transmissibility2p.hh

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#ifndef DUMUX_PNM_THROAT_TRANSMISSIBILITY_2P_HH
#define DUMUX_PNM_THROAT_TRANSMISSIBILITY_2P_HH
 
#include <dumux/porenetwork/common/throatproperties.hh>
#include "emptycache.hh"
 
namespace Dumux::PoreNetwork {
 
namespace WettingLayerTransmissibility {
 
struct CreviceResistanceFactorZhou
{
    template<class Scalar>
    static Scalar beta(const Scalar alpha, const Scalar theta, const Scalar f = 0)
    {
       using std::sin;
       using std::cos;
       using std::tan;
       const Scalar sinAlpha = sin(alpha);
       const Scalar sinSum = sin(alpha + theta);
       const Scalar cosSum = cos(alpha + theta);
       const Scalar phi1 = cosSum*cosSum + cosSum*sinSum*tan(alpha);
       const Scalar phi2 = 1 - theta/(M_PI/2 - alpha);
       const Scalar phi3 = cosSum / cos(alpha);
       const Scalar B = (M_PI/2 - alpha)*tan(alpha);
 
       Scalar result = 12*sinAlpha*sinAlpha*(1-B)*(1-B)*(phi1 - B*phi2)*(phi3 + f*B*phi2)*(phi3 + f*B*phi2);
       result /= (1-sinAlpha)*(1-sinAlpha)*B*B*(phi1 - B*phi2)*(phi1 - B*phi2)*(phi1 - B*phi2);
       return result;
    }
};
 
 
template<class Scalar, class CreviceResistanceFactor = CreviceResistanceFactorZhou>
struct RansohoffRadke
{
    class WettingLayerCache
    {
        using NumCornerVector = Dune::ReservedVector<Scalar, 4>;
    public:
        template<class Problem, class Element, class FVElementGeometry, class ElementVolumeVariables, class FluxVariablesCache>
        void fill(const Problem& problem,
                  const Element& element,
                  const FVElementGeometry& fvGeometry,
                  const typename FVElementGeometry::SubControlVolumeFace& scvf,
                  const ElementVolumeVariables& elemVolVars,
                  const FluxVariablesCache& fluxVarsCache,
                  const int phaseIdx)
        {
            const auto& spatialParams = problem.spatialParams();
            const auto& cornerHalfAngles = spatialParams.cornerHalfAngles(element);
            const Scalar contactAngle = spatialParams.contactAngle(element, elemVolVars);
 
            beta_.clear(); beta_.resize(cornerHalfAngles.size());
            for (int i = 0; i< cornerHalfAngles.size(); ++i)
                beta_[i] = CreviceResistanceFactor::beta(cornerHalfAngles[i], contactAngle);
        }
 
        Scalar creviceResistanceFactor(const int cornerIdx) const
        { return beta_[cornerIdx]; }
 
    private:
        NumCornerVector beta_;
    };
 
    template<class Element, class FVElementGeometry, class FluxVariablesCache>
    static Scalar wettingLayerTransmissibility(const Element& element,
                                               const FVElementGeometry& fvGeometry,
                                               const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                               const FluxVariablesCache& fluxVarsCache)
    {
        const Scalar throatLength = fluxVarsCache.throatLength();
        const Scalar rC = fluxVarsCache.curvatureRadius();
 
        const auto eIdx = fvGeometry.gridGeometry().elementMapper().index(element);
        const auto shape = fvGeometry.gridGeometry().throatCrossSectionShape(eIdx);
        const auto numCorners = Throat::numCorners(shape);
 
        // treat the wetting film layer in each corner of the throat individually (might have different corner half-angle and beta)
        Scalar result = 0.0;
        for (int i = 0; i < numCorners; ++i)
            result += fluxVarsCache.wettingLayerCrossSectionalArea(i) * rC*rC / (throatLength*fluxVarsCache.wettingLayerFlowVariables().creviceResistanceFactor(i));
 
        return result;
    }
};
} // end namespace WettingLayerTransmissibility
 
namespace NonWettingPhaseTransmissibility {
 
template<class Scalar>
struct Mogensen
{
    using NonWettingPhaseCache = EmptyCache;
 
    template<class Element, class FVElementGeometry, class FluxVariablesCache>
    static Scalar nonWettingPhaseTransmissibility(const Element& element,
                                                  const FVElementGeometry& fvGeometry,
                                                  const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                                  const FluxVariablesCache& fluxVarsCache)
    {
        // Mogensen et al. (1999), does not really revover the single phase value
        using std::sqrt;
        const Scalar throatLength = fluxVarsCache.throatLength();
        const auto nPhaseIdx = fluxVarsCache.nPhaseIdx();
        const Scalar aNw = fluxVarsCache.throatCrossSectionalArea(nPhaseIdx);
        const Scalar rEff = 0.5*(sqrt(aNw / M_PI) + fluxVarsCache.throatInscribedRadius());
        const Scalar result = M_PI/(8*throatLength) * rEff*rEff*rEff*rEff;
        return result;
    }
};
 
template<class Scalar, class SinglePhaseTransmissibilityLaw>
struct Valvatne
{
    using NonWettingPhaseCache = EmptyCache;
 
    template<class Element, class FVElementGeometry, class FluxVariablesCache>
    static Scalar nonWettingPhaseTransmissibility(const Element& element,
                                                  const FVElementGeometry& fvGeometry,
                                                  const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                                  const FluxVariablesCache& fluxVarsCache)
    {
        // Tora et al. (2012), also does not fully recover single-phase value, but is closer
        using std::sqrt;
        const auto nPhaseIdx = fluxVarsCache.nPhaseIdx();
        const Scalar aNw = fluxVarsCache.throatCrossSectionalArea(nPhaseIdx);
        const Scalar aTot = fluxVarsCache.throatCrossSectionalArea();
 
        const Scalar result = SinglePhaseTransmissibilityLaw::singlePhaseTransmissibility(element, fvGeometry, scvf, fluxVarsCache)
                              * aNw / aTot;
 
        return result;
    }
};
 
template<class Scalar>
struct BakkeOren
{
    using NonWettingPhaseCache = EmptyCache;
 
    template<class Element, class FVElementGeometry, class FluxVariablesCache>
    static Scalar nonWettingPhaseTransmissibility(const Element& element,
                                                  const FVElementGeometry& fvGeometry,
                                                  const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                                  const FluxVariablesCache& fluxVarsCache)
    {
        // Tora et al. (2012), quite close for single-phase value of square
        using std::sqrt;
        const Scalar throatLength = fluxVarsCache.throatLength();
        const auto nPhaseIdx = fluxVarsCache.nPhaseIdx();
        const Scalar aNw = fluxVarsCache.throatCrossSectionalArea(nPhaseIdx);
        const Scalar rEff = 0.5*(sqrt(aNw / M_PI) + fluxVarsCache.throatInscribedRadius());
        const Scalar result = rEff*rEff*aNw / (8.0*throatLength);
        return result;
    }
};
} // end namespace NonWettingPhaseTransmissibility
} // end namespace Dumux::PoreNetwork
 
#endif