Modelica.Fluid.Pipes.BaseClasses.FlowModels

Information

Package Content

Name	Description
PartialStaggeredFlowModel	Base class for momentum balances in flow models
NominalLaminarFlow	NominalLaminarFlow: Linear pressure loss for nominal values
PartialGenericPipeFlow	GenericPipeFlow: Pipe flow pressure loss and gravity with replaceable WallFriction package
NominalTurbulentPipeFlow	NominalTurbulentPipeFlow: Quadratic turbulent pressure loss for nominal values
TurbulentPipeFlow	TurbulentPipeFlow: Pipe wall friction in the quadratic turbulent regime (simple characteristic, mu not used)
DetailedPipeFlow	DetailedPipeFlow: Pipe wall friction in the laminar and turbulent regime (detailed characteristic)

Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialStaggeredFlowModel

Information

This paratial model defines a common interface for m=n-1 flow models between n device segments. The flow models provide a steady-state or dynamic momentum balance using an upwind discretization scheme per default. Extending models must add pressure loss terms for friction and gravity.

The fluid is specified in the interface with the thermodynamic states[n] for a given Medium model. The geometry is specified with the pathLengths[n-1] between the device segments as well as with the crossAreas[n] and the roughnesses[n] of the device segments. Moreover the fluid flow is characterized for different types of devices by the characteristic dimensions[n] and the average velocities vs[n] of fluid flow in the device segments. See Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber for examplary definitions.

The parameter Re_turbulent can be specified for the least mass flow rate of the turbulent regime. It defaults to 4000, which is appropriate for pipe flow. The m_flows_turbulent[n-1] resulting from Re_turbulent can optionally be calculated together with the Reynolds numbers Res[n] of the device segments (show_Res=true).

Using the thermodynamic states[n] of the device segments, the densities rhos[n] and the dynamic viscosities mus[n] of the segments as well as the actual densities rhos_act[n-1] and the actual viscosities mus_act[n-1] of the flows are predefined in this base model. Note that no events are raised on flow reversal. This needs to be treated by an extending model, e.g., with numerical smoothing or by raising events as appropriate.

Extends from Modelica.Fluid.Interfaces.PartialDistributedFlow (Base class for a distributed momentum balance).

Parameters

Type	Name	Default	Description
Integer	m	n - 1	Number of flow segments
ReynoldsNumber	Re_turbulent	4000	Start of turbulent regime, depending on type of flow device [1]
Advanced
Boolean	useUpstreamScheme	true	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Internal Interface
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Modelica definition

partial model PartialStaggeredFlowModel 
  "Base class for momentum balances in flow models"

  //
  // Internal interface
  // (not exposed to GUI; needs to be hard coded when using this model
  //
  replaceable package Medium =
    Modelica.Media.Interfaces.PartialMedium "Medium in the component";

  parameter Integer n=2 "Number of discrete flow volumes";

  // Inputs
  input Medium.ThermodynamicState[n] states 
    "Thermodynamic states along design flow";
  input Modelica.SIunits.Velocity[n] vs "Mean velocities of fluid flow";

  // Geometry parameters and inputs
  parameter Real nParallel "number of identical parallel flow devices";

  input SI.Area[n] crossAreas "Cross flow areas at segment boundaries";
  input SI.Length[n] dimensions 
    "Characteristic dimensions for fluid flow (diameters for pipe flow)";
  input SI.Height[n] roughnesses "Average height of surface asperities";

  // Static head
  input SI.Length[n-1] dheights "Height(states[2:n]) - Height(states[1:n-1])";

  parameter SI.Acceleration g=system.g "Constant gravity acceleration";

  // Assumptions
  parameter Boolean allowFlowReversal=system.allowFlowReversal 
    "= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])";
  parameter Modelica.Fluid.Types.Dynamics momentumDynamics=system.momentumDynamics 
    "Formulation of momentum balance";

  // Initialization
  parameter Medium.MassFlowRate m_flow_start=system.m_flow_start 
    "Start value of mass flow rates";
  parameter Medium.AbsolutePressure p_a_start 
    "Start value for p[1] at design inflow";
  parameter Medium.AbsolutePressure p_b_start 
    "Start value for p[n+1] at design outflow";

  //
  // Implementation of momentum balance
  //
  extends Modelica.Fluid.Interfaces.PartialDistributedFlow(
             final m = n-1);

  // Advanced parameters
  parameter Boolean useUpstreamScheme = true 
    "= false to average upstream and downstream properties across flow segments";

  parameter Boolean use_Ib_flows = momentumDynamics <> Types.Dynamics.SteadyState 
    "= true to consider differences in flow of momentum through boundaries";

  // Variables
  SI.Density[n] rhos = if use_rho_nominal then fill(rho_nominal, n) else Medium.density(states);
  SI.Density[n-1] rhos_act "Actual density per segment";

  SI.DynamicViscosity[n] mus = if use_mu_nominal then fill(mu_nominal, n) else Medium.dynamicViscosity(states);
  SI.DynamicViscosity[n-1] mus_act "Actual viscosity per segment";

  // Variables
  Modelica.SIunits.Pressure[n-1] dps_fg(each start = (p_a_start - p_b_start)/(n-1)) 
    "pressure drop between states";

  // Reynolds Number
  parameter SI.ReynoldsNumber Re_turbulent = 4000 
    "Start of turbulent regime, depending on type of flow device";
  parameter Boolean show_Res = false 
    "= true, if Reynolds numbers are included for plotting";
  SI.ReynoldsNumber[n] Res=Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber(
      vs,
      rhos,
      mus,
      dimensions) if show_Res "Reynolds numbers";
  Medium.MassFlowRate[n-1] m_flows_turbulent=
      {nParallel*(Modelica.Constants.pi/4)*0.5*(dimensions[i] + dimensions[i+1])*mus_act[i]*Re_turbulent for i in 1:n-1} if 
         show_Res "Start of turbulent flow";
protected 
  parameter Boolean use_rho_nominal = false 
    "= true, if rho_nominal is used, otherwise computed from medium";
  parameter SI.Density rho_nominal = Medium.density_pTX(Medium.p_default, Medium.T_default, Medium.X_default) 
    "Nominal density (e.g., rho_liquidWater = 995, rho_air = 1.2)";

  parameter Boolean use_mu_nominal = false 
    "= true, if mu_nominal is used, otherwise computed from medium";
  parameter SI.DynamicViscosity mu_nominal = Medium.dynamicViscosity(
                                                 Medium.setState_pTX(
                                                     Medium.p_default, Medium.T_default, Medium.X_default)) 
    "Nominal dynamic viscosity (e.g., mu_liquidWater = 1e-3, mu_air = 1.8e-5)";

equation 
  if not allowFlowReversal then
    rhos_act = rhos[1:n-1];
    mus_act = mus[1:n-1];
  elseif not useUpstreamScheme then
    rhos_act = 0.5*(rhos[1:n-1] + rhos[2:n]);
    mus_act = 0.5*(mus[1:n-1] + mus[2:n]);
  else
    for i in 1:n-1 loop
      rhos_act[i] = noEvent(if m_flows[i] > 0 then rhos[i] else rhos[i+1]);
      mus_act[i] = noEvent(if m_flows[i] > 0 then mus[i] else mus[i+1]);
    end for;
  end if;

  if use_Ib_flows then
    Ib_flows = {rhos[i]*vs[i]*vs[i]*crossAreas[i] - rhos[i+1]*vs[i+1]*vs[i+1]*crossAreas[i+1] for i in 1:n-1};
    // alternatively use densities rhos_act of actual streams, together with mass flow rates,
    // not conserving momentum if fluid density changes between flow segments:
    //Ib_flows = {((rhos[i]*vs[i])^2*crossAreas[i] - (rhos[i+1]*vs[i+1])^2*crossAreas[i+1])/rhos_act[i] for i in 1:n-1};
  else
    Ib_flows = zeros(n-1);
  end if;

  Fs_p = nParallel*{0.5*(crossAreas[i]+crossAreas[i+1])*(Medium.pressure(states[i+1])-Medium.pressure(states[i])) for i in 1:n-1};

  // Note: the equation is written for dps_fg instead of Fs_fg to help the translator
  dps_fg = {Fs_fg[i]/nParallel*2/(crossAreas[i]+crossAreas[i+1]) for i in 1:n-1};

end PartialStaggeredFlowModel;

Modelica.Fluid.Pipes.BaseClasses.FlowModels.NominalLaminarFlow

Information

This model defines a simple lineaer pressure loss assuming laminar flow for specified dp_nominal and m_flow_nominal.

Select show_Res = true to analyze the actual flow and the lengths of a pipe that would fulfill the specified nominal values for given geometry parameters crossAreas, dimensions and roughnesses.

Extends from Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialStaggeredFlowModel (Base class for momentum balances in flow models).

Parameters

Type	Name	Default	Description
ReynoldsNumber	Re_turbulent	4000	Start of turbulent regime, depending on type of flow device [1]
AbsolutePressure	dp_nominal		Nominal pressure loss [Pa]
MassFlowRate	m_flow_nominal		Mass flow rate for dp_nominal [kg/s]
Advanced
Boolean	useUpstreamScheme	true	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Modelica definition

model NominalLaminarFlow 
  "NominalLaminarFlow: Linear pressure loss for nominal values"
  extends Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialStaggeredFlowModel
    (use_mu_nominal=not show_Res);

  // Operational conditions
  parameter SI.AbsolutePressure dp_nominal "Nominal pressure loss";
  parameter SI.MassFlowRate m_flow_nominal "Mass flow rate for dp_nominal";

  // Inverse parameterization assuming pipe flow and WallFriction.Laminar
  // Laminar.massFlowRate_dp:
  //   m_flow = dp*pi*diameter^4*d/(128*length*mu);
  SI.Length[n-1] pathLengths_nominal=
    {(dp_nominal/(n-1)-g*dheights[i])*Modelica.Constants.pi*((dimensions[i]+dimensions[i+1])/2)^4*rhos_act[i]/(128*mus_act[i])/
     (m_flow_nominal/nParallel) for i in 1:n-1} if show_Res;

equation 
  // linear pressure loss
  if  not allowFlowReversal or use_rho_nominal or not useUpstreamScheme then
    dps_fg = {g*dheights[i]*rhos_act[i] for i in 1:n-1} + dp_nominal/(n-1)/m_flow_nominal*m_flows;
  else
    dps_fg = {g*dheights[i]*(if m_flows[i] > 0 then rhos[i] else rhos[i+1]) for i in 1:n-1} + dp_nominal/(n-1)/m_flow_nominal*m_flows;
  end if;

end NominalLaminarFlow;

Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow

Information

This model describes pressure losses due to wall friction in a pipe and due to gravity. Correlations of different complexity and validity can be seleted via the replaceable package WallFriction (see parameter menu below). The details of the pipe wall friction model are described in the UsersGuide. Basically, different variants of the equation

   dp = λ(Re,D)*(L/D)*ρ*v*|v|/2.

By default, the correlations are computed with media data at the actual time instant. In order to reduce non-linear equation systems, the parameters use_mu_nominal and use_rho_nominal provide the option to compute the correlations with constant media values at the desired operating point. This might speed-up the simulation and/or might give a more robust simulation.

Extends from Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialStaggeredFlowModel (Base class for momentum balances in flow models).

Parameters

Type	Name	Default	Description
ReynoldsNumber	Re_turbulent	4000	Start of turbulent regime, depending on type of flow device [1]
AbsolutePressure	dp_nominal		Nominal pressure loss (for nominal models) [Pa]
MassFlowRate	m_flow_nominal		Mass flow rate for dp_nominal (for nominal models) [kg/s]
Boolean	from_dp	momentumDynamics >= Types.Dy...	= true, use m_flow = f(dp), otherwise dp = f(m_flow)
AbsolutePressure	dp_small	system.dp_small	Within regularization if |dp| < dp_small (may be wider for large discontinuities in static head) [Pa]
MassFlowRate	m_flow_small	system.m_flow_small	Within regularization if |m_flows| < m_flow_small (may be wider for large discontinuities in static head) [kg/s]
Advanced
Boolean	useUpstreamScheme	true	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Modelica definition

partial model PartialGenericPipeFlow 
  "GenericPipeFlow: Pipe flow pressure loss and gravity with replaceable WallFriction package"
  extends Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialStaggeredFlowModel
    (
 final Re_turbulent=4000);

  replaceable package WallFriction =
    Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed
      constrainedby 
    Modelica.Fluid.Pipes.BaseClasses.WallFriction.PartialWallFriction 
    "Wall friction model";

  input SI.Length[n-1] pathLengths_internal 
    "pathLengths used internally; to be defined by extending class";

  // Parameters
  parameter SI.AbsolutePressure dp_nominal 
    "Nominal pressure loss (for nominal models)";
  parameter SI.MassFlowRate m_flow_nominal 
    "Mass flow rate for dp_nominal (for nominal models)";
  parameter Boolean from_dp = momentumDynamics >= Types.Dynamics.SteadyStateInitial 
    " = true, use m_flow = f(dp), otherwise dp = f(m_flow)";
  parameter SI.AbsolutePressure dp_small = system.dp_small 
    "Within regularization if |dp| < dp_small (may be wider for large discontinuities in static head)";
  parameter SI.MassFlowRate m_flow_small = system.m_flow_small 
    "Within regularization if |m_flows| < m_flow_small (may be wider for large discontinuities in static head)";

  final parameter Boolean constantPressureLossCoefficient=
     use_rho_nominal and (use_mu_nominal or not WallFriction.use_mu) 
    "= true if the pressure loss does not depend on fluid states";
  final parameter Boolean continuousFlowReversal=
     (not useUpstreamScheme)
     or constantPressureLossCoefficient
     or not allowFlowReversal 
    "= true if the pressure loss is continuous around zero flow";

  SI.Length[n-1] diameters = 0.5*(dimensions[1:n-1] + dimensions[2:n]) 
    "mean diameters between segments";

equation 
  for i in 1:n-1 loop
    assert(m_flows[i] > -m_flow_small or allowFlowReversal, "Reverting flow occurs even though allowFlowReversal is false");
  end for;

  if continuousFlowReversal then
    // simple regularization
    if from_dp and not WallFriction.dp_is_zero then
      m_flows = WallFriction.massFlowRate_dp(
        dps_fg - {g*dheights[i]*rhos_act[i] for i in 1:n-1},
        rhos_act,
        rhos_act,
        mus_act,
        mus_act,
        pathLengths_internal,
        diameters,
        (roughnesses[1:n-1]+roughnesses[2:n])/2,
        dp_small)*nParallel;
    else
      dps_fg = WallFriction.pressureLoss_m_flow(
        m_flows/nParallel,
        rhos_act,
        rhos_act,
        mus_act,
        mus_act,
        pathLengths_internal,
        diameters,
        (roughnesses[1:n-1]+roughnesses[2:n])/2,
        m_flow_small/nParallel) + {g*dheights[i]*rhos_act[i] for i in 1:n-1};
    end if;
  else
    // regularization for discontinuous flow reversal and static head
    if from_dp and not WallFriction.dp_is_zero then
      m_flows = WallFriction.massFlowRate_dp_staticHead(
        dps_fg,
        rhos[1:n-1],
        rhos[2:n],
        mus[1:n-1],
        mus[2:n],
        pathLengths_internal,
        diameters,
        g*dheights,
        (roughnesses[1:n-1]+roughnesses[2:n])/2,
        dp_small/n)*nParallel;
    else
      dps_fg = WallFriction.pressureLoss_m_flow_staticHead(
        m_flows/nParallel,
        rhos[1:n-1],
        rhos[2:n],
        mus[1:n-1],
        mus[2:n],
        pathLengths_internal,
        diameters,
        g*dheights,
        (roughnesses[1:n-1]+roughnesses[2:n])/2,
        m_flow_small/nParallel);
    end if;
  end if;

end PartialGenericPipeFlow;

Modelica.Fluid.Pipes.BaseClasses.FlowModels.NominalTurbulentPipeFlow

Information

This model defines the pressure loss assuming turbulent flow for specified dp_nominal and m_flow_nominal. It takes into account the fluid density of each flow segment and obtaines appropriate pathLengths_nominal values for an inverse parameterization of the TurbulentPipeFlow model. Per default the upstream and downstream densities are averaged with the setting useUpstreamScheme = false, in order to avoid discontinuous pathLengths_nominal values in the case of flow reversal.

The geometry parameters crossAreas, diameters and roughnesses do not effect simulation results of this nominal pressure loss model. As the geometry is specified however, the optionally calculated Reynolds number as well as m_flows_turbulent and dps_fg_turbulent become meaningful and can be related to m_flow_small and dp_small.

Optional Variables if show_Res

Extends from Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow (GenericPipeFlow: Pipe flow pressure loss and gravity with replaceable WallFriction package).

Parameters

Type	Name	Default	Description
Length	pathLengths_internal[n - 1]	pathLengths_nominal	pathLengths used internally; to be defined by extending class [m]
AbsolutePressure	dp_nominal		Nominal pressure loss (for nominal models) [Pa]
MassFlowRate	m_flow_nominal		Mass flow rate for dp_nominal (for nominal models) [kg/s]
Boolean	from_dp	momentumDynamics >= Types.Dy...	= true, use m_flow = f(dp), otherwise dp = f(m_flow)
AbsolutePressure	dp_small	system.dp_small	Within regularization if |dp| < dp_small (may be wider for large discontinuities in static head) [Pa]
MassFlowRate	m_flow_small	system.m_flow_small	Within regularization if |m_flows| < m_flow_small (may be wider for large discontinuities in static head) [kg/s]
Advanced
Boolean	useUpstreamScheme	false	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Wall friction
replaceable package WallFriction		Detailed	Wall friction model
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Connectors

Type	Name	Description
Wall friction
replaceable package WallFriction		Wall friction model

Modelica definition

model NominalTurbulentPipeFlow 
  "NominalTurbulentPipeFlow: Quadratic turbulent pressure loss for nominal values"
  extends Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow(
redeclare package WallFriction =
    Modelica.Fluid.Pipes.BaseClasses.WallFriction.QuadraticTurbulent,
use_mu_nominal=not show_Res,
pathLengths_internal=pathLengths_nominal,
useUpstreamScheme=false);

  import Modelica.Constants.pi;

  // variables for nominal pressure loss
  SI.Length[n-1] pathLengths_nominal 
    "pathLengths resulting from nominal pressure loss and geometry";
  Real[n-1] ks_inv "coefficient for quadratic flow";
  Real[n-1] zetas "coefficient for quadratic flow";

  // Reynolds Number
  Medium.AbsolutePressure[n-1] dps_fg_turbulent=
      {(mus_act[i]*diameters[i]*pi/4)^2*Re_turbulent^2/(ks_inv[i]*rhos_act[i]) for i in 1:n-1} if 
         show_Res "Start of turbulent flow";

equation 
  // Inverse parameterization for WallFriction.QuadraticTurbulent
  // Note: the code should be shared with the WallFriction.QuadraticTurbulent model,
  //       but this required a re-design of the WallFriction interfaces ...
  //   zeta = (length_nominal/diameter)/(2*Math.log10(3.7 /(roughness/diameter)))^2;
  //   k_inv = (pi*diameter*diameter)^2/(8*zeta);
  //   k = rho*k_inv "Factor in m_flow = sqrt(k*dp)";
  for i in 1:n-1 loop
    ks_inv[i] = (m_flow_nominal/nParallel)^2/((dp_nominal/(n-1)-g*dheights[i]*rhos_act[i]))/rhos_act[i];
    zetas[i] = (pi*diameters[i]*diameters[i])^2/(8*ks_inv[i]);
    pathLengths_nominal[i] =
      zetas[i]*diameters[i]*(2*Modelica.Math.log10(3.7 /((roughnesses[i]+roughnesses[i+1])/2/diameters[i])))^2;
  end for;

end NominalTurbulentPipeFlow;

Modelica.Fluid.Pipes.BaseClasses.FlowModels.TurbulentPipeFlow

Information

This model defines only the quadratic turbulent regime of wall friction: dp = k*m_flow*|m_flow|, where "k" depends on density and the roughness of the pipe and is not a function of the Reynolds number. This relationship is only valid for large Reynolds numbers. The turbulent pressure loss correlation might be useful to optimize models that are only facing turbular flow.

Extends from Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow (GenericPipeFlow: Pipe flow pressure loss and gravity with replaceable WallFriction package).

Parameters

Type	Name	Default	Description
Length	pathLengths_internal[n - 1]	pathLengths	pathLengths used internally; to be defined by extending class [m]
AbsolutePressure	dp_nominal	1e3*dp_small	Nominal pressure loss (for nominal models) [Pa]
MassFlowRate	m_flow_nominal	1e2*m_flow_small	Mass flow rate for dp_nominal (for nominal models) [kg/s]
Boolean	from_dp	momentumDynamics >= Types.Dy...	= true, use m_flow = f(dp), otherwise dp = f(m_flow)
AbsolutePressure	dp_small	system.dp_small	Within regularization if |dp| < dp_small (may be wider for large discontinuities in static head) [Pa]
MassFlowRate	m_flow_small	system.m_flow_small	Within regularization if |m_flows| < m_flow_small (may be wider for large discontinuities in static head) [kg/s]
Advanced
Boolean	useUpstreamScheme	true	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Wall friction
replaceable package WallFriction		Detailed	Wall friction model
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Connectors

Type	Name	Description
Wall friction
replaceable package WallFriction		Wall friction model

Modelica definition

model TurbulentPipeFlow 
  "TurbulentPipeFlow: Pipe wall friction in the quadratic turbulent regime (simple characteristic, mu not used)"
 extends Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow(
redeclare package WallFriction =
    Modelica.Fluid.Pipes.BaseClasses.WallFriction.QuadraticTurbulent,
use_mu_nominal=not show_Res,
pathLengths_internal=pathLengths,
dp_nominal=1e3*dp_small,
m_flow_nominal=1e2*m_flow_small);

end TurbulentPipeFlow;

Modelica.Fluid.Pipes.BaseClasses.FlowModels.DetailedPipeFlow

Information

This component defines the complete regime of wall friction. The details are described in the UsersGuide. The functional relationship of the friction loss factor λ is displayed in the next figure. Function massFlowRate_dp() defines the "red curve" ("Swamee and Jain"), where as function pressureLoss_m_flow() defines the "blue curve" ("Colebrook-White"). The two functions are inverses from each other and give slightly different results in the transition region between Re = 1500 .. 4000, in order to get explicit equations without solving a non-linear equation.

Additionally to wall friction, this component properly implements static head. With respect to the latter, two cases can be distinguished. In the case shown next, the change of elevation with the path from a to b has the opposite sign of the change of density.

In the case illustrated second, the change of elevation with the path from a to b has the same sign of the change of density.

Extends from Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow (GenericPipeFlow: Pipe flow pressure loss and gravity with replaceable WallFriction package).

Parameters

Type	Name	Default	Description
Length	pathLengths_internal[n - 1]	pathLengths	pathLengths used internally; to be defined by extending class [m]
AbsolutePressure	dp_nominal	1e3*dp_small	Nominal pressure loss (for nominal models) [Pa]
MassFlowRate	m_flow_nominal	1e2*m_flow_small	Mass flow rate for dp_nominal (for nominal models) [kg/s]
Boolean	from_dp	momentumDynamics >= Types.Dy...	= true, use m_flow = f(dp), otherwise dp = f(m_flow)
AbsolutePressure	dp_small	system.dp_small	Within regularization if |dp| < dp_small (may be wider for large discontinuities in static head) [Pa]
MassFlowRate	m_flow_small	system.m_flow_small	Within regularization if |m_flows| < m_flow_small (may be wider for large discontinuities in static head) [kg/s]
Advanced
Boolean	useUpstreamScheme	true	= false to average upstream and downstream properties across flow segments
Boolean	use_Ib_flows	momentumDynamics <> Types.Dy...	= true to consider differences in flow of momentum through boundaries
Diagnostics
Boolean	show_Res	false	= true, if Reynolds numbers are included for plotting
Wall friction
replaceable package WallFriction		Detailed	Wall friction model
Internal Interface
replaceable package Medium		PartialMedium	Medium in the component
Integer	n	2	Number of discrete flow volumes
Geometry
Real	nParallel		number of identical parallel flow devices
Static head
Acceleration	g	system.g	Constant gravity acceleration [m/s2]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (states[1] -> states[n+1])
Dynamics	momentumDynamics	system.momentumDynamics	Formulation of momentum balance
Initialization
MassFlowRate	m_flow_start	system.m_flow_start	Start value of mass flow rates [kg/s]
AbsolutePressure	p_a_start		Start value for p[1] at design inflow [Pa]
AbsolutePressure	p_b_start		Start value for p[n+1] at design outflow [Pa]

Connectors

Type	Name	Description
Wall friction
replaceable package WallFriction		Wall friction model

Modelica definition

model DetailedPipeFlow 
  "DetailedPipeFlow: Pipe wall friction in the laminar and turbulent regime (detailed characteristic)"
 extends Modelica.Fluid.Pipes.BaseClasses.FlowModels.PartialGenericPipeFlow(
redeclare package WallFriction =
    Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed,
pathLengths_internal=pathLengths,
dp_nominal=1e3*dp_small,
m_flow_nominal=1e2*m_flow_small);

end DetailedPipeFlow;