Public Member Functions | List of all members
PrinceBlanch Class Reference

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

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Public Member Functions

 TypeName ("PrinceBlanch")
 Runtime type information. More...
 
 PrinceBlanch (const populationBalanceModel &popBal, const dictionary &dict)
 
virtual ~PrinceBlanch ()
 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< coalescenceModelclone () const
 
virtual ~coalescenceModel ()
 Destructor. More...
 
virtual void correct ()
 Correct diameter independent expressions. More...
 

Additional Inherited Members

- Static Public Member Functions inherited from coalescenceModel
static autoPtr< coalescenceModelNew (const word &type, const populationBalanceModel &popBal, const dictionary &dict)
 
- Protected Attributes inherited from coalescenceModel
const populationBalanceModelpopBal_
 Reference to the populationBalanceModel. More...
 

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 continous 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]

References:

        "Bubble Coalescence and Break-Up in Air-Sparged Bubble-Columns"
        Prince, M.J., Blanch, H.W.
        AIChE Journal, Vol. 36, Issue 10, 1990, pp. 1485-1499
Usage
Property Description Required Default value
C1 Coefficient C1 no 0.089
Source files

Definition at line 208 of file PrinceBlanch.H.

Constructor & Destructor Documentation

◆ PrinceBlanch()

PrinceBlanch ( const populationBalanceModel popBal,
const dictionary dict 
)

◆ ~PrinceBlanch()

virtual ~PrinceBlanch ( )
inlinevirtual

Destructor.

Definition at line 248 of file PrinceBlanch.H.

References PrinceBlanch::addToCoalescenceRate().

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Member Function Documentation

◆ TypeName()

TypeName ( "PrinceBlanch"  )

Runtime type information.

◆ addToCoalescenceRate()

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

Add to coalescenceRate.

Implements coalescenceModel.

Referenced by PrinceBlanch::~PrinceBlanch().

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