Buildings.Fluid.HeatExchangers.BaseClasses

Information

Extends from Modelica.Fluid.Icons.BaseClassLibrary (Icon for library).

Package Content

Name	Description
CoilHeader	Header for a heat exchanger register
CoilRegister	Register for a heat exchanger
DuctManifoldFixedResistance	Manifold for a heat exchanger air duct connection
DuctManifoldNoResistance	Duct manifold without resistance
HADryCoil	Sensible convective heat transfer model for air to water coil
HexElement	Element of a heat exchanger
MassExchange	Block to compute the latent heat transfer based on the Lewis number
PartialEffectiveness	Partial model to implement heat exchangers based on effectiveness model
PartialDuctManifold	Partial manifold for heat exchanger duct connection
PartialDuctPipeManifold	Partial heat exchanger duct and pipe manifold
PartialPipeManifold	Partial pipe manifold for a heat exchanger
PipeManifoldFixedResistance	Pipe manifold for a heat exchanger connection
PipeManifoldNoResistance	Manifold for heat exchanger register
Examples	Collection of models that illustrate model use and test models
appartusDewPoint	Computes the apparatus dewpoint temperature
epsilon_C	Computes heat exchanger effectiveness for given capacity flow rates and heat exchanger flow regime
epsilon_ntuZ	Computes heat exchanger effectiveness for given number of transfer units and heat exchanger flow regime
ntu_epsilonZ	Computes number of transfer units for given heat exchanger effectiveness and heat exchanger flow regime
lmtd	Log-mean temperature difference
Internal	Solve f(x, data) for x with given f

Buildings.Fluid.HeatExchangers.BaseClasses.CoilHeader

Information

Header for a heat exchanger coil.

This model connects the flow between its ports without modeling flow friction. Currently, the ports are connected without redistributing the flow. In latter versions, the model may be changed to define different flow reroutings in the coil header.

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
Integer	nPipPar		Number of parallel pipes in each register
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

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

Modelica definition

model CoilHeader "Header for a heat exchanger register"
  extends Buildings.BaseClasses.BaseIcon;

  outer Modelica.Fluid.System system "System wide properties";

  replaceable package Medium =
      Modelica.Media.Interfaces.PartialMedium "Medium in the component";
  parameter Boolean allowFlowReversal = system.allowFlowReversal 
    "= true to allow flow reversal, false restricts to design direction (port_a -> port_b)";

  parameter Integer nPipPar(min=1) "Number of parallel pipes in each register";
  parameter Modelica.SIunits.MassFlowRate mStart_flow_a 
    "Guess value for mass flow rate at port_a";

  Modelica.Fluid.Interfaces.FluidPort_a port_a[nPipPar](
        redeclare each final package Medium = Medium,
        each m_flow(start=mStart_flow_a/nPipPar, min=if allowFlowReversal then -Modelica.Constants.inf else 0)) 
    "Fluid connector a for medium (positive design flow direction is from port_a to port_b)";
    

  Modelica.Fluid.Interfaces.FluidPort_b port_b[nPipPar](
        redeclare each final package Medium = Medium,
        each m_flow(start=-mStart_flow_a/nPipPar, max=if allowFlowReversal then +Modelica.Constants.inf else 0)) 
    "Fluid connector b for medium (positive design flow direction is from port_a to port_b)";
    

equation 
  connect(port_a, port_b);
end CoilHeader;

Buildings.Fluid.HeatExchangers.BaseClasses.CoilRegister

Information

Register of a heat exchanger with dynamics on the fluids and the solid. The register represents one array of pipes that are perpendicular to the air stream. The hA value for both fluids is an input. The driving force for the heat transfer is the temperature difference between the fluid volumes and the solid in each heat exchanger element.

Extends from Buildings.Fluid.Interfaces.FourPortFlowResistanceParameters (Parameters for flow resistance for models with four ports).

Parameters

Type	Name	Default	Description
Integer	nPipPar	2	Number of parallel pipes in each register
Integer	nPipSeg	3	Number of pipe segments per register used for discretization
Boolean	allowCondensation	true	Set to false to compute sensible heat transfer only
Nominal condition
Pressure	dp1_nominal		Pressure [Pa]
Pressure	dp2_nominal		Pressure [Pa]
ThermalConductance	UA_nominal		Thermal conductance at nominal flow, used to compute time constant [W/K]
MassFlowRate	m1_flow_nominal		Mass flow rate medim 1 [kg/s]
MassFlowRate	m2_flow_nominal		Mass flow rate medium 2 [kg/s]
Time	tau1	20	Time constant at nominal flow for medium 1 [s]
Time	tau2	1	Time constant at nominal flow for medium 2 [s]
Time	tau_m	60	Time constant of metal at nominal UA value [s]
Fluid 1
Boolean	steadyState_1	false	Set to true for steady state model for fluid 1
Fluid 2
Boolean	steadyState_2	false	Set to true for steady state model for fluid 2
Flow resistance
Medium 1
Boolean	computeFlowResistance1	true	=true, compute flow resistance. Set to false to assume no friction
Boolean	from_dp1	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance1	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM1	0.1	Fraction of nominal flow rate where flow transitions to laminar
Medium 2
Boolean	computeFlowResistance2	true	=true, compute flow resistance. Set to false to assume no friction
Boolean	from_dp2	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance2	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM2	0.1	Fraction of nominal flow rate where flow transitions to laminar
Assumptions
Boolean	allowFlowReversal1	system.allowFlowReversal	= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
Boolean	allowFlowReversal2	system.allowFlowReversal	= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	energyDynamics1	Modelica.Fluid.Types.Dynamic...	Default formulation of energy balances for volume 1
Dynamics	energyDynamics2	Modelica.Fluid.Types.Dynamic...	Default formulation of energy balances for volume 2

Connectors

Type	Name	Description
FluidPort_a	port_a1[nPipPar]	Fluid connector a for medium 1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1[nPipPar]	Fluid connector b for medium 1 (positive design flow direction is from port_a to port_b)
FluidPort_a	port_a2[nPipPar, nPipSeg]	Fluid connector a for medium 2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2[nPipPar, nPipSeg]	Fluid connector b for medium 2 (positive design flow direction is from port_a to port_b)
input RealInput	Gc_2	Signal representing the convective thermal conductance medium 2 in [W/K]
input RealInput	Gc_1	Signal representing the convective thermal conductance medium 1 in [W/K]

Modelica definition

model CoilRegister "Register for a heat exchanger"
  import Modelica.Constants;
  extends Buildings.Fluid.Interfaces.FourPortFlowResistanceParameters(
     final computeFlowResistance1=true, final computeFlowResistance2=true);
  replaceable package Medium1 =
      Modelica.Media.Interfaces.PartialMedium "Medium 1 in the component";
  replaceable package Medium2 =
      Modelica.Media.Interfaces.PartialMedium "Medium 2 in the component";
  outer Modelica.Fluid.System system "System wide properties";

  parameter Boolean allowFlowReversal1 = system.allowFlowReversal 
    "= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)";
  parameter Boolean allowFlowReversal2 = system.allowFlowReversal 
    "= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)";

  parameter Integer nPipPar(min=1)=2 
    "Number of parallel pipes in each register";
  parameter Integer nPipSeg(min=1)=3 
    "Number of pipe segments per register used for discretization";
  final parameter Integer nEle = nPipPar * nPipSeg 
    "Number of heat exchanger elements";

  Buildings.Fluid.HeatExchangers.BaseClasses.HexElement[
                      nPipPar, nPipSeg] ele(
    redeclare each package Medium1 = Medium1,
    redeclare each package Medium2 = Medium2,
    each allowFlowReversal1=allowFlowReversal1,
    each allowFlowReversal2=allowFlowReversal2,
    each tau1=tau1/nPipSeg,
    each m1_flow_nominal=m1_flow_nominal/nPipPar,
    each tau2=tau2,
    each m2_flow_nominal=m2_flow_nominal/nPipPar/nPipSeg,
    each tau_m=tau_m,
    each UA_nominal=UA_nominal/nPipPar/nPipSeg,
    each energyDynamics1=energyDynamics1,
    each energyDynamics2=energyDynamics2,
    each allowCondensation=allowCondensation,
    each from_dp1=from_dp1,
    each linearizeFlowResistance1=linearizeFlowResistance1,
    each deltaM1=deltaM1,
    each from_dp2=from_dp2,
    each linearizeFlowResistance2=linearizeFlowResistance2,
    each deltaM2=deltaM2,
    each dp1_nominal=dp1_nominal,
    each dp2_nominal=dp2_nominal) "Element of a heat exchanger";

  Modelica.Fluid.Interfaces.FluidPort_a[nPipPar] port_a1(
        redeclare each package Medium = Medium1,
        each m_flow(start=0, min=if allowFlowReversal1 then -Constants.inf else 0)) 
    "Fluid connector a for medium 1 (positive design flow direction is from port_a1 to port_b1)";
  Modelica.Fluid.Interfaces.FluidPort_b[nPipPar] port_b1(
        redeclare each package Medium = Medium1,
        each m_flow(start=0, max=if allowFlowReversal1 then +Constants.inf else 0)) 
    "Fluid connector b for medium 1 (positive design flow direction is from port_a to port_b)";
  Modelica.Fluid.Interfaces.FluidPort_a[nPipPar,nPipSeg] port_a2(
        redeclare each package Medium = Medium2,
        each m_flow(start=0, min=if allowFlowReversal2 then -Constants.inf else 0)) 
    "Fluid connector a for medium 2 (positive design flow direction is from port_a2 to port_b2)";
  Modelica.Fluid.Interfaces.FluidPort_b[nPipPar,nPipSeg] port_b2(
        redeclare each package Medium = Medium2,
        each m_flow(start=0, max=if allowFlowReversal2 then +Constants.inf else 0)) 
    "Fluid connector b for medium 2 (positive design flow direction is from port_a to port_b)";
    

  parameter Modelica.SIunits.ThermalConductance UA_nominal 
    "Thermal conductance at nominal flow, used to compute time constant";

  parameter Modelica.SIunits.MassFlowRate m1_flow_nominal 
    "Mass flow rate medim 1";
  parameter Modelica.SIunits.MassFlowRate m2_flow_nominal 
    "Mass flow rate medium 2";

  parameter Modelica.SIunits.Time tau1=20 
    "Time constant at nominal flow for medium 1";
  parameter Modelica.SIunits.Time tau2=1 
    "Time constant at nominal flow for medium 2";
  parameter Boolean steadyState_1=false 
    "Set to true for steady state model for fluid 1";
  parameter Boolean steadyState_2=false 
    "Set to true for steady state model for fluid 2";
  Modelica.SIunits.HeatFlowRate Q1_flow 
    "Heat transfered from solid into medium 1";
  Modelica.SIunits.HeatFlowRate Q2_flow 
    "Heat transfered from solid into medium 2";
  parameter Modelica.SIunits.Time tau_m=60 
    "Time constant of metal at nominal UA value";
  parameter Boolean allowCondensation = true 
    "Set to false to compute sensible heat transfer only";
  parameter Modelica.Fluid.Types.Dynamics energyDynamics1=
    Modelica.Fluid.Types.Dynamics.DynamicFreeInitial 
    "Default formulation of energy balances for volume 1";
  parameter Modelica.Fluid.Types.Dynamics energyDynamics2=
    Modelica.Fluid.Types.Dynamics.DynamicFreeInitial 
    "Default formulation of energy balances for volume 2";
  Modelica.Blocks.Interfaces.RealInput Gc_2 
    "Signal representing the convective thermal conductance medium 2 in [W/K]";
  Modelica.Blocks.Interfaces.RealInput Gc_1 
    "Signal representing the convective thermal conductance medium 1 in [W/K]";
protected 
  Modelica.Blocks.Math.Gain gai_1(k=1/nEle) 
    "Gain medium-side 1 to take discretization into account";
  Modelica.Blocks.Math.Gain gai_2(k=1/nEle) 
    "Gain medium-side 2 to take discretization into account";
equation 
  Q1_flow = sum(ele[i,j].Q1_flow for i in 1:nPipPar, j in 1:nPipSeg);
  Q2_flow = sum(ele[i,j].Q2_flow for i in 1:nPipPar, j in 1:nPipSeg);
  for i in 1:nPipPar loop
    // liquid side (pipes)
    connect(ele[i,1].port_a1,       port_a1[i]);
    connect(ele[i,nPipSeg].port_b1, port_b1[i]);
    for j in 1:nPipSeg-1 loop
      connect(ele[i,j].port_b1, ele[i,j+1].port_a1);
    end for;
    // gas side (duct)                                                                                      //water connections
    for j in 1:nPipSeg loop
      connect(ele[i,j].port_a2, port_a2[i,j]);
      connect(ele[i,j].port_b2, port_b2[i,j]);
    end for;
  end for;

  connect(Gc_1, gai_1.u);
  connect(Gc_2, gai_2.u);
  for i in 1:nPipPar loop

     for j in 1:nPipSeg loop
      connect(gai_1.y, ele[i,j].Gc_1);
      connect(gai_2.y, ele[i,j].Gc_2);
     end for;
  end for;

end CoilRegister;

Buildings.Fluid.HeatExchangers.BaseClasses.DuctManifoldFixedResistance

Information

Duct manifold with a fixed flow resistance.

This model causes the flow to be distributed equally into each flow path by using a fixed flow resistance for each flow path.

Extends from PartialDuctManifold (Partial manifold for heat exchanger duct connection).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Integer	nPipSeg		Number of pipe segments per register used for discretization
Boolean	use_dh	false	Set to true to specify hydraulic diameter
Length	dh	1	Hydraulic diameter of duct [m]
Real	ReC	4000	Reynolds number where transition to turbulent starts
Real	deltaM	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Length	dl	0.3	Length of mixing volume [m]
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Nominal Condition
MassFlowRate	m_flow_nominal		Mass flow rate at port_a [kg/s]
Pressure	dp_nominal		Pressure [Pa]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Default formulation of energy balances for volume
Advanced
Boolean	linearized	false	= true, use linear relation between m_flow and dp for any flow rate
Boolean	from_dp	false	= true, use m_flow = f(dp) else dp = f(m_flow)

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a for medium (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b[nPipPar, nPipSeg]	Fluid connector b for medium (positive design flow direction is from port_a to port_b)

Modelica definition

model DuctManifoldFixedResistance 
  "Manifold for a heat exchanger air duct connection"
  extends PartialDuctManifold;

  parameter Boolean use_dh = false "Set to true to specify hydraulic diameter";

  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Mass flow rate at port_a";
  parameter Modelica.SIunits.Pressure dp_nominal(min=0) "Pressure";
  parameter Modelica.SIunits.Length dh=1 "Hydraulic diameter of duct";
  parameter Real ReC=4000 
    "Reynolds number where transition to turbulent starts";
  parameter Boolean linearized = false 
    "= true, use linear relation between m_flow and dp for any flow rate";
  parameter Real deltaM(min=0) = 0.3 
    "Fraction of nominal mass flow rate where transition to turbulent occurs";
  parameter Boolean from_dp = false 
    "= true, use m_flow = f(dp) else dp = f(m_flow)";

  Fluid.FixedResistances.FixedResistanceDpM[nPipPar,nPipSeg] fixRes(
    redeclare each package Medium = Medium,
    each m_flow_nominal=m_flow_nominal/nPipPar/nPipSeg,
    each m_flow(start=mStart_flow_a/nPipPar/nPipSeg),
    each dp_nominal=dp_nominal,
    each dh=dh/sqrt(nPipPar*nPipSeg),
    each from_dp=from_dp,
    each deltaM=deltaM,
    each ReC=ReC,
    each use_dh=use_dh,
    each linearized=linearized) "Fixed resistance for each duct";
  parameter Modelica.SIunits.Length dl = 0.3 "Length of mixing volume";
  Fluid.MixingVolumes.MixingVolume vol(redeclare package Medium = Medium,
    final V=dh*dh*dl,
    final nPorts=1+nPipPar*nPipSeg,
    final energyDynamics=energyDynamics,
    final massDynamics=energyDynamics);
  parameter Modelica.Fluid.Types.Dynamics energyDynamics=
    Modelica.Fluid.Types.Dynamics.DynamicFreeInitial 
    "Default formulation of energy balances for volume";
equation 
  for i in 1:nPipPar loop
    for j in 1:nPipSeg loop
      connect(vol.ports[1+(i-1)*nPipSeg+j], fixRes[i, j].port_a);
    end for;
  end for;

  connect(port_a, vol.ports[1]);
  connect(fixRes.port_b, port_b);
end DuctManifoldFixedResistance;

Buildings.Fluid.HeatExchangers.BaseClasses.DuctManifoldNoResistance

Information

Duct manifold without flow resistance.

This model connects the flows between the ports without modeling flow friction. The model is used in conjunction with a manifold which contains pressure drop elements and that is added to the other side of the heat exchanger registers.

Extends from PartialDuctManifold (Partial manifold for heat exchanger duct connection).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Integer	nPipSeg		Number of pipe segments per register used for discretization
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a for medium (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b[nPipPar, nPipSeg]	Fluid connector b for medium (positive design flow direction is from port_a to port_b)

Modelica definition

model DuctManifoldNoResistance "Duct manifold without resistance"
  extends PartialDuctManifold;

equation 
  for i in 1:nPipPar loop
    for j in 1:nPipSeg loop
    connect(port_a, port_b[i, j]);
    end for;
  end for;
end DuctManifoldNoResistance;

Buildings.Fluid.HeatExchangers.BaseClasses.HADryCoil

Information

Model for sensible convective heat transfer coefficients for an air to water coil.

This model computes the convective heat transfer coefficient for an air to water coil. The parameters allow a user to enable or disable, individually for each medium, the mass flow and/or the temperature dependence of the convective heat transfer coefficients. For a detailed explanation of the equation, see the references below.

References

• Wetter Michael, Simulation model finned water-air-coil without condensation, LBNL-42355, Lawrence Berkeley National Laboratory, Berkeley, CA, 1999.
• Wetter Michael, Simulation model air-to-air plate heat exchanger, LBNL-42354, Lawrence Berkeley National Laboratory, Berkeley, CA, 1999.

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
Real	n_w	0.85	Water-side exponent for convective heat transfer coefficient, h~m_flow^n
Real	n_a	0.8	Air-side exponent for convective heat transfer coefficient, h~m_flow^n
Nominal condition
ThermalConductance	UA_nominal		Thermal conductance at nominal flow [W/K]
MassFlowRate	m_flow_nominal_w		Water mass flow rate [kg/s]
MassFlowRate	m_flow_nominal_a		Air mass flow rate [kg/s]
Real	r_nominal	0.5	Ratio between air-side and water-side convective heat transfer coefficient
ThermalConductance	hA_nominal_w	UA_nominal*(r_nominal + 1)/r...	Water side convective heat transfer coefficient [W/K]
ThermalConductance	hA_nominal_a	r_nominal*hA_nominal_w	Air side convective heat transfer coefficient, including fin resistance [W/K]
Temperature	T0_w	Modelica.SIunits.Conversions...	Water temperature [K]
Temperature	T0_a	Modelica.SIunits.Conversions...	Air temperature [K]
Advanced
Modeling detail
Boolean	waterSideFlowDependent	true	Set to false to make water-side hA independent of mass flow rate
Boolean	airSideFlowDependent	true	Set to false to make air-side hA independent of mass flow rate
Boolean	waterSideTemperatureDependent	true	Set to false to make water-side hA independent of temperature
Boolean	airSideTemperatureDependent	true	Set to false to make air-side hA independent of temperature

Connectors

Type	Name	Description
input RealInput	m1_flow	Mass flow rate medium 1
input RealInput	m2_flow	Mass flow rate medium 2
input RealInput	T_1	Temperature medium 1
input RealInput	T_2	Temperature medium 2
output RealOutput	hA_1	Convective heat transfer medium 1
output RealOutput	hA_2	Convective heat transfer medium 2

Modelica definition

model HADryCoil 
  "Sensible convective heat transfer model for air to water coil"
  extends Buildings.BaseClasses.BaseIcon;
  parameter Modelica.SIunits.ThermalConductance UA_nominal(min=0) 
    "Thermal conductance at nominal flow";

  parameter Modelica.SIunits.MassFlowRate m_flow_nominal_w 
    "Water mass flow rate";
  parameter Modelica.SIunits.MassFlowRate m_flow_nominal_a "Air mass flow rate";

  Modelica.Blocks.Interfaces.RealInput m1_flow "Mass flow rate medium 1";
  Modelica.Blocks.Interfaces.RealInput m2_flow "Mass flow rate medium 2";
  Modelica.Blocks.Interfaces.RealInput T_1 "Temperature medium 1";
  Modelica.Blocks.Interfaces.RealInput T_2 "Temperature medium 2";

  Modelica.Blocks.Interfaces.RealOutput hA_1 
    "Convective heat transfer medium 1";
  Modelica.Blocks.Interfaces.RealOutput hA_2 
    "Convective heat transfer medium 2";

  parameter Real r_nominal(min=0, max=1)=0.5 
    "Ratio between air-side and water-side convective heat transfer coefficient";
  parameter Modelica.SIunits.ThermalConductance hA_nominal_w(min=0)=UA_nominal * (r_nominal+1)/r_nominal 
    "Water side convective heat transfer coefficient";
  parameter Modelica.SIunits.ThermalConductance hA_nominal_a(min=0)=r_nominal * hA_nominal_w 
    "Air side convective heat transfer coefficient, including fin resistance";
  parameter Real n_w(min=0, max=1)=0.85 
    "Water-side exponent for convective heat transfer coefficient, h~m_flow^n";
  parameter Real n_a(min=0, max=1)=0.8 
    "Air-side exponent for convective heat transfer coefficient, h~m_flow^n";
  parameter Modelica.SIunits.Temperature T0_w=
          Modelica.SIunits.Conversions.from_degC(20) "Water temperature";
  parameter Modelica.SIunits.Temperature T0_a=
          Modelica.SIunits.Conversions.from_degC(20) "Air temperature";
  parameter Boolean waterSideFlowDependent=true 
    "Set to false to make water-side hA independent of mass flow rate";
  parameter Boolean airSideFlowDependent = true 
    "Set to false to make air-side hA independent of mass flow rate";
  parameter Boolean waterSideTemperatureDependent = true 
    "Set to false to make water-side hA independent of temperature";
  parameter Boolean airSideTemperatureDependent = true 
    "Set to false to make air-side hA independent of temperature";
protected 
  Real x_a(min=0) 
    "Factor for air side temperature dependent variation of heat transfer coefficient";
  Real x_w(min=0) 
    "Factor for water side temperature dependent variation of heat transfer coefficient";
  parameter Real s_w(min=0, fixed=false) 
    "Coefficient for temperature dependence of water side heat transfer coefficient";
  Real fm_w "Fraction of actual to nominal mass flow rate";
  Real fm_a "Fraction of actual to nominal mass flow rate";
initial equation 
  s_w =  if waterSideTemperatureDependent then 
            0.014/(1+0.014*Modelica.SIunits.Conversions.to_degC(T0_w)) else 
              1;
equation 
  fm_w = if waterSideFlowDependent then 
              m1_flow / m_flow_nominal_w else 1;
  fm_a = if airSideFlowDependent then 
              m2_flow / m_flow_nominal_a else 1;
  x_w = if waterSideTemperatureDependent then 
         1 + s_w * (T_1-T0_w) else 
              1;
  x_a = if airSideTemperatureDependent then 
         1 + 4.769E-3 * (T_2-T0_a) else 
              1;
  if waterSideFlowDependent then
    hA_1 = x_w * hA_nominal_w
               * Buildings.Utilities.Math.Functions.regNonZeroPower(fm_w, n_w, 0.1);
  else
    hA_1 = x_w * hA_nominal_w;
  end if;

  if airSideFlowDependent then
    hA_2 = x_a * hA_nominal_a
               * Buildings.Utilities.Math.Functions.regNonZeroPower(fm_a, n_a, 0.1);
  else
    hA_2 = x_a * hA_nominal_a;
  end if;
end HADryCoil;

Buildings.Fluid.HeatExchangers.BaseClasses.HexElement

Information

Element of a heat exchanger with dynamics on the fluids and the solid. The hA value for both fluids is an input. The driving force for the heat transfer is the temperature difference between the fluid volumes and the solid.

The heat capacity C of the metal is assigned as follows. Suppose the metal temperature is governed by

C dT ⁄ dt = (hA)₁ (T₁ - T) + (hA)₂ (T₂ - T)

C dT ⁄ dt = 2 (UA)₀ ( (T₁ - T) + (T₂ - T) )

C = 2 (UA)₀ τ_m

Extends from Buildings.Fluid.Interfaces.PartialDynamicFourPortTransformer (Partial model transporting two fluid streams between four ports with storing mass or energy).

Parameters

Type	Name	Default	Description
replaceable package Medium1		PartialMedium	Medium 1 in the component
replaceable package Medium2		PartialMedium	Medium 2 in the component
HeatCapacity	C	2*UA_nominal*tau_m	Heat capacity of metal (= cp*m) [J/K]
Boolean	allowCondensation	true	Set to false to compute sensible heat transfer only
Nominal condition
MassFlowRate	m1_flow_nominal		Nominal mass flow rate [kg/s]
MassFlowRate	m2_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp1_nominal		Pressure [Pa]
Pressure	dp2_nominal		Pressure [Pa]
Time	tau1	60	Time constant at nominal flow [s]
Time	tau2	60	Time constant at nominal flow [s]
ThermalConductance	UA_nominal		Thermal conductance at nominal flow, used to compute time constant [W/K]
Time	tau_m	60	Time constant of metal at nominal UA value [s]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Assumptions
Boolean	allowFlowReversal1	system.allowFlowReversal	= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
Boolean	allowFlowReversal2	system.allowFlowReversal	= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	energyDynamics	system.energyDynamics	Formulation of energy balance
Dynamics	massDynamics	system.massDynamics	Formulation of mass balance
Dynamics	substanceDynamics	energyDynamics	Formulation of substance balance
Dynamics	traceDynamics	energyDynamics	Formulation of trace substance balance
Dynamics	energyDynamics1	Modelica.Fluid.Types.Dynamic...	Default formulation of energy balances for volume 1
Dynamics	energyDynamics2	Modelica.Fluid.Types.Dynamic...	Default formulation of energy balances for volume 2
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
Advanced
MassFlowRate	m1_flow_small	1E-4*m1_flow_nominal	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*m2_flow_nominal	Small mass flow rate for regularization of zero flow [kg/s]
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)
Flow resistance
Medium 1
Boolean	from_dp1	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance1	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM1	0.1	Fraction of nominal flow rate where flow transitions to laminar
Medium 2
Boolean	from_dp2	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance2	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM2	0.1	Fraction of nominal flow rate where flow transitions to laminar

Connectors

Type	Name	Description
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
input RealInput	Gc_1	Signal representing the convective thermal conductance medium 1 in [W/K]
input RealInput	Gc_2	Signal representing the convective thermal conductance medium 2 in [W/K]

Modelica definition

model HexElement "Element of a heat exchanger"
  extends Buildings.Fluid.Interfaces.PartialDynamicFourPortTransformer(
    vol1(redeclare package Medium = Medium1,
          V=m1_flow_nominal*tau1/rho1_nominal,
          nPorts=2,
          final energyDynamics=energyDynamics1,
          final massDynamics=energyDynamics1),
    redeclare Buildings.Fluid.MixingVolumes.MixingVolumeDryAir vol2(
          redeclare package Medium = Medium2,
          nPorts = 2,
          V=m2_flow_nominal*tau2/rho2_nominal,
          final energyDynamics=energyDynamics2,
          final massDynamics=energyDynamics2));
  // Note that we MUST declare the value of vol2.V here.
  // Otherwise, if the class of vol2 is redeclared at a higher level,
  // it will overwrite the assignment of V in the base class
  // PartialDynamicFourPortTransformer, which will cause V=0.
  // Assigning the values for vol1 here is optional, but we added
  // it to be consistent in the implementation of vol1 and vol2.

  parameter Modelica.SIunits.ThermalConductance UA_nominal 
    "Thermal conductance at nominal flow, used to compute time constant";
  parameter Modelica.SIunits.Time tau_m(min=0) = 60 
    "Time constant of metal at nominal UA value";
  parameter Modelica.SIunits.HeatCapacity C=2*UA_nominal*tau_m 
    "Heat capacity of metal (= cp*m)";

  Modelica.Blocks.Interfaces.RealInput Gc_1 
    "Signal representing the convective thermal conductance medium 1 in [W/K]";
  Modelica.Blocks.Interfaces.RealInput Gc_2 
    "Signal representing the convective thermal conductance medium 2 in [W/K]";

  parameter Boolean allowCondensation = true 
    "Set to false to compute sensible heat transfer only";

  MassExchange masExc(
       redeclare package Medium = Medium2) if allowCondensation 
    "Model for mass exchange";

  parameter Modelica.Fluid.Types.Dynamics energyDynamics1=
    Modelica.Fluid.Types.Dynamics.DynamicFreeInitial 
    "Default formulation of energy balances for volume 1";
  parameter Modelica.Fluid.Types.Dynamics energyDynamics2=
    Modelica.Fluid.Types.Dynamics.DynamicFreeInitial 
    "Default formulation of energy balances for volume 2";

  Modelica.Thermal.HeatTransfer.Components.HeatCapacitor mas(
                                                  C=C, T(stateSelect=StateSelect.always)) 
    "Mass of metal";
  Modelica.Thermal.HeatTransfer.Components.Convection con1(dT(min=-200)) 
    "Convection (and conduction) on fluid side 1";
  Modelica.Thermal.HeatTransfer.Components.Convection con2(dT(min=-200)) 
    "Convection (and conduction) on fluid side 2";
  Modelica.Thermal.HeatTransfer.Sensors.TemperatureSensor temSen(
    T(final quantity="Temperature",
      final unit = "K", displayUnit = "degC", min=0)) 
    "Temperature sensor of metal";
  Modelica.Thermal.HeatTransfer.Sensors.HeatFlowSensor heaFloSen_1 
    "Heat input into fluid 1";
  Modelica.Thermal.HeatTransfer.Sensors.HeatFlowSensor heaFloSen_2 
    "Heat input into fluid 1";
equation 
  connect(Gc_1, con1.Gc);
  connect(Gc_2, con2.Gc);
  connect(temSen.T, masExc.TSur);
  connect(Gc_2, masExc.Gc);
  connect(masExc.mWat_flow, vol2.mWat_flow);
  connect(masExc.TLiq, vol2.TWat);
  connect(vol2.X_w, masExc.XInf);
  connect(con1.solid,mas. port);
  connect(con2.solid,mas. port);
  connect(mas.port,temSen. port);
  connect(con1.fluid,heaFloSen_1. port_a);
  connect(con2.fluid,heaFloSen_2. port_a);
  connect(heaFloSen_1.port_b, vol1.heatPort);
  connect(heaFloSen_2.port_b, vol2.heatPort);
end HexElement;

Buildings.Fluid.HeatExchangers.BaseClasses.MassExchange

Information

This model computes the mass transfer based on similarity laws between the convective sensible heat transfer coefficient and the mass transfer coefficient.

Using the Lewis number which is defined as the ratio between the heat and mass diffusion coefficients, one can obtain the ratio between convection heat transfer coefficient h in (W/(m^2*K)) and mass transfer coefficient h_m in (m/s) as follows:

h ⁄ h_m = ρ c_p Le^(1-n), h_m

n_A = G_c ⁄ (c_p Le^(1-n)) (X_s - X_∞),

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
Real	Le	1	Lewis number (around 1 for water vapor in air)
Real	n	1/3	Exponent in bondary layer ratio, delta/delta_t = Pr^n

Connectors

Type	Name	Description
input RealInput	XInf	Water mass fraction of medium
input RealInput	TSur	Surface temperature [K]
output RealOutput	mWat_flow	Water flow rate [kg/s]
output RealOutput	TLiq	Temperature at which condensate drains from system [K]
input RealInput	Gc	Signal representing the convective (sensible) thermal conductance in [W/K]

Modelica definition

model MassExchange 
  "Block to compute the latent heat transfer based on the Lewis number"
  import Buildings;
  extends Buildings.BaseClasses.BaseIcon;
  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium 
    "Fluid medium model";

  Modelica.Blocks.Interfaces.RealInput XInf "Water mass fraction of medium";
  Modelica.Blocks.Interfaces.RealInput TSur(final quantity="Temperature",
                                            final unit = "K", displayUnit = "degC", min=0) 
    "Surface temperature";
  Modelica.Blocks.Interfaces.RealOutput mWat_flow(final unit = "kg/s") 
    "Water flow rate";
  Modelica.Blocks.Interfaces.RealOutput TLiq(final quantity="Temperature",
                                             final unit = "K", displayUnit = "degC", min=0) 
    "Temperature at which condensate drains from system";
  Modelica.Blocks.Interfaces.RealInput Gc 
    "Signal representing the convective (sensible) thermal conductance in [W/K]";
  parameter Real Le = 1 "Lewis number (around 1 for water vapor in air)";
  parameter Real n = 1/3 
    "Exponent in bondary layer ratio, delta/delta_t = Pr^n";
public 
  Buildings.Utilities.Psychrometrics.X_pW humRatPre(              use_p_in=
        false) "Model to convert water vapor pressure into humidity ratio";
  Buildings.Utilities.Psychrometrics.pW_TDewPoi TDewPoi 
    "Model to compute the water vapor pressure at the dew point";
  Modelica.Blocks.Math.Gain gain(k=1/cpLe) 
    "Constant to convert from heat transfer to mass transfer";
  Modelica.Blocks.Math.Product mWat "Water flow rate";
  Modelica.Blocks.Math.Min min;
  Modelica.Blocks.Sources.Constant zero(k=0) "Constant for zero";
  Modelica.Blocks.Math.Add delX(k2=-1, k1=1) "Humidity difference";
protected 
 parameter Medium.ThermodynamicState sta0 = Medium.setState_phX(h=Medium.h_default,
       p=Medium.p_default, X=Medium.X_default);
 parameter Modelica.SIunits.SpecificHeatCapacity cp=Medium.specificHeatCapacityCp(sta0) 
    "Density, used to compute fluid volume";
 parameter Real cpLe(unit="J/(kg.K)") = cp * Le^(1-n);
equation 
  connect(TSur, TDewPoi.T);
  connect(TDewPoi.p_w, humRatPre.p_w);
  connect(TSur, TLiq);
  connect(Gc, gain.u);
  connect(gain.y, mWat.u2);
  connect(mWat.y, mWat_flow);
  connect(zero.y,min. u1);
  connect(delX.u2,XInf);
  connect(humRatPre.X_w, delX.u1);
  connect(delX.y, min.u2);
  connect(min.y, mWat.u1);
end MassExchange;

Buildings.Fluid.HeatExchangers.BaseClasses.PartialEffectiveness

Information

Partial model to implement heat exchanger models

Classes that extend this model need to implement heat and mass balance equations in a form like

  // transfered heat
  Q1_flow = eps * QMax_flow;
  // no heat loss to ambient
  0 = Q1_flow + Q2_flow;
  // no mass exchange
  mXi1_flow = zeros(Medium1.nXi);
  mXi2_flow = zeros(Medium2.nXi);

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

Parameters

Type	Name	Default	Description
replaceable package Medium1		PartialMedium	Medium 1 in the component
replaceable package Medium2		PartialMedium	Medium 2 in the component
Nominal condition
MassFlowRate	m1_flow_nominal		Nominal mass flow rate [kg/s]
MassFlowRate	m2_flow_nominal		Nominal mass flow rate [kg/s]
Pressure	dp1_nominal		Pressure [Pa]
Pressure	dp2_nominal		Pressure [Pa]
Initialization
MassFlowRate	m1_flow.start	0	Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) [kg/s]
Pressure	dp1.start	0	Pressure difference between port_a1 and port_b1 [Pa]
MassFlowRate	m2_flow.start	0	Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) [kg/s]
Pressure	dp2.start	0	Pressure difference between port_a2 and port_b2 [Pa]
Assumptions
Boolean	allowFlowReversal1	system.allowFlowReversal	= true to allow flow reversal in medium 1, false restricts to design direction (port_a -> port_b)
Boolean	allowFlowReversal2	system.allowFlowReversal	= true to allow flow reversal in medium 2, false restricts to design direction (port_a -> port_b)
Initialization
SpecificEnthalpy	h_outflow_a1_start	Medium1.h_default	Start value for enthalpy flowing out of port a1 [J/kg]
SpecificEnthalpy	h_outflow_b1_start	Medium1.h_default	Start value for enthalpy flowing out of port b1 [J/kg]
SpecificEnthalpy	h_outflow_a2_start	Medium2.h_default	Start value for enthalpy flowing out of port a2 [J/kg]
SpecificEnthalpy	h_outflow_b2_start	Medium2.h_default	Start value for enthalpy flowing out of port b2 [J/kg]
Advanced
MassFlowRate	m1_flow_small	1E-4*m1_flow_nominal	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*m2_flow_nominal	Small mass flow rate for regularization of zero flow [kg/s]
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
Medium 1
Boolean	from_dp1	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance1	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM1	0.1	Fraction of nominal flow rate where flow transitions to laminar
Medium 2
Boolean	from_dp2	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance2	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM2	0.1	Fraction of nominal flow rate where flow transitions to laminar

Connectors

Type	Name	Description
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)

Modelica definition

partial model PartialEffectiveness 
  "Partial model to implement heat exchangers based on effectiveness model"
  extends Fluid.Interfaces.PartialStaticFourPortHeatMassTransfer(final show_T=true);

  Modelica.SIunits.Temperature T_in1 "Inlet temperature medium 1";
  Modelica.SIunits.Temperature T_in2 "Inlet temperature medium 2";
  Modelica.SIunits.ThermalConductance C1_flow 
    "Heat capacity flow rate medium 1";
  Modelica.SIunits.ThermalConductance C2_flow 
    "Heat capacity flow rate medium 2";
  Modelica.SIunits.ThermalConductance CMin_flow(min=0) 
    "Minimum heat capacity flow rate";
  Modelica.SIunits.HeatFlowRate QMax_flow 
    "Maximum heat flow rate into medium 1";
protected 
  Real gai1(min=0, max=1) "Auxiliary variable for smoothing at zero flow";
  Real gai2(min=0, max=1) "Auxiliary variable for smoothing at zero flow";
  parameter Real delta=1E-3 "Parameter used for smoothing";

  parameter Modelica.SIunits.SpecificHeatCapacity cp1_default(fixed=false) 
    "Specific heat capacity of medium 1 at default medium state";
  parameter Modelica.SIunits.SpecificHeatCapacity cp2_default(fixed=false) 
    "Specific heat capacity of medium 2 at default medium state";
  parameter Modelica.SIunits.ThermalConductance CMin_flow_small(fixed=false) 
    "Small value for smoothing of minimum heat capacity flow rate";
  Real fra_a1(min=0, max=1) 
    "Fraction of incoming state taken from port a2 (used to avoid excessive calls to regStep)";
  Real fra_b1(min=0, max=1) 
    "Fraction of incoming state taken from port b2 (used to avoid excessive calls to regStep)";
  Real fra_a2(min=0, max=1) 
    "Fraction of incoming state taken from port a2 (used to avoid excessive calls to regStep)";
  Real fra_b2(min=0, max=1) 
    "Fraction of incoming state taken from port b2 (used to avoid excessive calls to regStep)";
initial equation 
  cp1_default = Medium1.specificHeatCapacityCp(Medium1.setState_pTX(
    Medium1.p_default,
    Medium1.T_default,
    Medium1.X_default));
  cp2_default = Medium2.specificHeatCapacityCp(Medium2.setState_pTX(
    Medium2.p_default,
    Medium2.T_default,
    Medium2.X_default));
  CMin_flow_small = min(m1_flow_small*cp1_default, m2_flow_small*cp2_default);
equation 
  if allowFlowReversal2 then
    fra_a2 = Modelica.Fluid.Utilities.regStep(
      m2_flow,
      1,
      0,
      m2_flow_small);
    fra_b2 = 1-fra_a2;
  else
    fra_a2 = 1;
    fra_b2 = 0;
  end if;
  if allowFlowReversal1 then
    fra_a1 = Modelica.Fluid.Utilities.regStep(
      m1_flow,
      1,
      0,
      m1_flow_small);
    fra_b1 = 1-fra_a1;
  else
    fra_a1 = 1;
    fra_b1 = 0;
  end if;

  // Compute a gain that goes to zero near zero flow rate.
  // This is required to smoothen the heat transfer at very small flow rates.
  // Note that gaiK = 1 for abs(mK_flow) > mK_flow_small
  gai1 = Modelica.Fluid.Utilities.regStep(
    abs(m1_flow) - 0.75*m1_flow_small,
    1,
    0,
    0.25*m1_flow_small);
  gai2 = Modelica.Fluid.Utilities.regStep(
    abs(m2_flow) - 0.75*m2_flow_small,
    1,
    0,
    0.25*m2_flow_small);

  /////////////////////////////////////////////////////////
  // Definitions for heat transfer effectiveness model
  T_in1 = if allowFlowReversal1 then 
    fra_a1 * Medium1.temperature(state_a1_inflow) + fra_b1 * Medium1.temperature(state_b1_inflow) else 
    Medium1.temperature(state_a1_inflow);
  T_in2 = if allowFlowReversal2 then 
    fra_a2 * Medium2.temperature(state_a2_inflow) + fra_b2 * Medium2.temperature(state_b2_inflow) else 
    Medium2.temperature(state_a2_inflow);

  C1_flow = abs(m1_flow)*
    ( if allowFlowReversal1 then 
           fra_a1 * Medium1.specificHeatCapacityCp(state_a1_inflow) +
           fra_b1 * Medium1.specificHeatCapacityCp(state_b1_inflow) else 
        Medium1.specificHeatCapacityCp(state_a1_inflow));
  C2_flow = abs(m2_flow)*
    ( if allowFlowReversal2 then 
           fra_a2 * Medium2.specificHeatCapacityCp(state_a2_inflow) +
           fra_b2 * Medium2.specificHeatCapacityCp(state_b2_inflow) else 
        Medium2.specificHeatCapacityCp(state_a2_inflow));
  CMin_flow = min(C1_flow, C2_flow);

  // QMax_flow is maximum heat transfer into medium 1
  // We multiply by gai1*gai2 to ensure that if one flow is zero, then QMax_flow = 0
  QMax_flow = CMin_flow*(T_in2 - T_in1);

end PartialEffectiveness;

Buildings.Fluid.HeatExchangers.BaseClasses.PartialDuctManifold

Information

Partial duct manifold for a heat exchanger.

This model defines the duct connection to a heat exchanger. It is extended by other models that model the flow connection between the ports with and without flow friction.

Extends from PartialDuctPipeManifold (Partial heat exchanger duct and pipe manifold).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Integer	nPipSeg		Number of pipe segments per register used for discretization
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a for medium (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b[nPipPar, nPipSeg]	Fluid connector b for medium (positive design flow direction is from port_a to port_b)

Modelica definition

partial model PartialDuctManifold 
  "Partial manifold for heat exchanger duct connection"
  extends PartialDuctPipeManifold;
  parameter Integer nPipSeg(min=1) 
    "Number of pipe segments per register used for discretization";

  Modelica.Fluid.Interfaces.FluidPort_b[nPipPar,nPipSeg] port_b(
        redeclare each package Medium = Medium,
        each m_flow(start=-mStart_flow_a/nPipSeg/nPipPar,
             max=if allowFlowReversal then +Modelica.Constants.inf else 0)) 
    "Fluid connector b for medium (positive design flow direction is from port_a to port_b)";
end PartialDuctManifold;

Buildings.Fluid.HeatExchangers.BaseClasses.PartialDuctPipeManifold

Information

Partial heat exchanger manifold. This partial model defines ports and parameters that are used for air-side and water-side heat exchanger manifolds.

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
Integer	nPipPar		Number of parallel pipes in each register
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

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

Modelica definition

partial model PartialDuctPipeManifold 
  "Partial heat exchanger duct and pipe manifold"
  extends Buildings.BaseClasses.BaseIcon;

  outer Modelica.Fluid.System system "System wide properties";

  replaceable package Medium =
      Modelica.Media.Interfaces.PartialMedium "Medium in the component";

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

  parameter Integer nPipPar(min=1) "Number of parallel pipes in each register";

  parameter Modelica.SIunits.MassFlowRate mStart_flow_a 
    "Guess value for mass flow rate at port_a";

  Modelica.Fluid.Interfaces.FluidPort_a port_a(
        redeclare package Medium = Medium,
        m_flow(start=mStart_flow_a, min=if allowFlowReversal then -Modelica.Constants.inf else 0)) 
    "Fluid connector a for medium (positive design flow direction is from port_a to port_b)";
end PartialDuctPipeManifold;

Buildings.Fluid.HeatExchangers.BaseClasses.PartialPipeManifold

Information

Partial pipe manifold for a heat exchanger.

This model defines the pipe connection to a heat exchanger. It is extended by other models that model the flow connection between the ports with and without flow friction.

Extends from PartialDuctPipeManifold (Partial heat exchanger duct and pipe manifold).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

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

Modelica definition

partial model PartialPipeManifold 
  "Partial pipe manifold for a heat exchanger"
  extends PartialDuctPipeManifold;
  Modelica.Fluid.Interfaces.FluidPort_b[nPipPar] port_b(
        redeclare each package Medium = Medium,
        each m_flow(start=-mStart_flow_a/nPipPar, max=if allowFlowReversal then +Modelica.Constants.inf else 0)) 
    "Fluid connector b for medium (positive design flow direction is from port_a to port_b)";
end PartialPipeManifold;

Buildings.Fluid.HeatExchangers.BaseClasses.PipeManifoldFixedResistance

Information

Pipe manifold with a fixed flow resistance.

This model causes the flow to be distributed equally into each flow path by using a fixed flow resistance for each flow path.

Extends from PartialPipeManifold (Partial pipe manifold for a heat exchanger).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Boolean	use_dh	false	Set to true to specify hydraulic diameter
Length	dh	0.025	Hydraulic diameter for each pipe [m]
Real	ReC	4000	Reynolds number where transition to turbulent starts
Real	deltaM	0.3	Fraction of nominal mass flow rate where transition to turbulent occurs
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Nominal Condition
MassFlowRate	m_flow_nominal		Mass flow rate at port_a [kg/s]
Pressure	dp_nominal		Pressure [Pa]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
Boolean	linearized	false	= true, use linear relation between m_flow and dp for any flow rate
Boolean	from_dp	false	= true, use m_flow = f(dp) else dp = f(m_flow)

Connectors

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

Modelica definition

model PipeManifoldFixedResistance 
  "Pipe manifold for a heat exchanger connection"
  extends PartialPipeManifold;

  parameter Modelica.SIunits.MassFlowRate m_flow_nominal 
    "Mass flow rate at port_a";
  parameter Modelica.SIunits.Pressure dp_nominal(min=0) "Pressure";

  parameter Boolean use_dh = false "Set to true to specify hydraulic diameter";
  parameter Modelica.SIunits.Length dh=0.025 "Hydraulic diameter for each pipe";
  parameter Real ReC=4000 
    "Reynolds number where transition to turbulent starts";
  parameter Boolean linearized = false 
    "= true, use linear relation between m_flow and dp for any flow rate";
  parameter Real deltaM(min=0) = 0.3 
    "Fraction of nominal mass flow rate where transition to turbulent occurs";
  parameter Boolean from_dp = false 
    "= true, use m_flow = f(dp) else dp = f(m_flow)";

  Fluid.FixedResistances.FixedResistanceDpM[nPipPar] fixRes(
    redeclare each package Medium = Medium,
    each m_flow_nominal=m_flow_nominal/nPipPar,
    each m_flow(start=mStart_flow_a),
    each dp_nominal=dp_nominal,
    each dh=dh,
    each from_dp=from_dp,
    each deltaM=deltaM,
    each ReC=ReC,
    each use_dh=use_dh,
    each linearized=linearized) "Fixed resistance for each duct";
equation 
  for i in 1:nPipPar loop
    connect(port_a, fixRes[i].port_a);
    connect(fixRes[i].port_b, port_b[i]);
  end for;
end PipeManifoldFixedResistance;

Buildings.Fluid.HeatExchangers.BaseClasses.PipeManifoldNoResistance

Information

Pipe manifold without flow resistance.

This model connects the flows between the ports without modeling flow friction. The model is used in conjunction with a manifold which contains pressure drop elements and that is added to the other side of the heat exchanger registers.

Extends from PartialPipeManifold (Partial pipe manifold for a heat exchanger).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Integer	nPipPar		Number of parallel pipes in each register
Boolean	connectAllPressures	true
Initialization
MassFlowRate	mStart_flow_a		Guess value for mass flow rate at port_a [kg/s]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

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

Modelica definition

model PipeManifoldNoResistance "Manifold for heat exchanger register"
  extends PartialPipeManifold;
 parameter Boolean connectAllPressures=true;
  Modelica.Fluid.Fittings.MultiPort mulPor(
      redeclare package Medium = Medium,
      final nPorts_b=nPipPar);
equation 
  connect(port_a, mulPor.port_a);
  connect(mulPor.ports_b, port_b);
end PipeManifoldNoResistance;

Buildings.Fluid.HeatExchangers.BaseClasses.appartusDewPoint

Information

This function does its own iterations to find a solution because a solution may not exist or not be unique because the saturation line is convex. Therefore, this function searches for the solution starting at the air inlet temperature and progressively reduces the guess value for the apparatus dew point temperature. When a temperature below the apparatus dew point temperature has been found, it is rejected, and the search continues with a smaller step until the step size is smaller than a prescribed value. This ensures that the solution corresponding to the higher temperature is found. If no solution can be found, the function stops the simulation.

References

Brandemuehl, Michael, Shauna Gabel and Inger Andresen. HVAC2 Toolkit, A toolkit for secondary HVAC system energy calculations. ASHRAE, Atlanta. 1993.

Inputs

Type	Name	Default	Description
Temperature	TAir_in		Air inlet temperature at design condition [K]
Temperature	TAir_out		Air inlet temperature at design condition [K]
MassFraction	XW_in		Water vapor concentration at coil inlet at design condition [1]
MassFraction	XW_out		Water vapor concentration at coil outlet at design condition [1]

Outputs

Type	Name	Description
Temperature	T_dp	Apparatus dew point temperature [K]
MassFraction	XW_dp	Water vapor concentration at apparatus dew point [1]
Real	m	Slope, used to compute apparatus dewpoint temperature [1/K]

Modelica definition

function appartusDewPoint 
  "Computes the apparatus dewpoint temperature"
  import psy = Buildings.Utilities.Psychrometrics.Functions;

  input Modelica.SIunits.Temperature TAir_in 
    "Air inlet temperature at design condition";
  input Modelica.SIunits.Temperature TAir_out 
    "Air inlet temperature at design condition";

  input Modelica.SIunits.MassFraction XW_in 
    "Water vapor concentration at coil inlet at design condition";
  input Modelica.SIunits.MassFraction XW_out 
    "Water vapor concentration at coil outlet at design condition";
  output Modelica.SIunits.Temperature T_dp "Apparatus dew point temperature";
  output Modelica.SIunits.MassFraction XW_dp 
    "Water vapor concentration at apparatus dew point";
  output Real m(unit="1/K") 
    "Slope, used to compute apparatus dewpoint temperature";

protected 
  Modelica.SIunits.Temperature T "Iteration variable for temperature";
  Modelica.SIunits.Temperature dT 
    "Temperature increment used in initial search";
  constant Modelica.SIunits.Temperature dTMin = 1E-10 
    "Minimum temperature increment used during search";

  Integer i "Number of iterations";
  constant Integer iMax = 1000 "Maximum number of iterations";

  Real m_nominal(unit="1/K") 
    "Slope based on nominal conditions, used to compute apparatus dewpoint temperature";
  Boolean converged "Flag to control iteration";

algorithm 
  // Slope at design condition
  m_nominal :=(XW_in - XW_out)/(TAir_in - TAir_out);
  // Start value for iteration
  T_dp :=TAir_in;
  dT :=1;
  converged :=false;
  i :=0;
  while not converged loop
    i :=i + 1;
    assert(i < iMax, "Maximum number of iterations exceeded in computing\n"
      + "apparatus dew point for coil at nominal conditions"
      + "\n  Best known approximation is T_dp = " + realString(T_dp)
      + "\n  Search step is dT = " + realString(dT));

    T :=T_dp - dT;
    // New trial value
    XW_dp :=psy.X_pW(psy.pW_TDewPoi(T));
    m :=(XW_in - XW_dp)/(TAir_in - T);
    if (m < m_nominal) then // T is above dew point
       T_dp :=T; // Accept T as new approximation to solution
    else // T is below dew point.
       if (dT < dTMin) then // achieved required accuracy
         T_dp :=T;
         converged :=true;
       else  // need to shorten step. Reject last iterate T
         dT:=dT/10;
         T :=T_dp; // Resets T to last known value above dew point
       end if;
    end if;
  end while;
end appartusDewPoint;

Buildings.Fluid.HeatExchangers.BaseClasses.epsilon_C

Information

The implementation allows for zero flow rate. As CMin_flow crosses delta*CMin_flow_nominal from above, the Number of Transfer Units and the heat exchanger effectiveness go to zero.

Inputs

Type	Name	Default	Description
ThermalConductance	UA		UA value [W/K]
ThermalConductance	C1_flow		Enthalpy flow rate medium 1 [W/K]
ThermalConductance	C2_flow		Enthalpy flow rate medium 2 [W/K]
HeatExchangerFlowRegime	flowRegime		Heat exchanger flow regime
ThermalConductance	CMin_flow_nominal		Minimum enthalpy flow rate at nominal condition [W/K]
ThermalConductance	CMax_flow_nominal		Maximum enthalpy flow rate at nominal condition [W/K]
Real	delta	1E-3	Small value used for smoothing

Outputs

Type	Name	Description
Real	eps	Heat exchanger effectiveness
Real	NTU	Number of transfer units
Real	Z	Ratio of capacity flow rate (CMin/CMax)

Modelica definition

function epsilon_C 
  "Computes heat exchanger effectiveness for given capacity flow rates and heat exchanger flow regime"
  import f = Buildings.Fluid.Types.HeatExchangerFlowRegime;
  input Modelica.SIunits.ThermalConductance UA "UA value";
  input Modelica.SIunits.ThermalConductance C1_flow 
    "Enthalpy flow rate medium 1";
  input Modelica.SIunits.ThermalConductance C2_flow 
    "Enthalpy flow rate medium 2";
  input Buildings.Fluid.Types.HeatExchangerFlowRegime flowRegime 
    "Heat exchanger flow regime";
  input Modelica.SIunits.ThermalConductance CMin_flow_nominal 
    "Minimum enthalpy flow rate at nominal condition";
  input Modelica.SIunits.ThermalConductance CMax_flow_nominal 
    "Maximum enthalpy flow rate at nominal condition";
  input Real delta = 1E-3 "Small value used for smoothing";
  output Real eps(min=0, max=1) "Heat exchanger effectiveness";
  output Real NTU "Number of transfer units";
  output Real Z(min=0, max=1) "Ratio of capacity flow rate (CMin/CMax)";
protected 
  Modelica.SIunits.ThermalConductance deltaCMin 
    "Small number for capacity flow rate";
  Modelica.SIunits.ThermalConductance deltaCMax 
    "Small number for capacity flow rate";
  Modelica.SIunits.ThermalConductance CMin_flow "Minimum capacity flow rate";
  Modelica.SIunits.ThermalConductance CMax_flow "Maximum capacity flow rate";
  Modelica.SIunits.ThermalConductance CMinNZ_flow 
    "Minimum capacity flow rate, bounded away from zero";
  Modelica.SIunits.ThermalConductance CMaxNZ_flow 
    "Maximum capacity flow rate, bounded away from zero";
  Real gai(min=0, max=1) 
    "Gain used to force UA to zero for very small flow rates";
algorithm 
  deltaCMin := delta*CMin_flow_nominal;
  deltaCMax := delta*CMax_flow_nominal;
  // effectiveness
  CMin_flow :=Buildings.Utilities.Math.Functions.smoothMin(
    C1_flow,
    C2_flow,
    deltaCMin/4);
  CMax_flow :=Buildings.Utilities.Math.Functions.smoothMax(
    C1_flow,
    C2_flow,
    deltaCMax/4);
  // CMin and CMax, constrained to be non-zero to compute eps-NTU-Z relationship
  CMinNZ_flow :=Buildings.Utilities.Math.Functions.smoothMax(
    CMin_flow,
    deltaCMin,
    deltaCMin/4);
  CMaxNZ_flow :=Buildings.Utilities.Math.Functions.smoothMax(
    CMax_flow,
    deltaCMax,
    deltaCMax/4);
  Z :=CMin_flow/CMaxNZ_flow;
  // Gain that goes to zero as CMin_flow gets below deltaCMin
  // This is needed to allow zero flow
  gai := Buildings.Utilities.Math.Functions.spliceFunction(
                 pos=1, neg=0, x=CMin_flow-deltaCMin, deltax=deltaCMin/2);
  if ( gai == 0) then
    NTU := 0;
    eps := 1; // around zero flow, eps=Q/(CMin*dT) should be one
  else
    NTU :=gai*UA/CMinNZ_flow;
    eps := gai*Buildings.Fluid.HeatExchangers.BaseClasses.epsilon_ntuZ(NTU=NTU, Z=Z, flowRegime=flowRegime);
  end if;

end epsilon_C;

Buildings.Fluid.HeatExchangers.BaseClasses.epsilon_ntuZ

Information

Inputs

Type	Name	Default	Description
Real	NTU		Number of transfer units
Real	Z		Ratio of capacity flow rate (CMin/CMax)
HeatExchangerFlowRegime	flowRegime		Heat exchanger flow regime

Outputs

Type	Name	Description
Real	eps	Heat exchanger effectiveness

Modelica definition

function epsilon_ntuZ 
  "Computes heat exchanger effectiveness for given number of transfer units and heat exchanger flow regime"
  import f = Buildings.Fluid.Types.HeatExchangerFlowRegime;
  input Real NTU "Number of transfer units";
  input Real Z(min=0, max=1) "Ratio of capacity flow rate (CMin/CMax)";
  input Buildings.Fluid.Types.HeatExchangerFlowRegime flowRegime 
    "Heat exchanger flow regime";
  output Real eps(min=0, max=1) "Heat exchanger effectiveness";
protected 
  Real a "Auxiliary variable";
algorithm 
  if (flowRegime == f.ParallelFlow) then // parallel flow
    a := 0;
    eps := (1 - Modelica.Math.exp(-NTU*(1 + Z)))/(1 + Z);
  elseif (flowRegime == f.CounterFlow) then// counter flow
   // a is constraining Z since eps is not defined for Z=1.
    a := smooth(1, if Z < 0.97 then Z else 
      Buildings.Utilities.Math.Functions.smoothMin(
      x1=Z,
      x2=0.98,
      deltaX=0.01));
    eps := (1 - Modelica.Math.exp(-NTU*(1 - a)))/(1 - a*Modelica.Math.exp(-NTU*(
      1 - a)));
  elseif (flowRegime == f.CrossFlowUnmixed) then
   a := NTU^(-0.22);
    eps := 1 - Modelica.Math.exp( ( Modelica.Math.exp( - NTU * Z * a)  - 1)  / (Z * a));
  elseif (flowRegime == f.CrossFlowCMinUnmixedCMaxMixed) then
    // cross flow, (single pass), CMax mixed, CMin unmixed. (Coil with one row.)
    a := 0;
    eps := (1 - Modelica.Math.exp(-Z*(1 - Modelica.Math.exp(-NTU))))/Z;
  elseif (flowRegime == f.CrossFlowCMinMixedCMaxUnmixed) then
    // cross flow, (single pass), CMin mixed, CMax unmixed.
    a := 0;
    eps := 1 - Modelica.Math.exp(-(1 - Modelica.Math.exp(-Z*NTU))/Z);
  else
    a := 0;
    eps := 0;
    assert(0 < flowRegime and flowRegime < 6, "Flow regime is not implemented.");
  end if;
end epsilon_ntuZ;

Buildings.Fluid.HeatExchangers.BaseClasses.ntu_epsilonZ

Information

Note that for the flow regime CrossFlowUnmixed, computing the function requires the numerical solution of an equation in one variable. This is handled internally and not exposed to the global solver.

Inputs

Type	Name	Default	Description
Real	eps		Heat exchanger effectiveness
Real	Z		Ratio of capacity flow rate (CMin/CMax)
HeatExchangerFlowRegime	flowRegime		Heat exchanger flow regime

Outputs

Type	Name	Description
Real	NTU	Number of transfer units

Modelica definition

function ntu_epsilonZ 
  "Computes number of transfer units for given heat exchanger effectiveness and heat exchanger flow regime"
  import f = Buildings.Fluid.Types.HeatExchangerFlowRegime;
  input Real eps(min=0, max=0.999) "Heat exchanger effectiveness";
  input Real Z(min=0, max=1) "Ratio of capacity flow rate (CMin/CMax)";
  input Buildings.Fluid.Types.HeatExchangerFlowRegime flowRegime 
    "Heat exchanger flow regime";
  output Real NTU "Number of transfer units";

protected 
  Real a "Auxiliary variable";
algorithm 
  if (flowRegime == f.ParallelFlow) then // parallel flow
    a := Z+1;
    assert(eps < 1/a,
      "Invalid input data. eps > 1/(1+Z) is physically not possible for parallel flow." +
      "\n  Received eps = " + realString(eps) +
      "\n             Z = " + realString(Z) +
      "\n       1/(Z+1) = " + realString(1/a));
    NTU := -(Modelica.Math.log(1-eps*a))/(a);
  elseif (flowRegime == f.CounterFlow) then// counter flow
   // a is constraining Z since eps is not defined for Z=1.
    a := smooth(1, if Z < 0.97 then Z else 
      Buildings.Utilities.Math.Functions.smoothMin(
      x1=Z,
      x2=0.98,
      deltaX=0.01));
    NTU := Modelica.Math.log((1-eps)/(1-eps*a)) / (a-1);

  elseif (flowRegime == f.CrossFlowUnmixed) then
    a := 0;
    NTU := Internal.solve(eps, 1E-20, 1E6, {Z});
  elseif (flowRegime == f.CrossFlowCMinUnmixedCMaxMixed) then
    // cross flow, (single pass), CMax mixed, CMin unmixed. (Coil with one row.)
   a := smooth(1, if Z > 0.03 then Z else 
      Buildings.Utilities.Math.Functions.smoothMin(
      x1=0.02,
      x2=Z,
      deltaX=0.01));
    NTU := -Modelica.Math.log(1+(Modelica.Math.log(1-eps*a)/a));
  elseif (flowRegime == f.CrossFlowCMinMixedCMaxUnmixed) then
    // cross flow, (single pass), CMin mixed, CMax unmixed.
   a := smooth(1, if Z > 0.03 then Z else 
      Buildings.Utilities.Math.Functions.smoothMin(
      x1=0.02,
      x2=Z,
      deltaX=0.01));
    NTU := -Modelica.Math.log(1+Z*Modelica.Math.log(1-eps))/Z;
  else
    a := 0;
    NTU := 0;
    assert(0 < flowRegime and flowRegime < 6, "Flow regime is not implemented.");
  end if;

end ntu_epsilonZ;

Buildings.Fluid.HeatExchangers.BaseClasses.lmtd

Information

This function computes the log mean temperature difference of a heat exchanger.

Note that the implementation requires the temperature differences to be non-zero.

Inputs

Type	Name	Default	Description
Temperature	T_a1		Temperature at port a1 [K]
Temperature	T_b1		Temperature at port b1 [K]
Temperature	T_a2		Temperature at port a2 [K]
Temperature	T_b2		Temperature at port b2 [K]

Outputs

Type	Name	Description
TemperatureDifference	lmtd	Log-mean temperature difference [K]

Modelica definition

function lmtd "Log-mean temperature difference"
  input Modelica.SIunits.Temperature T_a1 "Temperature at port a1";
  input Modelica.SIunits.Temperature T_b1 "Temperature at port b1";
  input Modelica.SIunits.Temperature T_a2 "Temperature at port a2";
  input Modelica.SIunits.Temperature T_b2 "Temperature at port b2";
  output Modelica.SIunits.TemperatureDifference lmtd 
    "Log-mean temperature difference";
protected 
  Modelica.SIunits.TemperatureDifference dT1 "Temperature difference side 1";
  Modelica.SIunits.TemperatureDifference dT2 "Temperature difference side 2";
algorithm 
  dT1 :=T_a1 - T_b2;
  dT2 :=T_b1 - T_a2;
  lmtd :=(dT2 - dT1)/Modelica.Math.log(dT2/dT1);
end lmtd;