Modelica.Fluid.Vessels.BaseClasses

Information

Package Content

Name	Description
PartialLumpedVessel	Lumped volume with a vector of fluid ports and replaceable heat transfer model
HeatTransfer	HeatTransfer models for vessels
VesselPortsData	Data to describe inlet/outlet ports at vessels: diameter -- Inner (hydraulic) diameter of inlet/outlet port height -- Height over the bottom of the vessel zeta_out -- Hydraulic resistance out of vessel, default 0.5 for small diameter mounted flush with the wall zeta_in -- Hydraulic resistance into vessel, default 1.04 for small diameter mounted flush with the wall
VesselFluidPorts_a	Fluid connector with filled, large icon to be used for horizontally aligned vectors of FluidPorts (vector dimensions must be added after dragging)
VesselFluidPorts_b	Fluid connector with outlined, large icon to be used for horizontally aligned vectors of FluidPorts (vector dimensions must be added after dragging)

Modelica.Fluid.Vessels.BaseClasses.PartialLumpedVessel

Information

This base class extends PartialLumpedVolume with a vector of fluid ports and a replaceable wall HeatTransfer model.

The following modeling assumption are made:

• homogenous medium, i.e., phase seperation is not taken into account,
• no kinetic energy in the fluid, i.e., kinetic energy dissipates into the internal energy,
• pressure loss definitions at vessel ports assume incompressible fluid,
• outflow of ambient media is prevented at each port assuming check valve behavior. If fluidlevel < portsData_height[i] and   ports[i].p < vessel_ps_static[i] massflow at the port is set to 0.

The following variables need to be defined by an extending model:

• input fluidVolume, the volume of the fluid in the vessel,
• vessel_ps_static[nPorts], the static pressures inside the vessel at the height of the corresponding ports, at zero flow velocity, and
• Wb_flow, work term of the energy balance, e.g., p*der(V) if the volume is not constant or stirrer power.

• parameter vesselArea (default: Modelica.Constants.inf m2), the area of the vessel, to be related to cross flow areas of the ports for the consideration of dynamic pressure effects.

• input fluidLevel (default: 0m), the level the fluid in the vessel, and
• parameter fluidLevel_max (default: 1m), the maximum level that must not be exceeded. Ports at or above fluidLevel_max can only receive inflow.

• portsData_diameter[nPorts]
,
• portsData_height[nPorts]
,
• portsData_zeta_in[nPorts]
, and
• portsData_zeta_out[nPorts]

Extends from Modelica.Fluid.Interfaces.PartialLumpedVolume (Lumped volume with mass and energy balance).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Ports
Boolean	use_portsData	true	= false to neglect pressure loss and kinetic energy
VesselPortsData	portsData[nPorts]		Data of inlet/outlet ports
Assumptions
Dynamics
Dynamics	energyDynamics	system.energyDynamics	Formulation of energy balance
Dynamics	massDynamics	system.massDynamics	Formulation of mass balance
Heat transfer
Boolean	use_HeatTransfer	false	= true to use the HeatTransfer model
Initialization
AbsolutePressure	p_start	system.p_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
Port properties
MassFlowRate	m_flow_small	system.m_flow_small	Regularization range at zero mass flow rate [kg/s]

Connectors

Type	Name	Description
VesselFluidPorts_b	ports[nPorts]	Fluid inlets and outlets
HeatPort_a	heatPort

Modelica definition

partial model PartialLumpedVessel 
  "Lumped volume with a vector of fluid ports and replaceable heat transfer model"
  extends Modelica.Fluid.Interfaces.PartialLumpedVolume;

  // Port definitions
  parameter Integer nPorts=0 "Number of ports";
  VesselFluidPorts_b ports[nPorts](redeclare each package Medium = Medium) 
    "Fluid inlets and outlets";

  // Port properties
  parameter Boolean use_portsData=true 
    "= false to neglect pressure loss and kinetic energy";
  parameter Modelica.Fluid.Vessels.BaseClasses.VesselPortsData[nPorts]
  portsData if   use_portsData "Data of inlet/outlet ports";

  parameter SI.MassFlowRate m_flow_small(min=0) = system.m_flow_small 
    "Regularization range at zero mass flow rate";
/*
  parameter Medium.AbsolutePressure dp_small = system.dp_small
    "Turbulent flow if |dp| >= dp_small (regularization of zero flow)"
    annotation(Dialog(tab="Advanced",group="Ports"));
*/
  Medium.EnthalpyFlowRate ports_H_flow[nPorts];
  Medium.MassFlowRate ports_mXi_flow[nPorts,Medium.nXi];
  Medium.MassFlowRate[Medium.nXi] sum_ports_mXi_flow 
    "Substance mass flows through ports";
  Medium.ExtraPropertyFlowRate ports_mC_flow[nPorts,Medium.nC];
  Medium.ExtraPropertyFlowRate[Medium.nC] sum_ports_mC_flow 
    "Trace substance mass flows through ports";

  // Heat transfer through boundary
  parameter Boolean use_HeatTransfer = false 
    "= true to use the HeatTransfer model";
  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,
    final states = {medium.state},
    final use_k = use_HeatTransfer);
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort if use_HeatTransfer;

  // Conservation of kinetic energy
  Medium.Density[nPorts] portDensities 
    "densites of the fluid at the device boudary";
  SI.Velocity[nPorts] portVelocities 
    "velocities of fluid flow at device boundary";
  SI.EnergyFlowRate[nPorts] ports_E_flow 
    "flow of kinetic and potential energy at device boundary";

  // Note: should use fluidLevel_start - portsData.height
  Real[nPorts] s(each start = fluidLevel_max) 
    "curve parameters for port flows vs. port pressures; for further details see, Modelica Tutorial: Ideal switching devices";
  Real[nPorts] ports_penetration 
    "penetration of port with fluid, depending on fluid level and port diameter";

  // treatment of pressure losses at ports
  SI.Area[nPorts] portAreas = {Modelica.Constants.pi/4*portsData_diameter[i]^2 for i in 1:nPorts};
  Medium.AbsolutePressure[nPorts] vessel_ps_static 
    "static pressures inside the vessel at the height of the corresponding ports, zero flow velocity";
protected 
  input SI.Height fluidLevel = 0 
    "level of fluid in the vessel for treating heights of ports";
  parameter SI.Height fluidLevel_max = 1 "maximum level of fluid in the vessel";
  parameter SI.Area vesselArea = Modelica.Constants.inf 
    "Area of the vessel used to relate to cross flow area of ports";

  // Treatment of use_portsData=false to neglect portsData and to not require its specification either in this case.
  // Remove portsData conditionally if use_portsData=false. Simplify their use in model equations by always
  // providing portsData_diameter and portsData_height, independend of the use_portsData setting.
  // Note: this moreover serves as work-around if a tool does not support a zero sized portsData record.
  Modelica.Blocks.Interfaces.RealInput[nPorts]
  portsData_diameter_internal =                                              portsData.diameter if use_portsData and nPorts > 0;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_height_internal = portsData.height if use_portsData and nPorts > 0;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_zeta_in_internal = portsData.zeta_in if use_portsData and nPorts > 0;
  Modelica.Blocks.Interfaces.RealInput[nPorts]
  portsData_zeta_out_internal =                                              portsData.zeta_out if use_portsData and nPorts > 0;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_diameter;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_height;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_zeta_in;
  Modelica.Blocks.Interfaces.RealInput[nPorts] portsData_zeta_out;

equation 
  mb_flow = sum(ports.m_flow);
  mbXi_flow = sum_ports_mXi_flow;
  mbC_flow  = sum_ports_mC_flow;
  Hb_flow = sum(ports_H_flow) + sum(ports_E_flow);
  Qb_flow = heatTransfer.Q_flows[1];

  // Only one connection allowed to a port to avoid unwanted ideal mixing
  for i in 1:nPorts loop
    assert(cardinality(ports[i]) <= 1,"
each ports[i] of volume can at most be connected to one component.
If two or more connections are present, ideal mixing takes
place with these connections, which is usually not the intention
of the modeller. Increase nPorts to add an additional port.
");
  end for;
  // Check for correct solution
  assert(fluidLevel <= fluidLevel_max, "Vessel is overflowing (fluidLevel > fluidLevel_max = " + String(fluidLevel) + ")");
  assert(fluidLevel > -1e-6*fluidLevel_max, "Fluid level (= " + String(fluidLevel) + ") is below zero meaning that the solution failed.");

  // Boundary conditions

  // treatment of conditional portsData
  connect(portsData_diameter, portsData_diameter_internal);
  connect(portsData_height, portsData_height_internal);
  connect(portsData_zeta_in, portsData_zeta_in_internal);
  connect(portsData_zeta_out, portsData_zeta_out_internal);
  if not use_portsData then
    portsData_diameter = zeros(nPorts);
    portsData_height = zeros(nPorts);
    portsData_zeta_in = zeros(nPorts);
    portsData_zeta_out = zeros(nPorts);
  end if;

  // actual definition of port variables
  for i in 1:nPorts loop
    if use_portsData then
      // dp = 0.5*zeta*d*v*|v|
      // Note: assume vessel_ps_static for portDensities to avoid algebraic loops for ports.p
      portDensities[i] = noEvent(Medium.density(Medium.setState_phX(vessel_ps_static[i], actualStream(ports[i].h_outflow), actualStream(ports[i].Xi_outflow))));
      portVelocities[i] = smooth(0, ports[i].m_flow/portAreas[i]/portDensities[i]);
      // Note: the penetration should not go too close to zero as this would prevent a vessel from running empty
      ports_penetration[i] = Utilities.regStep(fluidLevel - portsData_height[i] - 0.1*portsData_diameter[i], 1, 1e-3, 0.1*portsData_diameter[i]);
    else
      // an infinite port diameter is assumed
      portDensities[i] = medium.d;
      portVelocities[i] = 0;
      ports_penetration[i] = 1;
    end if;
    // fluid flow through ports
    if fluidLevel >= portsData_height[i] then
      // regular operation: fluidLevel is above ports[i]
      // Note: >= covers default values of zero as well
      if use_portsData then
        /* Without regularization
        ports[i].p = vessel_ps_static[i] + 0.5*ports[i].m_flow^2/portAreas[i]^2
                      * noEvent(if ports[i].m_flow>0 then zeta_in[i]/portDensities[i] else -zeta_out[i]/medium.d);
        */

        ports[i].p = vessel_ps_static[i] + (0.5/portAreas[i]^2*Utilities.regSquare2(ports[i].m_flow, m_flow_small,
                                     (portsData_zeta_in[i] - 1 + portAreas[i]^2/vesselArea^2)/portDensities[i]*ports_penetration[i],
                                     (portsData_zeta_out[i] + 1 - portAreas[i]^2/vesselArea^2)/medium.d/ports_penetration[i]));
        /*
        // alternative formulation m_flow=f(dp); not allowing the ideal portsData_zeta_in[i]=1 though
        ports[i].m_flow = smooth(2, portAreas[i]*Utilities.regRoot2(ports[i].p - vessel_ps_static[i], dp_small,
                                     2*portDensities[i]/portsData_zeta_in[i],
                                     2*medium.d/portsData_zeta_out[i]));
        */
      else
        ports[i].p = vessel_ps_static[i];
      end if;
      s[i] = fluidLevel - portsData_height[i];
    elseif s[i] > 0 or portsData_height[i] >= fluidLevel_max then
      // ports[i] is above fluidLevel and has inflow
      ports[i].p = vessel_ps_static[i];
      s[i] = ports[i].m_flow;
    else
      // ports[i] is above fluidLevel, preventing outflow
      ports[i].m_flow = 0;
      s[i] = (ports[i].p - vessel_ps_static[i])/Medium.p_default*(portsData_height[i] - fluidLevel);
    end if;

    ports[i].h_outflow  = medium.h;
    ports[i].Xi_outflow = medium.Xi;
    ports[i].C_outflow  = C;

    ports_H_flow[i] = ports[i].m_flow * actualStream(ports[i].h_outflow) 
      "Enthalpy flow";
    ports_E_flow[i] = ports[i].m_flow*(0.5*portVelocities[i]*portVelocities[i] + system.g*portsData_height[i]) 
      "Flow of kinetic and potential energy";
    ports_mXi_flow[i,:] = ports[i].m_flow * actualStream(ports[i].Xi_outflow) 
      "Component mass flow";
    ports_mC_flow[i,:]  = ports[i].m_flow * actualStream(ports[i].C_outflow) 
      "Trace substance mass flow";
  end for;

  for i in 1:Medium.nXi loop
    sum_ports_mXi_flow[i] = sum(ports_mXi_flow[:,i]);
  end for;

  for i in 1:Medium.nC loop
    sum_ports_mC_flow[i]  = sum(ports_mC_flow[:,i]);
  end for;

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

Modelica.Fluid.Vessels.BaseClasses.VesselPortsData

Information

Vessel Port Data

This record describes the ports of a vessel. The variables in it are mostly self-explanatory (see list below); only the ζ loss factors are discussed further. All data is quoted from Idelchik (1994).

Outlet Coefficients

If a straight pipe with constant cross section is mounted flush with the wall, its outlet pressure loss coefficient will be ζ = 0.5 (Idelchik, p. 160, Diagram 3-1, paragraph 2).

If a straight pipe with constant cross section is mounted into a vessel such that the entrance into it is at a distance b from the wall (inside) the following table can be used. Herein, δ is the tube wall thickness (Idelchik, p. 160, Diagram 3-1, paragraph 1).

If a straight pipe with a circular bellmouth inlet (collector) without baffle is mounted flush with the wall then its pressure loss coefficient can be established from the following table. Herein, r is the radius of the bellmouth inlet surface (Idelchik, p. 164 f., Diagram 3-4, paragraph b)

If a straight pipe with a circular bellmouth inlet (collector) without baffle is mounted at a distance from a wall then its pressure loss coefficient can be established from the following table. Herein, r is the radius of the bellmouth inlet surface (Idelchik, p. 164 f., Diagram 3-4, paragraph a)

Inlet Coefficients

If a straight pipe with constant circular cross section is mounted flush with the wall, its vessel inlet pressure loss coefficient will be according to the following table (Idelchik, p. 209 f., Diagram 4-2 with A_port/A_vessel = 0 and Idelchik, p. 640, Diagram 11-1, graph a). According to the text, m = 9 is appropriate for fully developed turbulent flow.

For larger port diameters, relative to the area of the vessel, the inlet pressure loss coefficient will be according to the following table (Idelchik, p. 209 f., Diagram 4-2 with m = 7).

References

Idelchik I.E. (1994):

Handbook of Hydraulic Resistance. 3rd edition, Begell House, ISBN 0-8493-9908-4

Extends from Modelica.Icons.Record (Icon for records).

Parameters

Type	Name	Default	Description
Diameter	diameter		Inner (hydraulic) diameter of inlet/outlet port [m]
Height	height	0	Height over the bottom of the vessel [m]
Real	zeta_out	0.5	Hydraulic resistance out of vessel, default 0.5 for small diameter mounted flush with the wall
Real	zeta_in	1.04	Hydraulic resistance into vessel, default 1.04 for small diameter mounted flush with the wall

Modelica definition

record VesselPortsData "Data to describe inlet/outlet ports at vessels:
    diameter -- Inner (hydraulic) diameter of inlet/outlet port
    height -- Height over the bottom of the vessel
    zeta_out -- Hydraulic resistance out of vessel, default 0.5 for small diameter mounted flush with the wall
    zeta_in -- Hydraulic resistance into vessel, default 1.04 for small diameter mounted flush with the wall"
      extends Modelica.Icons.Record;
  parameter SI.Diameter diameter 
    "Inner (hydraulic) diameter of inlet/outlet port";
  parameter SI.Height height = 0 "Height over the bottom of the vessel";
  parameter Real zeta_out(min=0)=0.5 
    "Hydraulic resistance out of vessel, default 0.5 for small diameter mounted flush with the wall";
  parameter Real zeta_in(min=0)=1.04 
    "Hydraulic resistance into vessel, default 1.04 for small diameter mounted flush with the wall";
end VesselPortsData;

Modelica.Fluid.Vessels.BaseClasses.VesselFluidPorts_a

Information

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium model

Contents

Type	Name	Description
flow MassFlowRate	m_flow	Mass flow rate from the connection point into the component [kg/s]
AbsolutePressure	p	Thermodynamic pressure in the connection point [Pa]
stream SpecificEnthalpy	h_outflow	Specific thermodynamic enthalpy close to the connection point if m_flow < 0 [J/kg]
stream MassFraction	Xi_outflow[Medium.nXi]	Independent mixture mass fractions m_i/m close to the connection point if m_flow < 0 [kg/kg]
stream ExtraProperty	C_outflow[Medium.nC]	Properties c_i/m close to the connection point if m_flow < 0

Modelica definition

connector VesselFluidPorts_a 
  "Fluid connector with filled, large icon to be used for horizontally aligned vectors of FluidPorts (vector dimensions must be added after dragging)"
  extends Interfaces.FluidPort;
end VesselFluidPorts_a;

Modelica.Fluid.Vessels.BaseClasses.VesselFluidPorts_b

Information

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium model

Contents

Type	Name	Description
flow MassFlowRate	m_flow	Mass flow rate from the connection point into the component [kg/s]
AbsolutePressure	p	Thermodynamic pressure in the connection point [Pa]
stream SpecificEnthalpy	h_outflow	Specific thermodynamic enthalpy close to the connection point if m_flow < 0 [J/kg]
stream MassFraction	Xi_outflow[Medium.nXi]	Independent mixture mass fractions m_i/m close to the connection point if m_flow < 0 [kg/kg]
stream ExtraProperty	C_outflow[Medium.nC]	Properties c_i/m close to the connection point if m_flow < 0

Modelica definition

connector VesselFluidPorts_b 
  "Fluid connector with outlined, large icon to be used for horizontally aligned vectors of FluidPorts (vector dimensions must be added after dragging)"
  extends Interfaces.FluidPort;
end VesselFluidPorts_b;

Modelica.Fluid.Vessels.BaseClasses.PartialLumpedVessel.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";