Modelica.Fluid.Pipes

Information

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
StaticPipe	Basic pipe flow model without storage of mass or energy
DynamicPipe	Dynamic pipe model with storage of mass and energy
BaseClasses	Base classes used in the Pipes package (only of interest to build new component models)

Modelica.Fluid.Pipes.StaticPipe

Information

Model of a straight pipe with constant cross section and with steady-state mass, momentum and energy balances, i.e., the model does not store mass or energy. There exist two thermodynamic states, one at each fluid port. The momentum balance is formulated for the two states, taking into account momentum flows, friction and gravity. The same result can be obtained by using DynamicPipe with steady-state dynamic settings. The intended use is to provide simple connections of vessels or other devices with storage, as it is done in:

• Examples.Tanks.EmptyTanks
• Examples.InverseParameterization

Numerical Issues

Extends from Modelica.Fluid.Pipes.BaseClasses.PartialStraightPipe (Base class for straight pipe models).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Geometry
Real	nParallel	1	Number of identical parallel pipes
Length	length		Length [m]
Boolean	isCircular	true	= true if cross sectional area is circular
Diameter	diameter		Diameter of circular pipe [m]
Area	crossArea	Modelica.Constants.pi*diamet...	Inner cross section area [m2]
Length	perimeter	Modelica.Constants.pi*diameter	Inner perimeter [m]
Height	roughness	2.5e-5	Average height of surface asperities (default: smooth steel pipe) [m]
Static head
Length	height_ab	0	Height(port_b) - Height(port_a) [m]
Pressure loss
replaceable model FlowModel		DetailedPipeFlow	Wall friction, gravity, momentum flow
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Initialization
AbsolutePressure	p_a_start	system.p_start	Start value of pressure at port a [Pa]
AbsolutePressure	p_b_start	p_a_start	Start value of pressure at port b [Pa]
MassFlowRate	m_flow_start	system.m_flow_start	Start value for mass flow rate [kg/s]

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)

Modelica definition

model StaticPipe 
  "Basic pipe flow model without storage of mass or energy"

  // extending PartialStraightPipe
  extends Modelica.Fluid.Pipes.BaseClasses.PartialStraightPipe;

  // Initialization
  parameter Medium.AbsolutePressure p_a_start=system.p_start 
    "Start value of pressure at port a";
  parameter Medium.AbsolutePressure p_b_start=p_a_start 
    "Start value of pressure at port b";
  parameter Medium.MassFlowRate m_flow_start = system.m_flow_start 
    "Start value for mass flow rate";

  FlowModel flowModel(
          redeclare final package Medium = Medium,
          final n=2,
          states={Medium.setState_phX(port_a.p, inStream(port_a.h_outflow), inStream(port_a.Xi_outflow)),
                 Medium.setState_phX(port_b.p, inStream(port_b.h_outflow), inStream(port_b.Xi_outflow))},
          vs={port_a.m_flow/Medium.density(flowModel.states[1])/flowModel.crossAreas[1],
              -port_b.m_flow/Medium.density(flowModel.states[2])/flowModel.crossAreas[2]}/nParallel,
          final momentumDynamics=Types.Dynamics.SteadyState,
          final allowFlowReversal=allowFlowReversal,
          final p_a_start=p_a_start,
          final p_b_start=p_b_start,
          final m_flow_start=m_flow_start,
          final nParallel=nParallel,
          final pathLengths={length},
          final crossAreas={crossArea, crossArea},
          final dimensions={4*crossArea/perimeter, 4*crossArea/perimeter},
          final roughnesses={roughness, roughness},
          final dheights={height_ab},
          final g=system.g) "Flow model";
equation 
  // Mass balance
  port_a.m_flow = flowModel.m_flows[1];
  0 = port_a.m_flow + port_b.m_flow;
  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);

  // Energy balance, considering change of potential energy
  // Wb_flow = v*A*dpdx + v*F_fric
  //         = m_flow/d/A * (A*dpdx + A*pressureLoss.dp_fg - F_grav)
  //         = m_flow/d/A * (-A*g*height_ab*d)
  //         = -m_flow*g*height_ab
  port_b.h_outflow = inStream(port_a.h_outflow) - system.g*height_ab;
  port_a.h_outflow = inStream(port_b.h_outflow) + system.g*height_ab;

end StaticPipe;

Modelica.Fluid.Pipes.DynamicPipe

Information

Model of a straight pipe with distributed mass, energy and momentum balances. It provides the complete balance equations for one-dimensional fluid flow as formulated in UsersGuide.ComponentDefinition.BalanceEquations.

The partial differential equations are treated with the finite volume method and a staggered grid scheme for momentum balances. The pipe is split into nNodes equally spaced segments along the flow path. The default value is nNodes=2. This results in two lumped mass and energy balances and one lumped momentum balance across the dynamic pipe.

Note that this generally leads to high-index DAEs for pressure states if dynamic pipes are directly connected to each other, or generally to models with storage exposing a thermodynamic state through the port. This may not be valid if the dynamic pipe is connected to a model with non-differentiable pressure, like a Sources.Boundary_pT with prescribed jumping pressure. The modelStructure can be configured as appropriate in such situations, in order to place a momentum balance between a pressure state of the pipe and a non-differentiable boundary condition.

The default modelStructure is av_vb (see Advanced tab). The simplest possible alternative symetric configuration, avoiding potential high-index DAEs at the cost of the potential introduction of nonlinear equation systems, is obtained with the setting nNodes=1, modelStructure=a_v_b. Depending on the configured model structure, the first and the last pipe segment, or the flow path length of the first and the last momentum balance, are of half size. See the documentation of the base class Pipes.BaseClasses.PartialTwoPortFlow, also covering asymmetric configurations.

The HeatTransfer component specifies the source term Qb_flows of the energy balance. The default component uses a constant coefficient for the heat transfer between the bulk flow and the segment boundaries exposed through the heatPorts. The HeatTransfer model is replaceable and can be exchanged with any model extended from BaseClasses.HeatTransfer.PartialFlowHeatTransfer.

The intended use is for complex networks of pipes and other flow devices, like valves. See e.g.

• Examples.BranchingDynamicPipes, or
• Examples.IncompressibleFluidNetwork.

Extends from Modelica.Fluid.Pipes.BaseClasses.PartialStraightPipe (Base class for straight pipe models), BaseClasses.PartialTwoPortFlow (Base class for distributed flow models).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Geometry
Real	nParallel	1	Number of identical parallel pipes
Length	length		Length [m]
Boolean	isCircular	true	= true if cross sectional area is circular
Diameter	diameter		Diameter of circular pipe [m]
Area	crossArea	Modelica.Constants.pi*diamet...	Inner cross section area [m2]
Length	perimeter	Modelica.Constants.pi*diameter	Inner perimeter [m]
Height	roughness	2.5e-5	Average height of surface asperities (default: smooth steel pipe) [m]
Length	lengths[n]	if n == 1 then {length} else...	lengths of flow segments [m]
Area	crossAreas[n]	fill(crossArea, n)	cross flow areas of flow segments [m2]
Length	dimensions[n]	fill(4*crossArea/perimeter, n)	hydraulic diameters of flow segments [m]
Height	roughnesses[n]	fill(roughness, n)	Average heights of surface asperities [m]
Static head
Length	height_ab	0	Height(port_b) - Height(port_a) [m]
Length	dheights[n]	height_ab*dxs	Differences in heigths of flow segments [m]
Pressure loss
replaceable model FlowModel		DetailedPipeFlow	Wall friction, gravity, momentum flow
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	energyDynamics	system.energyDynamics	Formulation of energy balances
Dynamics	massDynamics	system.massDynamics	Formulation of mass balances
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balances
Heat transfer
Boolean	use_HeatTransfer	false	= true to use the HeatTransfer model
Initialization
AbsolutePressure	p_a_start	system.p_start	Start value of pressure at port a [Pa]
AbsolutePressure	p_b_start	p_a_start	Start value of pressure at port b [Pa]
Boolean	use_T_start	true	Use T_start if true, 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
MassFlowRate	m_flow_start	system.m_flow_start	Start value for mass flow rate [kg/s]
Advanced
Integer	nNodes	2	Number of discrete flow volumes
ModelStructure	modelStructure	Types.ModelStructure.av_vb	Determines whether flow or volume models are present at the ports
Boolean	useLumpedPressure	false	=true to lump pressure states together
Boolean	useInnerPortProperties	false	=true to take port properties for flow models from internal control volumes

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)
HeatPorts_a	heatPorts[nNodes]

Modelica definition

model DynamicPipe 
  "Dynamic pipe model with storage of mass and energy"

  import Modelica.Fluid.Types.ModelStructure;

  // extending PartialStraightPipe
  extends Modelica.Fluid.Pipes.BaseClasses.PartialStraightPipe(
    final port_a_exposesState = (modelStructure == ModelStructure.av_b) or (modelStructure == ModelStructure.av_vb),
    final port_b_exposesState = (modelStructure == ModelStructure.a_vb) or (modelStructure == ModelStructure.av_vb));

  // extending PartialTwoPortFlow
  extends BaseClasses.PartialTwoPortFlow(
    final lengths=if n == 1 then 
                      {length} else 
                  if modelStructure == ModelStructure.av_vb then 
                      cat(1, {length/(n-1)/2}, fill(length/(n-1), n-2), {length/(n-1)/2}) else 
                  if modelStructure == ModelStructure.av_b then 
                      cat(1, {length/n/2}, fill(length*(1-1/n/2)/(n-1), n-1)) else 
                  if modelStructure == ModelStructure.a_vb then 
                      cat(1, fill(length*(1-1/n/2)/(n-1), n-1), {length/n/2}) else 
                      fill(length/n, n),
    final crossAreas=fill(crossArea, n),
    final dimensions=fill(4*crossArea/perimeter, n),
    final roughnesses=fill(roughness, n),
    final dheights=height_ab*dxs);

  // Wall heat transfer
  parameter Boolean use_HeatTransfer = false 
    "= true to use the HeatTransfer model";
  replaceable model HeatTransfer =
      Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer
    constrainedby 
    Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer 
    "Wall heat transfer";
  Interfaces.HeatPorts_a[nNodes] heatPorts if use_HeatTransfer;

  HeatTransfer heatTransfer(
    redeclare each final package Medium = Medium,
    final n=n,
    final nParallel=nParallel,
    final surfaceAreas=perimeter*lengths,
    final lengths=lengths,
    final dimensions=dimensions,
    final roughnesses=roughnesses,
    final states=mediums.state,
    final vs = vs,
    final use_k = use_HeatTransfer) "Heat transfer model";
  final parameter Real[n] dxs = lengths/sum(lengths);
equation 
  Qb_flows = heatTransfer.Q_flows;
  // Wb_flow = v*A*dpdx + v*F_fric
  //         = v*A*dpdx + v*A*flowModel.dp_fg - v*A*dp_grav
  if n == 1 or useLumpedPressure then
    Wb_flows = dxs * ((vs*dxs)*(crossAreas*dxs)*((port_b.p - port_a.p) + sum(flowModel.dps_fg) - system.g*(dheights*mediums.d)))*nParallel;
  else
    if modelStructure == ModelStructure.av_vb or modelStructure == ModelStructure.av_b then
      Wb_flows[2:n-1] = {vs[i]*crossAreas[i]*((mediums[i+1].p - mediums[i-1].p)/2 + (flowModel.dps_fg[i-1]+flowModel.dps_fg[i])/2 - system.g*dheights[i]*mediums[i].d) for i in 2:n-1}*nParallel;
    else
      Wb_flows[2:n-1] = {vs[i]*crossAreas[i]*((mediums[i+1].p - mediums[i-1].p)/2 + (flowModel.dps_fg[i]+flowModel.dps_fg[i+1])/2 - system.g*dheights[i]*mediums[i].d) for i in 2:n-1}*nParallel;
    end if;
    if modelStructure == ModelStructure.av_vb then
      Wb_flows[1] = vs[1]*crossAreas[1]*((mediums[2].p - mediums[1].p)/2 + flowModel.dps_fg[1]/2 - system.g*dheights[1]*mediums[1].d)*nParallel;
      Wb_flows[n] = vs[n]*crossAreas[n]*((mediums[n].p - mediums[n-1].p)/2 + flowModel.dps_fg[n-1]/2 - system.g*dheights[n]*mediums[n].d)*nParallel;
    elseif modelStructure == ModelStructure.av_b then
      Wb_flows[1] = vs[1]*crossAreas[1]*((mediums[2].p - mediums[1].p)/2 + flowModel.dps_fg[1]/2 - system.g*dheights[1]*mediums[1].d)*nParallel;
      Wb_flows[n] = vs[n]*crossAreas[n]*((port_b.p - mediums[n-1].p)/1.5 + flowModel.dps_fg[n-1]/2+flowModel.dps_fg[n] - system.g*dheights[n]*mediums[n].d)*nParallel;
    elseif modelStructure == ModelStructure.a_vb then
      Wb_flows[1] = vs[1]*crossAreas[1]*((mediums[2].p - port_a.p)/1.5 + flowModel.dps_fg[1]+flowModel.dps_fg[2]/2 - system.g*dheights[1]*mediums[1].d)*nParallel;
      Wb_flows[n] = vs[n]*crossAreas[n]*((mediums[n].p - mediums[n-1].p)/2 + flowModel.dps_fg[n]/2 - system.g*dheights[n]*mediums[n].d)*nParallel;
    elseif modelStructure == ModelStructure.a_v_b then
      Wb_flows[1] = vs[1]*crossAreas[1]*((mediums[2].p - port_a.p)/1.5 + flowModel.dps_fg[1]+flowModel.dps_fg[2]/2 - system.g*dheights[1]*mediums[1].d)*nParallel;
      Wb_flows[n] = vs[n]*crossAreas[n]*((port_b.p - mediums[n-1].p)/1.5 + flowModel.dps_fg[n]/2+flowModel.dps_fg[n+1] - system.g*dheights[n]*mediums[n].d)*nParallel;
    else
      assert(true, "Unknown model structure");
    end if;
  end if;

  connect(heatPorts, heatTransfer.heatPorts);
end DynamicPipe;

Modelica.Fluid.Pipes.DynamicPipe.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
Geometry
Real	nParallel		number of identical parallel flow devices

Connectors

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

Modelica definition

replaceable model HeatTransfer =
    Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer
  constrainedby 
  Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer 
  "Wall heat transfer";