Buildings.Fluid.HeatExchangers.Boreholes

Information

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
UTube	Single U-tube borehole heat exchanger
Examples	Example files for borehole heat exchanger
BaseClasses	Base classes for Borehole

Buildings.Fluid.HeatExchangers.Boreholes.UTube

Information

Model of a single U-tube borehole heat exchanger. The borehole heat exchanger is vertically discretized into n_seg elements of height h=h_Bor⁄n_seg. Each segment contains a model for the heat transfer in the borehole, for heat transfer in the soil and for the far-field boundary condition.

The heat transfer in the borehole is computed using a convective heat transfer coefficient that depends on the fluid velocity, a heat resistance between the two pipes, and a heat resistance between the pipes and the circumference of the borehole. The heat capacity of the fluid, and the heat capacity of the grout, is taken into account. All thermal mass is assumed to be at the two bulk temperatures of the down-flowing and up-flowing fluid.

The heat transfer in the soil is computed using transient heat conduction in cylindrical coordinates for the spatial domain r_bor ≤ r ≤ r_ext. In the radial direction, the spatial domain is discretized into n_hor segments with uniform material properties. Thermal properties can be specified separately for each horizontal layer. The vertical heat flow is assumed to be zero, and there is assumed to be no ground water flow.

The far-field temperature, i.e., the temperature at the radius r_ext, is computed using a power-series solution to a line-source heat transfer problem. This temperature boundary condition is updated every t_sample seconds.

The initial far-field temperature T_ext,start, which is the temperature of the soil at a radius r_ext, is computed as a function of the depth z > 0. For a depth between 0 ≤ z ≤ z₀, the temperature is set to T_ext,0,start. The value of z₀ is a parameter with a default of 10 meters. However, there is large variability in the depth where the undisturbed soil temperature starts. For a depth of z₀ ≤ z ≤ h_bor, the temperature is computed as

Tⁱ_ext,start = T_ext,0,start + (zⁱ - z₀) dT ⁄ dz

Implementation

Each horizontal layer is modeled using an instance of Buildings.HeatExchangers.Fluid.Boreholes.BaseClasses.BoreholeSegment. This model is composed of the model Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.HexInternalElement which computes the heat transfer in the pipes and the borehole filling, of the model Buildings.HeatTransfer.Conduction.SingleLayerCylinder which computes the heat transfer in the soil, and of the model Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.TemperatureBoundaryCondition which computes the far-field temperature boundary condition.

Extends from Buildings.Fluid.Interfaces.PartialTwoPortInterface (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

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Radius	rBor	0.1	Radius of the borehole [m]
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp_nominal		Pressure [Pa]
Initialization
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Tubes
Radius	rTub	0.02	Radius of the tubes [m]
ThermalConductivity	kTub	0.5	Thermal conductivity of the tube [W/(m.K)]
Length	eTub	0.002	Thickness of a tube [m]
Borehole
Generic	matFil	redeclare parameter Building...	Thermal properties of the borehole filling
Height	hBor		Total height of the borehole [m]
Integer	nVer	10	Number of segments used for discretization in the vertical direction
Length	xC	0.05	Shank spacing, defined as the distance between the center of a pipe and the center of the borehole [m]
Real	B0	17.44	Shape coefficient for grout resistance
Real	B1	-0.605	Shape coefficient for grout resistance
Soil
Generic	matSoi[nVer]	redeclare parameter Building...	Thermal properties of the soil
Radius	rExt	3	Radius of the soil used for the external boundary condition [m]
Integer	nHor	10	Number of state variables in each horizontal layer of the soil
Time	samplePeriod		Sample period for the external boundary condition [s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	true	= true, if actual temperature at port is computed (may lead to events)
Flow resistance
Boolean	computeFlowResistance	false	=true, compute flow resistance. Set to false to assume no friction
Boolean	from_dp	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM	0.1	Fraction of nominal flow rate where flow transitions to laminar
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Initial temperature
Soil
Temperature	TExt0_start	283.15	Initial far field temperature [K]
Temperature	TExt_start[nVer]	{if z[i] >= z0 then TExt0_st...	Temperature of the undisturbed ground [K]
Filling material
Temperature	TFil0_start	TExt0_start	Initial temperature of the filling material for h = 0...z0 [K]
Temperature	TFil_start[nVer]	TExt_start	Temperature of the undisturbed ground [K]
Temperature profile
Height	z0	10	Depth below which the temperature gradient starts [m]
Real	dT_dz	0.01	Vertical temperature gradient of the undisturbed soil for h below z0 [K/m]

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)

Modelica definition

model UTube "Single U-tube borehole heat exchanger"
  extends Buildings.Fluid.Interfaces.PartialTwoPortInterface(
    show_T=true);
  extends Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters(final 
      computeFlowResistance=false, final linearizeFlowResistance=false);
  extends Buildings.Fluid.Interfaces.LumpedVolumeDeclarations;

  parameter Modelica.SIunits.Radius rTub=0.02 "Radius of the tubes";
  parameter Modelica.SIunits.ThermalConductivity kTub=0.5 
    "Thermal conductivity of the tube";
  parameter Modelica.SIunits.Length eTub=0.002 "Thickness of a tube";

  replaceable parameter Buildings.HeatTransfer.Data.BoreholeFillings.Generic
    matFil "Thermal properties of the borehole filling";
  parameter Modelica.SIunits.Height hBor "Total height of the borehole";
  parameter Integer nVer=10 
    "Number of segments used for discretization in the vertical direction";
  parameter Modelica.SIunits.Radius rBor=0.1 "Radius of the borehole";

  replaceable parameter Buildings.HeatTransfer.Data.Soil.Generic
    matSoi[nVer] "Thermal properties of the soil";

  parameter Modelica.SIunits.Radius rExt=3 
    "Radius of the soil used for the external boundary condition";
  parameter Integer nHor(min=1) = 10 
    "Number of state variables in each horizontal layer of the soil";

  parameter Modelica.SIunits.Temperature TExt0_start=283.15 
    "Initial far field temperature";
  parameter Modelica.SIunits.Temperature TExt_start[nVer]={if z[i] >= z0 then 
      TExt0_start + (z[i] - z0)*dT_dz else TExt0_start for i in 1:nVer} 
    "Temperature of the undisturbed ground";

  parameter Modelica.SIunits.Temperature TFil0_start=TExt0_start 
    "Initial temperature of the filling material for h = 0...z0";
  parameter Modelica.SIunits.Temperature TFil_start[nVer]=TExt_start 
    "Temperature of the undisturbed ground";

  parameter Modelica.SIunits.Height z0=10 
    "Depth below which the temperature gradient starts";
  parameter Real dT_dz(unit="K/m") = 0.01 
    "Vertical temperature gradient of the undisturbed soil for h below z0";

  parameter Modelica.SIunits.Time samplePeriod 
    "Sample period for the external boundary condition";
  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=-0.605 "Shape coefficient for grout resistance";
  Buildings.Fluid.HeatExchangers.Boreholes.BaseClasses.BoreholeSegment borHol[nVer](
    redeclare each final package Medium = Medium,
    final matSoi=matSoi,
    each final matFil=matFil,
    each final hSeg=hBor/nVer,
    each final samplePeriod=samplePeriod,
    each final rTub=rTub,
    each final rBor=rBor,
    each final rExt=rExt,
    each final xC=xC,
    each final eTub=eTub,
    each final kTub=kTub,
    each final B0=B0,
    each final B1=B1,
    each final nSta=nHor,
    each final m_flow_nominal=m_flow_nominal,
    each final m_flow_small=m_flow_small,
    final dp_nominal={if i == 1 then dp_nominal else 0 for i in 1:nVer},
    TExt_start=TExt_start,
    TFil_start=TExt_start,
    each final homotopyInitialization=homotopyInitialization,
    each final show_V_flow=show_V_flow,
    each final show_T=show_T,
    each final computeFlowResistance=computeFlowResistance,
    each final from_dp=from_dp,
    each final linearizeFlowResistance=linearizeFlowResistance,
    each final deltaM=deltaM,
    each final energyDynamics=energyDynamics,
    each final massDynamics=massDynamics,
    each final p_start=p_start,
    each T_start=T_start,
    each X_start=X_start,
    each C_start=C_start,
    each C_nominal=C_nominal,
    each allowFlowReversal=allowFlowReversal) "Discretized borehole segments";

  Modelica.SIunits.Temperature Tdown[nVer] "Medium temperature in pipe 1";
  Modelica.SIunits.Temperature Tup[nVer] "Medium temperature in pipe 2";
protected 
  parameter Modelica.SIunits.Height z[nVer]={hBor/nVer*(i - 0.5) for i in 1:
      nVer} "Distance from the surface to the considered segment";
equation 
  Tdown[:] = borHol[:].pipFil.vol1.heatPort.T;
  Tup[:] = borHol[:].pipFil.vol2.heatPort.T;
  connect(port_a, borHol[1].port_a1);
  connect(port_b, borHol[1].port_b2);
  connect(borHol[nVer].port_b1, borHol[nVer].port_a2);
  for i in 1:nVer - 1 loop
    connect(borHol[i].port_b1, borHol[i + 1].port_a1);
    connect(borHol[i].port_a2, borHol[i + 1].port_b2);
  end for;
end UTube;