Buildings.Fluid.HeatExchangers.Radiators

Information

Package Content

Name	Description
RadiatorEN442_2	Dynamic radiator for space heating
Examples	Collection of models that illustrate model use and test models

Buildings.Fluid.HeatExchangers.Radiators.RadiatorEN442_2

Information

However, to allow for varying mass flow rates, the transferred heat is computed using a discretization along the water flow path, and heat is exchanged between each compartment and a uniform room air and radiation temperature. This discretization is different from the computation in EN 442-2, which may give water outlet temperatures that are below the room temperature at low mass flow rates. Also, rather than using only one room temperature, this model uses a room air and room radiation temperature.

The parameter energyDynamics (in the Assumptions tab), determines whether the model computes the dynamic or the steady-state response. For the transient response, heat storage is computed using a finite volume approach for the water and the metal mass, which are both assumed to be at the same temperature.

The default parameters are for a flat plate radiator without fins, with one plate of water carying fluid, and a height of 0.42 meters.

Extends from Fluid.Interfaces.PartialStaticTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Power	Q_flow_nominal		Nominal heating power [W]
Real	fraRad	0.35	Fraction radiant heat transfer
TemperatureDifference	dT_nominal	50	Nominal temperature difference (between water and air) [K]
Real	n	1.24	Exponent for heat transfer
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
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]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
Integer	nEle	5	Number of elements used in the discretization
Dynamics	energyDynamics	system.energyDynamics	Formulation of energy balance
Volume	VWat	5.8E-6*Q_flow_nominal	Water volume of radiator [m3]
Mass	mDry	0.0263*Q_flow_nominal	Dry mass of radiator that will be lumped to water heat capacity [kg]
Advanced
MassFlowRate	m_flow_small	1E-4*m_flow_nominal	Small mass flow rate for regularization of zero flow [kg/s]
TemperatureDifference	deltaT	0.1	Temperature difference used for smoothing of heat transfer coefficient [K]
Diagnostics
Boolean	show_V_flow	false	= true, if volume flow rate at inflowing port is computed
Boolean	show_T	false	= true, if actual temperature at port is computed (may lead to events)
Initialization
AbsolutePressure	p_start	system.p_start	Start value of pressure [Pa]
Boolean	use_T_start	true	= true, use T_start, otherwise h_start
Temperature	T_start	if use_T_start then system.T...	Start value of temperature [K]
SpecificEnthalpy	h_start	if use_T_start then Medium.s...	Start value of specific enthalpy [J/kg]
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

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)
HeatPort_a	heatPortCon	Heat port for convective heat transfer with room air temperature
HeatPort_a	heatPortRad	Heat port for radiative heat transfer with room radiation temperature

Modelica definition

model RadiatorEN442_2 "Dynamic radiator for space heating"
   extends Fluid.Interfaces.PartialStaticTwoPortInterface(
   showDesignFlowDirection = false);
  parameter Integer nEle(min=1) = 5 
    "Number of elements used in the discretization";
  parameter Modelica.SIunits.Power Q_flow_nominal "Nominal heating power";
  parameter Real fraRad(min=0, max=1) = 0.35 "Fraction radiant heat transfer";
  // Assumptions
  parameter Modelica.Fluid.Types.Dynamics energyDynamics=system.energyDynamics 
    "Formulation of energy balance";

 // Initialization
  parameter Medium.AbsolutePressure p_start = system.p_start 
    "Start value of pressure";
  parameter Boolean use_T_start = true "= true, use T_start, otherwise h_start";
  parameter Medium.Temperature T_start=
    if use_T_start then system.T_start else Medium.temperature_phX(p_start,h_start,X_start) 
    "Start value of temperature";
  parameter Medium.SpecificEnthalpy h_start=
    if use_T_start then Medium.specificEnthalpy_pTX(p_start, T_start, X_start) else Medium.h_default 
    "Start value of specific enthalpy";
  parameter Medium.MassFraction X_start[Medium.nX] = Medium.X_default 
    "Start value of mass fractions m_i/m";
  parameter Medium.ExtraProperty C_start[Medium.nC](
       quantity=Medium.extraPropertiesNames)=fill(0, Medium.nC) 
    "Start value of trace substances";

  parameter Modelica.SIunits.TemperatureDifference dT_nominal(min=0) = 50 
    "Nominal temperature difference (between water and air)";
  parameter Real n = 1.24 "Exponent for heat transfer";
  parameter Modelica.SIunits.Volume VWat = 5.8E-6*Q_flow_nominal 
    "Water volume of radiator";
  parameter Modelica.SIunits.Mass mDry = 0.0263*Q_flow_nominal if 
        not (energyDynamics == Modelica.Fluid.Types.Dynamics.SteadyState) 
    "Dry mass of radiator that will be lumped to water heat capacity";
  Modelica.SIunits.HeatFlowRate QCon_flow 
    "Heat input into the water due to convective heat transfer with room air";
  Modelica.SIunits.HeatFlowRate QRad_flow 
    "Heat input into the water due to radiative heat transfer with room";
  Modelica.SIunits.HeatFlowRate Q_flow "Heat input into the water";
  parameter Modelica.SIunits.TemperatureDifference deltaT=0.1 
    "Temperature difference used for smoothing of heat transfer coefficient";
public 
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPortCon 
    "Heat port for convective heat transfer with room air temperature";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPortRad 
    "Heat port for radiative heat transfer with room radiation temperature";

  Modelica.Thermal.HeatTransfer.Components.HeatCapacitor[nEle] heaCapDry(
      each C=500*mDry/nEle,
      each T(start=T_start)) if not (energyDynamics == Modelica.Fluid.Types.Dynamics.SteadyState) 
    "heat capacity of radiator metal";

  Modelica.Thermal.HeatTransfer.Sources.PrescribedHeatFlow[nEle] preHeaFloCon 
    "Heat input into radiator from convective heat transfer";
  Modelica.Thermal.HeatTransfer.Sources.PrescribedHeatFlow[nEle] preHeaFloRad 
    "Heat input into radiator from radiative heat transfer";

  Fluid.MixingVolumes.MixingVolume[nEle] vol(
    redeclare each package Medium = Medium,
    each nPorts = 2,
    each V=VWat/nEle,
    each final use_HeatTransfer=true,
    redeclare each model HeatTransfer =
        Modelica.Fluid.Vessels.BaseClasses.HeatTransfer.IdealHeatTransfer,
    each final energyDynamics=energyDynamics,
    each final massDynamics=energyDynamics,
    each final p_start=p_start,
    each final use_T_start=use_T_start,
    each final T_start=T_start,
    each final h_start=h_start,
    each final X_start=X_start,
    each final C_start=C_start) "Volume for fluid stream";
protected 
   Modelica.SIunits.TemperatureDifference[nEle] dTCon 
    "Temperature difference for convective heat transfer";
   Modelica.SIunits.TemperatureDifference[nEle] dTRad 
    "Temperature difference for radiative heat transfer";
   parameter Modelica.SIunits.ThermalConductance UA_nominaln = Q_flow_nominal /dT_nominal^n/nEle;
   Modelica.SIunits.ThermalConductance[nEle] UACon 
    "Thermal conductance between radiator and room for convective heat transfer";
   Modelica.SIunits.ThermalConductance[nEle] UARad 
    "Thermal conductance between radiator and room for radiative heat transfer";

equation 
  for i in 1:nEle loop
     dTCon[i] = heatPortCon.T - vol[i].medium.T;
     dTRad[i] = heatPortRad.T - vol[i].medium.T;
     UACon[i] = (1-fraRad)  * UA_nominaln *
                Buildings.Utilities.Math.Functions.regNonZeroPower(x=dTCon[i], n=n-1, delta=deltaT);
     UARad[i] = fraRad      * UA_nominaln *
                Buildings.Utilities.Math.Functions.regNonZeroPower(x=dTRad[i], n=n-1, delta=deltaT);
     preHeaFloCon[i].Q_flow = UACon[i] * dTCon[i];
     preHeaFloRad[i].Q_flow = UARad[i] * dTRad[i];
  end for;
  QCon_flow = sum(preHeaFloCon[i].Q_flow for i in 1:nEle);
  QRad_flow = sum(preHeaFloRad[i].Q_flow for i in 1:nEle);
  Q_flow = QCon_flow + QRad_flow;
  heatPortCon.Q_flow = QCon_flow;
  heatPortRad.Q_flow = QRad_flow;

  connect(preHeaFloCon.port, vol.heatPort);
  connect(preHeaFloRad.port, vol.heatPort);
  connect(heaCapDry.port, vol.heatPort);
  connect(port_a, vol[1].ports[1]);
  connect(vol[nEle].ports[2], port_b);
  for i in 1:nEle-1 loop

    connect(vol[i].ports[2], vol[i+1].ports[1]);
  end for;
end RadiatorEN442_2;