/*---------------------------------------------------------------------------*\
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Class
Foam::meltingEvaporationModels::kineticGasEvaporation
Description
Considering the Hertz Knudsen formula, which gives the
evaporation-condensation flux based on the kinetic theory for flat
interface:
\f[
Flux = C \sqrt{\frac{M}{2 \pi R T_{activate}}}(p - p_{sat})
\f]
where:
\vartable
Flux | mass flux rate [kg/s/m2]
M | molecular weight
T_{activate} | saturation temperature
C | accommodation coefficient
R | universal gas constant
p_{sat} | saturation pressure
p | vapor partial pressure
\endvartable
The Clapeyron-Clausius equation relates the pressure to the temperature
for the saturation condition:
\f[
\frac{dp}{dT} = - \frac{L}{T (\nu_v - \nu_l)}
\f]
where:
\vartable
L | latent heat
\nu_v | inverse of the vapor density
\nu_l | inverse of the liquid density
\endvartable
Using the above relations:
\f[
Flux =
2 \frac{C}{2 - C}
\sqrt{\frac{M}{2 \pi R {T_activate}^3}} L (\rho_{v})
(T - T_{activate})
\f]
This assumes liquid and vapour are in equilibrium, then the accommodation
coefficient are equivalent for the interface. This relation is known as the
Hertz-Knudsen-Schrage.
Based on the reference:
- Van P. Carey, Liquid-Vapor Phase Change Phenomena, ISBN 0-89116836,
1992, pp. 112-121.
Usage
Example usage:
\verbatim
massTransferModel
(
(liquid to gas)
{
type kineticGasEvaporation;
species vapour.gas;
C 0.1;
isoAlpha 0.1;
Tactivate 373;
}
);
\endverbatim
where:
\table
Property | Description | Required | Default value
C | Coefficient (C > 0 for evaporation, C < 0 for
condensation) | yes
includeVolChange | Volumen change | no | yes
isoAlpha | iso-alpha for interface | no | 0.5
Tactivate | Saturation temperature | yes
species | Specie name on the other phase | no | none
\endtable
SourceFiles
kineticGasEvaporation.C
\*---------------------------------------------------------------------------*/
#ifndef meltingEvaporationModels_kineticGasEvaporation_H
#define meltingEvaporationModels_kineticGasEvaporation_H
#include "InterfaceCompositionModel.H"
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//
namespace Foam
{
// Forward Declarations
class phasePair;
namespace meltingEvaporationModels
{
/*---------------------------------------------------------------------------*\
Class kineticGasEvaporation Declaration
\*---------------------------------------------------------------------------*/
template
class kineticGasEvaporation
:
public InterfaceCompositionModel
{
// Private Data
//- Evaporation coefficient
dimensionedScalar C_;
//- Activation temperature
const dimensionedScalar Tactivate_;
//- Molar weight of the vapour in the continuous phase
dimensionedScalar Mv_;
//- Interface area
volScalarField interfaceArea_;
//- Heat transfer coefficient
volScalarField htc_;
//- Mass source
volScalarField mDotc_;
//- Interface Iso-value
scalar isoAlpha_;
// Private Member Functions
//- Update interface
void updateInterface(const volScalarField& T);
public:
//- Runtime type information
TypeName("kineticGasEvaporation");
// Constructors
//- Construct from components
kineticGasEvaporation
(
const dictionary& dict,
const phasePair& pair
);
//- Destructor
virtual ~kineticGasEvaporation() = default;
// Member Functions
//- Explicit total mass transfer coefficient
virtual tmp Kexp
(
const volScalarField& field
);
//- Implicit mass transfer coefficient
virtual tmp KSp
(
label modelVariable,
const volScalarField& field
);
//- Explicit mass transfer coefficient
virtual tmp KSu
(
label modelVariable,
const volScalarField& field
);
//- Return Tactivate
virtual const dimensionedScalar& Tactivate() const noexcept
{
return Tactivate_;
}
//- Add/subtract alpha*div(U) as a source term
//- for alpha, substituting div(U) = mDot(1/rho1 - 1/rho2)
virtual bool includeDivU() const noexcept
{
return true;
}
};
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
} // End namespace meltingEvaporationModels
} // End namespace Foam
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
#ifdef NoRepository
# include "kineticGasEvaporation.C"
#endif
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
#endif
// ************************************************************************* //