ProcessLib::HeatTransportBHE::BHE::BHE_1U Class Reference

Detailed Description

The BHE_1U class is the realization of 1U type of Borehole Heate Exchanger. In this class, the pipe heat capacity, pipe heat conductiion, pie advection vectors are initialized according to the geometry of 1U type of BHE. For 1U type of BHE, 4 primary unknowns are assigned on the 1D BHE elements. They are the temperature in inflow pipe T_in, temperature in outflow pipe T_out temperature of the two grout zones surrounding the inflow and outflow pipe T_g1 and T_g2. These primary variables are solved according to heat convection and conduction equations on the pipes and also in the grout zones. The interaction of the 1U type of BHE and the surrounding soil is regulated through the thermal resistance values, which are calculated specifically during the initialization of the class.

Definition at line 41 of file BHE_1U.h.

#include <BHE_1U.h>

Inheritance diagram for ProcessLib::HeatTransportBHE::BHE::BHE_1U:

Collaboration diagram for ProcessLib::HeatTransportBHE::BHE::BHE_1U:

Public Member Functions
	BHE_1U (BoreholeGeometry const &borehole, RefrigerantProperties const &refrigerant, GroutParameters const &grout, FlowAndTemperatureControl const &flowAndTemperatureControl, PipeConfigurationUType const &pipes, bool const use_python_bcs)
std::array< double, number_of_unknowns >	pipeHeatCapacities () const
std::array< double, number_of_unknowns >	pipeHeatConductions () const
std::array< Eigen::Vector3d, number_of_unknowns >	pipeAdvectionVectors (Eigen::Vector3d const &) const
double	updateFlowRateAndTemperature (double T_out, double current_time)
	Return the inflow temperature for the boundary condition.
double	thermalResistance (int const unknown_index) const
std::array< double, number_of_unknowns >	crossSectionAreas () const
void	updateHeatTransferCoefficients (double const flow_rate)
Public Member Functions inherited from ProcessLib::HeatTransportBHE::BHE::BHECommonUType
	BHECommonUType (BoreholeGeometry const &borehole, RefrigerantProperties const &refrigerant, GroutParameters const &grout, FlowAndTemperatureControl const &flowAndTemperatureControl, PipeConfigurationUType const &pipes, bool const use_python_bcs)
Public Member Functions inherited from ProcessLib::HeatTransportBHE::BHE::BHECommon
constexpr bool	isPowerBC () const

Static Public Member Functions
template<int NPoints, typename SingleUnknownMatrixType , typename RMatrixType , typename RPiSMatrixType , typename RSMatrixType >
static void	assembleRMatrices (int const idx_bhe_unknowns, Eigen::MatrixBase< SingleUnknownMatrixType > const &matBHE_loc_R, Eigen::MatrixBase< RMatrixType > &R_matrix, Eigen::MatrixBase< RPiSMatrixType > &R_pi_s_matrix, Eigen::MatrixBase< RSMatrixType > &R_s_matrix)
static std::array< std::pair< std::size_t, int >, 2 >	getBHEInflowDirichletBCNodesAndComponents (std::size_t const top_node_id, std::size_t const, int const in_component_id)
static std::optional< std::array< std::pair< std::size_t, int >, 2 > >	getBHEBottomDirichletBCNodesAndComponents (std::size_t const bottom_node_id, int const in_component_id, int const out_component_id)

Static Public Attributes
static constexpr int	number_of_unknowns = 4
static constexpr int	number_of_grout_zones = 2
static constexpr std::pair< int, int >	inflow_outflow_bc_component_ids []

Private Member Functions
std::array< double, number_of_unknowns >	calcThermalResistances (double const Nu)
	Nu is the Nusselt number.

Private Attributes
std::array< double, number_of_unknowns >	_thermal_resistances

Additional Inherited Members
Public Attributes inherited from ProcessLib::HeatTransportBHE::BHE::BHECommon
BoreholeGeometry const	borehole_geometry
RefrigerantProperties const	refrigerant
GroutParameters const	grout
FlowAndTemperatureControl const	flowAndTemperatureControl
bool const	use_python_bcs
Protected Attributes inherited from ProcessLib::HeatTransportBHE::BHE::BHECommonUType
PipeConfigurationUType const	_pipes
double	_flow_velocity = std::numeric_limits<double>::quiet_NaN()
	Flow velocity inside the pipes. Depends on the flow_rate.

Constructor & Destructor Documentation

BHE_1U()

ProcessLib::HeatTransportBHE::BHE::BHE_1U::BHE_1U	(	BoreholeGeometry const &	borehole,
		RefrigerantProperties const &	refrigerant,
		GroutParameters const &	grout,
		FlowAndTemperatureControl const &	flowAndTemperatureControl,
		PipeConfigurationUType const &	pipes,
		bool const	use_python_bcs )

Definition at line 25 of file BHE_1U.cpp.

    : BHECommonUType{borehole, refrigerant,   grout, flowAndTemperatureControl,
                     pipes,    use_python_bcs}
{
    _thermal_resistances.fill(std::numeric_limits<double>::quiet_NaN());
 
    // Initialize thermal resistances.
    auto values = visit(
        [&](auto const& control) {
            return control(refrigerant.reference_temperature,
                           0. /* initial time */);
        },
        flowAndTemperatureControl);
    updateHeatTransferCoefficients(values.flow_rate);
}

References _thermal_resistances, ProcessLib::HeatTransportBHE::BHE::BHECommon::flowAndTemperatureControl, ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::reference_temperature, ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant, and updateHeatTransferCoefficients().

Member Function Documentation

assembleRMatrices()

template<int NPoints, typename SingleUnknownMatrixType , typename RMatrixType , typename RPiSMatrixType , typename RSMatrixType >

static void ProcessLib::HeatTransportBHE::BHE::BHE_1U::assembleRMatrices ( int const idx_bhe_unknowns, Eigen::MatrixBase< SingleUnknownMatrixType > const & matBHE_loc_R, Eigen::MatrixBase< RMatrixType > & R_matrix, Eigen::MatrixBase< RPiSMatrixType > & R_pi_s_matrix, Eigen::MatrixBase< RSMatrixType > & R_s_matrix )

inlinestatic

Definition at line 66 of file BHE_1U.h.

    {
        switch (idx_bhe_unknowns)
        {
            case 0:  // PHI_fig
                R_matrix.block(0, 2 * NPoints, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
                R_matrix.block(2 * NPoints, 0, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
 
                R_matrix.block(0, 0, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_i1
                R_matrix.block(2 * NPoints, 2 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_ig
                return;
            case 1:  // PHI_fog
                R_matrix.block(NPoints, 3 * NPoints, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
                R_matrix.block(3 * NPoints, NPoints, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
 
                R_matrix.block(NPoints, NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_o1
                R_matrix.block(3 * NPoints, 3 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_og
                return;
            case 2:  // PHI_gg
                R_matrix.block(2 * NPoints, 3 * NPoints, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
                R_matrix.block(3 * NPoints, 2 * NPoints, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
 
                R_matrix.block(2 * NPoints, 2 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_ig  // notice we only have
                                         // 1 PHI_gg term here.
                R_matrix.block(3 * NPoints, 3 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_og  // see Diersch 2013 FEFLOW
                                         // book page 954 Table M.2
                return;
            case 3:  // PHI_gs
                R_s_matrix.template block<NPoints, NPoints>(0, 0).noalias() +=
                    1.0 * matBHE_loc_R;
 
                R_pi_s_matrix.block(2 * NPoints, 0, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
                R_pi_s_matrix.block(3 * NPoints, 0, NPoints, NPoints) +=
                    -1.0 * matBHE_loc_R;
                R_matrix.block(2 * NPoints, 2 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_ig
                R_matrix.block(3 * NPoints, 3 * NPoints, NPoints, NPoints) +=
                    1.0 * matBHE_loc_R;  // K_og
                return;
            default:
                OGS_FATAL(
                    "Error!!! In the function BHE_1U::assembleRMatrices, "
                    "the index of bhe unknowns is out of range! ");
        }
    }

References OGS_FATAL.

calcThermalResistances()

std::array< double, BHE_1U::number_of_unknowns > ProcessLib::HeatTransportBHE::BHE::BHE_1U::calcThermalResistances ( double const Nu )

private

Nu is the Nusselt number.

Definition at line 173 of file BHE_1U.cpp.

{
    constexpr double pi = std::numbers::pi;
 
    double const lambda_r = refrigerant.thermal_conductivity;
    double const lambda_g = grout.lambda_g;
    double const lambda_p = _pipes.inlet.wall_thermal_conductivity;
 
    // thermal resistances due to advective flow of refrigerant in the _pipes
    // Eq. 36 in Diersch_2011_CG
    double const R_adv_i1 = 1.0 / (Nu * lambda_r * pi);
    double const R_adv_o1 = 1.0 / (Nu * lambda_r * pi);
 
    // thermal resistance due to thermal conductivity of the pipe wall material
    // Eq. 49
    double const R_con_a =
        std::log(_pipes.inlet.outsideDiameter() / _pipes.inlet.diameter) /
        (2.0 * pi * lambda_p);
 
    // the average outer diameter of the _pipes
    double const d0 = _pipes.inlet.outsideDiameter();
    double const D = borehole_geometry.diameter;
    // Eq. 51
    double const chi = std::log(std::sqrt(D * D + 2 * d0 * d0) / 2 / d0) /
                       std::log(D / std::sqrt(2) / d0);
    // Eq. 52
    // thermal resistances of the grout
    double const R_g =
        std::acosh((D * D + d0 * d0 - _pipes.distance * _pipes.distance) /
                   (2 * D * d0)) /
        (2 * pi * lambda_g) * (1.601 - 0.888 * _pipes.distance / D);
 
    // thermal resistance due to inter-grout exchange
    double const R_ar =
        std::acosh((2.0 * _pipes.distance * _pipes.distance - d0 * d0) / d0 /
                   d0) /
        (2.0 * pi * lambda_g);
 
    auto const [chi_new, R_gg, R_gs] =
        thermalResistancesGroutSoil(chi, R_ar, R_g);
 
    // thermal resistance due to the grout transition.
    double const R_con_b = chi_new * R_g;
    // Eq. 29 and 30
    double const R_fig = R_adv_i1 + R_con_a + R_con_b;
    double const R_fog = R_adv_o1 + R_con_a + R_con_b;
 
    return {{R_fig, R_fog, R_gg, R_gs}};
 
    // keep the following lines------------------------------------------------
    // when debugging the code, printing the R and phi values are needed--------
    // std::cout << "Rfig =" << R_fig << " Rfog =" << R_fog << " Rgg =" <<
    // R_gg << " Rgs =" << R_gs << "\n"; double phi_fig = 1.0 / (R_fig *
    // S_i); double phi_fog = 1.0 / (R_fog * S_o); double phi_gg = 1.0 / (R_gg
    // * S_g1); double phi_gs = 1.0 / (R_gs * S_gs); std::cout << "phi_fig ="
    // << phi_fig << " phi_fog =" << phi_fog << " phi_gg =" << phi_gg << "
    // phi_gs =" << phi_gs << "\n";
    // -------------------------------------------------------------------------
}

References ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_pipes, ProcessLib::HeatTransportBHE::BHE::BHECommon::borehole_geometry, ProcessLib::HeatTransportBHE::BHE::BoreholeGeometry::diameter, ProcessLib::HeatTransportBHE::BHE::Pipe::diameter, ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::distance, ProcessLib::HeatTransportBHE::BHE::BHECommon::grout, ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::inlet, ProcessLib::HeatTransportBHE::BHE::GroutParameters::lambda_g, ProcessLib::HeatTransportBHE::BHE::Pipe::outsideDiameter(), ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant, ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::thermal_conductivity, ProcessLib::HeatTransportBHE::BHE::thermalResistancesGroutSoil(), and ProcessLib::HeatTransportBHE::BHE::Pipe::wall_thermal_conductivity.

Referenced by updateHeatTransferCoefficients().

crossSectionAreas()

std::array< double, BHE_1U::number_of_unknowns > ProcessLib::HeatTransportBHE::BHE::BHE_1U::crossSectionAreas

(

)

const

Definition at line 255 of file BHE_1U.cpp.

{
    return {{_pipes.inlet.area(), _pipes.outlet.area(),
             borehole_geometry.area() / 2 - _pipes.inlet.outsideArea(),
             borehole_geometry.area() / 2 - _pipes.outlet.outsideArea()}};
}

References ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_pipes, ProcessLib::HeatTransportBHE::BHE::BoreholeGeometry::area(), ProcessLib::HeatTransportBHE::BHE::Pipe::area(), ProcessLib::HeatTransportBHE::BHE::BHECommon::borehole_geometry, ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::inlet, ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::outlet, and ProcessLib::HeatTransportBHE::BHE::Pipe::outsideArea().

getBHEBottomDirichletBCNodesAndComponents()

std::optional< std::array< std::pair< std::size_t, int >, 2 > > ProcessLib::HeatTransportBHE::BHE::BHE_1U::getBHEBottomDirichletBCNodesAndComponents ( std::size_t const bottom_node_id, int const in_component_id, int const out_component_id )

static

Definition at line 246 of file BHE_1U.cpp.

{
    return {{std::make_pair(bottom_node_id, in_component_id),
             std::make_pair(bottom_node_id, out_component_id)}};
}

getBHEInflowDirichletBCNodesAndComponents()

std::array< std::pair< std::size_t, int >, 2 > ProcessLib::HeatTransportBHE::BHE::BHE_1U::getBHEInflowDirichletBCNodesAndComponents ( std::size_t const top_node_id, std::size_t const , int const in_component_id )

static

Definition at line 235 of file BHE_1U.cpp.

{
    return {std::make_pair(top_node_id, in_component_id),
            std::make_pair(top_node_id, in_component_id + 1)};
}

pipeAdvectionVectors()

std::array< Eigen::Vector3d, BHE_1U::number_of_unknowns > ProcessLib::HeatTransportBHE::BHE::BHE_1U::pipeAdvectionVectors

(

Eigen::Vector3d const &

)

const

Definition at line 88 of file BHE_1U.cpp.

{
    double const& rho_r = refrigerant.density;
    double const& Cp_r = refrigerant.specific_heat_capacity;
 
    return {{// pipe i1, Eq. 19
             {0, 0, -rho_r * Cp_r * _flow_velocity},
             // pipe o1, Eq. 20
             {0, 0, rho_r * Cp_r * _flow_velocity},
             // grout g1, Eq. 21
             {0, 0, 0},
             // grout g2, Eq. 22
             {0, 0, 0}}};
}

References ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_flow_velocity, ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::density, ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant, and ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::specific_heat_capacity.

pipeHeatCapacities()

std::array< double, BHE_1U::number_of_unknowns > ProcessLib::HeatTransportBHE::BHE::BHE_1U::pipeHeatCapacities

(

)

const

Definition at line 46 of file BHE_1U.cpp.

{
    double const rho_r = refrigerant.density;
    double const specific_heat_capacity = refrigerant.specific_heat_capacity;
    double const rho_g = grout.rho_g;
    double const porosity_g = grout.porosity_g;
    double const heat_cap_g = grout.heat_cap_g;
 
    return {{/*i1*/ rho_r * specific_heat_capacity,
             /*o1*/ rho_r * specific_heat_capacity,
             /*g1*/ (1.0 - porosity_g) * rho_g * heat_cap_g,
             /*g2*/ (1.0 - porosity_g) * rho_g * heat_cap_g}};
}

References ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::density, ProcessLib::HeatTransportBHE::BHE::BHECommon::grout, ProcessLib::HeatTransportBHE::BHE::GroutParameters::heat_cap_g, ProcessLib::HeatTransportBHE::BHE::GroutParameters::porosity_g, ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant, ProcessLib::HeatTransportBHE::BHE::GroutParameters::rho_g, and ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::specific_heat_capacity.

pipeHeatConductions()

std::array< double, BHE_1U::number_of_unknowns > ProcessLib::HeatTransportBHE::BHE::BHE_1U::pipeHeatConductions

(

)

const

Definition at line 61 of file BHE_1U.cpp.

{
    double const lambda_r = refrigerant.thermal_conductivity;
    double const rho_r = refrigerant.density;
    double const Cp_r = refrigerant.specific_heat_capacity;
    double const alpha_L = _pipes.longitudinal_dispersion_length;
    double const porosity_g = grout.porosity_g;
    double const lambda_g = grout.lambda_g;
 
    double const velocity_norm = std::abs(_flow_velocity);
 
    // Here we calculate the laplace coefficients in the governing
    // equations of BHE. These governing equations can be found in
    // 1) Diersch (2013) FEFLOW book on page 952, M.120-122, or
    // 2) Diersch (2011) Comp & Geosci 37:1122-1135, Eq. 19-22.
    return {{// pipe i1, Eq. 19
             (lambda_r + rho_r * Cp_r * alpha_L * velocity_norm),
             // pipe o1, Eq. 20
             (lambda_r + rho_r * Cp_r * alpha_L * velocity_norm),
             // pipe g1, Eq. 21
             (1.0 - porosity_g) * lambda_g,
             // pipe g2, Eq. 22
             (1.0 - porosity_g) * lambda_g}};
}

References ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_flow_velocity, ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_pipes, ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::density, ProcessLib::HeatTransportBHE::BHE::BHECommon::grout, ProcessLib::HeatTransportBHE::BHE::GroutParameters::lambda_g, ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::longitudinal_dispersion_length, ProcessLib::HeatTransportBHE::BHE::GroutParameters::porosity_g, ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant, ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::specific_heat_capacity, and ProcessLib::HeatTransportBHE::BHE::RefrigerantProperties::thermal_conductivity.

thermalResistance()

double ProcessLib::HeatTransportBHE::BHE::BHE_1U::thermalResistance ( int const unknown_index ) const

inline

Definition at line 133 of file BHE_1U.h.

    {
        return _thermal_resistances[unknown_index];
    }

References _thermal_resistances.

updateFlowRateAndTemperature()

double ProcessLib::HeatTransportBHE::BHE::BHE_1U::updateFlowRateAndTemperature	(	double	T_out,
		double	current_time )

Return the inflow temperature for the boundary condition.

Definition at line 262 of file BHE_1U.cpp.

{
    auto values =
        visit([&](auto const& control) { return control(T_out, current_time); },
              flowAndTemperatureControl);
    updateHeatTransferCoefficients(values.flow_rate);
    return values.temperature;
}

References ProcessLib::HeatTransportBHE::BHE::BHECommon::flowAndTemperatureControl, and updateHeatTransferCoefficients().

updateHeatTransferCoefficients()

void ProcessLib::HeatTransportBHE::BHE::BHE_1U::updateHeatTransferCoefficients

(

double const

flow_rate

)

Definition at line 161 of file BHE_1U.cpp.

{
    auto const tm_flow_properties = calculateThermoMechanicalFlowPropertiesPipe(
        _pipes.inlet, borehole_geometry.length, refrigerant, flow_rate);
 
    _flow_velocity = tm_flow_properties.velocity;
    _thermal_resistances =
        calcThermalResistances(tm_flow_properties.nusselt_number);
}

References ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_flow_velocity, ProcessLib::HeatTransportBHE::BHE::BHECommonUType::_pipes, _thermal_resistances, ProcessLib::HeatTransportBHE::BHE::BHECommon::borehole_geometry, calcThermalResistances(), ProcessLib::HeatTransportBHE::BHE::calculateThermoMechanicalFlowPropertiesPipe(), ProcessLib::HeatTransportBHE::BHE::PipeConfigurationUType::inlet, ProcessLib::HeatTransportBHE::BHE::BoreholeGeometry::length, and ProcessLib::HeatTransportBHE::BHE::BHECommon::refrigerant.

Referenced by BHE_1U(), and updateFlowRateAndTemperature().

Member Data Documentation

_thermal_resistances

std::array<double, number_of_unknowns> ProcessLib::HeatTransportBHE::BHE::BHE_1U::_thermal_resistances

private

PHI_fig, PHI_fog, PHI_gg, PHI_gs; Here we store the thermal resistances needed for computation of the heat exchange coefficients in the governing equations of BHE. These governing equations can be found in 1) Diersch (2013) FEFLOW book on page 958, M.3, or 2) Diersch (2011) Comp & Geosci 37:1122-1135, Eq. 90-97.

Definition at line 168 of file BHE_1U.h.

Referenced by BHE_1U(), thermalResistance(), and updateHeatTransferCoefficients().

inflow_outflow_bc_component_ids

std::pair<int, int> ProcessLib::HeatTransportBHE::BHE::BHE_1U::inflow_outflow_bc_component_ids[]

staticconstexpr

Initial value:

= {
        {0, 1}}

Definition at line 138 of file BHE_1U.h.

                                                                           {
        {0, 1}};

number_of_grout_zones

int ProcessLib::HeatTransportBHE::BHE::BHE_1U::number_of_grout_zones = 2

staticconstexpr

Definition at line 52 of file BHE_1U.h.

number_of_unknowns

int ProcessLib::HeatTransportBHE::BHE::BHE_1U::number_of_unknowns = 4

staticconstexpr

Definition at line 51 of file BHE_1U.h.

---

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

• ProcessLib/HeatTransportBHE/BHE/BHE_1U.h
• ProcessLib/HeatTransportBHE/BHE/BHE_1U.cpp