASE 2 (M2)


( * POROUS MEDIA INPUTS FOR ZONE 1 *)-

IRF

(INERTIAL RESISTANCE FACTOR FOR ZONE 1)

4.0000E+02 INERTIAL FACTOR IN THE I-DIRN. FOR PHASE 1 (/M)

4.0000E+02 INERTIAL FACTOR IN THE J-DIRN. FOR PHASE 1 (/M)

1.0000E+02 INERTIAL FACTOR IN THE I-DIRN. FOR PHASE 2 (/M)

1.0000E+02 INERTIAL FACTOR IN THE J-DIRN. FOR PHASE 2 (/M)

NO INERTIAL TERM =(C2*DEN*Vi*ABS(Vi))/2 ELSE =(C2*DEN*Vi*Vmag)/2




As an example, consider a long narrow channel that is completelyExample�lled with a porous material.

CELL TYPES:

J I= 2 4 6 8 10 12 14 16 18 20

10 W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1 10

9 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 9

8 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 8

7 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 7

6 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 6

5 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 5

4 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 4

3 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 3

2 I1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1I2 2

1 W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1W1 1

J I= 2 4 6 8 10 12 14 16 18 20

The duct is initially �lled with oil with a density of 800 kg/m3 anda viscosity of 0.01 kg/m-sec. At t=0, water is allowed to enter thedomain from the left under the action of a total pressure of 104

Pascals. The water has a density of 1000 kg/m3 and a viscosity of9e-4 kg/m-sec. A zero pressure boundary serves as the exit for theduct on the right.

In this example, the porous media is modeled with a permeabilityonly. Under these conditions, the source term contribution to themomentum equation in the porous region has the form:

S = ��

kv (10.3-8)

Using permeability values of 5 �10�7 m2 for oil and 1 �10�8 m2

for water, the transient solution shows the front moving steadilythrough the domain (Figure 10.3.6).

The velocity is continuous across the interface, but the pressuredrop is not, due to the permeabilities speci�ed for the two uids.

10.3.11 Using the VOF Model in Mixing Tank Simulations

There are many industrial applications of mixing tanks involvingimpellers and a tank �lled partially with liquid. In these cases,the shape of the liquid surface can be of interest. At low impellerspeeds, the liquid surface will remain at. As the speed increases,the surface will be pulled downward near the impeller shaft. If the



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 6.600E+01


Motion of an Oil-Water Interface through a Porous Region

Fluent Inc.

Fluent 4.30

Oct 20 1994Y

XZ

Figure 10.3.6: Motion of an Oil-Water Interface Through a PorousRegion



impeller speed is too great, the surface can break, resulting in theentrainment of air or other gas from above.

The following model combinations are possible for simulating mix-ing tanks with impellers in FLUENT:

� Time-dependent VOF|with the default donor-acceptor scheme|and the sliding mesh model (described in Section 13.1).

� Time-dependent VOF|with either the donor-acceptor or theimplicit interpolation scheme (see Section 10.3.2 to determinewhich is more appropriate)|and the multiple reference framesmodel (described in Section 12.4).

� Time-dependent VOF|with either the donor-acceptor or theimplicit interpolation scheme|and the �x option (describedin Section 14.16).

If the mixing tank problem includes in ow and out ow boundariesfor the liquid, and a pressure boundary for the air on top of thetank, the following combinations are possible:

� Steady-state VOF and the multiple reference frames model.

� Steady-state VOF and the �x option.

In combining the VOF and slidingmesh models, two time-dependentUsing the SlidingMesh Model phenomena must be treated in a compatible manner. The standard

technique to use in the sliding mesh model (Chapter 13) is one wherecoarse time stepping is done to reach the steady-state, after whichthe time step is reduced to obtain a well converged periodic solution.In combination with the VOF model, coarse time-stepping can leadto convergence di�culties with the volume fraction equation. It isadvisable, therefore, that the impeller grid move no more than twogrid lines per time step in the early stages of the calculation.

Once you have created a 3D grid that represents a section of a mix-ing tank with one or more impellers, the sliding mesh model requiresa number of inputs in the EXPERT ROTOR-PARAMETERS table. Thistable can only be accessed from the SETUP1 menu.

SETUP1 �! EXPERT �! ROTOR-PARAMETERS



(SETUP1)-

EX

(EXPERT)-

RP

(ROTOR PARAMETERS)

30 ROTOR ANGULAR VELOCITY (RAD/S)

15 SLIP LINE IN RADIAL DIRECTION

25 SLIP PLANE 1 IN AXIAL DIRECTION

49 SLIP PLANE 2 IN AXIAL DIRECTION

2 NUMBER OF GRID SPACE PER TIME STEP


The inputs to the table are the same that would be used for anystandard sliding-mesh calculation with two exceptions (unless youare interested in modeling the rotor/free-surface interaction, whichis discussed below). First, the axial slip planes must not be suchthat the free surface interface crosses at any point. Whereas in anynon-VOF simulation the axial slip planes can be anywhere from thetop of the vessel to the bottom (with the exception of the boundaryplanes themselves), with the VOF model active they must both becompletely contained within one of the uids. Second, the numberof grid lines that the model can traverse within a time step shouldnot exceed 2. As the solution reaches a periodic steady-state, thisvalue should be reduced further, as is advised in any sliding-meshcalculation.

The next step in the setting of the ROTOR-PARAMETERS is the choiceto be made between automatic or manual time-step adjustment. Aswith any sliding-mesh calculation, an automatic time-step adjust-ment is advised, particularly in the early stages of the calculation.

(L)- AUTOMATIC TIME STEP ADJUSTMENT? (NO=MANUAL)?


Y

(*)- ** TIME STEP IS RE-ADJUSTED FOR MOVING MESH **

The �nal step is the setting of the TIME-DEPENDENT FLOW SOLUTION

PARAMETERS. As with other VOF simulations, the choice can bemade to use the same global time step for the volume fraction cal-culation, or use an automatic re�nement based upon the maximumallowable Courant Number at the interface. Since the sliding-mesh



calculation is by nature one in which the ow �eld changes witheach time step, it is advisable to choose the automatic re�nementscheme.

(TIME DEPENDENT FLOW SOLUTION PARAMETERS)

10 MAX. NO. ITNS PER TIME STEP

1.0000E-03 MIN. RESIDUAL SUM (DIM)

1.3523E-03 SET TIME STEP (S)

YES SOLVE VOF EVERY ITERATION

YES AUTOMATIC TIME STEP REFINEMENT FOR VOF

2.5000E-01 MAXIMUM COURANT NUMBER FOR VOF (DIM)

NO AUTOMATIC SAVING

NO ENABLE TIME VARYING GRAVITY VECTOR


At the start of the calculation, it is recommended to request fewerthan the default value of 100 iterations per time step, so as to reachthe steady state condition as quickly as possible. Once the steadystate has been reached, this value should be increased.

It is possible to use the sliding-mesh model in combination with theModelingRotor/Free-Surface

InteractionVOF model to simulate the action of an impeller in a mixing tankwhich is �lled only to the level of the impeller. In such instances,one axial slip plane will be immersed in one uid while the otherwill be immersed in the other. A very small time step is required forthis kind of model. You can keep the default entry for the NUMBER

OF GRID SPACE PER TIME STEP prompt in the ROTOR-PARAMETERStable and request a manual time step adjustment in the questionthat follows:

(L)- AUTOMATIC TIME STEP ADJUSTMENT? (NO=MANUAL)?


N

You should then choose a small time step in the TIME DEPENDENT

FLOW SOLUTION PARAMETERS table, such that several time steps arerequired for the sliding mesh to traverse a typical control volume.

In Figure 10.3.7, a sliding-mesh simulation is illustrated with a par-tially �lled tank. The impeller rotates with an angular speed of 26.4rad.sec. After roughly a half second, the surface of the water beginsto change shape as a result of the rotation in the liquid phase.



0.00E+00

5.00E-01

1.00E+00



Sliding Mesh Model of a Partially Filled Mixing Tank

Fluent Inc.

Fluent 4.30

Nov 07 1994

Y

X

Z

Figure 10.3.7: Sliding-Mesh Model of a Partially Filled CylindricalVessel

If the time-averaged e�ects of an impeller are su�cient for yourUsing the FixOption model, the FIX-OPTION can be used in place of the sliding mesh

model. With this choice, the velocity components in the vicinityof the impeller can be \�xed" for the duration of the calculation.This model, described in detail in Section 14.16, is enabled in theSOLUTION-PARAMETERS table in the EXPERT menu.

In the example below, a cylindrical vessel is modeled using an ax-isymmetric grid with 50 � 23 cells. A central shaft rotates withan angular velocity of 26.4 rad/sec. At the end of the shaft, u�,v�, and w� components of velocity are �xed to simulate the time-averaged action of an impeller rotating at the same frequency. Attime t=0, the vessel is half-�lled with water. After slightly morethan 1.5 seconds have passed, the surface of the water becomes dis-torted as shown in Figure 10.3.8, due to the action of the impeller.

Note that the location of the live cells where the �xes are appliedfor this problem are highlighted by setting these cells to be porouscells. If the loss factors for these porous cells are not changed fromtheir default values, the porous cells will function as regular livecells.



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 1.520E+00


Water in a Mixing Tank Modeled with the Fix Option

Fluent Inc.

Fluent 4.30

Nov 07 1994

Y

X

Z

Figure 10.3.8: Water Level in a Mixing Tank Modeled with VelocityFixes



10.3.12 Using the VOF Model with Species Mixing

If your model involves the calculation of species mixing or reacting ow, this can be accomplished in the primary phase uid only. Toset up a model of this type, begin with the Models panel and chooseboth the Calculate Species and the VOF Free Surface options.

The next steps are to de�ne the phases as well as the species. Thesesteps can be accomplished in the SETUP1 menu, using the text in-terface, with the DEFINE-PHASES and DEFINE-SPECIES commands.



(SETUP1)-

DP



1

(PHASE NAMES)



LIQUID PRIMARY PHASE

AIR PHASE 2


(SETUP1)-

DS

(SPECIES NAMES)

NOTE : SPECIES NAMES CANNOT CONSIST OF


OIL-A SPECIES 1

OIL-B SPECIES 2


You can also use the graphical user interface to name the species. Inthe De�ne pull-down menu, choose Species.... The resulting De�ne

Species panel can be edited to name the species.



Note that the setup of multiple phases and multiple species can bedone entirely with the text interface, if you prefer. The setup of themultiple phases is illustrated in Section 10.3; the additional setup ofspecies is shown below. Begin by selecting SPECIES-AND-CHEMISTRYfrom the DEFINE-MODELS menu.

SETUP1 �! DEFINE-MODELS �! SPECIES-AND-CHEMISTRY



(SETUP1)-

DM

COMMANDS AVAILABLE FROM DEFINE-MODELS:

W-VELOCITY HEAT-TRANSFER TURBULENCE

RADIATION SPECIES-AND-CHEMISTRY MULTIPLE-PHASES

QUIT HELP


(DEFINE-MODELS)-

SP

(CHEMISTRY MODEL (SELECT ONLY ONE))

YES NON-REACTING SPECIES

NO FINITE RATE REACTIONS

NO PDF DIFFUSION

NO PREMIXED FRONT TRACKING


After choosing between reacting and non-reacting ow options, setthe number of species, and then name them.



COMMANDS AVAILABLE FROM NON-REACTING SPECIES:

NUMBER-OF-SPECIES DEFINE-SPECIES QUIT

HELP


(NON-REACTING SPECIES)-

NU

(SPECIES)

2 TOTAL NUMBER OF CHEMICAL SPECIES

NO ENABLE MOLE FRACTION INPUTS (OTHERWISE MASS FRACTION)


COMMANDS AVAILABLE FROM NON-REACTING SPECIES:

NUMBER-OF-SPECIES DEFINE-SPECIES QUIT

HELP


(NON-REACTING SPECIES)-

DE

(SPECIES NAMES)

NOTE : SPECIES NAMES CANNOT CONSIST OF


OIL-A SPECIES 1

OIL-B SPECIES 2


To set the properties, commands in the PHYSICAL-CONSTANTS menuSetting theProperties are used in the usual manner. The following dialogue illustrates the

setting of the density when the gas law is not in use.


DE

(PHASE-SELECTION)-

LIQ

(L)- USE GAS LAW FOR LIQUID?


N

COMMANDS AVAILABLE FROM SPECIES-SELECTION:

OIL-A OIL-B QUIT HELP


(SPECIES-SELECTION)-



As with any problem involving species mixing, a menu appears con-taining the species names. The densities for each are set by selectingeach species in turn.


OIL-A

(R)- DENSITY OF OIL-A


800

COMMANDS AVAILABLE FROM SPECIES-SELECTION:

OIL-A OIL-B QUIT HELP



OIL-B

(R)- DENSITY OF OIL-B


810

Once the species densities are set, you can QUIT from theSPECIES-SELECTION menu and set the density of the second phase.


Q

(PHASE-SELECTION)-

AIR

(R)- DENSITY OF AIR


1.0

The gas law can only be used in the primary phase, which meansthat species mixing in combination with the gas law can only bedone when the species are a part of the gaseous phase. In thisevent, the setting of the density proceeds as it normally does whenthe gas law is elected with multiple species. The dialogue is followedby input of the density for the second phase, as shown above.

The viscosity is set in the usual way. By default, you will need tode�ne the viscosity of each of the phases.




VI

(PHASE-SELECTION)-

LIQ

(R)- VISCOSITY OF LIQUID


X


(PHASE-SELECTION)-

AIR

(R)- VISCOSITY OF AIR


X


Note that if you want to set the viscosity for each of the species indi-vidually, you need to enable the COMPOSITION DEPENDENT VISCOSITY

option in the PROPERTY-OPTIONS table.

The setting of other properties, such as thermal conductivity andspeci�c heat, is done in a manner similar to that shown for theviscosity.

The boundary conditions are set for the phases and species in theSetting theBoundaryConditions

same manner as when only one of these models is active. For ex-ample, consider the setting of boundary conditions at an inlet. Toset the VOLUME-FRACTION, you only need to specify it for the secondphase (if it is not zero, the default value).

(SETUP1)-

BC I 1

COMMANDS AVAILABLE FROM I1-ZONE-BOUNDARY-CONDITIONS:

CHEMICAL-SPECIES NORMAL-VELOCITY U-VELOCITY

V-VELOCITY VOLUME-FRACTION QUIT

HELP



VF

(R)- VOLUME FRACTION OF AIR


0



To set the CHEMICAL-SPECIES you need to specify the value of the�rst species named (for this example). If you have N species, youwill have to set all non-zero values for the �rst N-1 species.


CS

(R)- OIL-A MASS FRACTION


.5

Boundary conditions may also be set in the Boundary Conditions

panel. Choose the boundary from the Active Zones list and clickthe Set... button. The Phase information is set in the resultingboundary conditions panel, as shown below.



To set the species, click on the Species... button, and provide theinputs to the chemical species panel.

10.3.13 Postprocessing with the VOF Model

Postprocessing with the VOF model includes the display of the vol-ume fractions of the phases, as well as integral reports that arerelative to a single phase at a time. These features are discussed inthis section.

The volume fraction of the primary or one of the secondary phasesDisplay of theVolume Fraction may be examined using alphanumerics or graphically using con-

tours, �lled contours, or pro�les. As an example, consider a bowlwhich is partially �lled with water and spinning on its axis. Torequest a display of the volume fraction of water, begin with theDisplay pull-down menu and select the Contours... item. In theContours panel, choose Multiphase in the Contours Of box. To select�lled contours, click on the Filled check button. Note that WATER

is the current selection from the Phase drop-down list (so does notneed to be changed). The default number of Contour Levels is 30.For a crisp display of the interface, it is best to choose 2 levelsinstead.



The resulting �gure, shown in Figure 10.3.9 has been mirrored aboutthe y-min boundary, rotated about the z axis, and reduced in sizeto �t in the graphics window.

Note that the air-water interface occurs at a value of �2 = 0.5, whichis a common practice in the viewing of volume fraction results. Themaximum is light in color and the minimum is dark in this �gure.Had AIR been chosen from the Phase drop-down list on the Contourspanel, the colors would be switched (Figure 10.3.10).

Alphanumeric reporting is available from the *MAIN* menu usingAlphanumericReporting the VIEW-ALPHA command. Once in the VIEW-ALPHA menu, the

SELECT-VARIABLE command results in a large selection of variablesfrom which to choose. The VOLUME-FRACTION command results inthe display of one phase at a time, which you can choose from thePHASE-SELECTION menu.



0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 5.000E-01


Water in a Spinning Bowl

Fluent Inc.

Fluent 4.30

Oct 26 1994

Y

X

Z

Figure 10.3.9: Volume Fraction of Water

0.00E+00

5.00E-01

1.00E+00

Max = 1.000E+00 Min = 0.000E+00 Time = 5.000E-01

Air Volume Fraction (Dim)

Water in a Spinning Bowl

Fluent Inc.

Fluent 4.30

Oct 26 1994

Y

X

Z

Figure 10.3.10: Volume Fraction of Air



(VIEW-ALPHANUMERICS)-

SV

COMMANDS AVAILABLE FROM VARIABLE-SELECTION:

DENSITY EXCHANGE-MASS

EXCHANGE-X EXCHANGE-Y

MASS-FRACTION MOLE-FRACTION

MOLECULAR-VISCOSITY STATIC-PRESSURE-REL

STATIC-PRESSURE-ABS STREAM-FUNCTION

SURFACE-MASS-FLUX TOTAL-PRESSURE-REL

TOTAL-PRESSURE-ABS U-VELOCITY

V-VELOCITY VELOCITY-MAGNITUDE

VOLUME-FRACTION XMOM-SOURCE

YMOM-SOURCE INTEGRALS-I-DIRECTION

INTEGRALS-J-DIRECTION INTEGRAL-RANGES

WALL-FORCES XTENDED-XOPTIONS

QUIT HELP


(VARIABLE-SELECTION)-

VF


AIR WATER QUIT HELP


(PHASE-SELECTION)-

AIR

VIEW ALPHA: AIR VOLUME FRACTION (DIM) AT TIME T = 5.000E-01

J I= 1 2 3 4 5 6

33 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

32 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

31 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

30 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

29 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

. . . . . . .

. . . . . . .

. . . . . . .

Integral reports are also available for a single phase at a time. Forexample, to examine the I-direction integrals for the top surface ofthe cup, where only air is present, the corresponding inlet zone ischosen, and AIR is chosen from the PHASE-SELECTION menu.




II


W-WALL Z-WALL SYMMETRY .(LIVE)

CYCLIC OUTLET INLET AXIS

QUIT HELP


(BOUNDS)-

I 1

(L)- PRINT CELL-BY-CELL INFO (OTHERWISE SUMMARY ONLY)?


Y

(*)- SELECT PHASE FOR INTEGRALS


AIR WATER QUIT HELP


(PHASE-SELECTION)-

AIR

INTEGRATED QUANTITIES FOR CELL ZONE 'I1'

I-DIRECTION COMPONENTS, AIR

AREA VELOCITY VOL. FLOW MASS FLOW DELTA P PH.- VOL.

I, J, K M2 M/S M3/S KG/S PA M3

----------- ---------- ---------- ---------- ---------- ---------- ----------

1, 32, 1 3.174E-02 -1.418E+00 -4.500E-02 -4.500E-02 0.000E+00 1.232E-03

1, 31, 1 3.070E-02 -8.260E-01 -2.535E-02 -2.535E-02 0.000E+00 1.188E-03

1, 30, 1 2.966E-02 -7.476E-01 -2.217E-02 -2.217E-02 0.000E+00 1.144E-03

1, 29, 1 2.862E-02 -6.541E-01 -1.872E-02 -1.872E-02 0.000E+00 1.101E-03

1, 28, 1 2.758E-02 -5.355E-01 -1.477E-02 -1.477E-02 0.000E+00 1.057E-03

1, 27, 1 2.653E-02 -3.820E-01 -1.014E-02 -1.014E-02 0.000E+00 1.014E-03

1, 26, 1 2.549E-02 -1.836E-01 -4.681E-03 -4.681E-03 0.000E+00 9.713E-04

. . . . . . . .

. . . . . . . .

. . . . . . . .

1, 7, 1 5.723E-03 7.522E-01 4.305E-03 4.305E-03 -2.829E-01 2.048E-04

1, 6, 1 4.683E-03 7.613E-01 3.565E-03 3.565E-03 -2.898E-01 1.670E-04

1, 5, 1 3.642E-03 7.678E-01 2.796E-03 2.796E-03 -2.947E-01 1.294E-04

1, 4, 1 2.601E-03 7.712E-01 2.006E-03 2.006E-03 -2.974E-01 9.214E-05

1, 3, 1 1.561E-03 7.733E-01 1.207E-03 1.207E-03 -2.990E-01 5.510E-05

1, 2, 1 5.203E-04 7.746E-01 4.030E-04 4.030E-04 -3.000E-01 1.830E-05

-----------------------------------------------------------------------------

TOTALS 5.000E-01 2.066E-09 2.066E-09 1.882E-02



The column on the right side of the table reports the volume ofthe phase in question. This is computed as the volume fraction ofthat phase multiplied by the cell volume. This column is primarilyintended for use with LIVE cells. For INLET cells, the cell volume isnot computed accurately, so the numbers appearing here may not becorrect. A column in which the HEAT-RATE is reported is normallyamong those shown, but has been eliminated for the purpose of thisexample.

When an integral plane is chosen that passes through the interface(in LIVE cells), the PH. - VOL. column gives the correct volume ofthe selected phase. The value changes from non-zero values, wherethe phase is present, to zero values where it is not. This kind ofreport is obtained using the INTEGRAL-RANGES option, as shownbelow, where integral reports for the water are examined.


IR

(I)- SELECT DIRECTION (I = 1, J = 2)


1

(I)- SELECT I-PLANE


25

(L)- SELECT SUB-RANGE?


N


W-WALL Z-WALL SYMMETRY .(LIVE) CYCLIC

OUTLET INLET AXIS QUIT HELP


(BOUNDS)-

.



(L)- PRINT CELL-BY-CELL INFO (OTHERWISE SUMMARY ONLY)?


Y

(*)- SELECT PHASE FOR INTEGRALS


AIR WATER QUIT HELP


(PHASE-SELECTION)-

WATER

INTEGRATED QUANTITIES FOR CELL ZONE ' .'

I-DIRECTION COMPONENTS, WATER

AREA VELOCITY VOL. FLOW MASS FLOW DELTA P PH.- VOL.

I, J, K M2 M/S M3/S KG/S PA M3

----------- ---------- ---------- ---------- ---------- ---------- ---------

25, 32, 1 1.589E-02 -5.649E-02 -8.976E-04 -8.753E-01 1.372E+02 4.558E-04

25, 31, 1 1.537E-02 -1.678E-02 -2.578E-04 -3.392E-01 1.432E+02 4.400E-04

25, 30, 1 1.485E-02 -2.535E-02 -3.764E-04 -4.309E-01 1.490E+02 4.243E-04

25, 29, 1 1.433E-02 -3.075E-02 -4.405E-04 -4.703E-01 1.561E+02 4.087E-04

25, 13, 1 5.992E-03 5.292E-02 8.630E-05 8.081E-02 6.405E+01 4.512E-05

25, 12, 1 5.471E-03 5.029E-02 2.190E-05 2.138E-02 2.548E+01 1.202E-05

25, 11, 1 4.950E-03 6.230E-02 2.402E-05 2.270E-02 1.315E+01 1.063E-05

25, 10, 1 4.429E-03 0.000E+00 0.000E+00 0.000E+00 7.849E-02 0.000E+00

25, 9, 1 3.908E-03 0.000E+00 0.000E+00 0.000E+00 2.757E-02 0.000E+00

25, 8, 1 3.387E-03 0.000E+00 0.000E+00 0.000E+00 3.756E-02 0.000E+00

25, 3, 1 7.815E-04 0.000E+00 0.000E+00 0.000E+00 6.194E-02 0.000E+00

25, 2, 1 2.605E-04 0.000E+00 0.000E+00 0.000E+00 6.002E-02 0.000E+00

----------------------------------------------------------------------------

TOTALS 2.503E-01 -2.772E-03 -2.640E+00 5.785E-03


chapter 10. vof free surface model

Education

limitations model

phase change model

eulerian multiphase

vof free surface model

slidingmesh model

porous media model

reynolds stress model

free surface model information