Commit 13087868 authored by Klaus Mosthaf's avatar Klaus Mosthaf
Browse files

Bugfix: Corrected computation of l_dry as geometric mean of the thermal...

Bugfix: Corrected computation of l_dry as geometric mean of the thermal conductivity of the solid and the fluid phase, as it is done for l_sat. Adapted documentation.

git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@10328 2fb0f335-1f38-0410-981e-8018bf24f1b0
parent 51bbffff
......@@ -35,9 +35,25 @@ namespace Dumux
*
* The Somerton method 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. It is assumed, that the
* non-wetting phase does not contribute to the conduction due to a large contrast
* in the fluid conductivities.
* 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:
* \f[
\lambda_\text{eff} = \lambda_{\text{dry}} + \sqrt{(S_w)} \left(\lambda_\text{wet} - \lambda_\text{dry}\right)
\f]
*
* with
* \f[
\lambda_\text{wet} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi
\f]
* and
*
* \f[
\lambda_\text{dry} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_n^\phi.
\f]
*
*/
template<class Scalar>
class ThermalConductivitySomerton
......@@ -46,11 +62,6 @@ public:
/*!
* \brief Returns the effective thermal conductivity \f$[W/(m K)]\f$ after Somerton (1974).
*
* The material law is:
* \f[
l_eff = l_solid + \sqrt(S_w)(l_wet - l_solid)
\f]
*
* \param Sw The saturation of the wetting phase
* \param lambdaW the thermal conductivity of the wetting phase
* \param lambdaN the thermal conductivity of the non-wetting phase
......@@ -58,6 +69,12 @@ public:
* \param porosity The porosity
*
* \return Effective thermal conductivity \f$[W/(m K)]\f$ after Somerton (1974)
*
* 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 square root of the wetting saturation.
* See f.e. Ebigbo, A.: Thermal Effects of Carbon Dioxide Sequestration in the Subsurface, Diploma thesis.
*/
static Scalar effectiveThermalConductivity(const Scalar Sw,
const Scalar lambdaW,
......@@ -66,8 +83,9 @@ public:
const Scalar porosity)
{
const Scalar satW = std::max<Scalar>(0.0, Sw);
// geometric means
const Scalar lSat = std::pow(lambdaSolid, (1.0 - porosity)) * std::pow(lambdaW, porosity);
const Scalar lDry = std::pow(lambdaSolid, (1.0 - porosity));
const Scalar lDry = std::pow(lambdaSolid, (1.0 - porosity)) * std::pow(lambdaN, porosity);
return lDry + std::sqrt(satW) * (lSat - lDry);
}
......
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