Buildings.Fluid.Movers

Information

Package Content

Name	Description
UsersGuide	User's Guide
FlowMachine_y	Fan or pump with ideally controlled normalized speed y as input signal
FlowMachine_Nrpm	Fan or pump with ideally controlled speed Nrpm as input signal
FlowMachine_dp	Fan or pump with ideally controlled head dp as input signal
FlowMachine_m_flow	Fan or pump with ideally controlled mass flow rate as input signal
FlowMachinePolynomial	Fan or pump with head and efficiency declared by a non-dimensional polynomial
Examples	Collection of models that illustrate model use and test models
BaseClasses	Package with base classes for Buildings.Fluid.Movers

Buildings.Fluid.Movers.FlowMachine_y

Information

This model describes a fan or pump with prescribed normalized speed. The input connector provides the normalized rotational speed (between 0 and 1). The head is computed based on the performance curve that take as an argument the actual volume flow rate divided by the maximum flow rate and the relative speed of the fan. The efficiency of the device is computed based on the efficiency curves that take as an argument the actual volume flow rate divided by the maximum possible volume flow rate, or based on the motor performance curves.

See the User's Guide for more information.

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	addPowerToMedium	true	Set to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Characteristics
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
Boolean	motorCooledByFluid	true	If true, then motor heat is added to fluid stream
efficiencyParameters	motorEfficiency		Normalized volume flow rate vs. efficiency
efficiencyParameters	hydraulicEfficiency		Normalized volume flow rate vs. efficiency
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
flowParameters	pressure		Volume flow rate vs. total pressure rise
powerParameters	power		Volume flow rate vs. electrical power consumption
Initialization
Real	r_V.start	1	Ratio V_flow/V_flow_max [1]
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Advanced
Boolean	homotopyInitialization	true	= true, use homotopy method
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed
Dynamics
Filtered speed
Boolean	filteredSpeed	true	= true, if speed is filtered with a 2nd order CriticalDamping filter
Time	riseTime	30	Rise time of the filter (time to reach 99.6 % of the speed) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	N_start	0	Initial value of speed
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Boolean	dynamicBalance	true	Set to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Time	tau	1	Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

Type	Name	Description
output RealOutput	P	Electrical power consumed [W]
output RealOutput	N_actual	[1/min]
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_a	heatPort	Heat dissipation to environment
input RealInput	y	Constant normalized rotational speed [1]

Modelica definition

model FlowMachine_y 
  "Fan or pump with ideally controlled normalized speed y as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine(
  final N_nominal=1500 "fix N_nominal as it is used only for scaling");

  Modelica.Blocks.Interfaces.RealInput y(min=0, max=1, unit="1") 
    "Constant normalized rotational speed";

protected 
  Modelica.Blocks.Math.Gain gaiSpe(final k=N_nominal,
    u(min=0, max=1),
    y(final quantity="AngularVelocity",
      final unit="1/min",
      nominal=N_nominal)) "Gain for speed input signal";
equation 
  connect(y, gaiSpe.u);

   connect(filter.y, N_filtered);

  if filteredSpeed then
    connect(gaiSpe.y, filter.u);
    connect(filter.y, N_actual);
  else
    connect(gaiSpe.y, N_actual);
  end if;

end FlowMachine_y;

Buildings.Fluid.Movers.FlowMachine_Nrpm

Information

See the User's Guide for more information.

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	addPowerToMedium	true	Set to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Characteristics
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
Boolean	motorCooledByFluid	true	If true, then motor heat is added to fluid stream
efficiencyParameters	motorEfficiency		Normalized volume flow rate vs. efficiency
efficiencyParameters	hydraulicEfficiency		Normalized volume flow rate vs. efficiency
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
flowParameters	pressure		Volume flow rate vs. total pressure rise
powerParameters	power		Volume flow rate vs. electrical power consumption
Initialization
Real	r_V.start	1	Ratio V_flow/V_flow_max [1]
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Advanced
Boolean	homotopyInitialization	true	= true, use homotopy method
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed
Dynamics
Filtered speed
Boolean	filteredSpeed	true	= true, if speed is filtered with a 2nd order CriticalDamping filter
Time	riseTime	30	Rise time of the filter (time to reach 99.6 % of the speed) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Real	N_start	0	Initial value of speed
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Boolean	dynamicBalance	true	Set to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Time	tau	1	Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)

Connectors

Type	Name	Description
output RealOutput	P	Electrical power consumed [W]
output RealOutput	N_actual	[1/min]
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_a	heatPort	Heat dissipation to environment
input RealInput	Nrpm	Prescribed rotational speed [1/min]

Modelica definition

model FlowMachine_Nrpm 
  "Fan or pump with ideally controlled speed Nrpm as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.PrescribedFlowMachine;

  Modelica.Blocks.Interfaces.RealInput Nrpm(unit="1/min") 
    "Prescribed rotational speed";

equation 
  if filteredSpeed then
    connect(Nrpm, filter.u);
    connect(filter.y, N_actual);
    connect(filter.y, N_filtered);

  else
    connect(Nrpm, N_actual);
  end if;

end FlowMachine_Nrpm;

Buildings.Fluid.Movers.FlowMachine_dp

Information

This model describes a fan or pump with prescribed head. The input connector provides the difference between outlet minus inlet pressure. The efficiency of the device is computed based on the efficiency curves that take as an argument the actual volume flow rate divided by the maximum possible volume flow rate.

If filteredSpeed=true, then the parameter dp_nominal is used to normalize the filter. This is used to improve the numerics of the transient response. The actual pressure raise of the mover at steady-state is independent of the value of dp_nominal. It is recommended to set dp_nominal to approximately the pressure raise that the fan has during full speed.

See the User's Guide for more information.

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	addPowerToMedium	true	Set to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Boolean	control_m_flow	false	= false to control head instead of m_flow
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Real	r_V.start	1	Ratio V_flow/V_flow_max = V_flow/V_flow(dp=0, N=N_nominal)
Characteristics
Boolean	motorCooledByFluid	true	If true, then motor heat is added to fluid stream
efficiencyParameters	motorEfficiency		Normalized volume flow rate vs. efficiency
efficiencyParameters	hydraulicEfficiency		Normalized volume flow rate vs. efficiency
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Boolean	dynamicBalance	true	Set to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Time	tau	1	Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Filtered speed
Boolean	filteredSpeed	true	= true, if speed is filtered with a 2nd order CriticalDamping filter
Time	riseTime	30	Rise time of the filter (time to reach 99.6 % of the speed) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
Pressure	dp_start	0	Initial value of pressure raise [Pa]
Pressure	dp_nominal	10000	Nominal pressure raise, used to normalize filter [Pa]
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_a	heatPort	Heat dissipation to environment
output RealOutput	P	Electrical power consumed [W]
input RealInput	dp_in	Prescribed pressure rise [Pa]
output RealOutput	dp_actual	[Pa]

Modelica definition

model FlowMachine_dp 
  "Fan or pump with ideally controlled head dp as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine(
  final control_m_flow = false,
  preSou(
      dp_start=dp_start,
      m_flow_small=m_flow_small));

  // 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 Modelica.SIunits.Pressure dp_start(min=0, displayUnit="Pa")=0 
    "Initial value of pressure raise";
  parameter Modelica.SIunits.Pressure dp_nominal(min=0, displayUnit="Pa")=10000 
    "Nominal pressure raise, used to normalize filter";
  Modelica.Blocks.Interfaces.RealInput dp_in(min=0, final unit="Pa") 
    "Prescribed pressure rise";

  Modelica.Blocks.Interfaces.RealOutput dp_actual(min=0, final unit="Pa");

protected 
  Modelica.Blocks.Math.Gain gain(final k=-1);
  Modelica.Blocks.Continuous.Filter filter(
     order=2,
     f_cut=5/(2*Modelica.Constants.pi*riseTime),
     final init=init,
     final y_start=dp_start,
     u_nominal=abs(dp_nominal),
     x(each stateSelect=StateSelect.always),
     u(final unit="Pa"),
     y(final unit="Pa"),
     final analogFilter=Modelica.Blocks.Types.AnalogFilter.CriticalDamping,
     final filterType=Modelica.Blocks.Types.FilterType.LowPass) if filteredSpeed 
    "Second order filter to approximate transient of rotor, and to improve numerics";

  Modelica.Blocks.Interfaces.RealOutput dp_filtered(min=0, final unit="Pa") if 
     filteredSpeed "Filtered pressure";
equation 
  assert(dp_in >= -Modelica.Constants.eps,
    "dp_in cannot be negative. Obtained dp_in = " + String(dp_in));

  connect(dp_in, gain.u);

  if filteredSpeed then
    connect(gain.y, filter.u);
    connect(filter.y, dp_actual);
    connect(filter.y, dp_filtered);
  else
    connect(gain.y, dp_actual);
  end if;

  connect(dp_actual, preSou.dp_in);
end FlowMachine_dp;

Buildings.Fluid.Movers.FlowMachine_m_flow

Information

This model describes a fan or pump with prescribed mass flow rate. The efficiency of the device is computed based on the efficiency curves that take as an argument the actual volume flow rate divided by the maximum possible volume flow rate.

See the User's Guide for more information.

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	addPowerToMedium	true	Set to false to avoid any power (=heat and flow work) being added to medium (may give simpler equations)
Boolean	control_m_flow	true	= false to control head instead of m_flow
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Real	r_V.start	1	Ratio V_flow/V_flow_max = V_flow/V_flow(dp=0, N=N_nominal)
Characteristics
Boolean	motorCooledByFluid	true	If true, then motor heat is added to fluid stream
efficiencyParameters	motorEfficiency		Normalized volume flow rate vs. efficiency
efficiencyParameters	hydraulicEfficiency		Normalized volume flow rate vs. efficiency
Dynamics
Equations
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Boolean	dynamicBalance	true	Set to true to use a dynamic balance, which often leads to smaller systems of equations
Nominal condition
Time	tau	1	Time constant of fluid volume for nominal flow, used if dynamicBalance=true [s]
Filtered speed
Boolean	filteredSpeed	true	= true, if speed is filtered with a 2nd order CriticalDamping filter
Time	riseTime	30	Rise time of the filter (time to reach 99.6 % of the speed) [s]
Init	init	Modelica.Blocks.Types.Init.I...	Type of initialization (no init/steady state/initial state/initial output)
MassFlowRate	m_flow_start	0	Initial value of mass flow rate [kg/s]
Initialization
AbsolutePressure	p_start	Medium.p_default	Start value of pressure [Pa]
Temperature	T_start	Medium.T_default	Start value of temperature [K]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
ExtraProperty	C_nominal[Medium.nC]	fill(1E-2, Medium.nC)	Nominal value of trace substances. (Set to typical order of magnitude.)
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)
HeatPort_a	heatPort	Heat dissipation to environment
output RealOutput	P	Electrical power consumed [W]
input RealInput	m_flow_in	Prescribed mass flow rate [kg/s]
output RealOutput	m_flow_actual	Actual mass flow rate [kg/s]

Modelica definition

model FlowMachine_m_flow 
  "Fan or pump with ideally controlled mass flow rate as input signal"
  extends Buildings.Fluid.Movers.BaseClasses.ControlledFlowMachine(
  final control_m_flow=true, preSou(m_flow_start=m_flow_start, m_flow_small=
          m_flow_small));
  Modelica.Blocks.Interfaces.RealInput m_flow_in(final unit="kg/s",
                                                 nominal=m_flow_nominal) 
    "Prescribed mass flow rate";

  // 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 Modelica.SIunits.MassFlowRate m_flow_start(min=0)=0 
    "Initial value of mass flow rate";

  Modelica.Blocks.Interfaces.RealOutput m_flow_actual(final unit="kg/s",
                                                       nominal=m_flow_nominal) 
    "Actual mass flow rate";

protected 
  Modelica.Blocks.Continuous.Filter filter(
     order=2,
     f_cut=5/(2*Modelica.Constants.pi*riseTime),
     final init=init,
     final y_start=m_flow_start,
     u_nominal=m_flow_nominal,
     x(each stateSelect=StateSelect.always),
     u(final unit="kg/s"),
     y(final unit="kg/s"),
     final analogFilter=Modelica.Blocks.Types.AnalogFilter.CriticalDamping,
     final filterType=Modelica.Blocks.Types.FilterType.LowPass) if 
        filteredSpeed 
    "Second order filter to approximate transient of rotor, and to improve numerics";

  Modelica.Blocks.Interfaces.RealOutput m_flow_filtered(final unit="kg/s") if 
     filteredSpeed "Filtered mass flow rate";

equation 
  if filteredSpeed then
    connect(m_flow_in, filter.u);
    connect(filter.y, m_flow_actual);
  else
    connect(m_flow_in, m_flow_actual);
  end if;
    connect(filter.y, m_flow_filtered);
        connect(m_flow_actual, preSou.m_flow_in);

end FlowMachine_m_flow;

Buildings.Fluid.Movers.FlowMachinePolynomial

Information

This is a model of a flow machine (pump or fan).

The normalized pressure difference is computed using a function of the normalized mass flow rate. The function is a polynomial for which a user needs to supply the coefficients and two values that determine for what flow rate the polynomial is linearly extended.

Note: This model is here for compatibility with older versions of this library. For new models, use instead Buildings.Fluid.Movers.FlowMachine_y.

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Length	D		Diameter [m]
Real	a[:]		Polynomial coefficients for pressure=p(mNor_flow)
Real	b[:]		Polynomial coefficients for etaSha=p(mNor_flow)
Real	mNorMin_flow		Lowest valid normalized mass flow rate
Real	mNorMax_flow		Highest valid normalized mass flow rate
Real	scaM_flow	1	Factor used to scale the mass flow rate of the fan (used for quickly adjusting fan size)
Real	scaDp	1	Factor used to scale the pressure increase of the fan (used for quickly adjusting fan size)
Nominal condition
MassFlowRate	m_flow_nominal		Nominal mass flow rate [kg/s]
Initialization
MassFlowRate	m_flow.start	0	Mass flow rate from port_a to port_b (m_flow > 0 is design flow direction) [kg/s]
Pressure	dp.start	0	Pressure difference between port_a and port_b [Pa]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
MassFlowRate	m_flow_small	1E-4*abs(m_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed

Connectors

Type	Name	Description
FluidPort_a	port_a	Fluid connector a (positive design flow direction is from port_a to port_b)
FluidPort_b	port_b	Fluid connector b (positive design flow direction is from port_a to port_b)
input RealInput	N_in	Prescribed rotational speed

Modelica definition

model FlowMachinePolynomial 
  "Fan or pump with head and efficiency declared by a non-dimensional polynomial"
  extends Buildings.Fluid.Interfaces.PartialTwoPortInterface;
  extends Modelica.Icons.ObsoleteModel;

  Modelica.Blocks.Interfaces.RealInput N_in "Prescribed rotational speed";

  parameter Modelica.SIunits.Length D "Diameter";
  parameter Real[:] a "Polynomial coefficients for pressure=p(mNor_flow)";
  parameter Real[:] b "Polynomial coefficients for etaSha=p(mNor_flow)";
  parameter Real mNorMin_flow "Lowest valid normalized mass flow rate";
  parameter Real mNorMax_flow "Highest valid normalized mass flow rate";
  parameter Real scaM_flow = 1 
    "Factor used to scale the mass flow rate of the fan (used for quickly adjusting fan size)";
  parameter Real scaDp = 1 
    "Factor used to scale the pressure increase of the fan (used for quickly adjusting fan size)";

  Real pNor(min=0) "Normalized pressure";
  Real mNor_flow(start=mNorMax_flow) "Normalized mass flow rate";
  Real etaSha(min=0, max=1) "Efficiency, flow work divided by shaft power";
  Modelica.SIunits.Power PSha "Power input at shaft";

  Medium.Density rho "Medium density";
protected 
  parameter Real pNorMin1(fixed=false) 
    "Normalized pressure, used to test slope of polynomial outside [xMin, xMax]";
  parameter Real pNorMin2(fixed=false) 
    "Normalized pressure, used to test slope of polynomial outside [xMin, xMax]";
  parameter Real pNorMax1(fixed=false) 
    "Normalized pressure, used to test slope of polynomial outside [xMin, xMax]";
  parameter Real pNorMax2(fixed=false) 
    "Normalized pressure, used to test slope of polynomial outside [xMin, xMax]";

initial equation 
 Modelica.Utilities.Streams.print("The model Buildings.Fluid.Movers.FlowMachinePolynomial is deprecated.
 It will be removed in future releases.
 You should use Buildings.Fluid.Movers.FlowMachine_y 
 instead of Buildings.Fluid.Movers.FlowMachinePolynomial.");
 // check slope of polynomial outside the domain [mNorMin_flow, mNorMax_flow]
 pNorMin1 = Buildings.Fluid.Utilities.extendedPolynomial(
                                        c=a, x=mNorMin_flow/2, xMin=mNorMin_flow, xMax=mNorMax_flow);
 pNorMin2 = Buildings.Fluid.Utilities.extendedPolynomial(
                                        c=a, x=mNorMin_flow, xMin=mNorMin_flow, xMax=mNorMax_flow);
 pNorMax1 = Buildings.Fluid.Utilities.extendedPolynomial(
                                        c=a, x=mNorMax_flow, xMin=mNorMin_flow, xMax=mNorMax_flow);
 pNorMax2 = Buildings.Fluid.Utilities.extendedPolynomial(
                                        c=a, x=mNorMax_flow*2, xMin=mNorMin_flow, xMax=mNorMax_flow);
 assert(pNorMin1>pNorMin2,
    "Slope of pump pressure polynomial is non-negative for mNor_flow < mNorMin_flow. Check parameter a.");
 assert(pNorMax1>pNorMax2,
    "Slope of pump pressure polynomial is non-negative for mNorMax_flow < mNor_flow. Check parameter a.");

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

  -dp = scaDp     * pNor      * rho * D*D   * N_in * N_in;
  m_flow = scaM_flow * mNor_flow * rho * D*D*D * N_in;
  pNor = Buildings.Fluid.Utilities.extendedPolynomial(
                                        c=a, x=mNor_flow, xMin=mNorMin_flow, xMax=mNorMax_flow);
  etaSha = max(0.1, Buildings.Fluid.Utilities.polynomial(
                                                      c=b, x=mNor_flow));
  etaSha * PSha = -dp * m_flow / rho; // dp<0 and m_flow>0 for normal operation

  // Energy balance (no storage, no heat loss/gain)
  PSha = -m_flow*(port_a.h_outflow-inStream(port_b.h_outflow));
  PSha = m_flow*(port_b.h_outflow-inStream(port_a.h_outflow));

  // Mass balance (no storage)
  port_a.m_flow + port_b.m_flow = 0;

  // Transport of substances
  port_a.Xi_outflow = inStream(port_b.Xi_outflow);
  port_b.Xi_outflow = inStream(port_a.Xi_outflow);

  port_a.C_outflow = inStream(port_b.C_outflow);
  port_b.C_outflow = inStream(port_a.C_outflow);

end FlowMachinePolynomial;