Public Member Functions | List of all members
Luo Class Reference

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

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Public Member Functions

 TypeName ("Luo")
 Runtime type information. More...
 
 Luo (const populationBalanceModel &popBal, const dictionary &dict)
 
virtual ~Luo ()
 Destructor. More...
 
virtual void addToCoalescenceRate (volScalarField &coalescenceRate, const label i, const label j)
 Add to coalescenceRate. More...
 
- Public Member Functions inherited from coalescenceModel
 TypeName ("coalescenceModel")
 Runtime type information. More...
 
 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 ()
 Destructor. More...
 
virtual void precompute ()
 Precompute diameter independent expressions. More...
 

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. More...
 

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.

$ d_i $ = Diameter of bubble i [m]
$ d_j $ = Diameter of bubble j [m]
$ u_{ij} $ = Mean approach velocity [m/s]
$ \xi_{ij} $ = Bubble size ratio [-]
$ \rho_d $ = Density of dispersed phase [kg/m^3]
$ \rho_c $ = Density of continuous phase [kg/m^3]
$ \sigma $ = Surface tension [N/m]
$ C_{vm} $ = Virtual mass coefficient [-]
$ C_1 $ = Coefficient [-]
$ \beta $ = Coefficient [-]
$ \epsilon_c $ = Continuous phase turbulent dissipation rate [m^2/s^3]

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

Definition at line 166 of file Luo.H.

Constructor & Destructor Documentation

◆ Luo()

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

Definition at line 54 of file Luo.C.

◆ ~Luo()

virtual ~Luo ( )
inlinevirtual

Destructor.

Definition at line 194 of file Luo.H.

Member Function Documentation

◆ TypeName()

TypeName ( "Luo"  )

Runtime type information.

◆ addToCoalescenceRate()

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

Add to coalescenceRate.

Implements coalescenceModel.

Definition at line 69 of file Luo.C.

References Foam::cbrt(), dispersedVirtualMassModel::Cvm(), sizeGroup::dSph(), Foam::exit(), Foam::exp(), Foam::FatalError, FatalErrorInFunction, phaseModel::name(), sizeGroup::phase(), Foam::constant::mathematical::pi(), Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), and Foam::sqrt().

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