Dumux::ThermalConductivityJohansen< Scalar, Indices > Class Template Reference

Relation for the saturation-dependent effective thermal conductivity. More...

#include <dumux/material/fluidmatrixinteractions/2p/thermalconductivityjohansen.hh>

Description

template<class Scalar, class Indices = JohansenIndices>
class Dumux::ThermalConductivityJohansen< Scalar, Indices >

Relation for the saturation-dependent effective thermal conductivity.

The Johansen method (Johansen 1975 [35] ) computes the thermal conductivity of dry and the wet soil material and uses a root function of the wetting saturation to compute the effective thermal conductivity for a two-phase fluidsystem. The individual thermal conductivities are calculated as geometric mean of the thermal conductivity of the porous material and of the respective fluid phase. The material law is: $\mathrm{[ \lambda_\text{eff} = \lambda_{\text{dry}} + \sqrt{(S_w)} \left(\lambda_\text{wet} - \lambda_\text{dry}\right) }$

with $\mathrm{ \lambda_\text{wet} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi }$ and the semi-empirical relation

$\mathrm{ \lambda_\text{dry} = \frac{0.135*\rho_s*\phi + 64.7}{\rho_s - 0.947 \rho_s*\phi}. }$

Source: Phdthesis (Johansen1975) Johansen, O. Thermal conductivity of soils Norw. Univ. of Sci. Technol., Trondheim, Norway, 1975 [35]

Static Public Member Functions
template<class VolumeVariables , class SpatialParams , class Element , class FVGeometry >
static Scalar	effectiveThermalConductivity (const VolumeVariables &volVars, const SpatialParams &spatialParams, const Element &element, const FVGeometry &fvGeometry, const typename FVGeometry::SubControlVolume &scv)
	effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35] More...
template<class VolumeVariables >
static Scalar	effectiveThermalConductivity (const VolumeVariables &volVars)
	Returns the effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35] . More...
static Scalar	effectiveThermalConductivity (const Scalar Sw, const Scalar lambdaW, const Scalar lambdaN, const Scalar lambdaSolid, const Scalar porosity, const Scalar rhoSolid)
	Returns the effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35] . More...

Member Function Documentation

effectiveThermalConductivity() [1/3]

template<class Scalar , class Indices = JohansenIndices>

static Scalar Dumux::ThermalConductivityJohansen< Scalar, Indices >::effectiveThermalConductivity ( const Scalar  Sw, const Scalar  lambdaW, const Scalar  lambdaN, const Scalar  lambdaSolid, const Scalar  porosity, const Scalar  rhoSolid  )

inlinestatic

Returns the effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35] .

Parameters

Sw	The saturation of the wetting phase
lambdaW	The thermal conductivity of the wetting phase in $\mathrm{[W/(m K)]}$
lambdaN	The thermal conductivity of the non-wetting phase in $\mathrm{[W/(m K)]}$
lambdaSolid	The thermal conductivity of the solid phase in $\mathrm{[W/(m K)]}$
porosity	The porosity
rhoSolid	The density of solid phase in $\mathrm{[kg/m^3]}$

Returns

Effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35]

effectiveThermalConductivity() [2/3]

template<class Scalar , class Indices = JohansenIndices>

template<class VolumeVariables >

static Scalar Dumux::ThermalConductivityJohansen< Scalar, Indices >::effectiveThermalConductivity ( const VolumeVariables &  volVars )

inlinestatic

Returns the effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35] .

Parameters

volVars

volume variables

Returns

Effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35]

This formulation is semi-empirical and fitted to quartz sand. This gives an interpolation of the effective thermal conductivities of a porous medium filled with the non-wetting phase and a porous medium filled with the wetting phase. These two effective conductivities are computed as geometric mean of the solid and the fluid conductivities and interpolated with the Kersten number.
Johansen, O. 1975. Thermal conductivity of soils. Ph.D. diss. Norwegian Univ. of Sci. and Technol., Trondheim. (Draft Transl. 637. 1977. U.S. Army Corps of Eng., Cold Regions Res. and Eng. Lab., Hanover, NH.) [35]

effectiveThermalConductivity() [3/3]

template<class Scalar , class Indices = JohansenIndices>

template<class VolumeVariables , class SpatialParams , class Element , class FVGeometry >

static Scalar Dumux::ThermalConductivityJohansen< Scalar, Indices >::effectiveThermalConductivity ( const VolumeVariables &  volVars, const SpatialParams &  spatialParams, const Element &  element, const FVGeometry &  fvGeometry, const typename FVGeometry::SubControlVolume &  scv  )

inlinestatic

effective thermal conductivity $\mathrm{[W/(m K)]}$ after Johansen (1975) [35]

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

• thermalconductivityjohansen.hh