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:

[legend]

Collaboration diagram for populationBalanceModel:

[legend]

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)
	Construct for a fluid. More...

autoPtr< populationBalanceModel >	clone () const
	Return clone. More...

virtual	~populationBalanceModel ()
	Destructor. More...

bool	writeData (Ostream &) const
	Dummy write for regIOobject. More...

const phaseSystem &	fluid () const
	Return reference to the phaseSystem. More...

const phaseSystem::dmdtfTable &	dmdtfs () const
	Return reference to the interfacial mass transfer rates. More...

const fvMesh &	mesh () const
	Return reference to the mesh. More...

const dictionary &	dict () 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 phaseModel &	continuousPhase () 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 volScalarField &	Sp (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 volScalarField &	alphas () const
	Return total void of phases belonging to this populationBalance. More...

const volVectorField &	U () const
	Return average velocity. More...

const dimensionedScalar	eta (const label i, const dimensionedScalar &v) const
	Return allocation coefficient. More...

const tmp< volScalarField >	sigmaWithContinuousPhase (const phaseModel &dispersedPhase) const
	Return the surface tension coefficient between a given dispersed. More...

const phaseCompressible::momentumTransportModel &	continuousTurbulence () const
	Return reference to momentumTransport 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 fileName &	caseName () 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...

label &	eventNo ()
	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...

Istream &	readStream (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 labelList &	watchIndices () const
	Return file-monitoring handles. More...

labelList &	watchIndices ()
	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 &)

const fileName &	caseName (const bool global) 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	filePath (const word &typeName, const bool global) const
	Return complete path + object name if the file exists. More...

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< IOobject >	clone () const
	Clone. More...

autoPtr< IOobject >	clone (const objectRegistry &registry) const
	Clone resetting registry. More...

virtual	~IOobject ()
	Destructor. More...

const Time &	time () const
	Return time. More...

const objectRegistry &	db () const
	Return the local objectRegistry. More...

const word &	name () const
	Return name. More...

const word &	headerClassName () const
	Return name of the class name read from header. More...

word &	headerClassName ()
	Return name of the class name read from header. More...

string &	note ()
	Return non-constant access to the optional note. More...

const string &	note () const
	Return the optional note. More...

bool &	registerObject ()
	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

readOption &	readOpt ()

writeOption	writeOpt () const

writeOption &	writeOpt ()

word	group () const
	Return group (extension part of name) More...

word	member () const
	Return member (name without the extension) More...

const fileName &	rootPath () const

const fileName &	caseName (const bool global) const

fileName &	instance () 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 fileName &	local () 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< IOobject >	info () const
	Return info proxy. More...

void	operator= (const IOobject &)

template<class Name >
Foam::word	groupName (Name name, const word &group)

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 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 open‐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 exemplary 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 229 of file populationBalanceModel.H.

Constructor & Destructor Documentation

◆ populationBalanceModel()

populationBalanceModel	(	const phaseSystem &	fluid,
		const word &	name
	)

Construct for a fluid.

Definition at line 777 of file populationBalanceModel.C.

References IOobject::AUTO_WRITE, Foam::dimLength, Foam::dimless, Foam::dimTime, Foam::dimVelocity, Foam::dimVolume, Foam::exit(), Foam::FatalError, FatalErrorInFunction, forAll, IOobject::groupName(), Foam::inv(), IOobject::name(), dimensioned< Type >::name(), IOobject::NO_READ, populationBalanceModel::sizeGroups(), fvMesh::time(), IOobject::time(), and Foam::Zero.

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

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◆ ~populationBalanceModel()

~populationBalanceModel ( )

virtual

Destructor.

Definition at line 1050 of file populationBalanceModel.C.

Member Function Documentation

◆ TypeName()

TypeName ( "populationBalanceModel" )

Runtime type information.

◆ clone()

Foam::autoPtr< Foam::diameterModels::populationBalanceModel > clone ( ) const

Return clone.

Definition at line 1056 of file populationBalanceModel.C.

References notImplemented.

◆ writeData()

bool writeData ( Ostream & os ) const

virtual

Dummy write for regIOobject.

Implements regIOobject.

Definition at line 1063 of file populationBalanceModel.C.

References IOstream::good().

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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 velocityGroup::correct().

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◆ dmdtfs()

const Foam::phaseSystem::dmdtfTable & dmdtfs ( ) const

inline

Return reference to the interfacial mass transfer rates.

Definition at line 47 of file populationBalanceModelI.H.

◆ mesh()

const Foam::fvMesh & mesh ( ) const

inline

Return reference to the mesh.

Definition at line 54 of file populationBalanceModelI.H.

Referenced by fractal::correct(), velocityGroup::correct(), phaseChange::phaseChange(), and PrinceBlanch::PrinceBlanch().

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◆ dict()

const Foam::dictionary & dict ( ) const

inline

Return populationBalanceCoeffs dictionary.

Definition at line 61 of file populationBalanceModelI.H.

◆ nCorr()

Foam::label nCorr ( ) const

inline

Return the number of corrections.

Definition at line 67 of file populationBalanceModelI.H.

◆ solveOnFinalIterOnly()

Foam::Switch solveOnFinalIterOnly ( ) const

inline

Solve on final pimple iteration only.

Definition at line 74 of file populationBalanceModelI.H.

Referenced by velocityGroup::correct().

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◆ continuousPhase()

const Foam::phaseModel & continuousPhase ( ) const

inline

Return continuous phase.

Definition at line 86 of file populationBalanceModelI.H.

◆ velocityGroupPtrs()

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

inline

Return the velocity groups belonging to this populationBalance.

Definition at line 93 of file populationBalanceModelI.H.

◆ sizeGroups()

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

inline

Return the size groups belonging to this populationBalance.

Definition at line 100 of file populationBalanceModelI.H.

Referenced by fractal::correct(), sizeGroup::i(), and populationBalanceModel::populationBalanceModel().

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◆ Sp()

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

inline

Return implicit source terms.

Definition at line 107 of file populationBalanceModelI.H.

Referenced by fractal::correct().

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◆ sourceDilatation()

const HashTable<volScalarField>& sourceDilatation ( ) const

inline

Return dilatation obtained from source terms.

◆ coalescencePairs()

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

inline

Return coalescence relevant size group pairs.

Definition at line 114 of file populationBalanceModelI.H.

◆ binaryBreakupPairs()

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

inline

Return binary breakup relevant size group pairs.

Definition at line 121 of file populationBalanceModelI.H.

◆ alphas()

const Foam::volScalarField & alphas ( ) const

inline

Return total void of phases belonging to this populationBalance.

Definition at line 128 of file populationBalanceModelI.H.

◆ U()

const Foam::volVectorField & U ( ) const

inline

Return average velocity.

Definition at line 142 of file populationBalanceModelI.H.

◆ eta()

const Foam::dimensionedScalar eta	(	const label	i,
		const dimensionedScalar &	v
	)		const

Return allocation coefficient.

Definition at line 1070 of file populationBalanceModel.C.

References dimensioned< Type >::value().

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◆ sigmaWithContinuousPhase()

const Foam::tmp< Foam::volScalarField > sigmaWithContinuousPhase ( const phaseModel & dispersedPhase ) const

Return the surface tension coefficient between a given dispersed.

and the continuous phase

Definition at line 1110 of file populationBalanceModel.C.

References phaseInterface::sigma().

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◆ continuousTurbulence()

const Foam::phaseCompressible::momentumTransportModel & continuousTurbulence ( ) const

Return reference to momentumTransport model of the continuous phase.

Definition at line 1120 of file populationBalanceModel.C.

◆ solve()

void solve ( )

Solve the population balance equation.

Definition at line 1130 of file populationBalanceModel.C.

References alpha(), phaseModel::alphaPhi(), Foam::correction(), Foam::fvm::ddt(), Foam::fvm::div(), Foam::endl(), Foam::first(), forAll, Foam::Info, Foam::max(), phaseModel::name(), Foam::name(), sizeGroup::phase(), fvMatrix< Type >::relax(), phaseModel::residualAlpha(), phaseModel::rho(), rho, fvMatrix< Type >::solve(), Foam::fvm::Sp(), Foam::fvc::Su(), Foam::fvm::SuSp(), and DimensionedField< Type, GeoMesh >::weightedAverage().

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◆ correct()

void correct ( )

Correct derived quantities.

Definition at line 1227 of file populationBalanceModel.C.

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

applications/modules/multiphaseEuler/phaseSystems/populationBalanceModel/populationBalanceModel/populationBalanceModel.H
applications/modules/multiphaseEuler/phaseSystems/populationBalanceModel/populationBalanceModel/populationBalanceModel.C
applications/modules/multiphaseEuler/phaseSystems/populationBalanceModel/populationBalanceModel/populationBalanceModelI.H

Classes

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ populationBalanceModel()

◆ ~populationBalanceModel()

Member Function Documentation

◆ TypeName()

◆ clone()

◆ writeData()

◆ fluid()

◆ dmdtfs()

◆ mesh()

◆ dict()

◆ nCorr()

◆ solveOnFinalIterOnly()

◆ continuousPhase()

◆ velocityGroupPtrs()

◆ sizeGroups()

◆ Sp()

◆ sourceDilatation()

◆ coalescencePairs()

◆ binaryBreakupPairs()

◆ alphas()

◆ U()

◆ eta()

◆ sigmaWithContinuousPhase()

◆ continuousTurbulence()

◆ solve()

◆ correct()