Model of Luo (1993). The coalescence rate is calculated by. More...
Public Member Functions | |
TypeName ("Luo") | |
Runtime type information. More... | |
Luo (const populationBalanceModel &popBal, const dictionary &dict) | |
virtual | ~Luo ()=default |
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 ()=default |
Destructor. More... | |
virtual void | correct () |
Correct diameter independent expressions. More... | |
virtual void | addToCoalescenceRate (volScalarField &coalescenceRate, const label i, const label j)=0 |
Add to coalescenceRate. 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... | |
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/m3] |
\( \rho_c \) | = | Density of continuous phase [kg/m3] |
\( \sigma \) | = | Surface tension [N/m] |
\( C_{vm} \) | = | Virtual mass coefficient [-] |
\( C_1 \) | = | 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).
Property | Description | Required | Default value |
---|---|---|---|
beta | Coefficient beta | no | 2.0 |
C1 | Coefficient C1 | no | 1.0 |
Luo | ( | const populationBalanceModel & | popBal, |
const dictionary & | dict | ||
) |
Definition at line 59 of file Luo.C.
References Foam::dimless.
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virtualdefault |
Destructor.
TypeName | ( | "Luo" | ) |
Runtime type information.
|
virtual |
Add to coalescenceRate.
Implements coalescenceModel.
Definition at line 74 of file Luo.C.
References Foam::cbrt(), virtualMassModel::Cvm(), sizeGroup::d(), Foam::exit(), Foam::exp(), Foam::FatalError, FatalErrorInFunction, phaseModel::name(), sizeGroup::phase(), Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), and Foam::sqrt().