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Buildings.Fluid.Movers.BaseClasses

Package with base classes for Buildings.Fluid.Movers

Information

This package contains base classes that are used to construct the models in Buildings.Fluid.Movers.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

NameDescription
Buildings.Fluid.Movers.BaseClasses.Characteristics Characteristics Functions for fan or pump characteristics
Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine ControlledFlowMachine Partial model for fan or pump with ideally controlled mass flow rate or head as input signal
Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine PrescribedFlowMachine Partial model for fan or pump with speed (y or Nrpm) as input signal
Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine PartialFlowMachine Partial model to interface fan or pump models with the medium
Buildings.Fluid.Movers.BaseClasses.IdealSource IdealSource Base class for pressure and mass flow source with optional power input
Buildings.Fluid.Movers.BaseClasses.PowerInterface PowerInterface Partial model to compute power draw and heat dissipation of fans and pumps
Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface FlowMachineInterface Partial model with performance curves for fans or pumps

Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine

Partial model for fan or pump with ideally controlled mass flow rate or head as input signal

Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine

Information

This model describes a fan or pump that takes as an input the head or the mass flow rate.

Extends from Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine (Partial model to interface fan or pump models with the medium), Buildings.Fluid.Movers.BaseClasses.PowerInterface (Partial model to compute power draw and heat dissipation of fans and pumps).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
BooleanaddPowerToMediumtrueSet to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Densityrho_defaultMedium.density(sta_default)Fluid density at medium default state [kg/m3]
Booleancontrol_m_flow = false to control head instead of m_flow
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Initialization
MassFlowRatem_flow.start0Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressuredp.start0Pressure difference between port_a and port_b [Pa]
Characteristics
Booleanuse_powerCharacteristicfalseUse powerCharacteristic (vs. efficiencyCharacteristic)
BooleanmotorCooledByFluidtrueIf true, then motor heat is added to fluid stream
efficiencyParametersmotorEfficiency Normalized volume flow rate vs. efficiency
efficiencyParametershydraulicEfficiency Normalized volume flow rate vs. efficiency
Dynamics
Equations
DynamicsenergyDynamicsModelica.Fluid.Types.Dynamic...Formulation of energy balance
DynamicsmassDynamicsenergyDynamicsFormulation of mass balance
BooleandynamicBalancetrueSet to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Timetau1Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Initialization
AbsolutePressurep_startMedium.p_defaultStart value of pressure [Pa]
TemperatureT_startMedium.T_defaultStart value of temperature [K]
MassFractionX_start[Medium.nX]Medium.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC_start[Medium.nC]fill(0, Medium.nC)Start value of trace substances
ExtraPropertyC_nominal[Medium.nC]fill(1E-2, Medium.nC)Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
BooleanallowFlowReversalsystem.allowFlowReversal= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRatem_flow_small1E-4*abs(m_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
BooleanhomotopyInitializationtrue= true, use homotopy method
Diagnostics
Booleanshow_Tfalse= true, if actual temperature at port is computed

Connectors

TypeNameDescription
FluidPort_aport_aFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_bFluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_aheatPortHeat dissipation to environment
output RealOutputPElectrical power consumed [W]

Modelica definition

model ControlledFlowMachine 
  "Partial model for fan or pump with ideally controlled mass flow rate or head as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine(
   preSou(final control_m_flow=control_m_flow));

  extends Buildings.Fluid.Movers.BaseClasses.PowerInterface(
     final use_powerCharacteristic = false,
     final rho_default = Medium.density(sta_default));

  import cha = Buildings.Fluid.Movers.BaseClasses.Characteristics;
//  parameter Modelica.SIunits.MassFlowRate m_flow_nominal
//    "Nominal mass flow rate, used as flow rate if control_m_flow";
//  parameter Modelica.SIunits.MassFlowRate m_flow_max = m_flow_nominal
//    "Maximum mass flow rate (at zero head)";
  // what to control
  constant Boolean control_m_flow "= false to control head instead of m_flow";

  Real r_V(start=1) 
    "Ratio V_flow/V_flow_max = V_flow/V_flow(dp=0, N=N_nominal)";

protected 
  final parameter Medium.AbsolutePressure p_a_default(displayUnit="Pa") = Medium.p_default 
    "Nominal inlet pressure for predefined fan or pump characteristics";
  parameter Medium.ThermodynamicState sta_default = Medium.setState_pTX(
     T=Medium.T_default,
     p=Medium.p_default,
     X=Medium.X_default[1:Medium.nXi]) "Default medium state";

  Modelica.Blocks.Sources.RealExpression PToMedium_flow(y=Q_flow + WFlo) if  addPowerToMedium 
    "Heat and work input into medium";
initial equation 
  V_flow_max=m_flow_nominal/rho_default;
equation 
  r_V = VMachine_flow/V_flow_max;
  etaHyd = cha.efficiency(data=hydraulicEfficiency, r_V=r_V, d=hydDer);
  etaMot = cha.efficiency(data=motorEfficiency,     r_V=r_V, d=motDer);
  dpMachine = -dp;
  VMachine_flow = -port_b.m_flow/rho_in;
  // To compute the electrical power, we set a lower bound for eta to avoid
  // a division by zero.
  P = WFlo / Buildings.Utilities.Math.Functions.smoothMax(x1=eta, x2=1E-5, deltaX=1E-6);

  connect(PToMedium_flow.y, prePow.Q_flow);
end ControlledFlowMachine;

Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine

Partial model for fan or pump with speed (y or Nrpm) as input signal

Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine

Information

This is the base model for fans and pumps that take as input a control signal in the form of the pump speed Nrpm or the normalized pump speed y=Nrpm/N_nominal.

Extends from Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface (Partial model with performance curves for fans or pumps), Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine (Partial model to interface fan or pump models with the medium).

Parameters

TypeNameDefaultDescription
Densityrho_defaultMedium.density_pTX(p=Medium....Fluid density at medium default state [kg/m3]
replaceable package MediumPartialMediumMedium in the component
BooleanaddPowerToMediumtrueSet to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Characteristics
Booleanuse_powerCharacteristicfalseUse powerCharacteristic (vs. efficiencyCharacteristic)
BooleanmotorCooledByFluidtrueIf true, then motor heat is added to fluid stream
efficiencyParametersmotorEfficiency Normalized volume flow rate vs. efficiency
efficiencyParametershydraulicEfficiency Normalized volume flow rate vs. efficiency
AngularVelocity_rpmN_nominal1500Nominal rotational speed for flow characteristic [1/min]
flowParameterspressure Volume flow rate vs. total pressure rise
powerParameterspower Volume flow rate vs. electrical power consumption
Initialization
Realr_V.start1Ratio V_flow/V_flow_max [1]
MassFlowRatem_flow.start0Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressuredp.start0Pressure difference between port_a and port_b [Pa]
Nominal condition
MassFlowRatem_flow_nominalmax(pressure.V_flow)*rho_def...Nominal mass flow rate [kg/s]
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method
MassFlowRatem_flow_small1E-4*abs(m_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
Diagnostics
Booleanshow_Tfalse= true, if actual temperature at port is computed
Dynamics
Filtered speed
BooleanfilteredSpeedtrue= true, if speed is filtered with a 2nd order CriticalDamping filter
TimeriseTime30Rise time of the filter (time to reach 99.6 % of the speed) [s]
InitinitModelica.Blocks.Types.Init.I...Type of initialization (no init/steady state/initial state/initial output)
RealN_start0Initial value of speed
Equations
DynamicsenergyDynamicsModelica.Fluid.Types.Dynamic...Formulation of energy balance
DynamicsmassDynamicsenergyDynamicsFormulation of mass balance
BooleandynamicBalancetrueSet to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Timetau1Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Initialization
AbsolutePressurep_startMedium.p_defaultStart value of pressure [Pa]
TemperatureT_startMedium.T_defaultStart value of temperature [K]
MassFractionX_start[Medium.nX]Medium.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC_start[Medium.nC]fill(0, Medium.nC)Start value of trace substances
ExtraPropertyC_nominal[Medium.nC]fill(1E-2, Medium.nC)Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
BooleanallowFlowReversalsystem.allowFlowReversal= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

TypeNameDescription
output RealOutputPElectrical power consumed [W]
output RealOutputN_actual[1/min]
FluidPort_aport_aFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_bFluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_aheatPortHeat dissipation to environment

Modelica definition

partial model PrescribedFlowMachine 
  "Partial model for fan or pump with speed (y or Nrpm) as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface(
    V_flow_max(start=V_flow_nominal),
    final rho_default = Medium.density_pTX(
      p=Medium.p_default,
      T=Medium.T_default,
      X=Medium.X_default));

  extends Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine(
      final m_flow_nominal = max(pressure.V_flow)*rho_default,
      preSou(final control_m_flow=false));

  // Models
protected 
  Modelica.Blocks.Sources.RealExpression dpMac(y=-dpMachine) 
    "Pressure drop of the pump or fan";

  Modelica.Blocks.Sources.RealExpression PToMedium_flow(y=Q_flow + WFlo) if 
       addPowerToMedium "Heat and work input into medium";
equation 
 VMachine_flow = -port_b.m_flow/rho;
 rho = rho_in;

  connect(preSou.dp_in, dpMac.y);
  connect(PToMedium_flow.y, prePow.Q_flow);
end PrescribedFlowMachine;

Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine

Partial model to interface fan or pump models with the medium

Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine

Information

This is the base model for fans and pumps. It provides an interface between the equations that compute head and power consumption, and the implementation of the energy and pressure balance of the fluid.

Depending on the value of the parameter dynamicBalance, the fluid volume is computed using a dynamic balance or a steady-state balance.

The parameter addPowerToMedium determines whether any power is added to the fluid. The default is addPowerToMedium=true, and hence the outlet enthalpy is higher than the inlet enthalpy if the flow device is operating. The setting addPowerToMedium=false is physically incorrect (since the flow work, the flow friction and the fan heat do not increase the enthalpy of the medium), but this setting does in some cases lead to simpler equations and more robust simulation, in particular if the mass flow is equal to zero.

Extends from Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes), Buildings.Fluid.Interfaces.PartialTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
BooleanaddPowerToMediumtrueSet to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Nominal condition
MassFlowRatem_flow_nominal Nominal mass flow rate [kg/s]
Initialization
MassFlowRatem_flow.start0Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressuredp.start0Pressure difference between port_a and port_b [Pa]
Dynamics
Equations
DynamicsenergyDynamicsModelica.Fluid.Types.Dynamic...Formulation of energy balance
DynamicsmassDynamicsenergyDynamicsFormulation of mass balance
BooleandynamicBalancetrueSet to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Timetau1Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Initialization
AbsolutePressurep_startMedium.p_defaultStart value of pressure [Pa]
TemperatureT_startMedium.T_defaultStart value of temperature [K]
MassFractionX_start[Medium.nX]Medium.X_defaultStart value of mass fractions m_i/m [kg/kg]
ExtraPropertyC_start[Medium.nC]fill(0, Medium.nC)Start value of trace substances
ExtraPropertyC_nominal[Medium.nC]fill(1E-2, Medium.nC)Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
BooleanallowFlowReversalsystem.allowFlowReversal= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRatem_flow_small1E-4*abs(m_flow_nominal)Small mass flow rate for regularization of zero flow [kg/s]
BooleanhomotopyInitializationtrue= true, use homotopy method
Diagnostics
Booleanshow_Tfalse= true, if actual temperature at port is computed

Connectors

TypeNameDescription
HeatPort_aheatPortHeat dissipation to environment

Modelica definition

partial model PartialFlowMachine 
  "Partial model to interface fan or pump models with the medium"
  extends Buildings.Fluid.Interfaces.LumpedVolumeDeclarations;
  import Modelica.Constants;

  extends Buildings.Fluid.Interfaces.PartialTwoPortInterface(show_T=false,
    port_a(
      h_outflow(start=h_outflow_start),
      final m_flow(min = if allowFlowReversal then -Constants.inf else 0)),
    port_b(
      h_outflow(start=h_outflow_start),
      p(start=p_start),
      final m_flow(max = if allowFlowReversal then +Constants.inf else 0)),
      final showDesignFlowDirection=false);

  Delays.DelayFirstOrder vol(
    redeclare package Medium = Medium,
    tau=tau,
    energyDynamics=if dynamicBalance then energyDynamics else Modelica.Fluid.Types.Dynamics.SteadyState,
    massDynamics=if dynamicBalance then massDynamics else Modelica.Fluid.Types.Dynamics.SteadyState,
    T_start=T_start,
    X_start=X_start,
    C_start=C_start,
    m_flow_nominal=m_flow_nominal,
    p_start=p_start,
    prescribedHeatFlowRate=true,
    allowFlowReversal=allowFlowReversal,
    nPorts=2) "Fluid volume for dynamic model";
   parameter Boolean dynamicBalance = true 
    "Set to true to use a dynamic balance, which often leads to smaller systems of equations";

  parameter Boolean addPowerToMedium=true 
    "Set to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)";

  parameter Modelica.SIunits.Time tau=1 
    "Time constant of fluid volume for nominal flow, used if dynamicBalance=true";

  // Models
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort 
    "Heat dissipation to environment";

protected 
  Modelica.SIunits.Density rho_in "Density of inflowing fluid";

  Buildings.Fluid.Movers.BaseClasses.IdealSource preSou(
  redeclare package Medium = Medium,
    allowFlowReversal=allowFlowReversal) "Pressure source";

  Buildings.HeatTransfer.Sources.PrescribedHeatFlow prePow if addPowerToMedium 
    "Prescribed power (=heat and flow work) flow for dynamic model";

  parameter Medium.ThermodynamicState sta_start=Medium.setState_pTX(
      T=T_start, p=p_start, X=X_start) "Medium state at start values";
  parameter Modelica.SIunits.SpecificEnthalpy h_outflow_start = Medium.specificEnthalpy(sta_start) 
    "Start value for outflowing enthalpy";

equation 
  // For computing the density, we assume that the fan operates in the design flow direction.
  rho_in = Medium.density(
       Medium.setState_phX(port_a.p, inStream(port_a.h_outflow), inStream(port_a.Xi_outflow)));
  connect(prePow.port, vol.heatPort);

  connect(vol.heatPort, heatPort);
  connect(port_a, vol.ports[1]);
  connect(vol.ports[2], preSou.port_a);
  connect(preSou.port_b, port_b);
end PartialFlowMachine;

Buildings.Fluid.Movers.BaseClasses.IdealSource Buildings.Fluid.Movers.BaseClasses.IdealSource

Base class for pressure and mass flow source with optional power input

Buildings.Fluid.Movers.BaseClasses.IdealSource

Information

Model of a fictious pipe that is used as a base class for a pressure source or to prescribe a mass flow rate.

Note that for fans and pumps with dynamic balance, both the heat and the flow work are added to the volume of air or water. This simplifies the equations compared to adding heat to the volume, and flow work to this model.

Extends from Modelica.Fluid.Interfaces.PartialTwoPortTransport (Partial element transporting fluid between two ports without storage of mass or energy).

Parameters

TypeNameDefaultDescription
replaceable package MediumPartialMediumMedium in the component
Booleancontrol_m_flow = false to control dp instead of m_flow
Assumptions
BooleanallowFlowReversalsystem.allowFlowReversal= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
AbsolutePressuredp_start0.01*system.p_startGuess value of dp = port_a.p - port_b.p [Pa]
MassFlowRatem_flow_startsystem.m_flow_startGuess value of m_flow = port_a.m_flow [kg/s]
MassFlowRatem_flow_smallsystem.m_flow_smallSmall mass flow rate for regularization of zero flow [kg/s]
Diagnostics
Booleanshow_Tfalse= true, if temperatures at port_a and port_b are computed
Booleanshow_V_flowtrue= true, if volume flow rate at inflowing port is computed

Connectors

TypeNameDescription
FluidPort_aport_aFluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_bport_bFluid connector b (positive design flow direction is from port_a to port_b)
input RealInputm_flow_inPrescribed mass flow rate
input RealInputdp_inPrescribed outlet pressure

Modelica definition

model IdealSource 
  "Base class for pressure and mass flow source with optional power input"
  extends Modelica.Fluid.Interfaces.PartialTwoPortTransport(show_T=false);

  // what to control
  parameter Boolean control_m_flow "= false to control dp instead of m_flow";
  Modelica.Blocks.Interfaces.RealInput m_flow_in if control_m_flow 
    "Prescribed mass flow rate";
  Modelica.Blocks.Interfaces.RealInput dp_in if not control_m_flow 
    "Prescribed outlet pressure";

protected 
  Modelica.Blocks.Interfaces.RealInput m_flow_internal 
    "Needed to connect to conditional connector";
  Modelica.Blocks.Interfaces.RealInput dp_internal 
    "Needed to connect to conditional connector";
equation 

  // Ideal control
  if control_m_flow then
    m_flow = m_flow_internal;
    dp_internal = 0;
  else
    dp = dp_internal;
    m_flow_internal = 0;
  end if;

  connect(dp_internal, dp_in);
  connect(m_flow_internal, m_flow_in);

  // Energy balance (no storage)
  port_a.h_outflow = inStream(port_b.h_outflow);
  port_b.h_outflow = inStream(port_a.h_outflow);

end IdealSource;

Buildings.Fluid.Movers.BaseClasses.PowerInterface Buildings.Fluid.Movers.BaseClasses.PowerInterface

Partial model to compute power draw and heat dissipation of fans and pumps

Buildings.Fluid.Movers.BaseClasses.PowerInterface

Information

This is an interface that implements the functions to compute the power draw and the heat dissipation of fans and pumps. It is used by the model Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface.

Implementation

Models that extend this model need to provide an implementation of WFlo = eta * P. This equation is not implemented in this model to allow other models to properly guard against division by zero.

Parameters

TypeNameDefaultDescription
Densityrho_default Fluid density at medium default state [kg/m3]
Characteristics
Booleanuse_powerCharacteristicfalseUse powerCharacteristic (vs. efficiencyCharacteristic)
BooleanmotorCooledByFluidtrueIf true, then motor heat is added to fluid stream
efficiencyParametersmotorEfficiency Normalized volume flow rate vs. efficiency
efficiencyParametershydraulicEfficiency Normalized volume flow rate vs. efficiency
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method

Connectors

TypeNameDescription
output RealOutputPElectrical power consumed [W]

Modelica definition

partial model PowerInterface 
  "Partial model to compute power draw and heat dissipation of fans and pumps"

  import Modelica.Constants;

  parameter Boolean use_powerCharacteristic = false 
    "Use powerCharacteristic (vs. efficiencyCharacteristic)";

  parameter Boolean motorCooledByFluid = true 
    "If true, then motor heat is added to fluid stream";
  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.efficiencyParameters
      motorEfficiency(r_V={1}, eta={0.7}) 
    "Normalized volume flow rate vs. efficiency";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.efficiencyParameters
      hydraulicEfficiency(r_V={1}, eta={0.7}) 
    "Normalized volume flow rate vs. efficiency";

  parameter Modelica.SIunits.Density rho_default 
    "Fluid density at medium default state";

  Modelica.Blocks.Interfaces.RealOutput P(quantity="Modelica.SIunits.Power",
   unit="W") "Electrical power consumed";

  Modelica.SIunits.Power WHyd 
    "Hydraulic power input (converted to flow work and heat)";
  Modelica.SIunits.Power WFlo "Flow work";
  Modelica.SIunits.HeatFlowRate Q_flow "Heat input from fan or pump to medium";
  Real eta(min=0, max=1) "Global efficiency";
  Real etaHyd(min=0, max=1) "Hydraulic efficiency";
  Real etaMot(min=0, max=1) "Motor efficiency";

  Modelica.SIunits.Pressure dpMachine(displayUnit="Pa") "Pressure increase";
  Modelica.SIunits.VolumeFlowRate VMachine_flow "Volume flow rate";
protected 
  parameter Modelica.SIunits.VolumeFlowRate V_flow_max(fixed=false) 
    "Maximum volume flow rate, used for smoothing";
  //Modelica.SIunits.HeatFlowRate QThe_flow "Heat input into the medium";
  parameter Modelica.SIunits.VolumeFlowRate delta_V_flow = 1E-3*V_flow_max 
    "Factor used for setting heat input into medium to zero at very small flows";
  final parameter Real motDer[size(motorEfficiency.r_V, 1)](each fixed=false) 
    "Coefficients for polynomial of pressure vs. flow rate";
  final parameter Real hydDer[size(hydraulicEfficiency.r_V,1)](each fixed=false) 
    "Coefficients for polynomial of pressure vs. flow rate";

  Modelica.SIunits.HeatFlowRate QThe_flow 
    "Heat input from fan or pump to medium";

initial algorithm 
 // Compute derivatives for cubic spline
 motDer :=
   if use_powerCharacteristic then 
     zeros(size(motorEfficiency.r_V, 1))
   elseif ( size(motorEfficiency.r_V, 1) == 1)  then 
       {0}
   else 
      Buildings.Utilities.Math.Functions.splineDerivatives(
      x=motorEfficiency.r_V,
      y=motorEfficiency.eta,
      ensureMonotonicity=Buildings.Utilities.Math.Functions.isMonotonic(x=motorEfficiency.eta,
                                                                        strict=false));
  hydDer :=
     if use_powerCharacteristic then 
       zeros(size(hydraulicEfficiency.r_V, 1))
     elseif ( size(hydraulicEfficiency.r_V, 1) == 1)  then 
       {0}
     else 
       Buildings.Utilities.Math.Functions.splineDerivatives(
                   x=hydraulicEfficiency.r_V,
                   y=hydraulicEfficiency.eta);
equation 
  eta = etaHyd * etaMot;
//  WFlo = eta * P;
  // Flow work
  WFlo = dpMachine*VMachine_flow;
  // Hydraulic power (transmitted by shaft), etaHyd = WFlo/WHyd
  etaHyd * WHyd   = WFlo;
  // Heat input into medium
  QThe_flow +  WFlo = if motorCooledByFluid then P else WHyd;
  // At m_flow = 0, the solver may still obtain positive values for QThe_flow.
  // The next statement sets the heat input into the medium to zero for very small flow rates.
  if homotopyInitialization then
    Q_flow = homotopy(actual=Buildings.Utilities.Math.Functions.spliceFunction(pos=QThe_flow, neg=0,
                       x=noEvent(abs(VMachine_flow))-2*delta_V_flow, deltax=delta_V_flow),
                     simplified=0);
  else
    Q_flow = Buildings.Utilities.Math.Functions.spliceFunction(pos=QThe_flow, neg=0,
                       x=noEvent(abs(VMachine_flow))-2*delta_V_flow, deltax=delta_V_flow);
  end if;
end PowerInterface;

Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface

Partial model with performance curves for fans or pumps

Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface

Information

This is an interface that implements the functions to compute the head, power draw and efficiency of fans and pumps. It is used by the model PrescribedFlowMachine.

The nominal hydraulic characteristic (volume flow rate versus total pressure) is given by a set of data points. A cubic hermite spline with linear extrapolation is used to compute the performance at other operating points.

The fan or pump energy balance can be specified in two alternative ways:

Implementation

For numerical reasons, the user-provided data points for volume flow rate versus pressure rise are modified to add a fan internal flow resistance. Because this flow resistance is subtracted during the simulation when computing the fan pressure rise, the model reproduces the exact points that were provided by the user.

Also for numerical reasons, the pressure rise at zero flow rate and the flow rate at zero pressure rise is added to the user-provided data, unless the user already provides these data points. Since Modelica 3.2 does not allow dynamic memory allocation, this implementation required the use of three different arrays for the situation where no additional point is added, where one additional point is added and where two additional points are added. The parameter curve causes the correct data record to be used during the simulation.

Extends from Buildings.Fluid.Movers.BaseClasses.PowerInterface (Partial model to compute power draw and heat dissipation of fans and pumps).

Parameters

TypeNameDefaultDescription
Densityrho_default Fluid density at medium default state [kg/m3]
Characteristics
Booleanuse_powerCharacteristicfalseUse powerCharacteristic (vs. efficiencyCharacteristic)
BooleanmotorCooledByFluidtrueIf true, then motor heat is added to fluid stream
efficiencyParametersmotorEfficiency Normalized volume flow rate vs. efficiency
efficiencyParametershydraulicEfficiency Normalized volume flow rate vs. efficiency
AngularVelocity_rpmN_nominal1500Nominal rotational speed for flow characteristic [1/min]
flowParameterspressure Volume flow rate vs. total pressure rise
powerParameterspower Volume flow rate vs. electrical power consumption
Advanced
BooleanhomotopyInitializationtrue= true, use homotopy method
Dynamics
Filtered speed
BooleanfilteredSpeedtrue= true, if speed is filtered with a 2nd order CriticalDamping filter
TimeriseTime30Rise time of the filter (time to reach 99.6 % of the speed) [s]
InitinitModelica.Blocks.Types.Init.I...Type of initialization (no init/steady state/initial state/initial output)
RealN_start0Initial value of speed

Connectors

TypeNameDescription
output RealOutputPElectrical power consumed [W]
output RealOutputN_actual[1/min]

Modelica definition

partial model FlowMachineInterface 
  "Partial model with performance curves for fans or pumps"
  extends Buildings.Fluid.Movers.BaseClasses.PowerInterface(
    VMachine_flow(nominal=V_flow_nominal, start=V_flow_nominal),
    V_flow_max(nominal=V_flow_nominal, start=V_flow_nominal));

  import Modelica.Constants;
  import cha = Buildings.Fluid.Movers.BaseClasses.Characteristics;

  parameter Modelica.SIunits.Conversions.NonSIunits.AngularVelocity_rpm
    N_nominal = 1500 "Nominal rotational speed for flow characteristic";
  final parameter Modelica.SIunits.VolumeFlowRate V_flow_nominal=
    pressure.V_flow[size(pressure.V_flow,1)] 
    "Nominal volume flow rate, used for homotopy";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParameters pressure 
    "Volume flow rate vs. total pressure rise";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.powerParameters power 
    "Volume flow rate vs. electrical power consumption";

  parameter Boolean homotopyInitialization = true "= true, use homotopy method";

  // Classes used to implement the filtered speed
  parameter Boolean filteredSpeed=true 
    "= true, if speed is filtered with a 2nd order CriticalDamping filter";
  parameter Modelica.SIunits.Time riseTime=30 
    "Rise time of the filter (time to reach 99.6 % of the speed)";
  parameter Modelica.Blocks.Types.Init init=Modelica.Blocks.Types.Init.InitialOutput 
    "Type of initialization (no init/steady state/initial state/initial output)";
  parameter Real N_start=0 "Initial value of speed";

  // Speed
  Modelica.Blocks.Interfaces.RealOutput N_actual(min=0, max=N_nominal,
                                                 final quantity="AngularVelocity",
                                                 final unit="1/min",
                                                 nominal=N_nominal);

  // "Shaft rotational speed in rpm";
  Real r_N(min=0, start=N_start/N_nominal, unit="1") "Ratio N_actual/N_nominal";
  Real r_V(start=1, unit="1") "Ratio V_flow/V_flow_max";

protected 
  Modelica.Blocks.Interfaces.RealOutput N_filtered(min=0, start=N_start, max=N_nominal) if 
     filteredSpeed "Filtered speed in the range 0..N_nominal";
  Modelica.Blocks.Continuous.Filter filter(
     order=2,
     f_cut=5/(2*Modelica.Constants.pi*riseTime),
     final init=init,
     final y_start=N_start,
     x(each stateSelect=StateSelect.always),
     u_nominal=N_nominal,
     u(final quantity="AngularVelocity", final unit="1/min", nominal=N_nominal),
     y(final quantity="AngularVelocity", final unit="1/min", nominal=N_nominal),
     final analogFilter=Modelica.Blocks.Types.AnalogFilter.CriticalDamping,
     final filterType=Modelica.Blocks.Types.FilterType.LowPass) if 
        filteredSpeed 
    "Second order filter to approximate valve opening time, and to improve numerics";
  parameter Modelica.SIunits.VolumeFlowRate VDelta_flow(fixed=false, start=delta*V_flow_nominal) 
    "Small volume flow rate";
  parameter Modelica.SIunits.Pressure dpDelta(fixed=false, start=100) 
    "Small pressure";
  parameter Real delta = 0.05 
    "Small value used to transition to other fan curve";
  parameter Real cBar[2](each fixed=false) 
    "Coefficients for linear approximation of pressure vs. flow rate";
  parameter Modelica.SIunits.Pressure dpMax(min=0, fixed=false);
  parameter Real kRes(min=0, unit="kg/(s.m4)", fixed=false) 
    "Coefficient for internal pressure drop of fan or pump";

  parameter Integer curve(min=1, max=3, fixed=false) 
    "Flag, used to pick the right representatio of the fan or pump pressure curve";
  parameter Integer nOri = size(pressure.V_flow,1) 
    "Number of data points for pressure curve";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal
                                                                              pCur1(
    final n = nOri,
    V_flow(each fixed=false), dp(each fixed=false)) 
    "Volume flow rate vs. total pressure rise with correction for pump resistance added";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal
                                                                              pCur2(
   final n = nOri + 1,
    V_flow(each fixed=false), dp(each fixed=false)) 
    "Volume flow rate vs. total pressure rise with correction for pump resistance added";
  parameter Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal
                                                                              pCur3(
   final n = nOri + 2,
    V_flow(each fixed=false), dp(each fixed=false)) 
    "Volume flow rate vs. total pressure rise with correction for pump resistance added";
  parameter Real preDer1[nOri](each fixed=false) 
    "Derivatives of flow rate vs. pressure at the support points";
  parameter Real preDer2[nOri+1](each fixed=false) 
    "Derivatives of flow rate vs. pressure at the support points";
  parameter Real preDer3[nOri+2](each fixed=false) 
    "Derivatives of flow rate vs. pressure at the support points";
  parameter Real powDer[size(power.V_flow,1)]=
   if use_powerCharacteristic then 
     Buildings.Utilities.Math.Functions.splineDerivatives(
                   x=power.V_flow,
                   y=power.P,
                   ensureMonotonicity=Buildings.Utilities.Math.Functions.isMonotonic(x=power.P,
                                                                                     strict=false))
   else 
     zeros(size(power.V_flow,1)) 
    "Coefficients for polynomial of pressure vs. flow rate";

  parameter Boolean haveMinimumDecrease(fixed=false) "Flag used for reporting";
  parameter Boolean haveDPMax(fixed=false) 
    "Flag, true if user specified data that contain dpMax";
  parameter Boolean haveVMax(fixed=false) 
    "Flag, true if user specified data that contain V_flow_max";

  // Variables
  Modelica.SIunits.Density rho "Medium density";

function getPerformanceDataAsString
  input Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParameters pressure 
      "Performance data";
  input Real derivative[:](unit="kg/(s.m4)") "Derivative";
  input Integer minimumLength =  6 "Minimum width of result";
  input Integer significantDigits = 6 "Number of significant digits";
  output String str "String representation";
algorithm 
  str :="";
  for i in 1:size(derivative, 1) loop
    str :=str + "  V_flow[" + String(i) + "]=" + String(
        pressure.V_flow[i],
        minimumLength=minimumLength,
        significantDigits=significantDigits) + "\t" + "dp[" + String(i) + "]=" +
        String(
        pressure.dp[i],
        minimumLength=minimumLength,
        significantDigits=significantDigits) + "\tResulting derivative dp/dV_flow = "
         + String(
        derivative[i],
        minimumLength=minimumLength,
        significantDigits=significantDigits) + "\n";
  end for;
end getPerformanceDataAsString;

function getArrayAsString
  input Real array[:] "Array to be printed";
  input String varName "Variable name";
  input Integer minimumLength =  6 "Minimum width of result";
  input Integer significantDigits = 6 "Number of significant digits";
  output String str "String representation";
algorithm 
  str :="";
  for i in 1:size(array, 1) loop
    str :=str + "  " + varName + "[" + String(i) + "]=" + String(
        array[i],
        minimumLength=minimumLength,
        significantDigits=significantDigits) + "\n";
  end for;
end getArrayAsString;

initial algorithm 
  // Check validity of data
  assert(size(pressure.V_flow, 1) > 1, "Must have at least two data points for pressure.V_flow.");
  assert(Buildings.Utilities.Math.Functions.isMonotonic(x=pressure.V_flow, strict=true) and 
  pressure.V_flow[1] > -Modelica.Constants.eps,
  "The volume flow rate for the fan pressure rise must be a strictly decreasing sequence
  with the first element being non-zero.
The following performance data have been entered:
" + getArrayAsString(pressure.V_flow, "pressure.V_flow"));

  // Check if V_flow_max or dpMax are provided by user
  haveVMax  :=(abs(pressure.dp[nOri])   < Modelica.Constants.eps);
  haveDPMax :=(abs(pressure.V_flow[1])  < Modelica.Constants.eps);
  // Assign V_flow_max and dpMax
  if haveVMax then
    V_flow_max :=pressure.V_flow[nOri];
  else
    assert((pressure.V_flow[nOri]-pressure.V_flow[nOri-1])/((pressure.dp[nOri]-pressure.dp[nOri-1]))<0,
    "The last two pressure points for the fan or pump performance curve must be decreasing.
    You need to set more reasonable parameters.
Received 
" + getArrayAsString(pressure.dp, "dp"));
    V_flow_max :=pressure.V_flow[nOri] - (pressure.V_flow[nOri] - pressure.V_flow[
      nOri - 1])/((pressure.dp[nOri] - pressure.dp[nOri - 1]))*pressure.dp[nOri];
  end if;
  if haveDPMax then
    dpMax :=pressure.dp[1];
  else
    dpMax :=pressure.dp[1] - ((pressure.dp[2] - pressure.dp[1])/(pressure.V_flow[
      2] - pressure.V_flow[1]))*pressure.V_flow[1];
  end if;

  // Check if minimum decrease condition is satisfied
  haveMinimumDecrease :=true;
  kRes :=dpMax/V_flow_max*delta^2/10;
  for i in 1:nOri-1 loop
    if ((pressure.dp[i+1]-pressure.dp[i])/(pressure.V_flow[i+1]-pressure.V_flow[i]) >= -kRes) then
      haveMinimumDecrease :=false;
    end if;
  end for;
  // Write warning if the volumetric flow rate versus pressure curve does not satisfy
  // the minimum decrease condition
  if (not haveMinimumDecrease) then
    Modelica.Utilities.Streams.print("
Warning:
========
It is recommended that the volume flow rate versus pressure relation
of the fan or pump satisfies the minimum decrease condition

        (pressure.dp[i+1]-pressure.dp[i])
d[i] = ----------------------------------------- < " + String(-kRes) + "
       (pressure.V_flow[i+1]-pressure.V_flow[i])
 
is " + getArrayAsString({(pressure.dp[i+1]-pressure.dp[i])/(pressure.V_flow[i+1]-pressure.V_flow[i]) for i in 1:nOri-1}, "d") + "
Otherwise, a solution to the equations may not exist if the fan or pump speed is reduced.
In this situation, the solver will fail due to non-convergence and 
the simulation stops.");
  end if;

  // Correction for flow resistance of pump or fan
  // Case 1:
  if (haveVMax and haveDPMax) or (nOri == 2) then  // ----- Curve 1
    curve :=1; // V_flow_max and dpMax are provided by the user, or we only have two data points
    for i in 1:nOri loop
      pCur1.dp[i]  :=pressure.dp[i] + pressure.V_flow[i] * kRes;
      pCur1.V_flow[i] := pressure.V_flow[i];
    end for;
    pCur2.V_flow := zeros(nOri + 1);
    pCur2.dp     := zeros(nOri + 1);
    pCur3.V_flow := zeros(nOri + 2);
    pCur3.dp     := zeros(nOri + 2);
    preDer1:=Buildings.Utilities.Math.Functions.splineDerivatives(x=pCur1.V_flow, y=pCur1.dp);
    preDer2:=zeros(nOri+1);
    preDer3:=zeros(nOri+2);

    // Equation to compute dpDelta
    dpDelta :=cha.pressure(
      data=pCur1,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer1,
      cBar=zeros(2),
      kRes=  kRes);

    // Equation to compute VDelta_flow. By the affinity laws, the volume flow rate is proportional to the speed.
    VDelta_flow :=V_flow_max*delta;

    // Linear equations to determine cBar
    // Conditions for r_N=delta, V_flow = VDelta_flow
    // Conditions for r_N=delta, V_flow = 0
    cBar[1] :=cha.pressure(
      data=pCur1,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer1,
      cBar=zeros(2),
      kRes=  kRes) * (1-delta)/delta^2;

    cBar[2] :=((cha.pressure(
      data=pCur1,
      V_flow=VDelta_flow,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer1,
      cBar=zeros(2),
      kRes=  kRes) - delta*dpDelta)/delta^2 - cBar[1])/VDelta_flow;

  elseif haveVMax or haveDPMax then  // ----- Curve 2
    curve :=2; // V_flow_max or dpMax is provided by the user, but not both
    if haveVMax then
      pCur2.V_flow[1] := 0;
      pCur2.dp[1]     := dpMax;
      for i in 1:nOri loop
        pCur2.dp[i+1]  :=pressure.dp[i] + pressure.V_flow[i] * kRes;
        pCur2.V_flow[i+1] := pressure.dp[i];
      end for;
    else
      for i in 1:nOri loop
        pCur2.dp[i]  :=pressure.dp[i] + pressure.V_flow[i] * kRes;
        pCur2.V_flow[i] := pressure.V_flow[i];
      end for;
      pCur2.V_flow[nOri+1] := V_flow_max;
      pCur2.dp[nOri+1]     := 0;
    end if;
    pCur1.V_flow := zeros(nOri);
    pCur1.dp     := zeros(nOri);
    pCur3.V_flow := zeros(nOri + 2);
    pCur3.dp     := zeros(nOri + 2);
    preDer1:=zeros(nOri);
    preDer2:=Buildings.Utilities.Math.Functions.splineDerivatives(x=pCur2.V_flow, y=pCur2.dp);
    preDer3:=zeros(nOri+2);

    // Equation to compute dpDelta
    dpDelta :=cha.pressure(
      data=pCur2,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer2,
      cBar=zeros(2),
      kRes=  kRes);

    // Equation to compute VDelta_flow. By the affinity laws, the volume flow rate is proportional to the speed.
    VDelta_flow :=V_flow_max*delta;

    // Linear equations to determine cBar
    // Conditions for r_N=delta, V_flow = VDelta_flow
    // Conditions for r_N=delta, V_flow = 0
    cBar[1] :=cha.pressure(
      data=pCur2,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer2,
      cBar=zeros(2),
      kRes=  kRes) * (1-delta)/delta^2;

    cBar[2] :=((cha.pressure(
      data=pCur2,
      V_flow=VDelta_flow,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer2,
      cBar=zeros(2),
      kRes=  kRes) - delta*dpDelta)/delta^2 - cBar[1])/VDelta_flow;

  else  // ----- Curve 3
    curve :=3; // Neither V_flow_max nor dpMax are provided by the user
    pCur3.V_flow[1] := 0;
    pCur3.dp[1]     := dpMax;
    for i in 1:nOri loop
      pCur3.dp[i+1]  :=pressure.dp[i] + pressure.V_flow[i] * kRes;
      pCur3.V_flow[i+1] := pressure.V_flow[i];
    end for;
    pCur3.V_flow[nOri+2] := V_flow_max;
    pCur3.dp[nOri+2]     := 0;
    pCur1.V_flow := zeros(nOri);
    pCur1.dp     := zeros(nOri);
    pCur2.V_flow := zeros(nOri + 1);
    pCur2.dp     := zeros(nOri + 1);
    preDer1:=zeros(nOri);
    preDer2:=zeros(nOri+1);
    preDer3:=Buildings.Utilities.Math.Functions.splineDerivatives(x=pCur3.V_flow, y=pCur3.dp);

    // Equation to compute dpDelta
    dpDelta :=cha.pressure(
      data=pCur3,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer3,
      cBar=zeros(2),
      kRes=  kRes);

    // Equation to compute VDelta_flow. By the affinity laws, the volume flow rate is proportional to the speed.
    VDelta_flow :=V_flow_max*delta;

    // Linear equations to determine cBar
    // Conditions for r_N=delta, V_flow = VDelta_flow
    // Conditions for r_N=delta, V_flow = 0
    cBar[1] :=cha.pressure(
      data=pCur3,
      V_flow=0,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer3,
      cBar=zeros(2),
      kRes=  kRes) * (1-delta)/delta^2;

    cBar[2] :=((cha.pressure(
      data=pCur3,
      V_flow=VDelta_flow,
      r_N=delta,
      VDelta_flow=0,
      dpDelta=0,
      V_flow_max=Modelica.Constants.eps,
      dpMax=0,
      delta=0,
      d=preDer3,
      cBar=zeros(2),
      kRes=  kRes) - delta*dpDelta)/delta^2 - cBar[1])/VDelta_flow;

  end if;

equation 

  // Hydraulic equations
  r_N = N_actual/N_nominal;
  r_V = VMachine_flow/V_flow_max;
  // For the homotopy method, we approximate dpMachine by an equation
  // that is linear in VMachine_flow, and that goes linearly to 0 as r_N goes to 0.
  // The three branches below are identical, except that we pass either
  // pCur1, pCur2 or pCur3, and preDer1, preDer2 or preDer3
  if (curve == 1) then
    if homotopyInitialization then
       dpMachine = homotopy(actual=cha.pressure(data=pCur1,
                                                    V_flow=VMachine_flow, r_N=r_N,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer1, cBar=cBar, kRes=kRes),
                          simplified=r_N*
                              (cha.pressure(data=pCur1,
                                                    V_flow=V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer1, cBar=cBar, kRes=kRes)
                               +(VMachine_flow-V_flow_nominal)*
                                (cha.pressure(data=pCur1,
                                                    V_flow=(1+delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer1, cBar=cBar, kRes=kRes)
                                -cha.pressure(data=pCur1,
                                                    V_flow=(1-delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer1, cBar=cBar, kRes=kRes))
                                 /(2*delta*V_flow_nominal)));

     else
       dpMachine = cha.pressure(data=pCur1, V_flow=VMachine_flow, r_N=r_N,
                                                VDelta_flow=VDelta_flow, dpDelta=dpDelta, V_flow_max=V_flow_max, dpMax=dpMax,
                                                delta=delta, d=preDer1, cBar=cBar, kRes=kRes);
     end if;
     // end of computation for this branch
   elseif (curve == 2) then
    if homotopyInitialization then
       dpMachine = homotopy(actual=cha.pressure(data=pCur2,
                                                    V_flow=VMachine_flow, r_N=r_N,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer2, cBar=cBar, kRes=kRes),
                          simplified=r_N*
                              (cha.pressure(data=pCur2,
                                                    V_flow=V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer2, cBar=cBar, kRes=kRes)
                               +(VMachine_flow-V_flow_nominal)*
                                (cha.pressure(data=pCur2,
                                                    V_flow=(1+delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer2, cBar=cBar, kRes=kRes)
                                -cha.pressure(data=pCur2,
                                                    V_flow=(1-delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer2, cBar=cBar, kRes=kRes))
                                 /(2*delta*V_flow_nominal)));

     else
       dpMachine = cha.pressure(data=pCur2, V_flow=VMachine_flow, r_N=r_N,
                                                VDelta_flow=VDelta_flow, dpDelta=dpDelta, V_flow_max=V_flow_max, dpMax=dpMax,
                                                delta=delta, d=preDer2, cBar=cBar, kRes=kRes);
     end if;
     // end of computation for this branch
  else
    if homotopyInitialization then
       dpMachine = homotopy(actual=cha.pressure(data=pCur3,
                                                    V_flow=VMachine_flow, r_N=r_N,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer3, cBar=cBar, kRes=kRes),
                          simplified=r_N*
                              (cha.pressure(data=pCur3,
                                                    V_flow=V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer3, cBar=cBar, kRes=kRes)
                               +(VMachine_flow-V_flow_nominal)*
                                (cha.pressure(data=pCur3,
                                                    V_flow=(1+delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer3, cBar=cBar, kRes=kRes)
                                -cha.pressure(data=pCur3,
                                                    V_flow=(1-delta)*V_flow_nominal, r_N=1,
                                                    VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                    V_flow_max=V_flow_max, dpMax=dpMax,
                                                    delta=delta, d=preDer3, cBar=cBar, kRes=kRes))
                                 /(2*delta*V_flow_nominal)));

     else
       dpMachine = cha.pressure(data=pCur3, V_flow=VMachine_flow, r_N=r_N,
                                                VDelta_flow=VDelta_flow, dpDelta=dpDelta, V_flow_max=V_flow_max, dpMax=dpMax,
                                                delta=delta, d=preDer3, cBar=cBar, kRes=kRes);
     end if;
     // end of computation for this branch
  end if;
  // Power consumption
  if use_powerCharacteristic then
    // For the homotopy, we want P/V_flow to be bounded as V_flow -> 0 to avoid a very high medium
    // temperature near zero flow.
    if homotopyInitialization then
      P = homotopy(actual=cha.power(data=power, V_flow=VMachine_flow, r_N=r_N, d=powDer),
                      simplified=VMachine_flow/V_flow_nominal*
                            cha.power(data=power, V_flow=V_flow_nominal, r_N=1, d=powDer));
    else
      P = (rho/rho_default)*cha.power(data=power, V_flow=VMachine_flow, r_N=r_N, d=powDer);
    end if;
    // To compute the efficiency, we set a lower bound on the electricity consumption.
    // This is needed because WFlo can be close to zero when P is zero, thereby
    // causing a division by zero.
    // Earlier versions of the model computed WFlo = eta * P, but this caused
    // a division by zero.
    eta = WFlo / Buildings.Utilities.Math.Functions.smoothMax(x1=P, x2=1E-5, deltaX=1E-6);
    // In this configuration, we only now the total power consumption.
    // Because nothing is known about etaMot versus etaHyd, we set etaHyd=1. This will
    // cause etaMot=eta, because eta=etaHyd*etaMot.
    // Earlier versions used etaMot=sqrt(eta), but as eta->0, this function has
    // and infinite derivative.
    etaHyd = 1;
  else
    if homotopyInitialization then
      etaHyd = homotopy(actual=cha.efficiency(data=hydraulicEfficiency,     r_V=r_V, d=hydDer),
                        simplified=cha.efficiency(data=hydraulicEfficiency, r_V=1,   d=hydDer));
      etaMot = homotopy(actual=cha.efficiency(data=motorEfficiency,     r_V=r_V, d=motDer),
                        simplified=cha.efficiency(data=motorEfficiency, r_V=1,   d=motDer));
    else
      etaHyd = cha.efficiency(data=hydraulicEfficiency, r_V=r_V, d=hydDer);
      etaMot = cha.efficiency(data=motorEfficiency,     r_V=r_V, d=motDer);
    end if;
    // To compute the electrical power, we set a lower bound for eta to avoid
    // a division by zero.
    P = WFlo / Buildings.Utilities.Math.Functions.smoothMax(x1=eta, x2=1E-5, deltaX=1E-6);

  end if;

end FlowMachineInterface;
Automatically generated Wed Feb 12 08:16:52 2014.