Model of Lehr et al. (2002). The coalescence rate is calculated by. More...

#include <LehrMilliesMewesCoalescence.H>

Inheritance diagram for LehrMilliesMewesCoalescence:

Collaboration diagram for LehrMilliesMewesCoalescence:

Public Member Functions
	TypeName ("LehrMilliesMewes")
	Runtime type information.
	LehrMilliesMewesCoalescence (const populationBalanceModel &popBal, const dictionary &dict)
virtual	~LehrMilliesMewesCoalescence ()=default
	Destructor.
virtual void	addToCoalescenceRate (volScalarField &coalescenceRate, const label i, const label j)
	Add to coalescenceRate.
Public Member Functions inherited from coalescenceModel
	TypeName ("coalescenceModel")
	Runtime type information.
	declareRunTimeSelectionTable (autoPtr, coalescenceModel, dictionary,(const populationBalanceModel &popBal, const dictionary &dict),(popBal, dict))
	coalescenceModel (const populationBalanceModel &popBal, const dictionary &dict)
autoPtr< coalescenceModel >	clone () const
virtual	~coalescenceModel ()=default
	Destructor.
virtual void	correct ()
	Correct diameter independent expressions.

Additional Inherited Members
Static Public Member Functions inherited from coalescenceModel
static autoPtr< coalescenceModel >	New (const word &type, const populationBalanceModel &popBal, const dictionary &dict)
Protected Attributes inherited from coalescenceModel
const populationBalanceModel &	popBal_
	Reference to the populationBalanceModel.

Detailed Description

Model of Lehr et al. (2002). The coalescence rate is calculated by.

$\‍[ \frac{\pi}{4} (d_i + d_j)^2 \mathrm{min}(u^{\prime}, u_{\mathrm{crit}}) \mathrm{exp} \left[ - \left(\frac{\alpha_{\mathrm{max}}^{1/3}}{\alpha^{1/3}} - 1\right)^2 \right]\,, \‍]$

where

$\‍[ u^{\prime} = \mathrm{max} \left( \sqrt{2} \epsilon_c^{1/3} \sqrt{d_i^{2/3} + d_j^{2/3}}, |\vec{u}_i - \vec{u}_j| \right) \‍]$

is the characteristic velocity for coalescence. Note that a velocity difference between bubble i and j is only present if the corresponding size groups are assigned to different velocity groups.

	=	Diameter of bubble i [m]
	=	Diameter of bubble j [m]
$\epsilon_c$	=	Turbulent dissipation rate of continuous phase [m2/s3]
$\alpha$	=	Total void fraction of the bubbles [-]
$\alpha_{max}$	=	Maximum packing density of the bubbles [-]
$u_{crit}$	=	Critical velocity for coalescence [m/s]
$\vec{u}_i$	=	Velocity vector of bubble i [m/s]
$\vec{u}_j$	=	Velocity vector of bubble j [m/s]

Reference:

        Lehr, F., Millies, M., & Mewes, D. (2002).
        Bubble‐size distributions and flow fields in bubble columns.
        AIChE Journal, 48(11), 2426-2443.

Usage

Property	Description	Required	Default value
`uCrit`	Crit. coalescence velocity	no	0.08
`alphaMax`	Maximum packing density	no	0.6

Source files

Definition at line 146 of file LehrMilliesMewesCoalescence.H.

Constructor & Destructor Documentation

◆ LehrMilliesMewesCoalescence()

LehrMilliesMewesCoalescence	(	const populationBalanceModel &	popBal,
		const dictionary &	dict )

Definition at line 50 of file LehrMilliesMewesCoalescence.C.

References coalescenceModel::coalescenceModel(), dict, Foam::dimless, and Foam::dimVelocity.

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◆ ~LehrMilliesMewesCoalescence()

virtual ~LehrMilliesMewesCoalescence ( )

virtualdefault

Destructor.

Member Function Documentation

◆ TypeName()

TypeName ( "LehrMilliesMewes" )

Runtime type information.

References dict.

◆ addToCoalescenceRate()

void addToCoalescenceRate	(	volScalarField &	coalescenceRate,
		const label	i,
		const label	j )

virtual

Add to coalescenceRate.

Implements coalescenceModel.

Definition at line 72 of file LehrMilliesMewesCoalescence.C.

References Foam::cbrt(), sizeGroup::d(), Foam::exp(), Foam::mag(), Foam::max(), Foam::min(), sizeGroup::phase(), pi(), coalescenceModel::popBal_, phaseModel::residualAlpha(), Foam::sqr(), Foam::sqrt(), and phaseModel::U().