Model of Prince and Blanch (1990). The coalescence rate is calculated by. More...
Public Member Functions | |
| TypeName ("PrinceBlanch") | |
| Runtime type information. More... | |
| PrinceBlanch (const populationBalanceModel &popBal, const dictionary &dict) | |
| virtual | ~PrinceBlanch ()=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 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] |
| \( h_0 \) | = | Initial film thickness [m] |
| \( h_f \) | = | Critical film thickness [m] |
| \( \epsilon_c \) | = | Continuous phase turbulent dissipation rate [m2/s3] |
| \( d_i \) | = | Diameter of bubble i [m] |
| \( d_j \) | = | Diameter of bubble j [m] |
| \( u_{ri} \) | = | Rise velocity of bubble i [m/s] |
| \( S_{ij} \) | = | Collision cross sectional area [m2] |
| \( g \) | = | 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.| 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 |
Definition at line 240 of file PrinceBlanch.H.
| PrinceBlanch | ( | const populationBalanceModel & | popBal, |
| const dictionary & | dict | ||
| ) |
Definition at line 59 of file PrinceBlanch.C.
|
virtualdefault |
Destructor.
| TypeName | ( | "PrinceBlanch" | ) |
Runtime type information.
|
virtual |
Add to coalescenceRate.
Implements coalescenceModel.
Definition at line 96 of file PrinceBlanch.C.
References Foam::cbrt(), sizeGroup::d(), Foam::exit(), Foam::exp(), Foam::FatalError, FatalErrorInFunction, g, Foam::log(), Foam::mag(), sizeGroup::phase(), Foam::constant::mathematical::pi(), Foam::pow(), Foam::pow3(), phaseModel::rho(), Foam::sqr(), and Foam::sqrt().
1.8.17