Buildings.HeatTransfer.Conduction.BaseClasses

Information

This package contains base classes that are used to construct the models in Buildings.HeatTransfer.Conduction.

Package Content

Name	Description
PartialConductor	Partial model for heat conductor
PartialConstruction	Partial model for multi-layer constructions
der_temperature_u	Computes the derivative of the temperature of a phase change material with respect to specific internal energy
temperature_u	Computes the temperature of a phase change material for a given specific internal energy
Examples	Collection of models that illustrate model use and test models

Buildings.HeatTransfer.Conduction.BaseClasses.PartialConductor

Information

Parameters

Type	Name	Default	Description
Area	A		Heat transfer area [m2]
ThermalResistance	R		Thermal resistance of construction [K/W]

Connectors

Type	Name	Description
HeatPort_a	port_a	Heat port at surface a
HeatPort_b	port_b	Heat port at surface b

Modelica definition

partial model PartialConductor "Partial model for heat conductor"
  extends Buildings.BaseClasses.BaseIcon;
  parameter Modelica.SIunits.Area A "Heat transfer area";
  final parameter Modelica.SIunits.CoefficientOfHeatTransfer U = UA/A 
    "U-value (without surface heat transfer coefficients)";
  final parameter Modelica.SIunits.ThermalConductance UA = 1/R 
    "Thermal conductance of construction (without surface heat transfer coefficients)";
  parameter Modelica.SIunits.ThermalResistance R 
    "Thermal resistance of construction";
  Modelica.SIunits.TemperatureDifference dT "port_a.T - port_b.T";
public 
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a port_a 
    "Heat port at surface a";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b port_b 
    "Heat port at surface b";
equation 
  dT = port_a.T - port_b.T;
end PartialConductor;

Buildings.HeatTransfer.Conduction.BaseClasses.PartialConstruction

Information

Parameters

Type	Name	Default	Description
Area	A		Heat transfer area [m2]
Generic	layers	redeclare parameter Building...	Construction definition from Data.OpaqueConstructions
Initialization
Boolean	steadyStateInitial	false	=true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start and T_b_start
Temperature	T_a_start	293.15	Initial temperature at port_a, used if steadyStateInitial = false [K]
Temperature	T_b_start	293.15	Initial temperature at port_b, used if steadyStateInitial = false [K]

Modelica definition

model PartialConstruction 
  "Partial model for multi-layer constructions"
  extends Buildings.BaseClasses.BaseIcon;
  parameter Modelica.SIunits.Area A "Heat transfer area";

  replaceable parameter Buildings.HeatTransfer.Data.OpaqueConstructions.Generic
    layers "Construction definition from Data.OpaqueConstructions";

  final parameter Integer nLay(min=1, fixed=true) = layers.nLay 
    "Number of layers";
  final parameter Integer nSta[nLay](min=1)={layers.material[i].nSta for i in 1:nLay} 
    "Number of states";
  parameter Boolean steadyStateInitial=false 
    "=true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start and T_b_start";
  parameter Modelica.SIunits.Temperature T_a_start=293.15 
    "Initial temperature at port_a, used if steadyStateInitial = false";
  parameter Modelica.SIunits.Temperature T_b_start=293.15 
    "Initial temperature at port_b, used if steadyStateInitial = false";

end PartialConstruction;

Buildings.HeatTransfer.Conduction.BaseClasses.der_temperature_u

Information

This function computes at the support points T_d the derivatives dT/du of the cubic hermite spline approximation to the temperature vs. specific internal energy relation. These derivatives are then used by the function Buildings.HeatTransfer.Conduction.BaseClasses.temperature_u to compute for a given specific internal energy the temperature.

Inputs

Type	Name	Default	Description
Generic	material		Material properties

Outputs

Type	Name	Description
SpecificInternalEnergy	ud[Buildings.HeatTransfer.Conduction.nSupPCM]	Support points for derivatives [J/kg]
Temperature	Td[Buildings.HeatTransfer.Conduction.nSupPCM]	Support points for derivatives [K]
Real	dT_du[Buildings.HeatTransfer.Conduction.nSupPCM]	Derivatives dT/du at the support points [kg.K2/J]

Modelica definition

function der_temperature_u 
  "Computes the derivative of the temperature of a phase change material with respect to specific internal energy"
  input Buildings.HeatTransfer.Data.Solids.Generic material 
    "Material properties";
  output Modelica.SIunits.SpecificInternalEnergy ud[Buildings.HeatTransfer.Conduction.nSupPCM] 
    "Support points for derivatives";
  output Modelica.SIunits.Temperature Td[Buildings.HeatTransfer.Conduction.nSupPCM] 
    "Support points for derivatives";
  output Real dT_du[Buildings.HeatTransfer.Conduction.nSupPCM](fixed=false, unit="kg.K2/J") 
    "Derivatives dT/du at the support points";
protected 
  parameter Real scale=0.999 "Used to place points on the phase transition";
  parameter Modelica.SIunits.Temperature Tm1=material.TSol+(1-scale)*(material.TLiq-material.TSol);
  parameter Modelica.SIunits.Temperature Tm2=material.TSol+scale*(material.TLiq-material.TSol);
algorithm 
  assert(Buildings.HeatTransfer.Conduction.nSupPCM == 6,
    "The material must have exactly 6 support points for the u(T) relation.");
  assert(material.TLiq > material.TSol,
    "TLiq has to be larger than TSol.");
  // Get the derivative values at the support points
  ud:={material.c*scale*material.TSol,
       material.c*material.TSol,
       material.c*Tm1 + material.LHea*(Tm1 - material.TSol)/(material.TLiq - material.TSol),
       material.c*Tm2 + material.LHea*(Tm2 - material.TSol)/(material.TLiq - material.TSol),
       material.c*material.TLiq + material.LHea,
       material.c*(material.TLiq + material.TSol*(1 - scale)) + material.LHea};
  Td:={scale*material.TSol,
       material.TSol,
       Tm1,
       Tm2,
       material.TLiq,
       material.TLiq + material.TSol*(1 - scale)};
  dT_du := Buildings.Utilities.Math.Functions.splineDerivatives(
      x=ud,
      y=Td,
      ensureMonotonicity=material.ensureMonotonicity);
end der_temperature_u;

Buildings.HeatTransfer.Conduction.BaseClasses.temperature_u

Information

This function computes for a given specific internal energy u the temperature T(u), using a cubic hermite spline approximation to the temperature vs. specific internal energy relation. Input to the function are the derivatives dT/du at the support points. These derivatives can be computed using Buildings.HeatTransfer.Conduction.BaseClasses.der_temperature_u.

Implementation

The derivatives dT/du are an input to this function because they typically only need to be computed once, whereas T(u) must be evaluated at each time step.

Inputs

Type	Name	Default	Description
SpecificInternalEnergy	ud[Buildings.HeatTransfer.Conduction.nSupPCM]		Support points for derivatives [J/kg]
Temperature	Td[Buildings.HeatTransfer.Conduction.nSupPCM]		Support points for derivatives [K]
Real	dT_du[:]		Derivatives dT/du at the support points [kg.K2/J]
SpecificInternalEnergy	u		Specific internal energy [J/kg]

Outputs

Type	Name	Description
Temperature	T	Resulting temperature [K]

Modelica definition

function temperature_u 
  "Computes the temperature of a phase change material for a given specific internal energy"

  input Modelica.SIunits.SpecificInternalEnergy ud[Buildings.HeatTransfer.Conduction.nSupPCM] 
    "Support points for derivatives";
  input Modelica.SIunits.Temperature Td[Buildings.HeatTransfer.Conduction.nSupPCM] 
    "Support points for derivatives";
  input Real dT_du[:](each fixed=false, unit="kg.K2/J") 
    "Derivatives dT/du at the support points";

  input Modelica.SIunits.SpecificInternalEnergy u "Specific internal energy";

  output Modelica.SIunits.Temperature T "Resulting temperature";
protected 
  Integer i "Integer to select data interval";
algorithm 
  // i is a counter that is used to pick the derivative
  // that corresponds to the interval that contains x
  i := 1;
  for j in 1:size(ud,1) - 1 loop
    if u > ud[j] then
      i := j;
    end if;
  end for;
  // Extrapolate or interpolate the data
  T :=  Buildings.Utilities.Math.Functions.cubicHermiteLinearExtrapolation(
     x=u,
     x1=ud[i],
     x2=ud[i + 1],
     y1=Td[i],
     y2=Td[i + 1],
     y1d=dT_du[i],
     y2d=dT_du[i + 1]);
end temperature_u;