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Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses

Base classes for Borehole

Information

This package contains base classes that are used to construct the models in Buildings.Fluid.HeatExchangers.Boreholes.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

NameDescription
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeSegment BoreholeSegment Vertical segment of a borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement HexInternalElement Internal part of a borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeResistance BoreholeResistance Thermal resistance of the borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.InterferenceResistance InterferenceResistance Total interference resistance between the two pipes of a borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance PartialBoreholeResistance Partial model for thermal resistance of the borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.SingleUTubeBoundaryCondition SingleUTubeBoundaryCondition Prescribed temperature at the outer boundary of a single U tube borehole
ExtendableArray class used to create the external object: ExtendableArray
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeInternalResistance boreholeInternalResistance Calculate the internal resistance of the borehole
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance boreholeThermalResistance Calculate the total thermal resistance of the borehole from the fluid to the soil
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues exchangeValues Store the value u at the element n in the external object, and return the value of the element i
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.factorial factorial Calculates the factorial value of the input
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.powerSeries powerSeries Power series used to compute far-field temperature
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.temperatureDrop temperatureDrop Calculate the temperature drop of the soil at the external boundary of the cylinder
Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.Examples Examples Example models to test base classes


Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeSegment Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeSegment

Vertical segment of a borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeSegment

Information

Horizontal layer that is used to model a U-tube borehole heat exchanger. This model combines three models, each simulating a different aspect of a borehole heat exchanger.

The instance pipFil computes the heat transfer in the pipes and the filling material. This computation is done using the model Buildings.Fluid.Boreholes.BaseClasses.HexInternalElement.

The instance soi computes transient and steady state heat transfer in the soil using a vertical cylinder. The computation is done using the model Buildings.HeatTransfer.Conduction.SingleLayerCylinder.

The model TBouCon computes the far-field temperature boundary condition, i.e., the temperature at the outer surface of the above cylindrical heat transfer computation. The computation is done using the model Buildings.Fluid.Boreholes.BaseClasses.TemperatureBoundaryCondition.

Extends from Buildings.Fluid.Interfaces.PartialFourPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters (Parameters for flow resistance for models with two ports), Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes).

Parameters

TypeNameDefaultDescription
replaceable package Medium1PartialMediumMedium 1 in the component
replaceable package Medium2PartialMediumMedium 2 in the component
replaceable package MediumPartialMediumMedium in the component
RadiusrBor0.1Radius of the borehole [m]
HeighthSeg Height of the element [m]
LengthxC0.05Shank spacing, defined as the distance between the center of a pipe and the center of the borehole [m]
RealB017.44Shape coefficient for grout resistance
RealB1-0.6052Shape coefficient for grout resistance
Nominal condition
MassFlowRatem1_flow_nominalm_flow_nominalNominal mass flow rate [kg/s]
MassFlowRatem2_flow_nominalm_flow_nominalNominal mass flow rate [kg/s]
Pressuredp_nominal Pressure [Pa]
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Initialization
MassFlowRatem1_flow.start0Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressuredp1.start0Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRatem2_flow.start0Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressuredp2.start0Pressure difference between port_a2 and port_b2 [Pa]
Soil
GenericmatSoiredeclare parameter Building...Thermal properties of soil
RadiusrExt3Radius of the soil used for the external boundary condition [m]
TemperatureTExt_start283.15Initial far field temperature [K]
IntegernSta10Number of state variables in the soil
TimesamplePeriod604800Sample period for the external boundary condition [s]
Filling material
GenericmatFilredeclare parameter Building...Thermal properties of the filling material
TemperatureTFil_start283.15Initial temperature of the filling material [K]
Tubes
RadiusrTub0.02Radius of the tubes [m]
ThermalConductivitykTub0.5Thermal conductivity of the tubes [W/(m.K)]
LengtheTub0.002Thickness of the tubes [m]
Assumptions
BooleanallowFlowReversal1allowFlowReversal= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
BooleanallowFlowReversal2allowFlowReversal= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
BooleanallowFlowReversaltrue= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
Initialization
SpecificEnthalpyh_outflow_a1_startMedium1.h_defaultStart value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpyh_outflow_b1_startMedium1.h_defaultStart value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpyh_outflow_a2_startMedium2.h_defaultStart value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpyh_outflow_b2_startMedium2.h_defaultStart value for enthalpy flowing out of port b2 [J/kg]
MassFlowRatem1_flow_smallm_flow_smallSmall mass flow rate for regularization of zero flow [kg/s]
MassFlowRatem2_flow_smallm_flow_smallSmall mass flow rate for regularization of zero flow [kg/s]
BooleanhomotopyInitializationtrue= true, use homotopy method
MassFlowRatem_flow_small1E-4*abs(m_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
Diagnostics
Booleanshow_V_flowfalse= true, if volume flow rate at inflowing port is computed
Booleanshow_Tfalse= true, if actual temperature at port is computed (may lead to events)
Flow resistance
BooleancomputeFlowResistancetrue=true, compute flow resistance. Set to false to assume no friction
Booleanfrom_dpfalse= true, use m_flow = f(dp) else dp = f(m_flow)
BooleanlinearizeFlowResistancefalse= true, use linear relation between m_flow and dp for any flow rate
RealdeltaM0.1Fraction of nominal flow rate where flow transitions to laminar
Dynamics
Equations
DynamicsenergyDynamicsModelica.Fluid.Types.Dynamic...Formulation of energy balance
DynamicsmassDynamicsenergyDynamicsFormulation of mass balance
Initialization
AbsolutePressurep_startMedium.p_defaultStart value of pressure [Pa]
TemperatureT_startTFil_startStart value of temperature [K]
MassFractionX_start[Medium.nX]Medium.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC_start[Medium.nC]fill(0, Medium.nC)Start value of trace substances
ExtraPropertyC_nominal[Medium.nC]fill(1E-2, Medium.nC)Nominal value of trace substances. (Set to typical order of magnitude.)

Connectors

TypeNameDescription
replaceable package Medium1Medium 1 in the component
replaceable package Medium2Medium 2 in the component
FluidPort_aport_a1Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_bport_b1Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_aport_a2Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_bport_b2Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
replaceable package MediumMedium in the component

Modelica definition

model BoreholeSegment "Vertical segment of a borehole"
  extends Buildings.Fluid.Interfaces.PartialFourPortInterface(
     redeclare final package Medium1 = Medium,
     redeclare final package Medium2 = Medium,
     final m1_flow_nominal = m_flow_nominal,
     final m2_flow_nominal = m_flow_nominal,
     final m1_flow_small =   m_flow_small,
     final m2_flow_small =   m_flow_small,
     final allowFlowReversal1=allowFlowReversal,
     final allowFlowReversal2=allowFlowReversal);
  extends Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters;
  extends Buildings.Fluid.Interfaces.LumpedVolumeDeclarations(T_start=TFil_start);
  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium 
    "Medium in the component";
  replaceable parameter Buildings.HeatTransfer.Data.Soil.Generic
                                             matSoi 
    "Thermal properties of soil";
  replaceable parameter Buildings.HeatTransfer.Data.BoreholeFillings.Generic matFil 
    "Thermal properties of the filling material";

  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Nominal mass flow rate";
  parameter Modelica.SIunits.MassFlowRate m_flow_small(min=0) = 1E-4*abs(m_flow_nominal) 
    "Small mass flow rate for regularization of zero flow";
  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

  parameter Modelica.SIunits.Radius rTub=0.02 "Radius of the tubes";
  parameter Modelica.SIunits.ThermalConductivity kTub=0.5 
    "Thermal conductivity of the tubes";
  parameter Modelica.SIunits.Length eTub=0.002 "Thickness of the tubes";
  parameter Modelica.SIunits.Temperature TFil_start=283.15 
    "Initial temperature of the filling material";
  parameter Modelica.SIunits.Radius rExt=3 
    "Radius of the soil used for the external boundary condition";
  parameter Modelica.SIunits.Temperature TExt_start=283.15 
    "Initial far field temperature";
  parameter Integer nSta(min=1) = 10 "Number of state variables in the soil";
  parameter Modelica.SIunits.Time samplePeriod=604800 
    "Sample period for the external boundary condition";
  parameter Modelica.SIunits.Radius rBor=0.1 "Radius of the borehole";
  parameter Modelica.SIunits.Height hSeg "Height of the element";
  parameter Modelica.SIunits.Length xC=0.05 
    "Shank spacing, defined as the distance between the center of a pipe and the center of the borehole";
  parameter Real B0=17.44 "Shape coefficient for grout resistance";
  parameter Real B1=-0.6052 "Shape coefficient for grout resistance";

 parameter Boolean allowFlowReversal = true 
    "= true to allow flow reversal, false restricts to design direction (port_a -> port_b)";

 Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement pipFil(
    redeclare final package Medium = Medium,
    final matFil=matFil,
    final hSeg=hSeg,
    final rTub=rTub,
    final eTub=eTub,
    final kTub=kTub,
    final kSoi=matSoi.k,
    final xC=xC,
    final rBor=rBor,
    final TFil_start=TFil_start,
    final B0=B0,
    final B1=B1,
    final m1_flow_nominal=m_flow_nominal,
    final m2_flow_nominal=m_flow_nominal,
    final dp1_nominal=dp_nominal,
    final dp2_nominal=0,
    final from_dp1=from_dp,
    final from_dp2=from_dp,
    final linearizeFlowResistance1=linearizeFlowResistance,
    final linearizeFlowResistance2=linearizeFlowResistance,
    final deltaM1=deltaM,
    final deltaM2=deltaM,
    final m1_flow_small=m_flow_small,
    final m2_flow_small=m_flow_small,
    final allowFlowReversal1=allowFlowReversal,
    final allowFlowReversal2=allowFlowReversal,
    final homotopyInitialization=homotopyInitialization,
    final show_V_flow=show_V_flow,
    final energyDynamics=energyDynamics,
    final massDynamics=massDynamics,
    final p1_start=p_start,
    T1_start=T_start,
    X1_start=X_start,
    C1_start=C_start,
    C1_nominal=C_nominal,
    final p2_start=p_start,
    T2_start=T_start,
    X2_start=X_start,
    C2_start=C_start,
    C2_nominal=C_nominal) 
    "Internal part of the borehole including the pipes and the filling material";
  Buildings.HeatTransfer.Conduction.SingleLayerCylinder soi(
    final material=matSoi,
    final h=hSeg,
    final nSta=nSta,
    final r_a=rBor,
    final r_b=rExt,
    final steadyStateInitial=false,
    final TInt_start=TFil_start,
    final TExt_start=TExt_start) "Heat conduction in the soil";
  Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.SingleUTubeBoundaryCondition
    TBouCon(
    final matSoi=matSoi,
    final rExt=rExt,
    final hSeg=hSeg,
    final TExt_start=TExt_start,
    final samplePeriod=samplePeriod) 
    "Thermal boundary condition for the far-field";
protected 
  Modelica.Thermal.HeatTransfer.Sensors.HeatFlowSensor heaFlo;
equation 
  connect(pipFil.port_b1, port_b1);
  connect(pipFil.port_a2, port_a2);
  connect(pipFil.port_b2, port_b2);
  connect(pipFil.port, heaFlo.port_a);
  connect(heaFlo.port_b, soi.port_a);
  connect(soi.port_b, TBouCon.port);
  connect(port_a1, pipFil.port_a1);
  connect(heaFlo.Q_flow, TBouCon.Q_flow);
end BoreholeSegment;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement

Internal part of a borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement

Information

Model for the heat transfer between the fluid and within the borehole filling. This model computes the dynamic response of the fluid in the tubes, and the heat transfer between the fluid and the borehole filling, and the heat storage within the fluid and the borehole filling.

The heat conduction in the filling material is modeled using three three resistances model that are arranged in a triangular configuration. Two of these resistances represent the heat conduction from the fluids to the external radius of the borehole, and the other resistance represents the thermal interference between the two pipes.

The resistance between the fluid and the borehole wall are the sum of the convective resistance inside the tubes, the conductive resistance of the tube wall and the conductive resistance of the filling material. They are obtained using

GCon = 2 π hseg rtub hin ,

Gtub = 4 π ktub hseg ⁄ ln( ( rtub+etub ) ⁄ rtub ),

Gfil= kfil hseg β0 ( rBor ⁄ rtub ) β1 ,

where hseg is the height of the tube, hin is the convection coefficient, ktub is the thermal conductivity of the tube, etub is the thickness of the tube, and β0, β1 are the resistance shape factor coefficients (Paul, 1996). Paul's shape factors are based on experimental and finite element analysis of typical borehole. The default values used for these coefficients are β0= 20.100 and β1=-0.94467. Values listed by Paul are given in the table below.

pipe spacingβ0β1
close 20.100377 -0.94467
middle 17.44 -0.6052
spaced 21.91 -0.3796

Implementation

The resistances between the fluid and the borehole wall are computed in Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeResistance. The resistance for the interference of the pipes is computed in Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.InterferenceResistance.

Extends from Buildings.Fluid.Interfaces.FourPortHeatMassExchanger (Model transporting two fluid streams between four ports with storing mass or energy).

Parameters

TypeNameDefaultDescription
replaceable package Medium1PartialMediumMedium 1 in the component
replaceable package Medium2PartialMediumMedium 2 in the component
replaceable package MediumModelica.Media.Interfaces.Pa...Medium in the component
ThermalConductivitykSoi Thermal conductivity of the soil used for the calculation of the internal interference resistance [W/(m.K)]
RadiusrBor Radius of the borehole [m]
HeighthSeg Height of the element [m]
RealB017.44268Shape coefficient for grout resistance
RealB1-0.60515Shape coefficient for grout resistance
LengthxC0.05Shank spacing definied as half the center-to-center distance between the two pipes [m]
Nominal condition
MassFlowRatem1_flow_nominal Nominal mass flow rate [kg/s]
MassFlowRatem2_flow_nominal Nominal mass flow rate [kg/s]
Pressuredp1_nominal Pressure [Pa]
Pressuredp2_nominal Pressure [Pa]
Initialization
MassFlowRatem1_flow.start0Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressuredp1.start0Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRatem2_flow.start0Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressuredp2.start0Pressure difference between port_a2 and port_b2 [Pa]
Filling material
GenericmatFilredeclare parameter Building...Thermal properties of the filling material
TemperatureTFil_start283.15Initial temperature of the filling material [K]
Pipes
RadiusrTub0.02Radius of the tubes [m]
ThermalConductivitykTub0.5Thermal conductivity of the tubes [W/(m.K)]
LengtheTub0.002Thickness of the tubes [m]
Assumptions
BooleanallowFlowReversal1system.allowFlowReversal= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
BooleanallowFlowReversal2system.allowFlowReversal= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRatem1_flow_small1E-4*abs(m1_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRatem2_flow_small1E-4*abs(m2_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
BooleanhomotopyInitializationtrue= true, use homotopy method
Diagnostics
Booleanshow_V_flowfalse= true, if volume flow rate at inflowing port is computed
Booleanshow_Tfalse= true, if actual temperature at port is computed (may lead to events)
Flow resistance
Medium 1
Booleanfrom_dp1false= true, use m_flow = f(dp) else dp = f(m_flow)
BooleanlinearizeFlowResistance1false= true, use linear relation between m_flow and dp for any flow rate
RealdeltaM10.1Fraction of nominal flow rate where flow transitions to laminar
Medium 2
Booleanfrom_dp2false= true, use m_flow = f(dp) else dp = f(m_flow)
BooleanlinearizeFlowResistance2false= true, use linear relation between m_flow and dp for any flow rate
RealdeltaM20.1Fraction of nominal flow rate where flow transitions to laminar
Dynamics
Nominal condition
Timetau1Modelica.Constants.pi*rTub^2...Time constant at nominal flow [s]
Timetau2Modelica.Constants.pi*rTub^2...Time constant at nominal flow [s]
Equations
DynamicsenergyDynamicsModelica.Fluid.Types.Dynamic...Formulation of energy balance
DynamicsmassDynamicsenergyDynamicsFormulation of mass balance
Initialization
Medium 1
AbsolutePressurep1_startMedium1.p_defaultStart value of pressure [Pa]
TemperatureT1_startTFil_startStart value of temperature [K]
MassFractionX1_start[Medium1.nX]Medium1.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC1_start[Medium1.nC]fill(0, Medium1.nC)Start value of trace substances
ExtraPropertyC1_nominal[Medium1.nC]fill(1E-2, Medium1.nC)Nominal value of trace substances. (Set to typical order of magnitude.)
Medium 2
AbsolutePressurep2_startMedium2.p_defaultStart value of pressure [Pa]
TemperatureT2_startTFil_startStart value of temperature [K]
MassFractionX2_start[Medium2.nX]Medium2.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC2_start[Medium2.nC]fill(0, Medium2.nC)Start value of trace substances
ExtraPropertyC2_nominal[Medium2.nC]fill(1E-2, Medium2.nC)Nominal value of trace substances. (Set to typical order of magnitude.)

Connectors

TypeNameDescription
replaceable package Medium1Medium 1 in the component
replaceable package Medium2Medium 2 in the component
FluidPort_aport_a1Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_bport_b1Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_aport_a2Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_bport_b2Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
replaceable package MediumMedium in the component
HeatPort_aportHeat port that connects to filling material

Modelica definition

model HexInternalElement "Internal part of a borehole"
  extends Buildings.Fluid.Interfaces.FourPortHeatMassExchanger(
    redeclare final package Medium1 = Medium,
    redeclare final package Medium2 = Medium,
    T1_start=TFil_start,
    T2_start=TFil_start,
    final tau1=Modelica.Constants.pi*rTub^2*hSeg*rho1_nominal/m1_flow_nominal,
    final tau2=Modelica.Constants.pi*rTub^2*hSeg*rho2_nominal/m2_flow_nominal,
    final show_T=false,
    vol1(final energyDynamics=energyDynamics,
         final massDynamics=massDynamics,
         final prescribedHeatFlowRate=false,
         final homotopyInitialization=homotopyInitialization,
         final allowFlowReversal=allowFlowReversal1,
         final V=m2_flow_nominal*tau2/rho2_nominal,
         final m_flow_small=m1_flow_small),
    final vol2(final energyDynamics=energyDynamics,
         final massDynamics=massDynamics,
         final prescribedHeatFlowRate=false,
         final homotopyInitialization=homotopyInitialization,
         final V=m1_flow_nominal*tau1/rho1_nominal,
         final m_flow_small=m2_flow_small));

  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium 
    "Medium in the component";

  replaceable parameter Buildings.HeatTransfer.Data.BoreholeFillings.Generic matFil 
    "Thermal properties of the filling material";

  parameter Modelica.SIunits.Radius rTub=0.02 "Radius of the tubes";
  parameter Modelica.SIunits.ThermalConductivity kTub=0.5 
    "Thermal conductivity of the tubes";
  parameter Modelica.SIunits.Length eTub=0.002 "Thickness of the tubes";
  parameter Modelica.SIunits.ThermalConductivity kSoi 
    "Thermal conductivity of the soil used for the calculation of the internal interference resistance";

  parameter Modelica.SIunits.Temperature TFil_start=283.15 
    "Initial temperature of the filling material";

  parameter Modelica.SIunits.Radius rBor "Radius of the borehole";
  parameter Modelica.SIunits.Height hSeg "Height of the element";

  parameter Real B0=17.44268 "Shape coefficient for grout resistance";
  parameter Real B1=-0.60515 "Shape coefficient for grout resistance";

  parameter Modelica.SIunits.Length xC=0.05 
    "Shank spacing definied as half the center-to-center distance between the two pipes";

  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a port 
    "Heat port that connects to filling material";
protected 
  final parameter Modelica.SIunits.SpecificHeatCapacity cpFil=matFil.c 
    "Specific heat capacity of the filling material";
  final parameter Modelica.SIunits.ThermalConductivity kFil=matFil.k 
    "Thermal conductivity of the filling material";
  final parameter Modelica.SIunits.Density dFil=matFil.d 
    "Density of the filling material";
  parameter Modelica.SIunits.HeatCapacity Co_fil=0.5*dFil*cpFil*hSeg*Modelica.Constants.pi
      *(rBor^2 - 2*(rTub + eTub)^2) "Heat capacity of the filling material";
  Modelica.Thermal.HeatTransfer.Components.HeatCapacitor cap2(C=Co_fil, T(start=
         TFil_start)) "Heat capacity of the filling material";
  Modelica.Thermal.HeatTransfer.Components.HeatCapacitor cap1(C=Co_fil,T(start=
          TFil_start)) "Heat capacity of the filling material";
  BoreholeResistance con1(
    redeclare final package Medium = Medium,
    final rBor=rBor,
    final rTub=rTub,
    final eTub=eTub,
    final kTub=kTub,
    final kFil=kFil,
    final hSeg=hSeg,
    final B0=B0,
    final B1=B1,
    final m_flow_nominal=m1_flow_nominal,
    homotopyInitialization=homotopyInitialization) 
    "Thermal resistance from the fluid to the wall of the borehole";
  BoreholeResistance con2(
    redeclare final package Medium = Medium,
    final rBor=rBor,
    final rTub=rTub,
    final eTub=eTub,
    final kTub=kTub,
    final kFil=kFil,
    final hSeg=hSeg,
    final B0=B0,
    final B1=B1,
    final m_flow_nominal=m1_flow_nominal,
    homotopyInitialization=homotopyInitialization) 
    "Thermal resistance from the fluid to the wall of the borehole";

  InterferenceResistance con12(
    redeclare final package Medium = Medium,
    final rBor=rBor,
    final rTub=rTub,
    final eTub=eTub,
    final kTub=kTub,
    final kFil=kFil,
    final kSoi=kSoi,
    final hSeg=hSeg,
    final xC=xC,
    final B0=B0,
    final B1=B1,
    final m_flow_nominal=m1_flow_nominal,
    homotopyInitialization=homotopyInitialization) 
    "Interference resistance between the two pipes";

  Modelica.Blocks.Sources.RealExpression m_flow(y=port_a1.m_flow) 
    "Mass flow rate";
equation 
  connect(vol1.heatPort, cap1.port);
  connect(vol2.heatPort, cap2.port);
  connect(cap1.port, con12.port_a);
  connect(cap1.port, con1.port_a);
  connect(con12.port_b, cap2.port);
  connect(con2.port_a, cap2.port);
  connect(con1.port_b, port);
  connect(con2.port_b, port);
  connect(m_flow.y, con1.m_flow);
  connect(m_flow.y, con2.m_flow);
  connect(m_flow.y, con12.m_flow);
end HexInternalElement;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeResistance Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeResistance

Thermal resistance of the borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeResistance

Information

This model computes the total thermal resistance from the fluid to the borehole wall. This thermal resistance is then used for a three-resistance model. It assumes that the pipe configuration is symmetric. The resistance is obtain using

R = 2 Rb,

where Rb is the total borehole resistance as defined by Hellstrom (1991).

The resistance Rb includes three different thermal resistances:

  1. a convective resistance from the brine to the pipe wall,
  2. a thermal resistance of the pipe wall, and
  3. the thermal resistance of the filling material.

Implementation

The calculation of Rb is done using the function Buildings.Fluid.Boreholes.BaseClasses.boreholeThermalResistance.

References

Hellstrom, G (1991).
Thermal Performance of Borehole Heat Exchangers.
Department of Mathematical Physics, Lund Institute of Technology.

Extends from Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance (Partial model for thermal resistance of the borehole).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
RadiusrBor Radius of the borehole [m]
ThermalConductivitykFil [W/(m.K)]
HeighthSeg Height of the segment [m]
RealB017.44268Shape coefficient for grout resistance
RealB1-0.60515Shape coefficient for grout resistance
Pipes
RadiusrTub Radius of the tubes [m]
ThermalConductivitykTub4Thermal conductivity of the tubes [W/(m.K)]
LengtheTub0.002Thickness of the tubes [m]
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method

Connectors

TypeNameDescription
input RealInputm_flowMass flow rate [kg/s]
HeatPort_aport_a 
HeatPort_bport_b 

Modelica definition

model BoreholeResistance "Thermal resistance of the borehole"
  extends Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance;

equation 
  if homotopyInitialization then
    Rb = homotopy(actual=Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance(
          hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub, kFil=kFil,
          kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow, m_flow_nominal=m_flow_nominal,
          B0=B0, B1=B1),
                  simplified=  Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance(
          hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub, kFil=kFil,
          kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow_nominal, m_flow_nominal=m_flow_nominal,
          B0=B0, B1=B1));
  else
    Rb = Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance(
          hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub, kFil=kFil,
          kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow, m_flow_nominal=m_flow_nominal,
          B0=B0, B1=B1);
  end if;
  G = 1/(2*Rb);
end BoreholeResistance;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.InterferenceResistance Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.InterferenceResistance

Total interference resistance between the two pipes of a borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.InterferenceResistance

Information

This model computes the interference resistance between the two pipes of a U-tube borehole. It computes the resistance using the internal resistance Ra and the borehole total resistance Rb.

The coupling resistance is obtained using

Ri = 4 Rb Ra ⁄ (4 Rb- Ra).

Implementation

The two resistances are calculated by the functions Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance for Rb and Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeInternalResistance for Ra.

Extends from Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance (Partial model for thermal resistance of the borehole).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
RadiusrBor Radius of the borehole [m]
ThermalConductivitykFil [W/(m.K)]
HeighthSeg Height of the segment [m]
RealB017.44268Shape coefficient for grout resistance
RealB1-0.60515Shape coefficient for grout resistance
LengthxC Shank spacing definied as half the center-to-center distance between the two pipes [m]
ThermalConductivitykSoi Thermal conductivity of the soil used for the calculation of the internal interference resistance [W/(m.K)]
Pipes
RadiusrTub Radius of the tubes [m]
ThermalConductivitykTub4Thermal conductivity of the tubes [W/(m.K)]
LengtheTub0.002Thickness of the tubes [m]
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method

Connectors

TypeNameDescription
input RealInputm_flowMass flow rate [kg/s]
HeatPort_aport_a 
HeatPort_bport_b 

Modelica definition

model InterferenceResistance 
  "Total interference resistance between the two pipes of a borehole"
  extends Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance;

  parameter Modelica.SIunits.Length xC 
    "Shank spacing definied as half the center-to-center distance between the two pipes";

  parameter Modelica.SIunits.ThermalConductivity kSoi 
    "Thermal conductivity of the soil used for the calculation of the internal interference resistance";

protected 
  parameter Modelica.SIunits.ThermalResistance Ra=boreholeInternalResistance(
      hSeg=hSeg,
      rBor=rBor,
      rTub=rTub,
      eTub=eTub,
      xC=xC,
      kFil=kFil,
      kSoi=kSoi) "Borehole internal resistance";

equation 
  if homotopyInitialization then
    Rb = homotopy(actual=boreholeThermalResistance(
            hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub,
            kFil=kFil, kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow,
            m_flow_nominal=m_flow_nominal, B0=B0, B1=B1),
         simplified=boreholeThermalResistance(
            hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub,
            kFil=kFil, kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow_nominal,
            m_flow_nominal=m_flow_nominal, B0=B0, B1=B1));
  else
   Rb = boreholeThermalResistance(
    hSeg=hSeg, rBor=rBor, rTub=rTub, eTub=eTub, kTub=kTub,
    kFil=kFil, kMed=kMed, mueMed=mueMed, cpFluid=cpFluid, m_flow=m_flow,
    m_flow_nominal=m_flow_nominal, B0=B0, B1=B1);
  end if;
  G = (4*Rb - Ra)/(4*Rb*Ra);
end InterferenceResistance;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance

Partial model for thermal resistance of the borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.PartialBoreholeResistance

Information

Partial model for the thermal resistance of the borehole.

Parameters

TypeNameDefaultDescription
replaceable package MediumModelica.Media.Interfaces.Pa...Medium in the component
RadiusrBor Radius of the borehole [m]
ThermalConductivitykFil [W/(m.K)]
HeighthSeg Height of the segment [m]
RealB017.44268Shape coefficient for grout resistance
RealB1-0.60515Shape coefficient for grout resistance
Pipes
RadiusrTub Radius of the tubes [m]
ThermalConductivitykTub4Thermal conductivity of the tubes [W/(m.K)]
LengtheTub0.002Thickness of the tubes [m]
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method

Connectors

TypeNameDescription
replaceable package MediumMedium in the component
input RealInputm_flowMass flow rate [kg/s]
HeatPort_aport_a 
HeatPort_bport_b 

Modelica definition

partial model PartialBoreholeResistance 
  "Partial model for thermal resistance of the borehole"
  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium 
    "Medium in the component";
  parameter Modelica.SIunits.Radius rTub "Radius of the tubes";
  parameter Modelica.SIunits.ThermalConductivity kTub=4 
    "Thermal conductivity of the tubes";
  parameter Modelica.SIunits.Length eTub=0.002 "Thickness of the tubes";
  parameter Modelica.SIunits.Radius rBor "Radius of the borehole";
  parameter Modelica.SIunits.ThermalConductivity kFil;
  parameter Modelica.SIunits.Height hSeg "Height of the segment";
  parameter Real B0=17.44268 "Shape coefficient for grout resistance";
  parameter Real B1=-0.60515 "Shape coefficient for grout resistance";
  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Nominal mass flow rate";

  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

  Modelica.Blocks.Interfaces.RealInput m_flow(unit="kg/s") "Mass flow rate";

  Modelica.SIunits.ThermalConductance G "Thermal conductance";
  Modelica.SIunits.HeatFlowRate Q_flow "Heat flow rate from port_a to port_b";
  Modelica.SIunits.TemperatureDifference dT "= port_a.T - port_b.T";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a port_a;
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b port_b;

protected 
  parameter Modelica.SIunits.SpecificHeatCapacity cpFluid=
      Medium.specificHeatCapacityCp(Medium.setState_pTX(
      Medium.p_default,
      Medium.T_default,
      Medium.X_default)) "Specific heat capacity of the fluid";
  parameter Modelica.SIunits.ThermalConductivity kMed=
      Medium.thermalConductivity(Medium.setState_pTX(
      Medium.p_default,
      Medium.T_default,
      Medium.X_default)) "Thermal conductivity of the fluid";
  parameter Modelica.SIunits.DynamicViscosity mueMed=Medium.dynamicViscosity(
      Medium.setState_pTX(
      Medium.p_default,
      Medium.T_default,
      Medium.X_default)) "Dynamic viscosity of the fluid";
  Modelica.SIunits.ThermalResistance Rb "Borehole thermal resistance";
equation 
  dT = port_a.T - port_b.T;
  port_a.Q_flow = Q_flow;
  port_b.Q_flow = -Q_flow;
  Q_flow = G*dT;
end PartialBoreholeResistance;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.SingleUTubeBoundaryCondition Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.SingleUTubeBoundaryCondition

Prescribed temperature at the outer boundary of a single U tube borehole

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.SingleUTubeBoundaryCondition

Information

This model computes the temperature boundary condition at the outer boundary of the borehole. It takes as an input the heat flow rate at the center of the borehole. This heat flow rate is averaged over the sample period. At each sampling interval, typically every one week, a new temperature boundary conditions is computed using the analytical solution to a line source heat transfer problem.

Implementation

The computation of the temperature change of the boundary is computed using the function Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.temperatureDrop.

Parameters

TypeNameDefaultDescription
GenericmatSoiredeclare parameter Building...Thermal properties of the soil
RadiusrExt3Distance from the brine where the calculation is performed [m]
HeighthSeg10Height of the segment [m]
TemperatureTExt_start283.15Initial external temperature [K]
TimesamplePeriod604800Period between two samples [s]

Connectors

TypeNameDescription
input RealInputQ_flowHeat flow rate at the center of the borehole, positive if heat is added to soil [W]
HeatPort_bportHeat port

Modelica definition

model SingleUTubeBoundaryCondition 
  "Prescribed temperature at the outer boundary of a single U tube borehole"
  import Buildings;
  replaceable parameter Buildings.HeatTransfer.Data.Soil.Generic matSoi 
    "Thermal properties of the soil";
  parameter Modelica.SIunits.Radius rExt=3 
    "Distance from the brine where the calculation is performed";
  parameter Modelica.SIunits.Height hSeg=10 "Height of the segment";
  parameter Modelica.SIunits.Temperature TExt_start=283.15 
    "Initial external temperature";
  parameter Modelica.SIunits.Time samplePeriod=604800 
    "Period between two samples";
  ExtendableArray table=ExtendableArray() 
    "Extentable array, used to store history of rate of heat flows";
  Modelica.SIunits.HeatFlowRate QAve_flow 
    "Average heat flux over a time period";
  Modelica.Blocks.Interfaces.RealInput Q_flow(unit="W") 
    "Heat flow rate at the center of the borehole, positive if heat is added to soil";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b port "Heat port";
protected 
  Integer iSam(min=1) 
    "Counter for how many time the model was sampled. Defined as iSam=1 when called at t=0";
  final parameter Modelica.SIunits.SpecificHeatCapacity c= matSoi.c 
    "Specific heat capacity of the soil";
  final parameter Modelica.SIunits.ThermalConductivity k= matSoi.k 
    "Thermal conductivity of the soil";
  final parameter Modelica.SIunits.Density d = matSoi.d "Density of the soil";
  Modelica.SIunits.Energy UOld "Internal energy at the previous period";
  Modelica.SIunits.Energy U 
    "Current internal energy, defined as U=0 for t=tStart";
  Modelica.SIunits.Time startTime "Start time of the simulation";
initial algorithm 
  U    := 0;
  UOld := 0;
equation 
  der(U) = Q_flow;
algorithm 
  // Set the start time for the sampling
  when initial() then
    startTime:=time;
    iSam :=1;
  end when;

  when initial() or sample(startTime,samplePeriod) then
    QAve_flow := (U-UOld)/samplePeriod;
    UOld      := U;
    port.T    := TExt_start + Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.temperatureDrop(
                                 table=table, iSam=iSam,
                                 Q_flow=QAve_flow, samplePeriod=samplePeriod,
                                 rExt=rExt, hSeg=hSeg,
                                 k=k, d=d, c=c);
    iSam := iSam+1;
  end when;

end SingleUTubeBoundaryCondition;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.ExtendableArray

class used to create the external object: ExtendableArray

Information

Class derived from ExternalObject having two local external function definition, named destructor and constructor respectively.

These functions create and release an external object that allows the the storage of real parameters in an array of extendable dimension.

Extends from ExternalObject.

Modelica definition

class ExtendableArray 
  "class used to create the external object: ExtendableArray"
extends ExternalObject;
    function constructor 
    "Construct an extendable array that can be used to store double values"
    output ExtendableArray table;
    external "C" table = initArray();
    end constructor;

  function destructor 
    "Release storage of table and close the external object"
    input ExtendableArray  table;
    external "C" freeArray(table);
  end destructor;
end ExtendableArray;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeInternalResistance

Calculate the internal resistance of the borehole

Information

This model computes the internal resistance R of a single U-tube borehole, as defined by Hellstrom (1991), as

k = ( 2 P1 ( P22 + 1 ) W ) / ( P2 ( P22 - 1 )W ),

R = ln(k) / (π kfil hseg) ,

where P1 and P2 are two dimensionless geometrical factors and W is a conductivity ratio. The geometrical factors are defined as P1 = rbor/(rtub + etub), where rbor is the borehole radius and rtub + etub is the external radius of a pipe and P2 = rbor/ xc , where xc is the shank spacing defined as half the center-to-center distance between the two pipes, and W = kfil - ksoi/ (ksoi + kfil).

References

Hellstrom, G (1991).
Thermal Performance of Borehole Heat Exchangers.
Department of Mathematical Physics, Lund Institute of Technology.

Inputs

TypeNameDefaultDescription
HeighthSeg Height of the element [m]
RadiusrBor Radius of the borehole [m]
RadiusrTub Radius of the tube [m]
LengtheTub Thickness of the tubes [m]
LengthxC Shank spacing, defined as half the center-to-center distance between the two pipes [m]
ThermalConductivitykFil Thermal conductivity of the filling material [W/(m.K)]
ThermalConductivitykSoi Thermal conductivity of the soil [W/(m.K)]

Outputs

TypeNameDescription
ThermalResistanceRInternal resistance of the borehole [K/W]

Modelica definition

function boreholeInternalResistance 
  "Calculate the internal resistance of the borehole"
  input Modelica.SIunits.Height hSeg "Height of the element";
  input Modelica.SIunits.Radius rBor "Radius of the borehole";
  input Modelica.SIunits.Radius rTub "Radius of the tube";
  input Modelica.SIunits.Length eTub "Thickness of the tubes";
  input Modelica.SIunits.Length xC 
    "Shank spacing, defined as half the center-to-center distance between the two pipes";
  input Modelica.SIunits.ThermalConductivity kFil 
    "Thermal conductivity of the filling material";
  input Modelica.SIunits.ThermalConductivity kSoi 
    "Thermal conductivity of the soil";
  output Modelica.SIunits.ThermalResistance R 
    "Internal resistance of the borehole";
protected 
  final parameter Real P1=rBor/(rTub + eTub) 
    "Non-dimensional geometrical parameter ";
  final parameter Real P2=rBor/xC "Non-dimensional geometrical parameter ";
  final parameter Real P3=(kFil - kSoi)/(kFil + kSoi) 
    "Non-dimensional parameter for filling and soil conductivity";
algorithm 
  assert(xC > (rTub + eTub) and xC < rBor - (rTub + eTub),
  "Parameters do not correspond to physically possible location of borehole tube.
    xC   = " + String(xC) + "
    rTub = " + String(rTub) + "
    eTub = " + String(eTub) + ".");
  R := Modelica.Math.log((2*P1*(P2^2 + 1)^P3)/(P2*(P2^2 - 1)^P3))/
           (Modelica.Constants.pi*kFil*hSeg);
end boreholeInternalResistance;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.boreholeThermalResistance

Calculate the total thermal resistance of the borehole from the fluid to the soil

Information

This model computes the borehole total thermal resistance for a single U-tube. The computation is as defined in Hellstom (1991). The total thermal resistance is the contribution of three different resistances as

Rtot= RCon + Rtub + Rfil.

where RCon is the convective resistance of the fluid, Rtub is the conductive resistance of the tube wall and Rfil is the resistance of the filling material.

The convective resistance is obtained as

RCon = 1 ⁄ (4 π hseg rtub hin ),

where hseg is the height of the segment and hin is the convective heat transfer coefficient. The convective heat transfer coefficient is determined using the Dittus-Boelter correlation,

hin= 0.023 kmed Pr0.35 Re0.8 ⁄ 2 rtub,

where kmed is the thermal conductivity of the fluid, Pr is the Prandtl number, Re is the Reynolds number and rtub is the inside radius of the pipe.

The conductive resistance is determined using

Rtub= ln[ ( rtub+etub ) ⁄ rtub ] ⁄ 4 π ktub hseg,

where ktub the heat conductivity of the pipe and etub is the thickness of the wall.

The resistance of the filling material is determined using the correlation from Paul (1996) :

Rfil = kfil hseg β0 (rBor ⁄ (rtub + etub)) β1 ,

where kfil is the thermal conductivity of the filling material and β0, β1 are the resistance shape factors (Paul 1996) based on U-tube shank spacing. Paul's shape factors are based on experimental and finite element analysis of typical borehole. The default values used for these coefficients are β0= 20.100 and β1=-0.94467. Values listed by Paul are given in the table below.

pipe spacingβ0β1
close 20.100377 -0.94467
middle 17.44 -0.6052
spaced 21.91 -0.3796

References

Hellstrom, G (1991).
Thermal Performance of Borehole Heat Exchangers.
Department of Mathematical Physics, Lund Institute of Technology.

Paul, N.D (1996). The effect of grout thermal conductivity on vertical geothermal heat exchanger design and performance. Master of Science Thesis, South Dakota State University.

Inputs

TypeNameDefaultDescription
HeighthSeg Height of the element [m]
RadiusrBor Radius of the borehole [m]
RadiusrTub Radius of the tube [m]
LengtheTub Thickness of the tubes [m]
ThermalConductivitykTub Thermal conductivity of the tubes [W/(m.K)]
ThermalConductivitykFil Thermal conductivity of the filling material [W/(m.K)]
ThermalConductivitykMed Thermal conductivity of the fluid [W/(m.K)]
DynamicViscositymueMed Dynamic viscosity of the fluid [Pa.s]
SpecificHeatCapacitycpFluid Specific heat capacity of the fluid [J/(kg.K)]
MassFlowRatem_flow Mass flow rate of the fluid [kg/s]
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
RealB0 Shape coefficient for grout resistance
RealB1 Shape coefficient for grout resistance

Outputs

TypeNameDescription
ThermalResistanceRbBorehole thermal resistance [K/W]

Modelica definition

function boreholeThermalResistance 
  "Calculate the total thermal resistance of the borehole from the fluid to the soil"
  input Modelica.SIunits.Height hSeg "Height of the element";
  input Modelica.SIunits.Radius rBor "Radius of the borehole";
  input Modelica.SIunits.Radius rTub "Radius of the tube";
  input Modelica.SIunits.Length eTub "Thickness of the tubes";
  input Modelica.SIunits.ThermalConductivity kTub 
    "Thermal conductivity of the tubes";
  input Modelica.SIunits.ThermalConductivity kFil 
    "Thermal conductivity of the filling material";
  input Modelica.SIunits.ThermalConductivity kMed 
    "Thermal conductivity of the fluid";
  input Modelica.SIunits.DynamicViscosity mueMed 
    "Dynamic viscosity of the fluid";
  input Modelica.SIunits.SpecificHeatCapacity cpFluid 
    "Specific heat capacity of the fluid";
  input Modelica.SIunits.MassFlowRate m_flow "Mass flow rate of the fluid";
  input Modelica.SIunits.MassFlowRate m_flow_nominal "Nominal mass flow rate";
  input Real B0 "Shape coefficient for grout resistance";
  input Real B1 "Shape coefficient for grout resistance";
  output Modelica.SIunits.ThermalResistance Rb "Borehole thermal resistance";
protected 
  Modelica.SIunits.CoefficientOfHeatTransfer h 
    "Convective heat transfer coefficient of the fluid";
  Modelica.SIunits.ThermalResistance RCon 
    "Convective thermal resistance of the fluid";
  Modelica.SIunits.ThermalResistance RTub 
    "Thermal resistance of the pipe's wall";
  Modelica.SIunits.ThermalResistance RFil 
    "Thermal resistance of the filling material";
  Real k(unit="s/kg") 
    "Coefficient used in the computation of the convective heat transfer coefficient";
algorithm 
  k :=2/(mueMed*Modelica.Constants.pi*rTub);
  h := 0.023*kMed*(cpFluid*mueMed/kMed)^(0.35)/(2*rTub) *
    Buildings.Utilities.Math.Functions.regNonZeroPower(
    x=m_flow*k, n=0.8,
    delta=0.01*m_flow_nominal*k);
  RCon := 1/(4*Modelica.Constants.pi*rTub*hSeg*h);
  RTub := Modelica.Math.log((rTub + eTub)/rTub)/(4*Modelica.Constants.pi*hSeg*kTub);
  RFil := 1/(hSeg*kFil*B0*(rBor/(rTub + eTub))^B1);
  Rb := RCon + RTub + RFil;
end boreholeThermalResistance;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues

Store the value u at the element n in the external object, and return the value of the element i

Information

External function that stores the input value x as the element a[iX] in the array a = [a[1], a[2], ...], and that returns the element a[iY]. The size of the array a is automatically enlarged as needed.

Inputs

TypeNameDefaultDescription
ExtendableArraytable External object
IntegeriX One-based index where u needs to be stored in the array of the external object
Realx Value to store in the external object
IntegeriY One-based index of the element that needs to be returned from C to Modelica

Outputs

TypeNameDescription
RealyValue of the i-th element

Modelica definition

function exchangeValues 
  "Store the value u at the element n in the external object, and return the value of the element i"
  input ExtendableArray table "External object";
  input Integer iX 
    "One-based index where u needs to be stored in the array of the external object";
  input Real x "Value to store in the external object";
  input Integer iY 
    "One-based index of the element that needs to be returned from C to Modelica";
  output Real y "Value of the i-th element";
external"C" y = exchangeValues(table, iX, x, iY);
end exchangeValues;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.factorial

Calculates the factorial value of the input

Information

This function computes y = j!.

Inputs

TypeNameDefaultDescription
Integerj  

Outputs

TypeNameDescription
Integerf 

Modelica definition

function factorial "Calculates the factorial value of the input"
  input Integer j;
  output Integer f;
algorithm 
  f := 1;
  for i in 1:j loop
    f := f*i;
  end for;
end factorial;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.powerSeries

Power series used to compute far-field temperature

Information

This function computes the power series that is used to compute the far-field temperature.

Inputs

TypeNameDefaultDescription
Realu u
IntegerN Number of coefficients

Outputs

TypeNameDescription
RealWPower series

Modelica definition

function powerSeries 
  "Power series used to compute far-field temperature"
  input Real u "u";
  input Integer N "Number of coefficients";
  output Real W "Power series";
algorithm 
  W := -0.5772 - Modelica.Math.log(u) + sum((-1)^(j + 1)*u^j/(j*factorial(j))
    for j in 1:N);
end powerSeries;

Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.temperatureDrop

Calculate the temperature drop of the soil at the external boundary of the cylinder

Information

This function calculates the temperature drop of the soil at the outer boundary of the cylinder. The analytical formula of Hart and Couvillion (1986) for constant heat extraction is adapted to a non-constant heat flux. To adapt the formula for a variable rate of heat extraction, different constant heat extraction rates, starting at different time instances, are super-imposed. To obtain the temperature drop at the time t=n*Δt, the effects of constant rate of heat extractions are super-imposed as

ΔT ( r , t=n Δt )= 1 ⁄ ( 4 π k ) ∑ W(u(r, t= i Δt)) (qn-i+1-qn-i),

where r is the radius for which the temperature is computed, k is the thermal conductivity of the material, W is a solution of the heat conduction in polar coordinates and qi=Qi/h is the specific rate of heat extraction per unit lenght at time t=i Δt. The value of W is obtained using

W(u)=[-0.5772 - ln(u) + u - u2/(2   2!) +u3/(3   3!) - u4/(4   4!) + ....].

where u(r,t)= c ρ r2 ⁄ (4 t k) , ρ is the mass density and c is the specific heat capacity per unit mass.

Implementation

The rate of heat flow Qi is obtained from the function Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues.

References

Hart and Couvillion, (1986). Earth Coupled Heat Transfer. Publication of the National Water Well Association.

Inputs

TypeNameDefaultDescription
ExtendableArraytable External object that contains the history terms of the heat flux
IntegeriSam Counter for how many time the model was sampled. Defined as iSam=1 when called at t=0
HeatFlowRateQ_flow Heat flow rate to be stored in the external object [W]
TimesamplePeriod Period between two samples [s]
RadiusrExt External radius of the cylinder [m]
HeighthSeg Height of the cylinder [m]
ThermalConductivityk Thermal conductivity of the soil [W/(m.K)]
Densityd Density of the soil [kg/m3]
SpecificHeatCapacityc Specific heat capacity of the soil [J/(kg.K)]

Outputs

TypeNameDescription
TemperatureDifferencedTTemperature drop of the soil [K]

Modelica definition

function temperatureDrop 
  "Calculate the temperature drop of the soil at the external boundary of the cylinder"
input ExtendableArray table 
    "External object that contains the history terms of the heat flux";
input Integer iSam(min=1) 
    "Counter for how many time the model was sampled. Defined as iSam=1 when called at t=0";

input Modelica.SIunits.HeatFlowRate Q_flow 
    "Heat flow rate to be stored in the external object";
input Modelica.SIunits.Time samplePeriod "Period between two samples";
input Modelica.SIunits.Radius rExt "External radius of the cylinder";
input Modelica.SIunits.Height hSeg "Height of the cylinder";
input Modelica.SIunits.ThermalConductivity k "Thermal conductivity of the soil";
input Modelica.SIunits.Density d "Density of the soil";
input Modelica.SIunits.SpecificHeatCapacity c 
    "Specific heat capacity of the soil";
output Modelica.SIunits.TemperatureDifference dT "Temperature drop of the soil";
protected 
 Modelica.SIunits.Time minSamplePeriod= rExt^2/(4*(k/c/d)*3.8) 
    "Minimal lenght of the sampling period";
 Modelica.SIunits.HeatFlowRate QL_flow 
    "Intermediate variable for heat flow rate at the lower bound of the time interval";
 Modelica.SIunits.HeatFlowRate QU_flow 
    "Intermediate variable for heat flow rate at the upper bound of the time interval";

algorithm 
  assert(rExt*rExt/(4*(k/c/d)*samplePeriod)<=3.8,
  "The samplePeriod has to be bigger than " + String(minSamplePeriod) + " for convergence purpose.
  samplePeriod = "+ String(samplePeriod));
  if iSam == 1 then
    // First call, at t=0
    dT := 0;
    QL_flow := Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues(
                       table=table, iX=iSam, x=Q_flow, iY=iSam);
  else
    dT := 0;
    // The first evaluation is at iSam=2, in which case we have one term of the sum,
    // and t=samplePeriod=(iSam-1)*samplePeriod
   for i in 1:(iSam-1) loop
      QL_flow := Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues(
        table=table, iX=iSam, x=Q_flow, iY=iSam+1-i);
      QU_flow := Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.exchangeValues(
        table=table, iX=iSam, x=Q_flow, iY=iSam-i);
      // The division by hSeg is because QU_flow and QL_flow are in [W], but the equation
      // requires [W/m], i.e., heat flow rate per unit length of the line source.
      dT := dT + 1/(4*Modelica.Constants.pi*k)*
        Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.powerSeries(
           u=c*d/(4*k*i*samplePeriod)*rExt^2, N=10)*
        (QL_flow-QU_flow)/hSeg;
 end for;
  end if;
end temperatureDrop;

Automatically generated Wed May 15 11:55:27 2013.