Buildings.Fluid.Movers

Information

This package contains models that can be used for fans and pumps.

The models with names FlowMachine_* are similar to the pump models in the package Modelica.Fluid.Machines. However, the models in this package differ primarily in the following points:

• For the model with prescribed pressure, the input signal is the pressure difference between the two ports, and not the absolute pressure at port_b.
• The pressure calculations are based on total pressure in Pascals instead of the pump head in meters. This change was done to avoid ambiguities in the parameterization if the models are used as a fan with air as the medium. The original formulation in Modelica.Fluid.Machines converts head to pressure using the density medium.d. Therefore, for fans, head would be converted to pressure using the density of air. However, for fans, manufacturers typically publish the head in millimeters water (mmH20). Therefore, to avoid confusion when using these models with media other than water, they have been changed to use total pressure in Pascals instead of head in meters.
• Additional performance curves have been added to the package Buildings.Fluid.Movers.BaseClasses.Characteristics.

For a detailed description of the models with names FlowMachine_*, see their base class Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine.

Package Content

Name	Description
FlowMachine_dp	Pump or fan with ideally controlled pressure difference
FlowMachine_m_flow	Pump or fan with ideally controlled mass flow rate
FlowMachine_Nrpm	Centrifugal pump with ideally controlled speed
FlowMachine_y	Pump or fan with ideally controlled normalized speed
FlowMachinePolynomial	Pump or fan with head and efficiency declared by a non-dimensional polynomial
Examples	Collection of models that illustrate model use and test models
BaseClasses	Base classes used in the Machines package (only of interest to build new component models)

Buildings.Fluid.Movers.FlowMachine_dp

Information

This model describes a centrifugal pump (or a group of nParallel pumps) with prescribed pressure difference across the ports, either fixed or provided by an external signal. The model is identical to Modelica:Modelica.Fluid.Machines.ControlledPump but it defines parameters for easier configuration, and input is the pressure difference between the ports, and not the pressure at the port_b.

Extends from Buildings.Fluid.Movers.BaseClasses.FlowMachine (Fan or pump with ideally controlled mass flow rate or pressure difference).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
AbsolutePressure	p_a_nominal	system.p_start	Nominal inlet pressure for predefined fan or pump characteristics [Pa]
AbsolutePressure	dp_set_nominal	1000	Nominal total pressure difference, fixed if not control_m_flow and not use_dp_set [Pa]
MassFlowRate	m_flow_nominal		Nominal mass flow rate, fixed if control_m_flow and not use_m_flow_set [kg/s]
Boolean	control_m_flow	false	= false to control outlet pressure port_b.p instead of m_flow
Boolean	use_m_flow_set	false	= true to use input signal m_flow_set instead of m_flow_nominal
Boolean	use_dp_set	true	= true to use input signal dp_set instead of dp_set_nominal
Characteristics
Integer	nParallel	1	Number of fans or pumps in parallel
replaceable function flowCharacteristic		Characteristics.quadraticFlo...	Total pressure vs. V_flow characteristic at nominal speed
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
Density	rho_nominal	Medium.density_pTX(Medium.p_...	Nominal fluid density [kg/m3]
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
replaceable function powerCharacteristic		Characteristics.quadraticPow...	Power consumption vs. V_flow at nominal speed and density
replaceable function efficiencyCharacteristic		Characteristics.constantEffi...	Efficiency vs. V_flow at nominal speed and density
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Boolean	checkValve	false	= true to prevent reverse flow
Volume	V	0	Volume inside the pump [m3]
Dynamics
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use a HeatTransfer model, e.g. for a housing
replaceable model HeatTransfer		IdealHeatTransfer	Wall heat transfer
Initialization
AbsolutePressure	p_a_start	system.p_start	Guess value for inlet pressure [Pa]
AbsolutePressure	p_b_start	p_a_start	Guess value for outlet pressure [Pa]
MassFlowRate	m_flow_start	1	Guess value of m_flow = port_a.m_flow [kg/s]
Boolean	use_T_start	true	= true, use T_start, otherwise h_start
Temperature	T_start	if use_T_start then system.T...	Start value of temperature [K]
SpecificEnthalpy	h_start	if use_T_start then Medium.s...	Start value of specific enthalpy [J/kg]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
Advanced
Diagnostics
Boolean	show_NPSHa	false	= true to compute Net Positive Suction Head available

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
input RealInput	m_flow_set	Prescribed mass flow rate
input RealInput	dp_set	Prescribed outlet pressure

Modelica definition

model FlowMachine_dp 
  "Pump or fan with ideally controlled pressure difference"
  extends Buildings.Fluid.Movers.BaseClasses.FlowMachine(
  final control_m_flow = false,
  final use_dp_set=true,
  final use_m_flow_set=false);
end FlowMachine_dp;

Buildings.Fluid.Movers.FlowMachine_m_flow

Information

This model describes a centrifugal pump (or a group of nParallel pumps) with prescribed mass flow rate, either fixed or provided by an external signal. The model is identical to Modelica.Fluid.Machines.ControlledPump but it defines parameters for easier configuration.

Extends from Buildings.Fluid.Movers.BaseClasses.FlowMachine (Fan or pump with ideally controlled mass flow rate or pressure difference).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
AbsolutePressure	p_a_nominal	system.p_start	Nominal inlet pressure for predefined fan or pump characteristics [Pa]
AbsolutePressure	dp_set_nominal	1000	Nominal total pressure difference, fixed if not control_m_flow and not use_dp_set [Pa]
MassFlowRate	m_flow_nominal		Nominal mass flow rate, fixed if control_m_flow and not use_m_flow_set [kg/s]
Boolean	control_m_flow	true	= false to control outlet pressure port_b.p instead of m_flow
Boolean	use_m_flow_set	true	= true to use input signal m_flow_set instead of m_flow_nominal
Boolean	use_dp_set	false	= true to use input signal dp_set instead of dp_set_nominal
Characteristics
Integer	nParallel	1	Number of fans or pumps in parallel
replaceable function flowCharacteristic		Characteristics.quadraticFlo...	Total pressure vs. V_flow characteristic at nominal speed
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
Density	rho_nominal	Medium.density_pTX(Medium.p_...	Nominal fluid density [kg/m3]
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
replaceable function powerCharacteristic		Characteristics.quadraticPow...	Power consumption vs. V_flow at nominal speed and density
replaceable function efficiencyCharacteristic		Characteristics.constantEffi...	Efficiency vs. V_flow at nominal speed and density
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Boolean	checkValve	false	= true to prevent reverse flow
Volume	V	0	Volume inside the pump [m3]
Dynamics
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use a HeatTransfer model, e.g. for a housing
replaceable model HeatTransfer		IdealHeatTransfer	Wall heat transfer
Initialization
AbsolutePressure	p_a_start	system.p_start	Guess value for inlet pressure [Pa]
AbsolutePressure	p_b_start	p_a_start	Guess value for outlet pressure [Pa]
MassFlowRate	m_flow_start	1	Guess value of m_flow = port_a.m_flow [kg/s]
Boolean	use_T_start	true	= true, use T_start, otherwise h_start
Temperature	T_start	if use_T_start then system.T...	Start value of temperature [K]
SpecificEnthalpy	h_start	if use_T_start then Medium.s...	Start value of specific enthalpy [J/kg]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
Advanced
Diagnostics
Boolean	show_NPSHa	false	= true to compute Net Positive Suction Head available

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
input RealInput	m_flow_set	Prescribed mass flow rate
input RealInput	dp_set	Prescribed outlet pressure

Modelica definition

model FlowMachine_m_flow 
  "Pump or fan with ideally controlled mass flow rate"
  extends Buildings.Fluid.Movers.BaseClasses.FlowMachine(
  final control_m_flow=true,
  final use_m_flow_set=true,
  final use_dp_set=false);
end FlowMachine_m_flow;

Buildings.Fluid.Movers.FlowMachine_Nrpm

Information

This model describes a centrifugal pump (or a group of nParallel pumps) with prescribed speed, either fixed or provided by an external signal.

The model extends PartialPump

If the N_in input connector is wired, it provides rotational speed of the pumps (rpm); otherwise, a constant rotational speed equal to N_const (which can be different from N_nominal) is assumed.

Extends from Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine (Base model for fans or pumps).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	use_N_in	true	Get the rotational speed from the input connector
AngularVelocity_rpm	N_const	N_nominal	Constant rotational speed [1/min]
Characteristics
Integer	nParallel	1	Number of fans or pumps in parallel
replaceable function flowCharacteristic		Characteristics.baseFlow	Total pressure vs. V_flow characteristic at nominal speed
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
Density	rho_nominal	Medium.density_pTX(Medium.p_...	Nominal fluid density [kg/m3]
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
replaceable function powerCharacteristic		Characteristics.quadraticPow...	Power consumption vs. V_flow at nominal speed and density
replaceable function efficiencyCharacteristic		Characteristics.constantEffi...	Efficiency vs. V_flow at nominal speed and density
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Boolean	checkValve	false	= true to prevent reverse flow
Volume	V	0	Volume inside the pump [m3]
Dynamics
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use a HeatTransfer model, e.g. for a housing
replaceable model HeatTransfer		IdealHeatTransfer	Wall heat transfer
Initialization
AbsolutePressure	p_a_start	system.p_start	Guess value for inlet pressure [Pa]
AbsolutePressure	p_b_start	p_a_start	Guess value for outlet pressure [Pa]
MassFlowRate	m_flow_start	1	Guess value of m_flow = port_a.m_flow [kg/s]
Boolean	use_T_start	true	= true, use T_start, otherwise h_start
Temperature	T_start	if use_T_start then system.T...	Start value of temperature [K]
SpecificEnthalpy	h_start	if use_T_start then Medium.s...	Start value of specific enthalpy [J/kg]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
Advanced
Diagnostics
Boolean	show_NPSHa	false	= true to compute Net Positive Suction Head available

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
input RealInput	N_in	Prescribed rotational speed [1/min]

Modelica definition

model FlowMachine_Nrpm 
  "Centrifugal pump with ideally controlled speed"
  extends Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine;
  parameter Boolean use_N_in = true 
    "Get the rotational speed from the input connector";
  parameter Modelica.SIunits.Conversions.NonSIunits.AngularVelocity_rpm N_const = N_nominal 
    "Constant rotational speed";
  Modelica.Blocks.Interfaces.RealInput N_in(unit="1/min") if use_N_in 
    "Prescribed rotational speed";

protected 
  Modelica.Blocks.Interfaces.RealInput N_in_internal(unit="1/min") 
    "Needed to connect to conditional connector";
equation 
  // Connect statement active only if use_p_in = true
  connect(N_in, N_in_internal);
  // Internal connector value when use_p_in = false
  if not use_N_in then
    N_in_internal = N_const;
  end if;
  // Set N with a lower limit to avoid singularities at zero speed
  N = max(N_in_internal,1e-3) "Rotational speed";

end FlowMachine_Nrpm;

Buildings.Fluid.Movers.FlowMachine_y

Information

This model describes a centrifugal pump (or a group of nParallel pumps) with prescribed speed, either fixed or provided by an external signal.

If the y_in input connector is wired, it provides the normalized rotational speed of the pumps (between 0 and 1); otherwise, a constant rotational speed equal to y_const is assumed.

Extends from Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine (Base model for fans or pumps).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Boolean	use_y_in	true	Get the rotational speed from the input connector
Real	y_const	1	Constant normalized rotational speed
Characteristics
Integer	nParallel	1	Number of fans or pumps in parallel
replaceable function flowCharacteristic		Buildings.Fluid.Movers.BaseC...	Total pressure vs. V_flow characteristic at nominal speed
AngularVelocity_rpm	N_nominal	1500	Nominal rotational speed for flow characteristic [1/min]
Density	rho_nominal	Medium.density_pTX(Medium.p_...	Nominal fluid density [kg/m3]
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
replaceable function powerCharacteristic		Characteristics.quadraticPow...	Power consumption vs. V_flow at nominal speed and density
replaceable function efficiencyCharacteristic		Characteristics.constantEffi...	Efficiency vs. V_flow at nominal speed and density
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Boolean	checkValve	false	= true to prevent reverse flow
Volume	V	0	Volume inside the pump [m3]
Dynamics
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Formulation of energy balance
Dynamics	massDynamics	energyDynamics	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use a HeatTransfer model, e.g. for a housing
replaceable model HeatTransfer		IdealHeatTransfer	Wall heat transfer
Initialization
AbsolutePressure	p_a_start	system.p_start	Guess value for inlet pressure [Pa]
AbsolutePressure	p_b_start	p_a_start	Guess value for outlet pressure [Pa]
MassFlowRate	m_flow_start	1	Guess value of m_flow = port_a.m_flow [kg/s]
Boolean	use_T_start	true	= true, use T_start, otherwise h_start
Temperature	T_start	if use_T_start then system.T...	Start value of temperature [K]
SpecificEnthalpy	h_start	if use_T_start then Medium.s...	Start value of specific enthalpy [J/kg]
MassFraction	X_start[Medium.nX]	Medium.X_default	Start value of mass fractions m_i/m [kg/kg]
ExtraProperty	C_start[Medium.nC]	fill(0, Medium.nC)	Start value of trace substances
Advanced
Diagnostics
Boolean	show_NPSHa	false	= true to compute Net Positive Suction Head available

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
input RealInput	y_in	Constant normalized rotational speed
Characteristics
replaceable function flowCharacteristic		Total pressure vs. V_flow characteristic at nominal speed

Modelica definition

model FlowMachine_y 
  "Pump or fan with ideally controlled normalized speed"
  extends Buildings.Fluid.Movers.BaseClasses.PartialFlowMachine(
  final N_nominal=1500 "fix N_nominal as it is used only for scaling",
  redeclare replaceable function flowCharacteristic = 
      Buildings.Fluid.Movers.BaseClasses.Characteristics.baseFlow);
  parameter Boolean use_y_in = true 
    "Get the rotational speed from the input connector";
  parameter Real y_const(min=0, max=1) = 1 
    "Constant normalized rotational speed";
  Modelica.Blocks.Interfaces.RealInput y_in(min=0, max=1) if use_y_in 
    "Constant normalized rotational speed";

protected 
  Modelica.Blocks.Interfaces.RealInput y_in_internal(min=0, max=1) 
    "Needed to connect to conditional connector";
equation 
  // Connect statement active only if use_y_in = true
  connect(y_in, y_in_internal);
  // Internal connector value when use_p_in = false
  if not use_y_in then
    y_in_internal = y_const;
  end if;
  // Set N with a lower limit to avoid singularities at zero speed
  N = max(y_in_internal*N_nominal,1e-3) "Rotational speed";

end FlowMachine_y;

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.

Extends from Buildings.Fluid.Interfaces.PartialStaticTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy).

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*m_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
Initialization
AbsolutePressure	p_a_start	system.p_start	Guess value for inlet pressure [Pa]
AbsolutePressure	p_b_start	p_a_start	Guess value for outlet pressure [Pa]

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 
  "Pump or fan with head and efficiency declared by a non-dimensional polynomial"
  extends Buildings.Fluid.Interfaces.PartialStaticTwoPortInterface;


  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 den "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 
 // 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 
  den = Medium.density(sta_a);
  -dp = scaDp     * pNor      * den * D*D   * N_in * N_in;
  m_flow = scaM_flow * mNor_flow * den * 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 / den; // 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;