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... | |
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 | ||
| ) |
|
virtualdefault |
Destructor.
| TypeName | ( | "Luo" | ) |
Runtime type information.
|
virtual |
Add to coalescenceRate.
Implements coalescenceModel.
Definition at line 76 of file Luo.C.
References Foam::cbrt(), virtualMassModel::Cvm(), sizeGroup::d(), 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().
1.8.17