Buildings.Fluid.HeatExchangers.RadiantSlabs

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Buildings.Fluid.HeatExchangers.RadiantSlabs

Package with radiant slab models

Information

This package contains models for radiant slabs with pipes or a capillary heat exchanger embedded in the construction.

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

Package Content

Name Description

SingleCircuitSlab Model of a single circuit of a radiant slab

ParallelCircuitsSlab Model of multiple parallel circuits of a radiant slab

Examples Collection of models that illustrate model use and test models

BaseClasses Package with base classes for Buildings.Fluid.HeatExchangers.RadiantSlabs

Name	Description
SingleCircuitSlab	Model of a single circuit of a radiant slab
ParallelCircuitsSlab	Model of multiple parallel circuits of a radiant slab
Examples	Collection of models that illustrate model use and test models
BaseClasses	Package with base classes for Buildings.Fluid.HeatExchangers.RadiantSlabs

Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab

Model of a single circuit of a radiant slab

Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab

Information

This is a model of a single flow circuit of a radiant slab with pipes or a capillary heat exchanger embedded in the construction. For a model with multiple parallel flow circuits, see Buildings.Fluid.HeatExchangers.RadiantSlabs.ParallelCircuitsSlab.

The figure below shows the thermal resistance network of the model for an example in which the pipes are embedded in the concrete slab, and the layers below the pipes are insulation and reinforced concrete.

The construction con_a computes transient heat conduction between the surface heat port surf_a and the plane that contains the pipes, with the heat port con_a.port_a connecting to surf_a. Similarly, the construction con_b is between the plane that contains the pipes and the surface heat port sur_b, with the heat port con_b.port_b connecting to surf_b. The temperature of the plane that contains the pipes is computes using a fictitious resistance RFic, which is computed by Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.AverageResistance. There is also a resistance for the pipe wall RPip and a convective heat transfer coefficient between the fluid and the pipe inside wall. The convective heat transfer coefficient is a function of the mass flow rate and is computed by Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.InternalFlowConvection.

This resistance network is instantiated several times along the flow path. The parameter nSeg determines how many instances are used. However, all instances connect to the same surface temperature heat ports surf_a and surf_b.

The material layers are declared by the parameter layers, which is an instance of Buildings.HeatTransfer.Data.OpaqueConstructions. The first layer of this material is the one at the heat port surf_a, and the last layer is at the heat port surf_b. The parameter iLayPip must be set to the number of the interface in which the pipes are located. For example, consider the following floor slab.

Then, the construction definition is

  Buildings.HeatTransfer.Data.OpaqueConstructions.Generic layers(
        nLay=3, 
        material={
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.08,
            k=1.13,
            c=1000,
            d=1400,
            nSta=5),
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.05,
            k=0.04,
            c=1400,
            d=10),
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.2,
            k=1.8,
            c=1100,
            d=2400)}) "Material definition for floor construction";

Note that we set nSta=5 in the first material layer. In this example, this material layer is the concrete layer in which the pipes are embedded. By setting nSta=5 the simulation is forced to be done with five state variables in this layer. The default setting would have led to only one state variable in this layer.

Since the pipes are at the interface of the concrete and the insulation, we set iLayPip=1.

Initialization

The initialization of the fluid in the pipes and of the slab temperature are independent of each other.

To initialize the medium, the same mechanism is used as for any other fluid volume, such as Buildings.Fluid.MixingVolumes.MixingVolume. Specifically, the parameters energyDynamics and massDynamics on the Dynamics tab are used. Depending on the values of these parameters, the medium is initialized using the values p_start, T_start, X_start and C_start, provided that the medium model contains species concentrations X and trace substances C.

To initialize the construction temperatures, the parameters steadyStateInitial, T_a_start, T_b_start and T_c_start are used. By default, T_c_start is set to the temperature that leads to steady-state heat transfer between the surfaces surf_a and surf_b, whose temperatures are both set to T_a_start and T_b_start.

The parameter pipe, which is an instance of the record Buildings.Fluid.Data.Pipes, defines the pipe material and geometry. The parameter disPip declares the spacing between the pipes and the parameter length, with default length=A/disPip where A is the slab surface area, declares the whole length of the pipe circuit.

The parameter sysTyp is used to select the equation that is used to compute the average temperature in the plane of the pipes. It needs to be set to the following values:

sysTyp System type

BaseClasses.Types.SystemType.Floor Radiant heating or cooling systems with pipes embedded in the concrete slab above the thermal insulation.

BaseClasses.Types.SystemType.Ceiling_Wall_or_Capillary Radiant heating or cooling systems with pipes embedded in the concrete slab in the ceiling, or radiant wall systems. Radiant heating and cooling systems with capillary heat exchanger at the construction surface.

sysTyp	System type
BaseClasses.Types.SystemType.Floor	Radiant heating or cooling systems with pipes embedded in the concrete slab above the thermal insulation.
BaseClasses.Types.SystemType.Ceiling_Wall_or_Capillary	Radiant heating or cooling systems with pipes embedded in the concrete slab in the ceiling, or radiant wall systems. Radiant heating and cooling systems with capillary heat exchanger at the construction surface.

Limitations

The analogy with a three-resistance network and the corresponding equation for Rx is based on a steady-state heat transfer analysis. Therefore, it is only valid during steady-state. For a fully dynamic model, a three-dimensional finite element method for the radiant slab would need to be implemented.

Implementation

To separate the material declaration layers into layers between the pipes and heat port surf_a, and between the pipes and surf_b, the vector layers.material[nLay] is partitioned into layers.material[1:iLayPip] and layers.material[iLayPip+1:nLay]. The respective partitions are then assigned to the models for heat conduction between the plane with the pipes and the construction surfaces, con_a and con_b.

Extends from Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab (Base class for radiant slab), Buildings.Fluid.FixedResistances.BaseClasses.Pipe (Model of a pipe with finite volume discretization along the flow path).

Parameters

Type Name Default Description

SystemType sysTyp Radiant system type

Distance disPip Pipe distance [m]

Generic pipe Record for pipe geometry and material

replaceable package Medium PartialMedium Medium in the component

Integer nSeg 10 Number of volume segments

Length thicknessIns 0 Thickness of insulation [m]

ThermalConductivity lambdaIns 0.04 Heat conductivity of insulation [W/(m.K)]

Length diameter pipe.dIn Pipe diameter (without insulation) [m]

Length length A/disPip Length of the pipe [m]

Construction

Generic layers Definition of the construction, which must have at least two material layers

Integer iLayPip Number of the interface layer in which the pipes are located

Area A Surface area of radiant slab [m2]

Nominal condition

MassFlowRate m_flow_nominal Nominal mass flow rate [kg/s]

Pressure dp_nominal Modelica.Fluid.Pipes.BaseCla... 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]

Initialization

Construction

Boolean steadyStateInitial false =true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start, T_c_start and T_b_start

Temperature T_a_start 293.15 Initial temperature at surf_a, used if steadyStateInitial = false [K]

Temperature T_b_start 293.15 Initial temperature at surf_b, used if steadyStateInitial = false [K]

Temperature T_c_start (T_a_start*con_b[1].layers.R... Initial construction temperature in the layer that contains the pipes, used if steadyStateInitial = false [K]

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.)

Dynamics

Equations

Dynamics energyDynamics Modelica.Fluid.Types.Dynamic... Formulation of energy balance

Dynamics massDynamics energyDynamics Formulation of mass balance

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

Flow resistance

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

Real ReC 4000 Reynolds number where transition to turbulent starts

Type	Name	Default	Description
SystemType	sysTyp		Radiant system type
Distance	disPip		Pipe distance [m]
Generic	pipe		Record for pipe geometry and material
replaceable package Medium	PartialMedium	Medium in the component
Integer	nSeg	10	Number of volume segments
Length	thicknessIns	0	Thickness of insulation [m]
ThermalConductivity	lambdaIns	0.04	Heat conductivity of insulation [W/(m.K)]
Length	diameter	pipe.dIn	Pipe diameter (without insulation) [m]
Length	length	A/disPip	Length of the pipe [m]
Construction
Generic	layers		Definition of the construction, which must have at least two material layers
Integer	iLayPip		Number of the interface layer in which the pipes are located
Area	A		Surface area of radiant slab [m2]
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp_nominal	Modelica.Fluid.Pipes.BaseCla...	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]
Initialization
Construction
Boolean	steadyStateInitial	false	=true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start, T_c_start and T_b_start
Temperature	T_a_start	293.15	Initial temperature at surf_a, used if steadyStateInitial = false [K]
Temperature	T_b_start	293.15	Initial temperature at surf_b, used if steadyStateInitial = false [K]
Temperature	T_c_start	(T_a_start*con_b[1].layers.R...	Initial construction temperature in the layer that contains the pipes, used if steadyStateInitial = false [K]
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.)
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
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
Flow resistance
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
Real	ReC	4000	Reynolds number where transition to turbulent starts

Connectors

Type Name Description

HeatPort_a surf_a Heat port at construction surface

HeatPort_a surf_b Heat port at construction surface

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)

Type	Name	Description
HeatPort_a	surf_a	Heat port at construction surface
HeatPort_a	surf_b	Heat port at construction surface
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 SingleCircuitSlab "Model of a single circuit of a radiant slab"
  extends Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab;
  extends Buildings.Fluid.FixedResistances.BaseClasses.Pipe(
     final diameter=pipe.dIn,
     length=A/disPip,
     final thicknessIns=0,
     final lambdaIns = 0.04,
     dp_nominal = Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed.pressureLoss_m_flow(
      m_flow=m_flow_nominal,
      rho_a=rho_nominal,
      rho_b=rho_nominal,
      mu_a=mu_nominal,
      mu_b=mu_nominal,
      length=length,
      diameter=pipe.dIn,
      roughness=pipe.roughness,
      m_flow_small=m_flow_small),
      res(dp(nominal=200*length)));
  parameter Modelica.SIunits.Area A "Surface area of radiant slab";
  parameter Modelica.SIunits.Temperature T_c_start=(T_a_start*con_b[1].layers.R+T_b_start*con_a[1].layers.R)/layers.R 
    "Initial construction temperature in the layer that contains the pipes, used if steadyStateInitial = false";
  final parameter Modelica.SIunits.Velocity v_nominal = 4*m_flow_nominal/pipe.dIn^2/Modelica.Constants.pi/rho_nominal 
    "Velocity at m_flow_nominal";

  Buildings.HeatTransfer.Conduction.MultiLayer con_a[nSeg](
    each final A=A/nSeg,
    each steadyStateInitial=steadyStateInitial,
    each layers(
      final nLay = iLayPip,
      final material={layers.material[i] for i in 1:iLayPip},
      absIR_a=layers.absIR_a,
      absIR_b=layers.absIR_b,
      absSol_a=layers.absSol_a,
      absSol_b=layers.absSol_b,
      roughness_a=layers.roughness_a),
      each T_a_start=T_a_start,
      each T_b_start=T_c_start) "Construction near the surface port surf_a";
  Buildings.HeatTransfer.Conduction.MultiLayer con_b[nSeg](
      each final A=A/nSeg,
      each steadyStateInitial=steadyStateInitial,
      each layers(
      final nLay = layers.nLay-iLayPip,
      final material={layers.material[i] for i in iLayPip + 1:layers.nLay},
      absIR_a=layers.absIR_a,
      absIR_b=layers.absIR_b,
      absSol_a=layers.absSol_a,
      absSol_b=layers.absSol_b,
      roughness_a=layers.roughness_a),
      each T_a_start=T_c_start,
      each T_b_start=T_b_start) "Construction near the surface port surf_b";

protected 
  Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.InternalFlowConvection
    hPip[nSeg](
    each kc_IN_con=
        Modelica.Fluid.Dissipation.HeatTransfer.StraightPipe.kc_overall_IN_con(
        d_hyd=pipe.dIn,
        L=length/nSeg,
        K=pipe.roughness),
    redeclare each final package Medium = Medium,
    each final A=Modelica.Constants.pi*pipe.dIn*length/nSeg) 
    "Liquid side convective heat transfer";
  Modelica.Blocks.Sources.RealExpression mFlu_flow[nSeg](each y=m_flow) 
    "Input signal for mass flow rate";
  Modelica.Thermal.HeatTransfer.Components.ThermalConductor RWal[nSeg](each G=2*
        Modelica.Constants.pi*pipe.k*(length/nSeg)/Modelica.Math.log(pipe.dOut/pipe.dIn)) 
    "Thermal conduction through the pipe wall";

  Modelica.Thermal.HeatTransfer.Components.ThermalCollector colAllToOne(
     final m=nSeg) "Connector to assign multiple heat ports to one heat port";
  Modelica.Thermal.HeatTransfer.Components.ThermalCollector colAllToOne1(
     final m=nSeg) "Connector to assign multiple heat ports to one heat port";
 Modelica.Thermal.HeatTransfer.Components.ThermalConductor RFic[nSeg](each G=A/nSeg/Rx) 
    "Average fictitious thermal resistance between pipe surface and plane that contains pipe";
    

  final parameter Modelica.SIunits.ThermalInsulance Rx=
      Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.AverageResistance(
        disPip=disPip,
        dPipOut=pipe.dOut,
        k=layers.material[iLayPip].k,
        sysTyp=sysTyp,
        kIns=layers.material[iLayPip+1].k,
        dIns=layers.material[iLayPip+1].x) 
    "Thermal insulance for average temperature in plane with pipes";
equation 
  connect(hPip.fluid, vol.heatPort);
  connect(RWal.port_b, hPip.solid);
  connect(RFic.port_b, RWal.port_a);
  connect(colAllToOne1.port_b,surf_a);
  connect(colAllToOne.port_b,surf_b);
  connect(colAllToOne1.port_a, con_a.port_a);
  connect(con_a.port_b, RFic.port_a);
  connect(colAllToOne.port_a, con_b.port_b);
  connect(con_b.port_a, RFic.port_a);

  connect(mFlu_flow.y, hPip.m_flow);
end SingleCircuitSlab;

Buildings.Fluid.HeatExchangers.RadiantSlabs.ParallelCircuitsSlab

Model of multiple parallel circuits of a radiant slab

Buildings.Fluid.HeatExchangers.RadiantSlabs.ParallelCircuitsSlab

Information

This is a model of a radiant slab with pipes or a capillary heat exchanger embedded in the construction. The model is a composition of multiple models of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab that are arranged in a parallel.

The parameter nCir declares the number of parallel flow circuits. Each circuit will have the same mass flow rate, and it is exposed to the same port variables for the heat port at the two surfaces, and for the flow inlet and outlet.

A typical model application is as follows: Suppose a large room has a radiant slab with two parallel circuits with the same pipe spacing and pipe length. Then, rather than using two instances of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab, this system can be modelled using one instance of this model in order to reduce computing effort. See Buildings.Fluid.HeatExchangers.RadiantSlabs.Examples.SingleCircuitMultipleCircuit for an example that shows that the models give identical results.

Since this model is a parallel arrangment of nCir models of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab, we refer to Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab for the model documentation.

Implementation

To allow a better comment for the nominal mass flow rate, i.e., to specify that its value is for all circuits combined, this model does not inherit Buildings.Fluid.Interfaces.PartialTwoPortInterface.

Extends from Modelica.Fluid.Interfaces.PartialTwoPort (Partial component with two ports), Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab (Base class for radiant slab), Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes), Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters (Parameters for flow resistance for models with two ports).

Parameters

Type Name Default Description

replaceable package Medium PartialMedium Medium in the component

SystemType sysTyp Radiant system type

Distance disPip Pipe distance [m]

Generic pipe Record for pipe geometry and material

Integer nCir 1 Number of parallel circuits

Integer nSeg 10 Number of volume segments in each circuit (along flow path)

Length length A/disPip/nCir Length of the pipe of a single circuit [m]

Construction

Generic layers Definition of the construction, which must have at least two material layers

Integer iLayPip Number of the interface layer in which the pipes are located

Area A Surface area of radiant slab (all circuits combined) [m2]

Nominal condition

Pressure dp_nominal Modelica.Fluid.Pipes.BaseCla... Pressure [Pa]

MassFlowRate m_flow_nominal Nominal mass flow rate of all circuits combined [kg/s]

Assumptions

Boolean allowFlowReversal system.allowFlowReversal = true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Initialization

Construction

Boolean steadyStateInitial false =true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start, T_c_start and T_b_start

Temperature T_a_start 293.15 Initial temperature at surf_a, used if steadyStateInitial = false [K]

Temperature T_b_start 293.15 Initial temperature at surf_b, used if steadyStateInitial = false [K]

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.)

Dynamics

Equations

Dynamics energyDynamics Modelica.Fluid.Types.Dynamic... Formulation of energy balance

Dynamics massDynamics energyDynamics Formulation of mass balance

Flow resistance

Boolean computeFlowResistance true =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

Advanced

MassFlowRate m_flow_small 1E-4*abs(m_flow_nominal) Small mass flow rate of all circuits combined 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 false = true, if actual temperature at port is computed (may lead to events)

Type	Name	Default	Description
replaceable package Medium	PartialMedium	Medium in the component
SystemType	sysTyp		Radiant system type
Distance	disPip		Pipe distance [m]
Generic	pipe		Record for pipe geometry and material
Integer	nCir	1	Number of parallel circuits
Integer	nSeg	10	Number of volume segments in each circuit (along flow path)
Length	length	A/disPip/nCir	Length of the pipe of a single circuit [m]
Construction
Generic	layers		Definition of the construction, which must have at least two material layers
Integer	iLayPip		Number of the interface layer in which the pipes are located
Area	A		Surface area of radiant slab (all circuits combined) [m2]
Nominal condition
Pressure	dp_nominal	Modelica.Fluid.Pipes.BaseCla...	Pressure [Pa]
MassFlowRate	m_flow_nominal		Nominal mass flow rate of all circuits combined [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Initialization
Construction
Boolean	steadyStateInitial	false	=true initializes dT(0)/dt=0, false initializes T(0) at fixed temperature using T_a_start, T_c_start and T_b_start
Temperature	T_a_start	293.15	Initial temperature at surf_a, used if steadyStateInitial = false [K]
Temperature	T_b_start	293.15	Initial temperature at surf_b, used if steadyStateInitial = false [K]
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.)
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Flow resistance
Boolean	computeFlowResistance	true	=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
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate of all circuits combined 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	false	= true, if actual temperature at port is computed (may lead to events)

Connectors

Type Name Description

HeatPort_a surf_a Heat port at construction surface

HeatPort_a surf_b Heat port at construction surface

Type	Name	Description
HeatPort_a	surf_a	Heat port at construction surface
HeatPort_a	surf_b	Heat port at construction surface

Modelica definition

model ParallelCircuitsSlab 
  "Model of multiple parallel circuits of a radiant slab"
  extends Modelica.Fluid.Interfaces.PartialTwoPort(
    port_a(p(start=Medium.p_default,
             nominal=Medium.p_default)),
    port_b(p(start=Medium.p_default,
           nominal=Medium.p_default)));
  extends Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab;
  extends Buildings.Fluid.Interfaces.LumpedVolumeDeclarations;
  extends Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters(
   dp_nominal = Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed.pressureLoss_m_flow(
      m_flow=m_flow_nominal/nCir,
      rho_a=rho_nominal,
      rho_b=rho_nominal,
      mu_a=mu_nominal,
      mu_b=mu_nominal,
      length=length,
      diameter=pipe.dIn,
      roughness=pipe.roughness,
      m_flow_small=m_flow_small/nCir));

  parameter Integer nCir(min=1) = 1 "Number of parallel circuits";
  parameter Integer nSeg(min=2) = 10 
    "Number of volume segments in each circuit (along flow path)";

  parameter Modelica.SIunits.Area A 
    "Surface area of radiant slab (all circuits combined)";
  parameter Modelica.SIunits.Length length = A/disPip/nCir 
    "Length of the pipe of a single circuit";

  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Nominal mass flow rate of all circuits combined";
  parameter Modelica.SIunits.MassFlowRate m_flow_small(min=0) = 1E-4*abs(m_flow_nominal) 
    "Small mass flow rate of all circuits combined for regularization of zero flow";

  final parameter Modelica.SIunits.Velocity v_nominal = 4*m_flow_nominal/pipe.dIn^2/Modelica.Constants.pi/rho_nominal/nCir 
    "Velocity at m_flow_nominal";

  // Parameters used for the fluid model implementation
  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

  // Diagnostics
   parameter Boolean show_V_flow = false 
    "= true, if volume flow rate at inflowing port is computed";
   parameter Boolean show_T = false 
    "= true, if actual temperature at port is computed (may lead to events)";

  Modelica.SIunits.VolumeFlowRate V_flow=
      m_flow/Medium.density(sta_a) if show_V_flow 
    "Volume flow rate at inflowing port (positive when flow from port_a to port_b)";

  Modelica.SIunits.MassFlowRate m_flow(start=0) = port_a.m_flow 
    "Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) for all circuits combined";
  Modelica.SIunits.Pressure dp(start=0, displayUnit="Pa") = port_a.p - port_b.p 
    "Pressure difference between port_a and port_b";

  Medium.ThermodynamicState sta_a=if homotopyInitialization then 
      Medium.setState_phX(port_a.p,
                          homotopy(actual=actualStream(port_a.h_outflow),
                                   simplified=inStream(port_a.h_outflow)),
                          homotopy(actual=actualStream(port_a.Xi_outflow),
                                   simplified=inStream(port_a.Xi_outflow)))
    else 
      Medium.setState_phX(port_a.p,
                          actualStream(port_a.h_outflow),
                          actualStream(port_a.Xi_outflow)) if 
         show_T or show_V_flow "Medium properties in port_a";

  Medium.ThermodynamicState sta_b=if homotopyInitialization then 
      Medium.setState_phX(port_b.p,
                          homotopy(actual=actualStream(port_b.h_outflow),
                                   simplified=port_b.h_outflow),
                          homotopy(actual=actualStream(port_b.Xi_outflow),
                            simplified=port_b.Xi_outflow))
    else 
      Medium.setState_phX(port_b.p,
                          actualStream(port_b.h_outflow),
                          actualStream(port_b.Xi_outflow)) if 
          show_T "Medium properties in port_b";

  Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab sla(
    redeclare final package Medium = Medium,
    final sysTyp=sysTyp,
    final A=A/nCir,
    final disPip=disPip,
    final pipe=pipe,
    final layers=layers,
    final steadyStateInitial=steadyStateInitial,
    final iLayPip=iLayPip,
    final T_a_start=T_a_start,
    final T_b_start=T_b_start,
    final energyDynamics=energyDynamics,
    final massDynamics=massDynamics,
    final p_start=p_start,
    final T_start=T_start,
    final X_start=X_start,
    final C_start=C_start,
    final C_nominal=C_nominal,
    final allowFlowReversal=allowFlowReversal,
    final m_flow_nominal=m_flow_nominal/nCir,
    final m_flow_small=m_flow_small/nCir,
    final homotopyInitialization=homotopyInitialization,
    final show_V_flow=show_V_flow,
    final from_dp=from_dp,
    final dp_nominal=dp_nominal,
    final linearizeFlowResistance=linearizeFlowResistance,
    final deltaM=deltaM,
    final nSeg=nSeg,
    final length=length,
    final ReC=4000) "Single parallel circuit of the radiant slab";
protected 
  parameter Medium.ThermodynamicState state_start = Medium.setState_pTX(
      T=T_start,
      p=p_start,
      X=X_start[1:Medium.nXi]) "Start state";
  parameter Modelica.SIunits.Density rho_nominal = Medium.density(state_start);
  parameter Modelica.SIunits.DynamicViscosity mu_nominal = Medium.dynamicViscosity(state_start) 
    "Dynamic viscosity at nominal condition";

  Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.MassFlowRateMultiplier
                                                                                 masFloMul_a(
      redeclare final package Medium = Medium,
      final k=nCir) 
    "Mass flow multiplier, used to avoid having to instanciate multiple slab models";
  Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.MassFlowRateMultiplier
                                                                                 masFloMul_b(
      redeclare final package Medium = Medium,
      final k=nCir) 
    "Mass flow multiplier, used to avoid having to instanciate multiple slab models";
  Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.HeatFlowRateMultiplier
                                                                                 heaFloMul_a(
      final k=nCir) 
    "Heat flow rate multiplier, used to avoid having to instanciate multiple slab models";
  Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.HeatFlowRateMultiplier
                                                                                 heaFloMul_b(
     final k=nCir) 
    "Heat flow rate multiplier, used to avoid having to instanciate multiple slab models";
equation 
  connect(sla.port_b, masFloMul_b.port_a);

  connect(masFloMul_b.port_b, port_b);

  connect(port_a, masFloMul_a.port_b);

  connect(masFloMul_a.port_a, sla.port_a);

  connect(sla.surf_a,heaFloMul_a. port_a);
  connect(heaFloMul_a.port_b, surf_a);
  connect(sla.surf_b,heaFloMul_b. port_a);
  connect(heaFloMul_b.port_b, surf_b);
end ParallelCircuitsSlab;

Automatically generated Wed May 15 11:56:05 2013.