populationBalanceModel Class Reference

Model for tracking the evolution of a dispersed phase size distribution due to coalescence (synonymous with coagulation, aggregation, agglomeration) and breakup events as well as density or phase changes. Provides an approximate solution of the population balance equation by means of a class method. The underlying theory is described in the article of Lehnigk et al. (2021). More...

Inheritance diagram for populationBalanceModel:
Collaboration diagram for populationBalanceModel:

Classes

class  iNew
 Return a pointer to a new populationBalanceModel object created on. More...
 

Public Member Functions

 TypeName ("populationBalanceModel")
 Runtime type information. More...
 
 populationBalanceModel (const phaseSystem &fluid, const word &name, HashPtrTable< volScalarField, phaseInterfaceKey, phaseInterfaceKey::hash > &pDmdt)
 
autoPtr< populationBalanceModelclone () const
 Return clone. More...
 
virtual ~populationBalanceModel ()
 Destructor. More...
 
bool writeData (Ostream &) const
 Dummy write for regIOobject. More...
 
const phaseSystemfluid () const
 Return reference to the phaseSystem. More...
 
const fvMeshmesh () const
 Return reference to the mesh. More...
 
const dictionarydict () const
 Return populationBalanceCoeffs dictionary. More...
 
label nCorr () const
 Return the number of corrections. More...
 
Switch solveOnFinalIterOnly () const
 Solve on final pimple iteration only. More...
 
const phaseModelcontinuousPhase () const
 Return continuous phase. More...
 
const HashTable< const velocityGroup * > & velocityGroupPtrs () const
 Return the velocity groups belonging to this populationBalance. More...
 
const UPtrList< sizeGroup > & sizeGroups () const
 Return the size groups belonging to this populationBalance. More...
 
const volScalarFieldSp (const label i) const
 Return implicit source terms. More...
 
const HashTable< volScalarField > & sourceDilatation () const
 Return dilatation obtained from source terms. More...
 
const List< labelPair > & coalescencePairs () const
 Return coalescence relevant size group pairs. More...
 
const List< labelPair > & binaryBreakupPairs () const
 Return binary breakup relevant size group pairs. More...
 
const volScalarFieldalphas () const
 Return total void of phases belonging to this populationBalance. More...
 
const volVectorFieldU () const
 Return average velocity. More...
 
const dimensionedScalar eta (const label i, const dimensionedScalar &v) const
 Return allocation coefficient. More...
 
const tmp< volScalarFieldsigmaWithContinuousPhase (const phaseModel &dispersedPhase) const
 Return the surface tension coefficient between a given dispersed. More...
 
const phaseCompressible::momentumTransportModelcontinuousTurbulence () const
 Return reference to turbulence model of the continuous phase. More...
 
void solve ()
 Solve the population balance equation. More...
 
void correct ()
 Correct derived quantities. More...
 
- Public Member Functions inherited from regIOobject
 TypeName ("regIOobject")
 Runtime type information. More...
 
 regIOobject (const IOobject &, const bool isTime=false)
 Construct from IOobject. Optional flag for if IOobject is the. More...
 
 regIOobject (const regIOobject &)
 Copy constructor. More...
 
 regIOobject (const regIOobject &&)
 Move constructor. More...
 
 regIOobject (const regIOobject &, bool registerCopy)
 Copy constructor, transferring registry registration to copy. More...
 
 regIOobject (const word &newName, const regIOobject &, bool registerCopy)
 Copy constructor with new name, transferring registry registration. More...
 
 regIOobject (const IOobject &, const regIOobject &)
 Copy constructor with new IO parameters. More...
 
virtual ~regIOobject ()
 Destructor. More...
 
virtual bool global () const
 Return true if object is global, i.e. same for all processors. More...
 
virtual bool globalFile () const
 Return true if object is global, i.e. same for all processors. More...
 
const fileNamecaseName () const
 
fileName path () const
 Return complete path. More...
 
fileName objectPath () const
 Return complete path + object name. More...
 
fileName filePath () const
 Return complete path + object name if the file exists. More...
 
bool checkIn ()
 Add object to registry. More...
 
bool checkOut ()
 Remove object from registry. More...
 
void addWatch ()
 Add file watch on object (if registered and READ_IF_MODIFIED) More...
 
bool registered () const
 Is this object registered with the registry? More...
 
bool ownedByRegistry () const
 Is this object owned by the registry? More...
 
void store ()
 Transfer ownership of this object to its registry. More...
 
void release ()
 Release ownership of this object from its registry. More...
 
label eventNo () const
 Event number at last update. More...
 
labeleventNo ()
 Event number at last update. More...
 
bool upToDate (const regIOobject &) const
 Return true if up-to-date with respect to given object. More...
 
bool upToDate (const regIOobject &, const regIOobject &) const
 Return true if up-to-date with respect to given objects. More...
 
bool upToDate (const regIOobject &, const regIOobject &, const regIOobject &) const
 Return true if up-to-date with respect to given objects. More...
 
bool upToDate (const regIOobject &, const regIOobject &, const regIOobject &, const regIOobject &) const
 Return true if up-to-date with respect to given objects. More...
 
void setUpToDate ()
 Set up to date (obviously) More...
 
virtual void rename (const word &newName)
 Rename. More...
 
bool headerOk ()
 Read and check header info. More...
 
IstreamreadStream (const word &, const bool read=true)
 Return Istream and check object type against that given. More...
 
void close ()
 Close Istream. More...
 
virtual bool readData (Istream &)
 Virtual readData function. More...
 
virtual bool read ()
 Read object. More...
 
const labelListwatchIndices () const
 Return file-monitoring handles. More...
 
labelListwatchIndices ()
 Return file-monitoring handles. More...
 
virtual bool modified () const
 Return true if the object's file (or files for objectRegistry) More...
 
virtual bool readIfModified ()
 Read object if modified (as set by call to modified) More...
 
virtual bool writeObject (IOstream::streamFormat, IOstream::versionNumber, IOstream::compressionType, const bool write) const
 Write using given format, version and compression. More...
 
virtual bool write (const bool write=true) const
 Write using setting from DB. More...
 
void operator= (const IOobject &)
 
- Public Member Functions inherited from IOobject
 TypeName ("IOobject")
 Runtime type information. More...
 
 IOobject (const word &name, const fileName &instance, const objectRegistry &registry, readOption r=NO_READ, writeOption w=NO_WRITE, bool registerObject=true)
 Construct from name, instance, registry, io options. More...
 
 IOobject (const word &name, const fileName &instance, const fileName &local, const objectRegistry &registry, readOption r=NO_READ, writeOption w=NO_WRITE, bool registerObject=true)
 Construct from name, instance, local, registry, io options. More...
 
 IOobject (const fileName &path, const objectRegistry &registry, readOption r=NO_READ, writeOption w=NO_WRITE, bool registerObject=true)
 Construct from path, registry, io options. More...
 
 IOobject (const IOobject &io, const objectRegistry &registry)
 Construct from copy resetting registry. More...
 
 IOobject (const IOobject &io, const word &name)
 Construct from copy resetting name. More...
 
 IOobject (const IOobject &io)=default
 Copy constructor. More...
 
autoPtr< IOobjectclone () const
 Clone. More...
 
autoPtr< IOobjectclone (const objectRegistry &registry) const
 Clone resetting registry. More...
 
virtual ~IOobject ()
 Destructor. More...
 
const Timetime () const
 Return time. More...
 
const objectRegistrydb () const
 Return the local objectRegistry. More...
 
const wordname () const
 Return name. More...
 
const wordheaderClassName () const
 Return name of the class name read from header. More...
 
wordheaderClassName ()
 Return name of the class name read from header. More...
 
stringnote ()
 Return non-constant access to the optional note. More...
 
const stringnote () const
 Return the optional note. More...
 
boolregisterObject ()
 Register object created from this IOobject with registry if true. More...
 
bool registerObject () const
 Register object created from this IOobject with registry if true. More...
 
readOption readOpt () const
 
readOptionreadOpt ()
 
writeOption writeOpt () const
 
writeOptionwriteOpt ()
 
word group () const
 Return group (extension part of name) More...
 
word member () const
 Return member (name without the extension) More...
 
word modelName (const char *name) const
 Return the name of the object within this model. More...
 
const fileNamerootPath () const
 
const fileNamecaseName (const bool global) const
 
fileNameinstance () const
 Return the instance directory, constant, system, <time> etc. More...
 
void updateInstance () const
 If the instance is a time directory update to the current time. More...
 
const fileNamelocal () const
 
fileName path (const bool global) const
 Return complete path including the processor sub-directory. More...
 
fileName objectPath (const bool global) const
 Return complete path + object name including the processor. More...
 
fileName relativePath () const
 Return the path relative to the case directory. More...
 
fileName relativeObjectPath () const
 Return complete relativePath + object name. More...
 
fileName filePath (const word &typeName, const bool global) const
 Return complete path + object name if the file exists. More...
 
bool readHeader (Istream &)
 Read header. More...
 
bool headerOk ()
 Read header of local object without type-checking. More...
 
template<class Type >
void warnNoRereading () const
 Helper: warn that type does not support re-reading. More...
 
bool writeHeader (Ostream &) const
 Write header. More...
 
bool writeHeader (Ostream &, const word &objectType) const
 Write header. Allow override of type. More...
 
bool good () const
 
bool bad () const
 
InfoProxy< IOobjectinfo () const
 Return info proxy. More...
 
void operator= (const IOobject &)
 
template<class Name >
Foam::word groupName (Name name, const word &group)
 
template<class Name >
Foam::word modelName (Name name, const word &model)
 

Additional Inherited Members

- Public Types inherited from IOobject
enum  objectState { GOOD, BAD }
 Enumeration defining the valid states of an IOobject. More...
 
enum  readOption { MUST_READ, MUST_READ_IF_MODIFIED, READ_IF_PRESENT, NO_READ }
 Enumeration defining the read options. More...
 
enum  writeOption { AUTO_WRITE = 0, NO_WRITE = 1 }
 Enumeration defining the write options. More...
 
enum  fileCheckTypes { timeStamp, timeStampMaster, inotify, inotifyMaster }
 Enumeration defining the file checking options. More...
 
- Static Public Member Functions inherited from regIOobject
template<class Type >
static Type & store (Type *)
 Transfer ownership of the given object pointer to its registry. More...
 
template<class Type >
static Type & store (autoPtr< Type > &)
 Transfer ownership of the given object pointer to its registry. More...
 
- Static Public Member Functions inherited from IOobject
static bool fileNameComponents (const fileName &path, fileName &instance, fileName &local, word &name)
 Split path into instance, local, name components. More...
 
template<class Name >
static word groupName (Name name, const word &group)
 
static word group (const word &name)
 Return group (extension part of name) More...
 
static word member (const word &name)
 Return member (name without the extension) More...
 
template<class Name >
static word modelName (Name name, const word &model)
 Return the name of the object within the given model. More...
 
template<class Stream >
static Stream & writeBanner (Stream &os, bool noHint=false)
 Write the standard OpenFOAM file/dictionary banner. More...
 
template<class Stream >
static Stream & writeDivider (Stream &os)
 Write the standard file section divider. More...
 
template<class Stream >
static Stream & writeEndDivider (Stream &os)
 Write the standard end file divider. More...
 
- Static Public Attributes inherited from regIOobject
static float fileModificationSkew
 
- Static Public Attributes inherited from IOobject
static constexpr const char * foamFile = "FoamFile"
 Keyword for the FoamFile header sub-dictionary. More...
 
static const NamedEnum< fileCheckTypes, 4 > fileCheckTypesNames
 
static fileCheckTypes fileModificationChecking
 Type of file modification checking. More...
 
- Protected Member Functions inherited from regIOobject
bool readHeaderOk (const IOstream::streamFormat defaultFormat, const word &typeName)
 Read header, check readOpt flags and read data if necessary. More...
 
- Protected Member Functions inherited from IOobject
void setBad (const string &)
 Set the object state to bad. More...
 
template<class Type >
bool typeHeaderOk (const bool checkType)
 Read header using typeGlobalFile to find file. More...
 

Detailed Description

Model for tracking the evolution of a dispersed phase size distribution due to coalescence (synonymous with coagulation, aggregation, agglomeration) and breakup events as well as density or phase changes. Provides an approximate solution of the population balance equation by means of a class method. The underlying theory is described in the article of Lehnigk et al. (2021).

The size distribution, expressed through a volume-based number density function, is discretised using the fixot pivot technique of Kumar and Ramkrishna (1996). Thereby, the population balance equation is transformed into a series of transport equations for the particle (bubble, droplet) number concentrations in separate size classes that are coupled through their source terms. The discretisation is based on representative particle volumes, which are provided by the user through the corresponding sphere equivalent diameters.

Since the representative volumes are fixed a priori and the total dispersed phase volume already available from solving the phase continuity equation, the model only determines the evolution of the individual size class fractions

\[ f_{i,\varphi} = \frac{\alpha_{i,\varphi}}{\alpha_{\varphi}}\,, \]

where $\alpha_{i,\varphi}$ is the volume fraction of the size class and $\alpha_{\varphi}$ the total phase fraction of phase $\varphi$.

The source terms are formulated such that the first and second moment of the distribution, i.e. the total particle number and volume, are conserved irrespective of the discretisation of the size domain. The treatment of particle breakup depends on the selected breakup submodels. For models which provide a total breakup frequency and a separate daughter size distribution function, the formulation provided Kumar and Ramkrishna (1996) is utilised, which is applicable both for binary and multiple breakup events. Currently, only field-independent daughter size distribution models are allowed. In case of binary breakup models that provide the breakup frequency between a size class pair directly, the formulation of Liao et al. (2018) is adopted, which is computationally more efficient compared to first extracting the field-dependent daughter size distribution and then consuming it in the formulation of Kumar and Ramkrishna. The source terms describing a drift of the size distribution through particle growth or shrinkage are derived using upwind differencing, thus ensuring conservation of the total particle number and volume. Note that due to the volume-based implementation, both density as well as phase change lead to a drift of the size distribution function. Further, users can specify multiple submodels for each mechanism, whose contributions are added up.

The model also allows to distribute the size classes over multiple representative phases with identical physical properties that collectively define the dispersed phase. Thereby, size class fields can be transported with different velocity fields in order to account for the size dependency of the particle motion. A possible mass transfer between representative phases by means of coalescence, breakup and drift is taken into account. Similarly, the spatial evolution of secondary particle properties such as the particle surface area can be tracked.

The key variable during a simulation is the Sauter diameter, which is computed from the size class fractions of the corresponding phase. The underlying size distribution can be extracted from the simulation using the functionObject 'sizeDistribution'. Integral and mean properties of a size distribution can be computed with the functionObject 'moments'.

Verification cases for the population balance modeling functionality are provided in test/multiphase/multiphaseEulerFoam/populationBalance.

References:

    Lehnigk, R., Bainbridge, W., Liao, Y., Lucas, D., Niemi, T.,
    Peltola, J., & Schlegel, F. (2021).
    An openā€source population balance modeling framework for the simulation
    of polydisperse multiphase flows.
    AIChE Journal, 68(3), e17539.
    Coalescence and breakup term formulation:
    Kumar, S., & Ramkrishna, D. (1996).
    On the solution of population balance equations by discretization-I. A
    fixed pivot technique.
    Chemical Engineering Science, 51(8), 1311-1332.
    Binary breakup term formulation:
    Liao, Y., Oertel, R., Kriebitzsch, S., Schlegel, F., & Lucas, D. (2018).
    A discrete population balance equation for binary breakage.
    International Journal for Numerical Methods in Fluids, 87(4), 202-215.
Usage
Excerpt from an examplary phaseProperties dictionary:
type populationBalanceMultiphaseSystem;

...

populationBalances (bubbles);

air
{
    type            pureIsothermalPhaseModel;

    diameterModel   velocityGroup;

    velocityGroupCoeffs
    {
        populationBalance    bubbles;

        shapeModel           spherical;

        sizeGroups
        (
            f1 {dSph  1e-3; value 1.0;}
            f2 {dSph  2e-3; value 0.0;}
            f3 {dSph  3e-3; value 0.0;}
            f4 {dSph  4e-3; value 0.0;}
            f5 {dSph  5e-3; value 0.0;}
            ...
        );
    }

    residualAlpha   1e-6;
}

...

populationBalanceCoeffs
{
    bubbles
    {
        continuousPhase water;

        coalescenceModels
        (
            LehrMilliesMewes{}
        );

        binaryBreakupModels
        (
            LehrMilliesMewes{}
        );

        breakupModels
        ();

        driftModels
        (
            densityChange{}
        );

        nucleationModels
        ();
    }
}
See also
Foam::PopulationBalancePhaseSystem Foam::diameterModels::sizeGroup Foam::diameterModels::velocityGroup Foam::diameterModels::SecondaryPropertyModel Foam::diameterModels::coalescenceModel Foam::diameterModels::breakupModel Foam::diameterModels::daughterSizeDistributionModel Foam::diameterModels::binaryBreakupModel Foam::diameterModels::driftModel Foam::diameterModels::nucleationModel Foam::functionObjects::sizeDistribution Foam::functionObjects::moments
Source files

Definition at line 230 of file populationBalanceModel.H.

Constructor & Destructor Documentation

◆ populationBalanceModel()

Referenced by populationBalanceModel::iNew::operator()().

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◆ ~populationBalanceModel()

virtual ~populationBalanceModel ( )
virtual

Destructor.

Referenced by populationBalanceModel::iNew::operator()().

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Member Function Documentation

◆ TypeName()

TypeName ( "populationBalanceModel"  )

Runtime type information.

◆ clone()

autoPtr<populationBalanceModel> clone ( ) const

Return clone.

◆ writeData()

bool writeData ( Ostream ) const
virtual

Dummy write for regIOobject.

Implements regIOobject.

Referenced by populationBalanceModel::iNew::operator()().

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◆ fluid()

const Foam::phaseSystem & fluid ( ) const
inline

Return reference to the phaseSystem.

Definition at line 40 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ mesh()

const Foam::fvMesh & mesh ( ) const
inline

Return reference to the mesh.

Definition at line 47 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ dict()

const Foam::dictionary & dict ( ) const
inline

Return populationBalanceCoeffs dictionary.

Definition at line 54 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ nCorr()

Foam::label nCorr ( ) const
inline

Return the number of corrections.

Definition at line 60 of file populationBalanceModelI.H.

References dictionary::lookup(), fvMesh::solution(), and solution::solverDict().

Referenced by populationBalanceModel::iNew::operator()().

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◆ solveOnFinalIterOnly()

Foam::Switch solveOnFinalIterOnly ( ) const
inline

Solve on final pimple iteration only.

Definition at line 67 of file populationBalanceModelI.H.

References dictionary::lookupOrDefault(), fvMesh::solution(), and solution::solverDict().

Referenced by populationBalanceModel::iNew::operator()().

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◆ continuousPhase()

const Foam::phaseModel & continuousPhase ( ) const
inline

Return continuous phase.

Definition at line 79 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ velocityGroupPtrs()

const Foam::HashTable< const Foam::diameterModels::velocityGroup * > & velocityGroupPtrs ( ) const
inline

Return the velocity groups belonging to this populationBalance.

Definition at line 86 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ sizeGroups()

const Foam::UPtrList< Foam::diameterModels::sizeGroup > & sizeGroups ( ) const
inline

Return the size groups belonging to this populationBalance.

Definition at line 93 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ Sp()

const Foam::volScalarField & Sp ( const label  i) const
inline

Return implicit source terms.

Definition at line 100 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ sourceDilatation()

const HashTable<volScalarField>& sourceDilatation ( ) const
inline

Return dilatation obtained from source terms.

Referenced by populationBalanceModel::iNew::operator()().

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◆ coalescencePairs()

const Foam::List< Foam::Pair< Foam::label > > & coalescencePairs ( ) const
inline

Return coalescence relevant size group pairs.

Definition at line 107 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ binaryBreakupPairs()

const Foam::List< Foam::Pair< Foam::label > > & binaryBreakupPairs ( ) const
inline

Return binary breakup relevant size group pairs.

Definition at line 114 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ alphas()

const Foam::volScalarField & alphas ( ) const
inline

Return total void of phases belonging to this populationBalance.

Definition at line 121 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ U()

const Foam::volVectorField & U ( ) const
inline

Return average velocity.

Definition at line 135 of file populationBalanceModelI.H.

Referenced by populationBalanceModel::iNew::operator()().

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◆ eta()

const dimensionedScalar eta ( const label  i,
const dimensionedScalar v 
) const

Return allocation coefficient.

Referenced by populationBalanceModel::iNew::operator()().

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◆ sigmaWithContinuousPhase()

const tmp<volScalarField> sigmaWithContinuousPhase ( const phaseModel dispersedPhase) const

Return the surface tension coefficient between a given dispersed.

and the continuous phase

Referenced by populationBalanceModel::iNew::operator()().

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◆ continuousTurbulence()

const phaseCompressible::momentumTransportModel& continuousTurbulence ( ) const

Return reference to turbulence model of the continuous phase.

Referenced by populationBalanceModel::iNew::operator()().

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◆ solve()

void solve ( )

Solve the population balance equation.

Referenced by populationBalanceModel::iNew::operator()().

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◆ correct()

void correct ( )

Correct derived quantities.

Referenced by populationBalanceModel::iNew::operator()().

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The documentation for this class was generated from the following files: