Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent

Information

This library provides pressure loss factors of a pipe segment (orifice, bending etc.) with a minimum amount of data. If available, data can be provided for both flow directions, i.e., flow from port_a to port_b and from port_b to port_a, as well as for the laminar and the turbulent region. It is also an option to provide the loss factor only for the turbulent region for a flow from port_a to port_b. Basically, the pressure drop is defined by the following equation:

   Δp = 0.5*ζ*ρ*v*|v|
      = 0.5*ζ/A^2 * (1/ρ) * m_flow*|m_flow|
      = 8*ζ/(π^2*D^4*ρ) * m_flow*|m_flow|

where

• Δp is the pressure drop: Δp = port_a.p - port_b.p
• v is the mean velocity.
• ρ is the density.
• ζ is the loss factor that depends on the geometry of the pipe. In the turbulent flow regime, it is assumed that ζ is constant and is given by "zeta1" and "zeta2" depending on the flow direction.
• D is the diameter of the pipe segment. If this is not a circular cross section, D = 4*A/P, where A is the cross section area and P is the wetted perimeter.

Package Content

Name	Description
LossFactorData	Data structure defining constant loss factor data for dp = zeta*rho*v*|v|/2 and functions providing the data for some loss types
massFlowRate_dp	Return mass flow rate from constant loss factor data and pressure drop (m_flow = f(dp))
massFlowRate_dp_and_Re	Return mass flow rate from constant loss factor data, pressure drop and Re (m_flow = f(dp))
pressureLoss_m_flow	Return pressure drop from constant loss factor and mass flow rate (dp = f(m_flow))
pressureLoss_m_flow_and_Re	Return pressure drop from constant loss factor, mass flow rate and Re (dp = f(m_flow))
BaseModel	Generic pressure drop component with constant turbulent loss factor data and without an icon
TestWallFriction	Pressure drop in pipe due to wall friction (only for test purposes; if needed use Pipes.StaticPipe instead)
BaseModelNonconstantCrossSectionArea	Generic pressure drop component with constant turbulent loss factor data and without an icon, for non-constant cross section area
pressureLoss_m_flow_totalPressure	Return pressure drop from constant loss factor and mass flow rate (dp = f(m_flow))

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.LossFactorData

Information

This record defines the pressure loss factors of a pipe segment (orifice, bending etc.) with a minimum amount of data. If available, data should be provided for both flow directions, i.e., flow from port_a to port_b and from port_b to port_a, as well as for the laminar and the turbulent region. It is also an option to provide the loss factor only for the turbulent region for a flow from port_a to port_b.

The following equations are used:

   Δp = 0.5*ζ*ρ*v*|v|
      = 0.5*ζ/A^2 * (1/ρ) * m_flow*|m_flow|
      = 8*ζ/(π^2*D^4*ρ) * m_flow*|m_flow|
        Re = |v|*D*ρ/μ

where

• Δp is the pressure drop: Δp = port_a.p - port_b.p
• v is the mean velocity.
• ρ is the density.
• ζ is the loss factor that depends on the geometry of the pipe. In the turbulent flow regime, it is assumed that ζ is constant and is given by "zeta1" and "zeta2" depending on the flow direction.
  When the Reynolds number Re is below "Re_turbulent", the flow is laminar for small flow velocities. For higher velocities there is a transition region from laminar to turbulent flow. The loss factor for laminar flow at small velocities is defined by the often occuring approximation c0/Re. If c0 is different for the two flow directions, the mean value has to be used (c0 = (c0_ab + c0_ba)/2).
• The equation "Δp = 0.5*ζ*ρ*v*|v|" is either with respect to port_a or to port_b, depending on the definition of the particular loss factor ζ (in some references loss factors are defined with respect to port_a, in other references with respect to port_b).
• Re = |v|*D_Re*ρ/μ = |m_flow|*D_Re/(A_Re*μ) is the Reynolds number at the smallest cross section area. This is often at port_a or at port_b, but can also be between the two ports. In the record, the diameter D_Re of this smallest cross section area has to be provided, as well, as Re_turbulent, the absolute value of the Reynolds number at which the turbulent flow starts. If Re_turbulent is different for the two flow directions, use the smaller value as Re_turbulent.
• D is the diameter of the pipe. If the pipe has not a circular cross section, D = 4*A/P, where A is the cross section area and P is the wetted perimeter.
• A is the cross section area with A = π(D/2)^2.
• μ is the dynamic viscosity.

The laminar and the transition region is usually of not much technical interest because the operating point is mostly in the turbulent regime. For simplification and for numercial reasons, this whole region is described by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The polynomials start at Re = |m_flow|*4/(π*D_Re*μ), where D_Re is the smallest diameter between port_a and port_b. The common derivative of the two polynomials at Re = 0 is computed from the equation "c0/Re". Note, the pressure drop equation above in the laminar region is always defined with respect to the smallest diameter D_Re.

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

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

Parameters

Type	Name	Default	Description
Diameter	diameter_a		Diameter at port_a [m]
Diameter	diameter_b		Diameter at port_b [m]
Real	zeta1		Loss factor for flow port_a -> port_b
Real	zeta2		Loss factor for flow port_b -> port_a
ReynoldsNumber	Re_turbulent		Loss factors suited for Re >= Re_turbulent [1]
Diameter	D_Re		Diameter used to compute Re [m]
Boolean	zeta1_at_a	true	dp = zeta1*(if zeta1_at_a then rho_a*v_a^2/2 else rho_b*v_b^2/2)
Boolean	zeta2_at_a	false	dp = -zeta2*(if zeta2_at_a then rho_a*v_a^2/2 else rho_b*v_b^2/2)
Boolean	zetaLaminarKnown	false	= true, if zeta = c0/Re in laminar region
Real	c0	1	zeta = c0/Re; dp = zeta*rho_Re*v_Re^2/2, Re=v_Re*D_Re*rho_Re/mu_Re)

Modelica definition

record LossFactorData 
  "Data structure defining constant loss factor data for dp = zeta*rho*v*|v|/2 and functions providing the data for some loss types"

       extends Modelica.Icons.Record;

 SI.Diameter diameter_a "Diameter at port_a";
 SI.Diameter diameter_b "Diameter at port_b";
 Real zeta1 "Loss factor for flow port_a -> port_b";
 Real zeta2 "Loss factor for flow port_b -> port_a";
 SI.ReynoldsNumber Re_turbulent "Loss factors suited for Re >= Re_turbulent";
 SI.Diameter D_Re "Diameter used to compute Re";
 Boolean zeta1_at_a = true 
    "dp = zeta1*(if zeta1_at_a then rho_a*v_a^2/2 else rho_b*v_b^2/2)";
 Boolean zeta2_at_a = false 
    "dp = -zeta2*(if zeta2_at_a then rho_a*v_a^2/2 else rho_b*v_b^2/2)";
 Boolean zetaLaminarKnown = false "= true, if zeta = c0/Re in laminar region";
 Real c0 = 1 
    "zeta = c0/Re; dp = zeta*rho_Re*v_Re^2/2, Re=v_Re*D_Re*rho_Re/mu_Re)";

  encapsulated function wallFriction 
    "Return pressure loss data due to friction in a straight pipe with walls of nonuniform roughness (not useful for smooth pipes, since zeta is no function of Re)"
     import Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.LossFactorData;
     import lg = Modelica.Math.log10;
     import SI = Modelica.SIunits;

    input SI.Length length "Length of pipe";
    input SI.Diameter diameter "Inner diameter of pipe";
    input SI.Length roughness(min=1e-10) 
      "Absolute roughness of pipe (> 0 required, details see info layer)";
    output LossFactorData data "Pressure loss factors for both flow directions";
  protected 
    Real Delta = roughness/diameter "relative roughness";
  algorithm 
    data.diameter_a          := diameter;
    data.diameter_b          := diameter;
    data.zeta1        := (length/diameter)/(2*lg(3.7 /Delta))^2;
    data.zeta2        := data.zeta1;
    data.Re_turbulent := 4000 
      ">= 560/Delta flow does not depend on Re, but interpolation is bad";
    data.D_Re         := diameter;
    data.zeta1_at_a   := true;
    data.zeta2_at_a   := false;
    data.zetaLaminarKnown := true;
    data.c0               := 64*(length/diameter);
  end wallFriction;

  encapsulated function suddenExpansion 
    "Return pressure loss data for sudden expansion or contraction in a pipe (for both flow directions)"
     import Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.LossFactorData;
     import SI = Modelica.SIunits;
    input SI.Diameter diameter_a "Inner diameter of pipe at port_a";
    input SI.Diameter diameter_b "Inner diameter of pipe at port_b";
    output LossFactorData data "Pressure loss factors for both flow directions";
  protected 
    Real A_rel;
  algorithm 
    data.diameter_a          := diameter_a;
    data.diameter_b          := diameter_b;
    data.Re_turbulent := 100;
    data.zetaLaminarKnown := true;
    data.c0 := 30;

    if diameter_a <= diameter_b then
       A_rel :=(diameter_a/diameter_b)^2;
       data.zeta1 :=(1 - A_rel)^2;
       data.zeta2 :=0.5*(1 - A_rel)^0.75;
       data.zeta1_at_a :=true;
       data.zeta2_at_a :=true;
       data.D_Re := diameter_a;
    else
       A_rel :=(diameter_b/diameter_a)^2;
       data.zeta1 :=0.5*(1 - A_rel)^0.75;
       data.zeta2 :=(1 - A_rel)^2;
       data.zeta1_at_a :=false;
       data.zeta2_at_a :=false;
       data.D_Re := diameter_b;
    end if;
  end suddenExpansion;

  encapsulated function sharpEdgedOrifice 
    "Return pressure loss data for sharp edged orifice (for both flow directions)"
     import NonSI = Modelica.SIunits.Conversions.NonSIunits;
     import Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.LossFactorData;
     import SI = Modelica.SIunits;
     input SI.Diameter diameter 
      "Inner diameter of pipe (= same at port_a and port_b)";
     input SI.Diameter leastDiameter "Smallest diameter of orifice";
     input SI.Diameter length "Length of orifice";
     input NonSI.Angle_deg alpha "Angle of orifice";
     output LossFactorData data 
      "Pressure loss factors for both flow directions";
  protected 
     Real D_rel=leastDiameter/diameter;
     Real LD=length/leastDiameter;
     Real k=0.13 + 0.34*10^(-(3.4*LD + 88.4*LD^2.3));
  algorithm 
     data.diameter_a := diameter;
     data.diameter_b := diameter;
     data.zeta1 := ((1 - D_rel) + 0.707*(1 - D_rel)^0.375)^2*(1/D_rel)^2;
     data.zeta2 := k*(1 - D_rel)^0.75 + (1 - D_rel)^2 + 2*sqrt(k*(1 -
       D_rel)^0.375) + (1 - D_rel);
     data.Re_turbulent := 1e4;
     data.D_Re := leastDiameter;
     data.zeta1_at_a := true;
     data.zeta2_at_a := false;
     data.zetaLaminarKnown := false;
     data.c0 := 0;
  end sharpEdgedOrifice;

end LossFactorData;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.massFlowRate_dp

Information

Compute mass flow rate from constant loss factor and pressure drop (m_flow = f(dp)). For small pressure drops (dp < dp_small), the characteristic is approximated by a polynomial in order to have a finite derivative at zero mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Pressure	dp		Pressure drop (dp = port_a.p - port_b.p) [Pa]
Density	rho_a		Density at port_a [kg/m3]
Density	rho_b		Density at port_b [kg/m3]
LossFactorData	data		Constant loss factors for both flow directions
AbsolutePressure	dp_small	1	Turbulent flow if |dp| >= dp_small [Pa]

Outputs

Type	Name	Description
MassFlowRate	m_flow	Mass flow rate from port_a to port_b [kg/s]

Modelica definition

function massFlowRate_dp 
  "Return mass flow rate from constant loss factor data and pressure drop (m_flow = f(dp))"
        //import Modelica.Fluid.PressureLosses.BaseClasses.lossConstant_D_zeta;
  extends Modelica.Icons.Function;

  input SI.Pressure dp "Pressure drop (dp = port_a.p - port_b.p)";
  input SI.Density rho_a "Density at port_a";
  input SI.Density rho_b "Density at port_b";
  input LossFactorData data "Constant loss factors for both flow directions";
  input SI.AbsolutePressure dp_small = 1 "Turbulent flow if |dp| >= dp_small";
  output SI.MassFlowRate m_flow "Mass flow rate from port_a to port_b";

protected 
  Real k1 = lossConstant_D_zeta(if data.zeta1_at_a then data.diameter_a else data.diameter_b,data.zeta1);
  Real k2 = lossConstant_D_zeta(if data.zeta2_at_a then data.diameter_a else data.diameter_b,data.zeta2);
algorithm 
  /*
   dp = 0.5*zeta*rho*v*|v|
      = 0.5*zeta*rho*1/(rho*A)^2 * m_flow * |m_flow|
      = 0.5*zeta/A^2 *1/rho * m_flow * |m_flow|
      = k/rho * m_flow * |m_flow|
   k  = 0.5*zeta/A^2
      = 0.5*zeta/(pi*(D/2)^2)^2
      = 8*zeta/(pi*D^2)^2
  */
  m_flow :=Utilities.regRoot2(dp, dp_small, rho_a/k1, rho_b/k2);
end massFlowRate_dp;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.massFlowRate_dp_and_Re

Information

Compute mass flow rate from constant loss factor and pressure drop (m_flow = f(dp)). If the Reynolds-number Re ≥ data.Re_turbulent, the flow is treated as a turbulent flow with constant loss factor zeta. If the Reynolds-number Re < data.Re_turbulent, the flow is laminar and/or in a transition region between laminar and turbulent. This region is approximated by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The common derivative of the two polynomials at Re = 0 is computed from the equation "data.c0/Re".

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Pressure	dp		Pressure drop (dp = port_a.p - port_b.p) [Pa]
Density	rho_a		Density at port_a [kg/m3]
Density	rho_b		Density at port_b [kg/m3]
DynamicViscosity	mu_a		Dynamic viscosity at port_a [Pa.s]
DynamicViscosity	mu_b		Dynamic viscosity at port_b [Pa.s]
LossFactorData	data		Constant loss factors for both flow directions

Outputs

Type	Name	Description
MassFlowRate	m_flow	Mass flow rate from port_a to port_b [kg/s]

Modelica definition

function massFlowRate_dp_and_Re 
  "Return mass flow rate from constant loss factor data, pressure drop and Re (m_flow = f(dp))"
        extends Modelica.Icons.Function;

  input SI.Pressure dp "Pressure drop (dp = port_a.p - port_b.p)";
  input SI.Density rho_a "Density at port_a";
  input SI.Density rho_b "Density at port_b";
  input SI.DynamicViscosity mu_a "Dynamic viscosity at port_a";
  input SI.DynamicViscosity mu_b "Dynamic viscosity at port_b";
  input LossFactorData data "Constant loss factors for both flow directions";
  output SI.MassFlowRate m_flow "Mass flow rate from port_a to port_b";

protected 
  constant Real pi=Modelica.Constants.pi;
  Real k0=2*data.c0/(pi*data.D_Re^3);
  Real k1 = lossConstant_D_zeta(if data.zeta1_at_a then data.diameter_a else data.diameter_b,data.zeta1);
  Real k2 = lossConstant_D_zeta(if data.zeta2_at_a then data.diameter_a else data.diameter_b,data.zeta2);
  Real yd0 "Derivative of m_flow=m_flow(dp) at zero, if data.zetaLaminarKnown";
  SI.AbsolutePressure dp_turbulent 
    "The turbulent region is: |dp| >= dp_turbulent";
algorithm 
/*
Turbulent region:
   Re = m_flow*(4/pi)/(D_Re*mu)
   dp = 0.5*zeta*rho*v*|v|
      = 0.5*zeta*rho*1/(rho*A)^2 * m_flow * |m_flow|
      = 0.5*zeta/A^2 *1/rho * m_flow * |m_flow|
      = k/rho * m_flow * |m_flow|
   k  = 0.5*zeta/A^2
      = 0.5*zeta/(pi*(D/2)^2)^2
      = 8*zeta/(pi*D^2)^2
   m_flow_turbulent = (pi/4)*D_Re*mu*Re_turbulent
   dp_turbulent     =  k/rho *(D_Re*mu*pi/4)^2 * Re_turbulent^2

   The start of the turbulent region is computed with mean values
   of dynamic viscosity mu and density rho. Otherwise, one has
   to introduce different "delta" values for both flow directions.
   In order to simplify the approach, only one delta is used.

Laminar region:
   dp = 0.5*zeta/(A^2*d) * m_flow * |m_flow|
      = 0.5 * c0/(|m_flow|*(4/pi)/(D_Re*mu)) / ((pi*(D_Re/2)^2)^2*d) * m_flow*|m_flow|
      = 0.5 * c0*(pi/4)*(D_Re*mu) * 16/(pi^2*D_Re^4*d) * m_flow*|m_flow|
      = 2*c0/(pi*D_Re^3) * mu/rho * m_flow
      = k0 * mu/rho * m_flow
   k0 = 2*c0/(pi*D_Re^3)

   In order that the derivative of dp=f(m_flow) is continuous
   at m_flow=0, the mean values of mu and d are used in the
   laminar region: mu/rho = (mu_a + mu_b)/(rho_a + rho_b)
   If data.zetaLaminarKnown = false then mu_a and mu_b are potentially zero
   (because dummy values) and therefore the division is only performed
   if zetaLaminarKnown = true.
*/
   dp_turbulent :=(k1 + k2)/(rho_a + rho_b)*
                  ((mu_a + mu_b)*data.D_Re*pi/8)^2*data.Re_turbulent^2;
   yd0 :=if data.zetaLaminarKnown then 
            (rho_a + rho_b)/(k0*(mu_a + mu_b)) else 0;
   m_flow := Utilities.regRoot2(dp, dp_turbulent, rho_a/k1, rho_b/k2,
                                               data.zetaLaminarKnown, yd0);
end massFlowRate_dp_and_Re;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.pressureLoss_m_flow

Information

Compute pressure drop from constant loss factor and mass flow rate (dp = f(m_flow)). For small mass flow rates(|m_flow| < m_flow_small), the characteristic is approximated by a polynomial in order to have a finite derivative at zero mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
MassFlowRate	m_flow		Mass flow rate from port_a to port_b [kg/s]
Density	rho_a		Density at port_a [kg/m3]
Density	rho_b		Density at port_b [kg/m3]
LossFactorData	data		Constant loss factors for both flow directions
MassFlowRate	m_flow_small	0.01	Turbulent flow if |m_flow| >= m_flow_small [kg/s]

Outputs

Type	Name	Description
Pressure	dp	Pressure drop (dp = port_a.p - port_b.p) [Pa]

Modelica definition

function pressureLoss_m_flow 
  "Return pressure drop from constant loss factor and mass flow rate (dp = f(m_flow))"
        extends Modelica.Icons.Function;

  input SI.MassFlowRate m_flow "Mass flow rate from port_a to port_b";
  input SI.Density rho_a "Density at port_a";
  input SI.Density rho_b "Density at port_b";
  input LossFactorData data "Constant loss factors for both flow directions";
  input SI.MassFlowRate m_flow_small = 0.01 
    "Turbulent flow if |m_flow| >= m_flow_small";
  output SI.Pressure dp "Pressure drop (dp = port_a.p - port_b.p)";

protected 
  Real k1 = lossConstant_D_zeta(if data.zeta1_at_a then data.diameter_a else data.diameter_b,data.zeta1);
  Real k2 = lossConstant_D_zeta(if data.zeta2_at_a then data.diameter_a else data.diameter_b,data.zeta2);
algorithm 
  /*
   dp = 0.5*zeta*rho*v*|v|
      = 0.5*zeta*rho*1/(rho*A)^2 * m_flow * |m_flow|
      = 0.5*zeta/A^2 *1/rho * m_flow * |m_flow|
      = k/rho * m_flow * |m_flow|
   k  = 0.5*zeta/A^2
      = 0.5*zeta/(pi*(D/2)^2)^2
      = 8*zeta/(pi*D^2)^2
  */
  dp :=Utilities.regSquare2(m_flow, m_flow_small, k1/rho_a, k2/rho_b);
end pressureLoss_m_flow;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.pressureLoss_m_flow_and_Re

Information

Compute pressure drop from constant loss factor and mass flow rate (dp = f(m_flow)). If the Reynolds-number Re ≥ data.Re_turbulent, the flow is treated as a turbulent flow with constant loss factor zeta. If the Reynolds-number Re < data.Re_turbulent, the flow is laminar and/or in a transition region between laminar and turbulent. This region is approximated by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The common derivative of the two polynomials at Re = 0 is computed from the equation "data.c0/Re".

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
MassFlowRate	m_flow		Mass flow rate from port_a to port_b [kg/s]
Density	rho_a		Density at port_a [kg/m3]
Density	rho_b		Density at port_b [kg/m3]
DynamicViscosity	mu_a		Dynamic viscosity at port_a [Pa.s]
DynamicViscosity	mu_b		Dynamic viscosity at port_b [Pa.s]
LossFactorData	data		Constant loss factors for both flow directions

Outputs

Type	Name	Description
Pressure	dp	Pressure drop (dp = port_a.p - port_b.p) [Pa]

Modelica definition

function pressureLoss_m_flow_and_Re 
  "Return pressure drop from constant loss factor, mass flow rate and Re (dp = f(m_flow))"
        extends Modelica.Icons.Function;

  input SI.MassFlowRate m_flow "Mass flow rate from port_a to port_b";
  input SI.Density rho_a "Density at port_a";
  input SI.Density rho_b "Density at port_b";
  input SI.DynamicViscosity mu_a "Dynamic viscosity at port_a";
  input SI.DynamicViscosity mu_b "Dynamic viscosity at port_b";
  input LossFactorData data "Constant loss factors for both flow directions";
  output SI.Pressure dp "Pressure drop (dp = port_a.p - port_b.p)";

protected 
  constant Real pi=Modelica.Constants.pi;
  Real k0 = 2*data.c0/(pi*data.D_Re^3);
  Real k1 = lossConstant_D_zeta(if data.zeta1_at_a then data.diameter_a else data.diameter_b,data.zeta1);
  Real k2 = lossConstant_D_zeta(if data.zeta2_at_a then data.diameter_a else data.diameter_b,data.zeta2);
  Real yd0 "Derivative of dp = f(m_flow) at zero, if data.zetaLaminarKnown";
  SI.MassFlowRate m_flow_turbulent 
    "The turbulent region is: |m_flow| >= m_flow_turbulent";
algorithm 
/*
Turbulent region:
   Re = m_flow*(4/pi)/(D_Re*mu)
   dp = 0.5*zeta*rho*v*|v|
      = 0.5*zeta*rho*1/(rho*A)^2 * m_flow * |m_flow|
      = 0.5*zeta/A^2 *1/rho * m_flow * |m_flow|
      = k/rho * m_flow * |m_flow|
   k  = 0.5*zeta/A^2
      = 0.5*zeta/(pi*(D/2)^2)^2
      = 8*zeta/(pi*D^2)^2
   m_flow_turbulent = (pi/4)*D_Re*mu*Re_turbulent
   dp_turbulent     =  k/rho *(D_Re*mu*pi/4)^2 * Re_turbulent^2

   The start of the turbulent region is computed with mean values
   of dynamic viscosity mu and density rho. Otherwise, one has
   to introduce different "delta" values for both flow directions.
   In order to simplify the approach, only one delta is used.

Laminar region:
   dp = 0.5*zeta/(A^2*d) * m_flow * |m_flow|
      = 0.5 * c0/(|m_flow|*(4/pi)/(D_Re*mu)) / ((pi*(D_Re/2)^2)^2*d) * m_flow*|m_flow|
      = 0.5 * c0*(pi/4)*(D_Re*mu) * 16/(pi^2*D_Re^4*d) * m_flow*|m_flow|
      = 2*c0/(pi*D_Re^3) * mu/rho * m_flow
      = k0 * mu/rho * m_flow
   k0 = 2*c0/(pi*D_Re^3)

   In order that the derivative of dp=f(m_flow) is continuous
   at m_flow=0, the mean values of mu and d are used in the
   laminar region: mu/rho = (mu_a + mu_b)/(rho_a + rho_b)
   If data.zetaLaminarKnown = false then mu_a and mu_b are potentially zero
   (because dummy values) and therefore the division is only performed
   if zetaLaminarKnown = true.
*/
  m_flow_turbulent :=(pi/8)*data.D_Re*(mu_a + mu_b)*data.Re_turbulent;
  yd0 :=if data.zetaLaminarKnown then k0*(mu_a + mu_b)/(rho_a + rho_b) else 0;
  dp :=Utilities.regSquare2(m_flow, m_flow_turbulent, k1/rho_a, k2/rho_b,
                                           data.zetaLaminarKnown, yd0);
end pressureLoss_m_flow_and_Re;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.BaseModel

Information

This model computes the pressure loss of a pipe segment (orifice, bending etc.) with a minimum amount of data provided via parameter data. If available, data should be provided for both flow directions, i.e., flow from port_a to port_b and from port_b to port_a, as well as for the laminar and the turbulent region. It is also an option to provide the loss factor only for the turbulent region for a flow from port_a to port_b.

The following equations are used:

   Δp = 0.5*ζ*ρ*v*|v|
      = 0.5*ζ/A^2 * (1/ρ) * m_flow*|m_flow|
        Re = |v|*D*ρ/μ

where

• Δp is the pressure drop: Δp = port_a.p - port_b.p
• v is the mean velocity.
• ρ is the density.
• ζ is the loss factor that depends on the geometry of the pipe. In the turbulent flow regime, it is assumed that ζ is constant and is given by "zeta1" and "zeta2" depending on the flow direction.
  When the Reynolds number Re is below "Re_turbulent", the flow is laminar for small flow velocities. For higher velocities there is a transition region from laminar to turbulent flow. The loss factor for laminar flow at small velocities is defined by the often occuring approximation c0/Re. If c0 is different for the two flow directions, the mean value has to be used (c0 = (c0_ab + c0_ba)/2).
• The equation "Δp = 0.5*ζ*ρ*v*|v|" is either with respect to port_a or to port_b, depending on the definition of the particular loss factor ζ (in some references loss factors are defined with respect to port_a, in other references with respect to port_b).
• Re = |v|*D_Re*ρ/μ = |m_flow|*D_Re/(A_Re*μ) is the Reynolds number at the smallest cross section area. This is often at port_a or at port_b, but can also be between the two ports. In the record, the diameter D_Re of this smallest cross section area has to be provided, as well, as Re_turbulent, the absolute value of the Reynolds number at which the turbulent flow starts. If Re_turbulent is different for the two flow directions, use the smaller value as Re_turbulent.
• D is the diameter of the pipe. If the pipe has not a circular cross section, D = 4*A/P, where A is the cross section area and P is the wetted perimeter.
• A is the cross section area with A = π(D/2)^2.
• μ is the dynamic viscosity.

The laminar and the transition region is usually of not much technical interest because the operating point is mostly in the turbulent regime. For simplification and for numercial reasons, this whole region is described by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The polynomials start at Re = |m_flow|*4/(π*D_Re*μ), where D_Re is the smallest diameter between port_a and port_b. The common derivative of the two polynomials at Re = 0 is computed from the equation "c0/Re". Note, the pressure drop equation above in the laminar region is always defined with respect to the smallest diameter D_Re.

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

Extends from Modelica.Fluid.Interfaces.PartialTwoPortTransport (Partial element transporting fluid between two ports without storage of mass or energy), Modelica.Fluid.Interfaces.PartialLumpedFlow (Base class for a lumped momentum balance).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Length	pathLength	0	Length flow path [m]
LossFactorData	data		Loss factor data
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	momentumDynamics	Types.Dynamics.SteadyState	Formulation of momentum balance
Advanced
AbsolutePressure	dp_start	0.01*system.p_start	Guess value of dp = port_a.p - port_b.p [Pa]
MassFlowRate	m_flow_start	system.m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
MassFlowRate	m_flow_small	system.m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	from_dp	true	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	use_Re	false	= true, if turbulent region is defined by Re, otherwise by dp_small or m_flow_small
AbsolutePressure	dp_small	system.dp_small	Turbulent flow if |dp| >= dp_small [Pa]
Diagnostics
Boolean	show_T	true	= true, if temperatures at port_a and port_b are computed
Boolean	show_V_flow	true	= true, if volume flow rate at inflowing port is computed
Boolean	show_Re	false	= true, if Reynolds number is included for plotting

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

partial model BaseModel 
  "Generic pressure drop component with constant turbulent loss factor data and without an icon"

  extends Modelica.Fluid.Interfaces.PartialTwoPortTransport;
  extends Modelica.Fluid.Interfaces.PartialLumpedFlow(
    final pathLength = 0,
    final momentumDynamics = Types.Dynamics.SteadyState);

  parameter LossFactorData data "Loss factor data";

  // Advanced
  parameter Boolean from_dp = true 
    "= true, use m_flow = f(dp) else dp = f(m_flow)";
  parameter Boolean use_Re = false 
    "= true, if turbulent region is defined by Re, otherwise by dp_small or m_flow_small";
  parameter Medium.AbsolutePressure dp_small = system.dp_small 
    "Turbulent flow if |dp| >= dp_small";
  parameter Medium.MassFlowRate m_flow_small = system.m_flow_small 
    "Turbulent flow if |m_flow| >= m_flow_small";

  // Diagnostics
  parameter Boolean show_Re = false 
    "= true, if Reynolds number is included for plotting";
  SI.ReynoldsNumber Re = Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber_m_flow(
        m_flow,
        noEvent(if m_flow>0 then Medium.dynamicViscosity(state_a) else Medium.dynamicViscosity(state_b)),
        data.D_Re) if show_Re "Reynolds number at diameter data.D_Re";

  // Variables
  Modelica.SIunits.Pressure dp_fg "pressure loss due to friction and gravity";
  Modelica.SIunits.Area A_mean = Modelica.Constants.pi/4*(data.diameter_a^2+data.diameter_b^2)/2 
    "mean cross flow area";

equation 
  Ib_flow = 0;
  F_p = A_mean*(Medium.pressure(state_b) - Medium.pressure(state_a));
  F_fg = A_mean*dp_fg;
  if from_dp then
     m_flow = if use_Re then 
                 massFlowRate_dp_and_Re(
                    dp_fg, Medium.density(state_a), Medium.density(state_b),
                    Medium.dynamicViscosity(state_a),
                    Medium.dynamicViscosity(state_b),
                    data) else 
                 massFlowRate_dp(dp_fg, Medium.density(state_a), Medium.density(state_b), data, dp_small);
  else
     dp_fg = if use_Re then 
             pressureLoss_m_flow_and_Re(
                 m_flow, Medium.density(state_a), Medium.density(state_b),
                 Medium.dynamicViscosity(state_a),
                 Medium.dynamicViscosity(state_b),
                 data) else 
             pressureLoss_m_flow(m_flow, Medium.density(state_a), Medium.density(state_b), data, m_flow_small);
  end if;

  // Isenthalpic state transformation (no storage and no loss of energy)
  port_a.h_outflow = inStream(port_b.h_outflow);
  port_b.h_outflow = inStream(port_a.h_outflow);

end BaseModel;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.TestWallFriction

Information

Extends from BaseModel (Generic pressure drop component with constant turbulent loss factor data and without an icon).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
LossFactorData	data	LossFactorData.wallFriction(...	Loss factor data
Length	length		Length of pipe [m]
Diameter	diameter		Inner diameter of pipe [m]
Length	roughness		Absolute roughness of pipe (> 0 required, details see info layer) [m]
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Advanced
AbsolutePressure	dp_start	0.01*system.p_start	Guess value of dp = port_a.p - port_b.p [Pa]
MassFlowRate	m_flow_start	system.m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
MassFlowRate	m_flow_small	system.m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	from_dp	true	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	use_Re	false	= true, if turbulent region is defined by Re, otherwise by dp_small or m_flow_small
AbsolutePressure	dp_small	system.dp_small	Turbulent flow if |dp| >= dp_small [Pa]
Diagnostics
Boolean	show_T	true	= true, if temperatures at port_a and port_b are computed
Boolean	show_V_flow	true	= true, if volume flow rate at inflowing port is computed
Boolean	show_Re	false	= true, if Reynolds number is included for plotting

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 TestWallFriction 
  "Pressure drop in pipe due to wall friction (only for test purposes; if needed use Pipes.StaticPipe instead)"
        extends BaseModel(final data=
          LossFactorData.wallFriction(
          length,
          diameter,
          roughness));
  parameter SI.Length length "Length of pipe";
  parameter SI.Diameter diameter "Inner diameter of pipe";
  parameter SI.Length roughness(min=1e-10) 
    "Absolute roughness of pipe (> 0 required, details see info layer)";
end TestWallFriction;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.BaseModelNonconstantCrossSectionArea

Information

This model computes the pressure loss of a pipe segment (orifice, bending etc.) with a minimum amount of data provided via parameter data. If available, data should be provided for both flow directions, i.e., flow from port_a to port_b and from port_b to port_a, as well as for the laminar and the turbulent region. It is also an option to provide the loss factor only for the turbulent region for a flow from port_a to port_b.

The following equations are used:

   Δp = 0.5*ζ*ρ*v*|v|
      = 0.5*ζ/A^2 * (1/ρ) * m_flow*|m_flow|
        Re = |v|*D*ρ/μ

where

• Δp is the pressure drop: Δp = port_a.p - port_b.p
• v is the mean velocity.
• ρ is the density.
• ζ is the loss factor that depends on the geometry of the pipe. In the turbulent flow regime, it is assumed that ζ is constant and is given by "zeta1" and "zeta2" depending on the flow direction.
  When the Reynolds number Re is below "Re_turbulent", the flow is laminar for small flow velocities. For higher velocities there is a transition region from laminar to turbulent flow. The loss factor for laminar flow at small velocities is defined by the often occuring approximation c0/Re. If c0 is different for the two flow directions, the mean value has to be used (c0 = (c0_ab + c0_ba)/2).
• The equation "Δp = 0.5*ζ*ρ*v*|v|" is either with respect to port_a or to port_b, depending on the definition of the particular loss factor ζ (in some references loss factors are defined with respect to port_a, in other references with respect to port_b).
• Re = |v|*D_Re*ρ/μ = |m_flow|*D_Re/(A_Re*μ) is the Reynolds number at the smallest cross section area. This is often at port_a or at port_b, but can also be between the two ports. In the record, the diameter D_Re of this smallest cross section area has to be provided, as well, as Re_turbulent, the absolute value of the Reynolds number at which the turbulent flow starts. If Re_turbulent is different for the two flow directions, use the smaller value as Re_turbulent.
• D is the diameter of the pipe. If the pipe has not a circular cross section, D = 4*A/P, where A is the cross section area and P is the wetted perimeter.
• A is the cross section area with A = π(D/2)^2.
• μ is the dynamic viscosity.

The laminar and the transition region is usually of not much technical interest because the operating point is mostly in the turbulent regime. For simplification and for numercial reasons, this whole region is described by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The polynomials start at Re = |m_flow|*4/(π*D_Re*μ), where D_Re is the smallest diameter between port_a and port_b. The common derivative of the two polynomials at Re = 0 is computed from the equation "c0/Re". Note, the pressure drop equation above in the laminar region is always defined with respect to the smallest diameter D_Re.

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

Extends from Modelica.Fluid.Interfaces.PartialTwoPortTransport (Partial element transporting fluid between two ports without storage of mass or energy), Modelica.Fluid.Interfaces.PartialLumpedFlow (Base class for a lumped momentum balance).

Parameters

Type	Name	Default	Description
replaceable package Medium		PartialMedium	Medium in the component
Length	pathLength	0	Length flow path [m]
LossFactorData	data		Loss factor data
Assumptions
Boolean	allowFlowReversal	system.allowFlowReversal	= true to allow flow reversal, false restricts to design direction (port_a -> port_b)
Dynamics
Dynamics	momentumDynamics	Types.Dynamics.SteadyState	Formulation of momentum balance
Advanced
AbsolutePressure	dp_start	0.01*system.p_start	Guess value of dp = port_a.p - port_b.p [Pa]
MassFlowRate	m_flow_start	system.m_flow_start	Guess value of m_flow = port_a.m_flow [kg/s]
MassFlowRate	m_flow_small	system.m_flow_small	Small mass flow rate for regularization of zero flow [kg/s]
AbsolutePressure	dp_small	system.dp_small	Turbulent flow if |dp| >= dp_small [Pa]
Diagnostics
Boolean	show_T	true	= true, if temperatures at port_a and port_b are computed
Boolean	show_V_flow	true	= true, if volume flow rate at inflowing port is computed
Boolean	show_Re	false	= true, if Reynolds number is included for plotting
Boolean	show_totalPressures	false	= true, if total pressures are included for plotting
Boolean	show_portVelocities	false	= true, if port velocities are included for plotting

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

partial model BaseModelNonconstantCrossSectionArea 
  "Generic pressure drop component with constant turbulent loss factor data and without an icon, for non-constant cross section area"

  extends Modelica.Fluid.Interfaces.PartialTwoPortTransport;
  extends Modelica.Fluid.Interfaces.PartialLumpedFlow(
    final pathLength = 0,
    final momentumDynamics = Types.Dynamics.SteadyState);

  parameter LossFactorData data "Loss factor data";

  // Advanced
  /// Other settings than the final values are not yet implemented ///
  final parameter Boolean from_dp = false 
    "= true, use m_flow = f(dp) else dp = f(m_flow)";
  final parameter Boolean use_Re = false 
    "= true, if turbulent region is defined by Re, otherwise by dp_small or m_flow_small";
  // End not yet implemented /////////////////////////////////////////
  parameter Medium.AbsolutePressure dp_small = system.dp_small 
    "Turbulent flow if |dp| >= dp_small";
  parameter Medium.MassFlowRate m_flow_small = system.m_flow_small 
    "Turbulent flow if |m_flow| >= m_flow_small";

  // Diagnostics
  parameter Boolean show_Re = false 
    "= true, if Reynolds number is included for plotting";
  SI.ReynoldsNumber Re = Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber_m_flow(
        m_flow,
        noEvent(if m_flow>0 then Medium.dynamicViscosity(state_a) else Medium.dynamicViscosity(state_b)),
        data.D_Re) if show_Re "Reynolds number at diameter data.D_Re";
  parameter Boolean show_totalPressures = false 
    "= true, if total pressures are included for plotting";
  SI.AbsolutePressure p_total_a = port_a.p + 0.5 * m_flow^2 /((Modelica.Constants.pi/4 * data.diameter_a^2)^2 * noEvent(if port_a.m_flow > 0 then Medium.density(state_a) else Medium.density(state_b))) if 
    show_totalPressures "Total pressure at port_a";
  SI.AbsolutePressure p_total_b = port_b.p + 0.5 * m_flow^2 /((Modelica.Constants.pi/4 * data.diameter_b^2)^2 * noEvent(if port_b.m_flow > 0 then Medium.density(state_b) else Medium.density(state_a))) if 
    show_totalPressures "Total pressure at port_a";
  parameter Boolean show_portVelocities = false 
    "= true, if port velocities are included for plotting";
  SI.Velocity v_a = port_a.m_flow /(Modelica.Constants.pi/4 * data.diameter_a^2 * noEvent(if port_a.m_flow > 0 then Medium.density(state_a) else Medium.density(state_b))) if 
    show_portVelocities "Fluid velocity into port_a";
  SI.Velocity v_b = port_b.m_flow /(Modelica.Constants.pi/4 * data.diameter_b^2 * noEvent(if port_b.m_flow > 0 then Medium.density(state_b) else Medium.density(state_a))) if 
    show_portVelocities "Fluid velocity into port_b";

  // Variables
  Modelica.SIunits.Pressure dp_fg "pressure loss due to friction and gravity";
  Modelica.SIunits.Area A_mean = Modelica.Constants.pi/4*(data.diameter_a^2+data.diameter_b^2)/2 
    "mean cross flow area";

  Medium.ThermodynamicState state_b_des 
    "Thermodynamic state at port b for flow a -> b";
  Medium.ThermodynamicState state_a_nondes 
    "Thermodynamic state at port a for flow a <- b";

equation 
  Ib_flow = 0;
  F_p = A_mean*(Medium.pressure(state_b) - Medium.pressure(state_a));
  F_fg = A_mean*dp_fg;
  if from_dp then
     m_flow = if use_Re then 
                 massFlowRate_dp_and_Re(
                    dp_fg, Medium.density(state_a), Medium.density(state_b),
                    Medium.dynamicViscosity(state_a),
                    Medium.dynamicViscosity(state_b),
                    data) else 
                 massFlowRate_dp(dp_fg, Medium.density(state_a), Medium.density(state_b), data, dp_small);
  else
     dp_fg = if use_Re then 
             pressureLoss_m_flow_and_Re(
                 m_flow, Medium.density(state_a), Medium.density(state_b),
                 Medium.dynamicViscosity(state_a),
                 Medium.dynamicViscosity(state_b),
                 data) else 
             pressureLoss_m_flow_totalPressure(m_flow,
               Medium.density(state_a),
               Medium.density(state_b_des),
               Medium.density(state_b),
               Medium.density(state_a_nondes),
               data, m_flow_small);
  end if;

  // Isenthalpic state transformation (no storage and no loss of energy)
  port_a.h_outflow = inStream(port_b.h_outflow);
  port_b.h_outflow = inStream(port_a.h_outflow);

  // medium states for downstream properties, may want to change this neglecting the only difference from state_a, state_b, which is in pressure
  // This will remove the extra interation variables
  state_b_des = Medium.setState_phX(port_b.p, inStream(port_a.h_outflow), inStream(port_a.Xi_outflow));
  state_a_nondes = Medium.setState_phX(port_a.p, inStream(port_b.h_outflow), inStream(port_b.Xi_outflow));

end BaseModelNonconstantCrossSectionArea;

Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.pressureLoss_m_flow_totalPressure

Information

Compute pressure drop from constant loss factor and mass flow rate (dp = f(m_flow)). For small mass flow rates(|m_flow| < m_flow_small), the characteristic is approximated by a polynomial in order to have a finite derivative at zero mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
MassFlowRate	m_flow		Mass flow rate from port_a to port_b [kg/s]
Density	rho_a_des		Density at port_a, mass flow in design direction a -> b [kg/m3]
Density	rho_b_des		Density at port_b, mass flow in design direction a -> b [kg/m3]
Density	rho_b_nondes		Density at port_b, mass flow against design direction a <- b [kg/m3]
Density	rho_a_nondes		Density at port_a, mass flow against design direction a <- b [kg/m3]
LossFactorData	data		Constant loss factors for both flow directions
MassFlowRate	m_flow_small	0.01	Turbulent flow if |m_flow| >= m_flow_small [kg/s]

Outputs

Type	Name	Description
Pressure	dp	Pressure drop (dp = port_a.p - port_b.p) [Pa]

Modelica definition

function pressureLoss_m_flow_totalPressure 
  "Return pressure drop from constant loss factor and mass flow rate (dp = f(m_flow))"
        extends Modelica.Icons.Function;

  input SI.MassFlowRate m_flow "Mass flow rate from port_a to port_b";
  input SI.Density rho_a_des 
    "Density at port_a, mass flow in design direction a -> b";
  input SI.Density rho_b_des 
    "Density at port_b, mass flow in design direction a -> b";
  input SI.Density rho_b_nondes 
    "Density at port_b, mass flow against design direction a <- b";
  input SI.Density rho_a_nondes 
    "Density at port_a, mass flow against design direction a <- b";
  input LossFactorData data "Constant loss factors for both flow directions";
  input SI.MassFlowRate m_flow_small = 0.01 
    "Turbulent flow if |m_flow| >= m_flow_small";
  output SI.Pressure dp "Pressure drop (dp = port_a.p - port_b.p)";

protected 
  SI.Area A_a = Modelica.Constants.pi * data.diameter_a^2/4 
    "Cross section area at port_a";
  SI.Area A_b = Modelica.Constants.pi * data.diameter_b^2/4 
    "Cross section area at port_b";
algorithm 
    dp := 1/2 * m_flow^2 *( if m_flow > 0 then 
      data.zeta1/(if data.zeta1_at_a then rho_a_des    * A_a^2 else    rho_b_des * A_b^2) - 1/(rho_a_des    * A_a^2) + 1/(rho_b_des    * A_b^2) else 
      -data.zeta2/(if data.zeta2_at_a then rho_a_nondes * A_a^2 else rho_b_nondes * A_b^2) - 1/(rho_a_nondes * A_a^2) + 1/(rho_b_nondes * A_b^2));
end pressureLoss_m_flow_totalPressure;