Description

template<class Scalar>
class Dumux::ThermalConductivitySomertonThreeP< Scalar >

Somerton (three fluid phases)

The Somerton method [73] computes the thermal conductivity of dry and the wet soil material. It is extended here to a three phase system of water (w), NAPL (n) and gas (g). It uses a root function of the water and NAPL saturation to compute the effective thermal conductivity for a three-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 effective thermal conductivity of ThermalConductivitySomertonThreeP is given by

\[ \lambda_\text{eff} = \lambda_\text{g,eff} + \sqrt{S_\text{w}} \left(\lambda_\text{w,eff} - \lambda_\text{g,eff}\right) + \sqrt{S_\text{n}} \left(\lambda_\text{n,eff} - \lambda_\text{g,eff}\right) \]

with \( S_\text{w} \) the water saturation, \( S_\text{n} \) the NAPL saturation, the effective phase saturations given by \( \lambda_{\alpha,\text{eff}} = (\lambda_\text{s})^{\left(1-\phi\right)} (\lambda_\alpha)^\phi, \alpha \in \{\text{w,n,g}\}\) (geometric mean) and \( \lambda_\text{s} \) is the thermal conductivity of the solid phase.

Static Public Member Functions
template<class VolumeVariables >
static Scalar	effectiveThermalConductivity (const VolumeVariables &volVars)
	Effective thermal conductivity in \(\mathrm{W/(m K)}\) for three phases. More...

static Scalar	effectiveThermalConductivity (const Scalar sw, const Scalar sn, const Scalar lambdaW, const Scalar lambdaN, const Scalar lambdaG, const Scalar lambdaSolid, const Scalar porosity)
	Effective thermal conductivity in \(\mathrm{W/(m K)}\) for three phases. More...

Member Function Documentation

◆ effectiveThermalConductivity() [1/2]

template<class Scalar >

static Scalar Dumux::ThermalConductivitySomertonThreeP< Scalar >::effectiveThermalConductivity	(	const Scalar	sw,
		const Scalar	sn,
		const Scalar	lambdaW,
		const Scalar	lambdaN,
		const Scalar	lambdaG,
		const Scalar	lambdaSolid,
		const Scalar	porosity
	)

inlinestatic

Parameters

sw	The saturation of the wetting phase
sn	The saturation of the nonwetting phase
lambdaW	The thermal conductivity of the water phase in \(\mathrm{W/(m K)}\)
lambdaN	The thermal conductivity of the NAPL phase in \(\mathrm{W/(m K)}\)
lambdaG	The thermal conductivity of the gas phase in \(\mathrm{W/(m K)}\)
lambdaSolid	The thermal conductivity of the solid phase in \(\mathrm{W/(m K)}\)
porosity	The porosity

Returns: Effective thermal conductivity in \(\mathrm{W/(m K)}\) for three phases

◆ effectiveThermalConductivity() [2/2]

template<class Scalar >

template<class VolumeVariables >

static Scalar Dumux::ThermalConductivitySomertonThreeP< Scalar >::effectiveThermalConductivity ( const VolumeVariables & volVars )