Model of Luo (1993). The coalescence rate is calculated by. More...

#include <Luo.H>

Inheritance diagram for Luo:

Collaboration diagram for Luo:

Public Member Functions
	TypeName ("Luo")
	Runtime type information.
	Luo (const populationBalanceModel &popBal, const dictionary &dict)
virtual	~Luo ()=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 Luo (1993). The coalescence rate is calculated by.

$\‍[ \frac{\pi}{4} (d_i + d_j)^2 u_{ij} \mathrm{exp} \left[ - C_1 \frac {[0.75(1 + \xi_{ij}^2)(1 + \xi_{ij}^3)]^{1/2}} {(\rho_d/\rho_c + C_{vm})^{1/2} (1 + \xi_{ij})^3} \left(\frac{\rho_c d_i u_{ij}^2}{\sigma}\right)^{1/2} \right]\,, \‍]$

where

$\‍[ u_{ij} = \sqrt{\beta} (\epsilon_c d_i)^{1/3} \sqrt{1 + \xi_{ij}^{-2/3}} \‍]$

is the mean approach velocity of the bubbles and

$\‍[ \xi_{ij} = d_i/d_j \‍]$

their size ratio.

	=	Diameter of bubble i [m]
	=	Diameter of bubble j [m]
$u_{ij}$	=	Mean approach velocity [m/s]
$\xi_{ij}$	=	Bubble size ratio [-]
$\rho_d$	=	Density of dispersed phase [kg/m3]
$\rho_c$	=	Density of continuous phase [kg/m3]
$\sigma$	=	Surface tension [N/m]
$C_{vm}$	=	Virtual mass coefficient [-]
	=	Coefficient [-]
$\beta$	=	Coefficient [-]
$\epsilon_c$	=	Continuous phase turbulent dissipation rate [m2/s3]

Reference:

        Luo, H. (1993).
        Coalescence, breakup and liquid circulation in bubble column reactors.
        Dr. Ing (Doctoral dissertation, Thesis, Department of Chemical
        Engineering, The Norwegian Institute of Technology, Trondheim, Norway).

Usage

Property	Description	Required	Default value
`beta`	Coefficient beta	no	2.0
`C1`	Coefficient C1	no	1.0

Source files

Luo.H
Luo.C

Definition at line 164 of file Luo.H.

Constructor & Destructor Documentation

◆ Luo()

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

Definition at line 52 of file Luo.C.

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

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◆ ~Luo()

virtual ~Luo ( )

virtualdefault

Destructor.

Member Function Documentation

◆ TypeName()

TypeName ( "Luo" )

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 67 of file Luo.C.

References Foam::cbrt(), virtualMassModel::Cvm(), sizeGroup::d(), Foam::exit(), Foam::exp(), Foam::FatalError, FatalErrorInFunction, phaseModel::name(), sizeGroup::phase(), pi(), coalescenceModel::popBal_, Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), and Foam::sqrt().