Class that solves the univariate population balance equation by means of a class method (also called sectional or discrete method). The internal coordinate is set to the particle volume, so the equation is based on a transport equation of the volume-based number density function. The discretisation is done using the fixed pivot technique of Kumar and Ramkrishna (1996). The source terms are written in a way that particle number and mass are preserved. Coalescence (coagulation), breakup, drift (growth and surface loss) as well as nucleation are supported. For the discrete breakup term two recipes are available, depending on the model choice. For models which state a total breakup rate and a separate daughter size distribution function, the formulation of Kumar and Ramkrishna (1996) is applied which is applicable for binary and multiple breakup events. The second formulation is given by Liao et al. (2018). It is useful for binary breakup models which give the breakup rate between a sizeGroup pair directly, without an explicit expression for the daughter size distribution. The drift term is implemented using a finite difference upwind scheme. Although it is diffusive, it ensures a stable and number-conservative solution. More...

Inheritance diagram for populationBalanceModel:

[legend]

Collaboration diagram for populationBalanceModel:

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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, phasePairKey, phasePairKey::hash > &pDmdt)

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

const dictionary &	dict () const
	Return populationBalanceCoeffs dictionary. More...

const phaseModel &	continuousPhase () const
	Return continuous phase. More...

const UPtrList< velocityGroup > &	velocityGroups () const
	Return the velocityGroups belonging to this populationBalance. More...

const UPtrList< sizeGroup > &	sizeGroups () const
	Return the sizeGroups belonging to this populationBalance. More...

const phasePairTable &	phasePairs () const
	Return list of unordered phasePairs in this populationBalance. More...

const volScalarField &	Sp (const label i) const
	Return implicit 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...

bool	isVelocityGroupPair (const phasePair &pair) const
	Returns true if both phases are velocity groups and. 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 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 &, 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...

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	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...

virtual fileName	filePath () const
	Return complete path + object name if the file exists. 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	global () const
	Is object same for all processors. 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< 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...

word	modelName (const char *name) const
	Return the name of the object within this model. More...

const fileName &	rootPath () const

const fileName &	caseName () const

const fileName &	instance () const

fileName &	instance ()

const fileName &	local () const

fileName	path () const
	Return complete path. More...

fileName	path (const word &instance, const fileName &local="") const
	Return complete path with alternative instance and local. More...

fileName	localPath () const
	Return the path relative to the case. More...

fileName	objectPath () const
	Return complete path + object name. More...

fileName	localObjectPath () const
	Return complete localPath + object name. More...

fileName	localFilePath (const word &typeName) const
	Helper for filePath that searches locally. More...

fileName	globalFilePath (const word &typeName) const
	Helper for filePath that searches up if in parallel. More...

bool	readHeader (Istream &)
	Read header. More...

template<class Type >
bool	typeHeaderOk (const bool checkType=true)
	Read header (uses typeFilePath to find file) and check header. 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)

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...

Detailed Description

Class that solves the univariate population balance equation by means of a class method (also called sectional or discrete method). The internal coordinate is set to the particle volume, so the equation is based on a transport equation of the volume-based number density function. The discretisation is done using the fixed pivot technique of Kumar and Ramkrishna (1996). The source terms are written in a way that particle number and mass are preserved. Coalescence (coagulation), breakup, drift (growth and surface loss) as well as nucleation are supported. For the discrete breakup term two recipes are available, depending on the model choice. For models which state a total breakup rate and a separate daughter size distribution function, the formulation of Kumar and Ramkrishna (1996) is applied which is applicable for binary and multiple breakup events. The second formulation is given by Liao et al. (2018). It is useful for binary breakup models which give the breakup rate between a sizeGroup pair directly, without an explicit expression for the daughter size distribution. The drift term is implemented using a finite difference upwind scheme. Although it is diffusive, it ensures a stable and number-conservative solution.

The implementation allows to split the population balance over multiple velocity fields using the capability of multiphaseEulerFoam to solve for n momentum equations. It is also possible to define multiple population balances, e.g. bubbles and droplets simultaneously.

References:

    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

Example excerpt from a phaseProperties dictionary.

type populationBalanceTwoPhaseSystem;

phases (air water);

populationBalances (bubbles);

air
{
    type            purePhaseModel;
    diameterModel   velocityGroup;
    velocityGroupCoeffs
    {
        populationBalance    bubbles;

        shapeModel           constant;

        sizeGroups
        (
            f0{dSph  1.00e-3; value 0;}
            f1{dSph  1.08e-3; value 0;}
            f2{dSph  1.16e-3; value 0.25;}
            f3{dSph  1.25e-3; value 0.5;}
            f4{dSph  1.36e-3; value 0.25;}
            f5{dSph  1.46e-3; value 0;}
            ...
        );
    }

    residualAlpha   1e-6;
}

populationBalanceCoeffs
{
    bubbles
    {
        continuousPhase water;

        coalescenceModels
        (
            hydrodynamic
            {
                C 0.25;
            }
        );

        binaryBreakupModels
        ();

        breakupModels
        (
            exponential
            {
                C 0.5;
                exponent 0.01;
                daughterSizeDistributionModel uniform;
            }
        );

        driftModels
        (
            densityChange{}
        );

        nucleationModels
        ();
    }
}

See also: Foam::diameterModels::sizeGroup Foam::diameterModels::velocityGroup

Source files

Definition at line 178 of file populationBalanceModel.H.

Constructor & Destructor Documentation

◆ populationBalanceModel()

populationBalanceModel	(	const phaseSystem &	fluid,
		const word &	name,
		HashPtrTable< volScalarField, phasePairKey, phasePairKey::hash > &	pDmdt
	)

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 46 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 53 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 60 of file populationBalanceModelI.H.

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

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◆ continuousPhase()

const Foam::phaseModel & continuousPhase ( ) const

inline

Return continuous phase.

Definition at line 67 of file populationBalanceModelI.H.

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

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◆ velocityGroups()

const Foam::UPtrList< Foam::diameterModels::velocityGroup > & velocityGroups ( ) const

inline

Return the velocityGroups belonging to this populationBalance.

Definition at line 74 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 sizeGroups belonging to this populationBalance.

Definition at line 81 of file populationBalanceModelI.H.

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

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◆ phasePairs()

const Foam::diameterModels::populationBalanceModel::phasePairTable & phasePairs ( ) const

inline

Return list of unordered phasePairs in this populationBalance.

Definition at line 88 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 95 of file populationBalanceModelI.H.

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 102 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 109 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 116 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 130 of file populationBalanceModelI.H.

References populationBalanceModel::isVelocityGroupPair().

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

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◆ isVelocityGroupPair()

bool isVelocityGroupPair ( const phasePair & pair ) const

inline

Returns true if both phases are velocity groups and.

belong to this populationBalance

Definition at line 144 of file populationBalanceModelI.H.

References phaseModel::dPtr(), phasePair::phase1(), phasePair::phase2(), and velocityGroup::popBalName().

Referenced by populationBalanceModel::iNew::operator()(), and populationBalanceModel::U().

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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:

applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/populationBalanceModel/populationBalanceModel/populationBalanceModel.H
applications/solvers/multiphase/multiphaseEulerFoam/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()

◆ mesh()

◆ dict()

◆ continuousPhase()

◆ velocityGroups()

◆ sizeGroups()

◆ phasePairs()

◆ Sp()

◆ coalescencePairs()

◆ binaryBreakupPairs()

◆ alphas()

◆ U()

◆ isVelocityGroupPair()

◆ eta()

◆ sigmaWithContinuousPhase()

◆ continuousTurbulence()

◆ solve()

◆ correct()