Name | Description |
---|---|
![]() | Collection of models that illustrate model use and test models |
![]() | Dynamic radiator for space heating |
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 Fluids.Interfaces.PartialStaticTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy).
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 | true | = true, if volume flow rate at inflowing port is computed |
Initialization | |||
AbsolutePressure | p_a_start | system.p_start | Guess value for inlet pressure [Pa] |
AbsolutePressure | p_b_start | p_a_start | Guess value for outlet pressure [Pa] |
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 |
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 |
model RadiatorEN442_2 "Dynamic radiator for space heating" extends Fluids.Interfaces.PartialStaticTwoPortInterface; 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"; Fluids.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, each final m_flow_small=m_flow_small) "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;