Model of Prince and Blanch (1990). The coalescence rate is calculated by. More...

#include <PrinceBlanch.H>

Inheritance diagram for PrinceBlanch:

Collaboration diagram for PrinceBlanch:

Public Member Functions
	TypeName ("PrinceBlanch")
	Runtime type information.
	PrinceBlanch (const populationBalanceModel &popBal, const dictionary &dict)
virtual	~PrinceBlanch ()=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 Prince and Blanch (1990). The coalescence rate is calculated by.

$\‍[ \left( \theta_{ij}^{T} + \theta_{ij}^{B} + \theta_{ij}^{LS} \right) \lambda_{ij} \‍]$

with the coalescence efficiency

$\‍[ \lambda_{ij} = \mathrm{exp} \left( - \sqrt{\frac{r_{ij}^3 \rho_c}{16 \sigma}} \mathrm{ln} \left(\frac{h_0}{h_f}\right) \epsilon_c^{1/3}/r_{ij}^{2/3} \right)\;, \‍]$

the turbulent collision rate

$\‍[ \theta_{ij}^{T} = C_1 \pi (d_i + d_j)^{2} \epsilon_c^{1/3} \sqrt{d_{i}^{2/3} + d_{j}^{2/3}}\;, \‍]$

and the buoyancy-driven collision rate

$\‍[ \theta_{ij}^{B} = S_{ij} \left| u_{ri} - u_{rj} \right|\;, \‍]$

where the rise velocity of bubble i is calculated by

$\‍[ u_{ri} = \sqrt{2.14 \sigma / \left(\rho_c d_i \right) + 0.505 g d_i}\;, \‍]$

the equivalent radius by

$\‍[ r_{ij} = \left( \frac{1}{d_i} + \frac{1}{d_j} \right)^{-1} \‍]$

and the collision cross sectional area by

$\‍[ S_{ij} = \frac{\pi}{4} \left(d_i + d_j\right)^{2}\;. \‍]$

Note that in equation 2, the bubble radius has been substituted by the bubble diameter. Also the expression for the equivalent radius r_ij (equation 19 in the paper of Prince and Blanch (1990)) was corrected. The collision rate contribution due to laminar shear in the continuous phase is currently neglected.

$\theta_{ij}^{T}$	=	Turbulent collision rate [m3/s]
$\theta_{ij}^{B}$	=	Buoyancy-driven collision rate [m3/s]
$\theta_{ij}^{LS}$	=	Laminar shear collision rate [m3/s]
$\lambda_{ij}$	=	Coalescence efficiency [-]
$r_{ij}$	=	Equivalent radius [m]
$\rho_c$	=	Density of continuous phase [kg/m3]
$\sigma$	=	Surface tension [N/m]
	=	Initial film thickness [m]
	=	Critical film thickness [m]
$\epsilon_c$	=	Continuous phase turbulent dissipation rate [m2/s3]
	=	Diameter of bubble i [m]
	=	Diameter of bubble j [m]
$u_{ri}$	=	Rise velocity of bubble i [m/s]
$S_{ij}$	=	Collision cross sectional area [m2]
	=	Gravitational constant [m/s2]

Reference:

        Prince, M. J., & Blanch, H. W. (1990).
        Bubble coalescence and break‐up in air‐sparged bubble columns.
        AIChE journal, 36(10), 1485-1499.

Usage

Property	Description	Required	Default value
`C1`	coefficient C1	no	0.089
`h0`	initial film thickness	no	1e-4m
`hf`	critical film thickness	no	1e-8m
`turbulence`	Switch for collisions due to turbulence	yes	none
`buoyancy`	Switch for collisions due to buoyancy	yes	none
`laminarShear`	Switch for collisions due to laminar shear	yes	none

Source files

Definition at line 236 of file PrinceBlanch.H.

Constructor & Destructor Documentation

◆ PrinceBlanch()

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

Definition at line 50 of file PrinceBlanch.C.

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

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◆ ~PrinceBlanch()

virtual ~PrinceBlanch ( )

virtualdefault

Destructor.

Member Function Documentation

◆ TypeName()

TypeName ( "PrinceBlanch" )

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 87 of file PrinceBlanch.C.

References Foam::cbrt(), sizeGroup::d(), Foam::exit(), Foam::exp(), Foam::FatalError, FatalErrorInFunction, g, Foam::log(), Foam::mag(), sizeGroup::phase(), pi(), coalescenceModel::popBal_, Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), Foam::sqrt(), and Foam::type().