Modelica.Fluid.Machines.BaseClasses

Information

Package Content

Name	Description
PartialPump	Base model for centrifugal pumps
PumpCharacteristics	Functions for pump characteristics
assertPositiveDifference

Modelica.Fluid.Machines.BaseClasses.PartialPump

Information

This is the base model for pumps.

The model describes a centrifugal pump, or a group of nParallel identical pumps. The pump model is based on the theory of kinematic similarity: the pump characteristics are given for nominal operating conditions (rotational speed and fluid density), and then adapted to actual operating condition, according to the similarity equations.

Pump characteristics

The nominal hydraulic characteristic (head vs. volume flow rate) is given by the the replaceable function flowCharacteristic.

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

• use_powerCharacteristic = false (default option): the replaceable function efficiencyCharacteristic (efficiency vs. volume flow rate in nominal conditions) is used to determine the efficiency, and then the power consumption. The default is a constant efficiency of 0.8.
• use_powerCharacteristic = true: the replaceable function powerCharacteristic (power consumption vs. volume flow rate in nominal conditions) is used to determine the power consumption, and then the efficiency. Use powerCharacteristic to specify a non-zero power consumption for zero flow rate.

Several functions are provided in the package PumpCharacteristics to specify the characteristics as a function of some operating points at nominal conditions.

Depending on the value of the checkValve parameter, the model either supports reverse flow conditions, or includes a built-in check valve to avoid flow reversal.

It is possible to take into account the mass and energy storage of the fluid inside the pump by specifying its volume V, and by selecting appropriate dynamic mass and energy balance assumptions (see below); this is recommended to avoid singularities in the computation of the outlet enthalpy in case of zero flow rate. If zero flow rate conditions are always avoided, this dynamic effect can be neglected by leaving the default value V = 0, thus avoiding fast state variables in the model.

Dynamics options

Steady-state mass and energy balances are assumed per default, neglecting the holdup of fluid in the pump; this configuration works well if the flow rate is always positive. Dynamic mass and energy balance can be used by setting the corresponding dynamic parameters. This is recommended to avoid singularities at zero or reversing mass flow rate. If the initial conditions imply non-zero mass flow rate, it is possible to use the SteadyStateInitial condition, otherwise it is recommended to use FixedInitial in order to avoid undetermined initial conditions.

Heat transfer

The boolean paramter use_HeatTransfer can be set to true if heat exchanged with the environment should be taken into account or to model a housing. This might be desirable if a pump with realistic powerCharacteristic for zero flow operates while a valve prevents fluid flow.

Diagnostics of Cavitation

The boolean parameter show_NPSHa can set true to compute the Net Positive Suction Head available and check for cavitation, provided a two-phase medium model is used.

Extends from Modelica.Fluid.Interfaces.PartialTwoPort (Partial component with two ports), Modelica.Fluid.Interfaces.PartialLumpedVolume (Lumped volume with mass and energy balance).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Volume	fluidVolume	V	Volume [m3]
Characteristics
Integer	nParallel	1	Number of pumps in parallel
AngularVelocity_rpm	N_nominal		Nominal rotational speed for flow characteristic [1/min]
Density	rho_nominal	Medium.density_pTX(Medium.p_...	Nominal fluid density for characteristic [kg/m3]
Boolean	use_powerCharacteristic	false	Use powerCharacteristic (vs. efficiencyCharacteristic)
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	Types.Dynamics.SteadyState	Formulation of energy balance
Dynamics	massDynamics	Types.Dynamics.SteadyState	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use a HeatTransfer model, e.g., for a housing
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]
AbsolutePressure	p_start	p_b_start	Start value of pressure [Pa]
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
HeatPort_a	heatPort

Modelica definition

partial model PartialPump "Base model for centrifugal pumps"
    import Modelica.SIunits.Conversions.NonSIunits.*;
    import Modelica.Constants;

  extends Modelica.Fluid.Interfaces.PartialTwoPort(
    port_b_exposesState = energyDynamics<>Types.Dynamics.SteadyState or massDynamics<>Types.Dynamics.SteadyState,
    port_a(
      p(start=p_a_start),
      m_flow(start = m_flow_start,
             min = if allowFlowReversal and not checkValve then -Constants.inf else 0)),
    port_b(
      p(start=p_b_start),
      m_flow(start = -m_flow_start,
             max = if allowFlowReversal and not checkValve then +Constants.inf else 0)));

  // Initialization
  parameter Medium.AbsolutePressure p_a_start=system.p_start 
    "Guess value for inlet pressure";
  parameter Medium.AbsolutePressure p_b_start=p_a_start 
    "Guess value for outlet pressure";
  parameter Medium.MassFlowRate m_flow_start = 1 
    "Guess value of m_flow = port_a.m_flow";

  // Characteristics
  parameter Integer nParallel(min=1) = 1 "Number of pumps in parallel";
  replaceable function flowCharacteristic =
      PumpCharacteristics.baseFlow 
    "Head vs. V_flow characteristic at nominal speed and density";
  parameter AngularVelocity_rpm N_nominal 
    "Nominal rotational speed for flow characteristic";
  parameter Medium.Density rho_nominal = Medium.density_pTX(Medium.p_default, Medium.T_default, Medium.X_default) 
    "Nominal fluid density for characteristic";
  parameter Boolean use_powerCharacteristic = false 
    "Use powerCharacteristic (vs. efficiencyCharacteristic)";
  replaceable function powerCharacteristic =
        PumpCharacteristics.quadraticPower (
       V_flow_nominal={0,0,0},W_nominal={0,0,0}) 
    "Power consumption vs. V_flow at nominal speed and density";
  replaceable function efficiencyCharacteristic =
    PumpCharacteristics.constantEfficiency(eta_nominal = 0.8) constrainedby 
    PumpCharacteristics.baseEfficiency 
    "Efficiency vs. V_flow at nominal speed and density";

  // Assumptions
  parameter Boolean checkValve=false "= true to prevent reverse flow";

  parameter SI.Volume V = 0 "Volume inside the pump";

  // Energy and mass balance
  extends Modelica.Fluid.Interfaces.PartialLumpedVolume(
      final fluidVolume = V,
      energyDynamics = Types.Dynamics.SteadyState,
      massDynamics = Types.Dynamics.SteadyState,
      final p_start = p_b_start);

  // Heat transfer through boundary, e.g., to add a housing
  parameter Boolean use_HeatTransfer = false 
    "= true to use a HeatTransfer model, e.g., for a housing";
  replaceable model HeatTransfer =
      Modelica.Fluid.Vessels.BaseClasses.HeatTransfer.IdealHeatTransfer
    constrainedby 
    Modelica.Fluid.Vessels.BaseClasses.HeatTransfer.PartialVesselHeatTransfer 
    "Wall heat transfer";
  HeatTransfer heatTransfer(
    redeclare final package Medium = Medium,
    final n=1,
    surfaceAreas={4*Modelica.Constants.pi*(3/4*V/Modelica.Constants.pi)^(2/3)},
    final states = {medium.state},
    final use_k = use_HeatTransfer);
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort if use_HeatTransfer;

  // Variables
  final parameter SI.Acceleration g=system.g;
  Medium.Density rho = medium.d;
  SI.Pressure dp_pump = port_b.p - port_a.p "Pressure increase";
  SI.Height head = dp_pump/(rho*g) "Pump head";
  SI.MassFlowRate m_flow = port_a.m_flow "Mass flow rate (total)";
  SI.MassFlowRate m_flow_single = m_flow/nParallel 
    "Mass flow rate (single pump)";
  SI.VolumeFlowRate V_flow = m_flow/rho "Volume flow rate (total)";
  SI.VolumeFlowRate V_flow_single(start = m_flow_start/rho_nominal/nParallel) = V_flow/nParallel 
    "Volume flow rate (single pump)";
  AngularVelocity_rpm N(start = N_nominal) "Shaft rotational speed";
  SI.Power W_single "Power Consumption (single pump)";
  SI.Power W_total = W_single*nParallel "Power Consumption (total)";
  Real eta "Global Efficiency";
  Real s(start = m_flow_start) 
    "Curvilinear abscissa for the flow curve in parametric form (either mass flow rate or head)";

  // Diagnostics
  parameter Boolean show_NPSHa = false 
    "= true to compute Net Positive Suction Head available";
  Medium.ThermodynamicState state_a=
    Medium.setState_phX(port_a.p, inStream(port_a.h_outflow), inStream(port_a.Xi_outflow)) if 
       show_NPSHa "state for medium inflowing through port_a";
  Medium.Density rho_in = Medium.density(state_a) if show_NPSHa 
    "Liquid density at the inlet port_a";
  SI.Length NPSHa=NPSPa/(rho_in*system.g) if show_NPSHa 
    "Net Positive Suction Head available";
  SI.Pressure NPSPa=assertPositiveDifference(port_a.p, Medium.saturationPressure(Medium.temperature(state_a)),
                                             "Cavitation occurs at the pump inlet") if show_NPSHa 
    "Net Positive Suction Pressure available";
  SI.Pressure NPDPa=assertPositiveDifference(port_b.p, Medium.saturationPressure(medium.T),
                                             "Cavitation occurs in the pump") if show_NPSHa 
    "Net Positive Discharge Pressure available";
protected 
  constant SI.Height unitHead = 1;
  constant SI.MassFlowRate unitMassFlowRate = 1;

equation 
  // Flow equations
  if not checkValve then
    // Regular flow characteristics without check valve
    head = (N/N_nominal)^2*flowCharacteristic(V_flow_single*(N_nominal/N));
    s = 0;
  elseif s > 0 then
    // Flow characteristics when check valve is open
    head = (N/N_nominal)^2*flowCharacteristic(V_flow_single*(N_nominal/N));
    V_flow_single = s*unitMassFlowRate/rho;
  else
    // Flow characteristics when check valve is closed
    head = (N/N_nominal)^2*flowCharacteristic(0) - s*unitHead;
    V_flow_single = 0;
  end if;

  // Power consumption
  if use_powerCharacteristic then
    W_single = (N/N_nominal)^3*(rho/rho_nominal)*powerCharacteristic(V_flow_single*(N_nominal/N));
    eta = dp_pump*V_flow_single/W_single;
  else
    eta = efficiencyCharacteristic(V_flow_single*(N_nominal/N));
    W_single = dp_pump*V_flow_single/eta;
  end if;

  // Energy balance
  Wb_flow = W_total;
  Qb_flow = heatTransfer.Q_flows[1];
  Hb_flow = port_a.m_flow*actualStream(port_a.h_outflow) +
            port_b.m_flow*actualStream(port_b.h_outflow);

  // Ports
  port_a.h_outflow = medium.h;
  port_b.h_outflow = medium.h;
  port_b.p = medium.p 
    "outlet pressure is equal to medium pressure, which includes Wb_flow";

  // Mass balance
  mb_flow = port_a.m_flow + port_b.m_flow;

  mbXi_flow = port_a.m_flow*actualStream(port_a.Xi_outflow) +
              port_b.m_flow*actualStream(port_b.Xi_outflow);
  port_a.Xi_outflow = medium.Xi;
  port_b.Xi_outflow = medium.Xi;

  mbC_flow = port_a.m_flow*actualStream(port_a.C_outflow) +
             port_b.m_flow*actualStream(port_b.C_outflow);
  port_a.C_outflow = C;
  port_b.C_outflow = C;

  connect(heatTransfer.heatPorts[1], heatPort);
end PartialPump;

Modelica.Fluid.Machines.BaseClasses.assertPositiveDifference

Information

Inputs

Type	Name	Default	Description
Pressure	p		[Pa]
Pressure	p_sat		[Pa]
String	message

Outputs

Type	Name	Description
Pressure	dp	[Pa]

Modelica definition

function assertPositiveDifference
  extends Modelica.Icons.Function;
  input SI.Pressure p;
  input SI.Pressure p_sat;
  input String message;
  output SI.Pressure dp;
algorithm 
  dp := p - p_sat;
  assert(p >= p_sat, message);
end assertPositiveDifference;

Modelica.Fluid.Machines.BaseClasses.PartialPump.HeatTransfer

Parameters

Type	Name	Default	Description
Ambient
CoefficientOfHeatTransfer	k	0	Heat transfer coefficient to ambient [W/(m2.K)]
Temperature	T_ambient	system.T_ambient	Ambient temperature [K]
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	1	Number of heat transfer segments
Boolean	use_k	false	= true to use k value for thermal isolation

Connectors

Type	Name	Description
HeatPorts_a	heatPorts[n]	Heat port to component boundary

Modelica definition

replaceable model HeatTransfer =
    Modelica.Fluid.Vessels.BaseClasses.HeatTransfer.IdealHeatTransfer
  constrainedby 
  Modelica.Fluid.Vessels.BaseClasses.HeatTransfer.PartialVesselHeatTransfer 
  "Wall heat transfer";