Modelica.Fluid.Dissipation.PressureLoss.Channel

Package for pressure loss calculation of channels

Information

Channel

Internal overall flow

Calculation of pressure loss for an internal flow through different geometries at laminar and turbulent flow regime considering surface roughness. See more information.

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

Package Content

Name Description

dp_internalFlowOverall_DP Pressure loss of internal flow | calculate pressure loss | overall flow regime | surface roughness | several geometries

dp_internalFlowOverall_MFLOW Pressure loss of internal flow | calculate mass flow rate | overall flow regime | surface roughness | several geometries

dp_internalFlowOverall_IN_con Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW

dp_internalFlowOverall_IN_var Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW

Name	Description
dp_internalFlowOverall_DP	Pressure loss of internal flow \| calculate pressure loss \| overall flow regime \| surface roughness \| several geometries
dp_internalFlowOverall_MFLOW	Pressure loss of internal flow \| calculate mass flow rate \| overall flow regime \| surface roughness \| several geometries
dp_internalFlowOverall_IN_con	Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW
dp_internalFlowOverall_IN_var	Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_DP

Pressure loss of internal flow | calculate pressure loss | overall flow regime | surface roughness | several geometries

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_DP

Information

Calculation of pressure loss for an internal flow through different geometries at overall flow regime for incompressible and single-phase fluid flow considering surface roughness.

Generally this function is numerically best used for the incompressible case , where the mass flow rate (m_flow) is known (as state variable) in the used model and the corresponding pressure loss (DP) has to be calculated. On the other hand the function dp_internalFlowOverall_MFLOW is numerically best used for the compressible case if the pressure loss (dp) is known (out of pressures as state variable) and the mass flow rate (M_FLOW) has to be calculated. See more information.

Extends from Modelica.Fluid.Dissipation.Utilities.Icons.PressureLoss.Channel_d (Geometry figure for channel).

Inputs

Type Name Default Description

Constant inputs

dp_internalFlowOverall_IN_con IN_con Input record for function dp_internalFlowOverall_DP

Variable inputs

dp_internalFlowOverall_IN_var IN_var Input record for function dp_internalFlowOverall_DP

Input

MassFlowRate m_flow Mass flow rate [kg/s]

Type	Name	Description
Constant inputs
dp_internalFlowOverall_IN_con	IN_con	Input record for function dp_internalFlowOverall_DP
Variable inputs
dp_internalFlowOverall_IN_var	IN_var	Input record for function dp_internalFlowOverall_DP
Input
MassFlowRate	m_flow	Mass flow rate [kg/s]

Outputs

Type Name Description

Pressure DP Output for function dp_internalFlowOverall_DP [Pa]

Type	Name	Description
Pressure	DP	Output for function dp_internalFlowOverall_DP [Pa]

Modelica definition

function dp_internalFlowOverall_DP 
  "Pressure loss of internal flow | calculate pressure loss | overall flow regime | surface roughness | several geometries"
  //SOURCE_1: Idelchik, I.E.: HANDBOOK OF HYDRAULIC RESISTANCE, 3rd edition, 2006.
  //SOURCE_2: Miller, D.S.: INTERNAL FLOW SYSTEMS, 1978.
  //SOURCE_3: VDI-Waermeatlas, 9th edition, Springer-Verlag, 2002
  //Notation of equations according to SOURCES

  import FD = Modelica.Fluid.Dissipation.PressureLoss.Channel;
  import SMOOTH = Modelica.Fluid.Dissipation.Utilities.Functions.General.Stepsmoother;

  //icon
  extends Modelica.Fluid.Dissipation.Utilities.Icons.PressureLoss.Channel_d;

  //input records
  input Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_con
    IN_con "Input record for function dp_internalFlowOverall_DP";
  input Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_var
    IN_var "Input record for function dp_internalFlowOverall_DP";
  input SI.MassFlowRate m_flow "Mass flow rate";

  //output variables
  output SI.Pressure DP "Output for function dp_internalFlowOverall_DP";

protected 
  type TYP =
      Modelica.Fluid.Dissipation.Utilities.Types.GeometryOfInternalFlow;

  Real MIN=Modelica.Constants.eps;

  SI.Area A_cross=max(MIN, if IN_con.geometry == TYP.Annular then (PI/4)*((
      IN_con.D_ann)^2 - (IN_con.d_ann)^2) else if IN_con.geometry == TYP.Circular then 
            PI/4*(IN_con.d_cir)^2 else if IN_con.geometry == TYP.Elliptical then 
            PI*IN_con.a_ell*IN_con.b_ell else if IN_con.geometry == TYP.Rectangular then 
            IN_con.a_rec*IN_con.b_rec else if IN_con.geometry == TYP.Isosceles then 
            0.5*(IN_con.a_tri*IN_con.h_tri) else 0) "Cross sectional area";
  SI.Length perimeter=max(MIN, if IN_con.geometry == TYP.Annular then PI*(
      IN_con.D_ann + IN_con.d_ann) else if IN_con.geometry == TYP.Circular then 
            PI*IN_con.d_cir else if IN_con.geometry == TYP.Elliptical then PI*(
      IN_con.a_ell + IN_con.b_ell) else if IN_con.geometry == TYP.Rectangular then 
            2*(IN_con.a_rec + IN_con.b_rec) else if IN_con.geometry == TYP.Isosceles then 
            IN_con.a_tri + 2*((IN_con.h_tri)^2 + (IN_con.a_tri/2)^2)^0.5 else 0) 
    "Perimeter";
  SI.Diameter d_hyd=4*A_cross/perimeter "Hydraulic diameter";
  Real beta=IN_con.beta*180/PI "Top angle";

  //SOURCE_2: p.138, sec 8.5
  Real Dd_ann=min(max(MIN, IN_con.d_ann), IN_con.D_ann)/max(MIN, max(IN_con.d_ann,
      IN_con.D_ann)) "Ratio of small to large diameter of annular geometry";
  Real CF_ann=98.7378*Dd_ann^0.0589 "Correction factor for annular geometry";
  Real ab_rec=min(IN_con.a_rec, IN_con.b_rec)/max(MIN, max(IN_con.a_rec, IN_con.b_rec)) 
    "Aspect ratio of rectangular geometry";
  Real CF_rec=-59.85*(ab_rec)^3 + 148.67*(ab_rec)^2 - 128.1*(ab_rec) + 96.1 
    "Correction factor for rectangular geometry";
  Real ab_ell=min(IN_con.a_ell, IN_con.b_ell)/max(MIN, max(IN_con.a_ell, IN_con.b_ell)) 
    "Ratio of small to large length of annular geometry";
  Real CF_ell=-169.2211*(ab_ell)^4 + 260.9028*(ab_ell)^3 - 113.7890*(ab_ell)^2
       + 9.2588*(ab_ell)^1 + 78.7124 
    "Correction factor for elliptical geometry";
  Real CF_tri=-0.0013*(min(90, beta))^2 + 0.1577*(min(90, beta)) + 48.5575 
    "Correction factor for triangular geometry";
  Real CF_lam=if IN_con.geometry == TYP.Annular then CF_ann else if IN_con.geometry
       == TYP.Circular then 64 else if IN_con.geometry == TYP.Elliptical then 
      CF_ell else if IN_con.geometry == TYP.Rectangular then CF_rec else if 
      IN_con.geometry == TYP.Isosceles then CF_tri else 0 
    "Correction factor for laminar flow";

  //SOURCE_1: p.81, fig. 2-3, sec 21-22: definition of flow regime boundaries
  Real k=max(MIN, abs(IN_con.K)/d_hyd) "Relative roughness";
  SI.ReynoldsNumber Re_lam_min=1e3 "Minimum Reynolds number for laminar regime";
  SI.ReynoldsNumber Re_lam_max=2090*(1/max(0.007, k))^0.0635 
    "Maximum Reynolds number for laminar regime";
  SI.ReynoldsNumber Re_lam_leave=min(Re_lam_max, max(Re_lam_min, 754*
      Modelica.Math.exp(if k <= 0.007 then 0.0065/0.007 else 0.0065/k))) 
    "Start of transition regime for increasing Reynolds number (leaving laminar regime)";

  //Adapted mass flow rate for function dp_turbulent of a straight pipe
  SI.MassFlowRate m_flow_turb=m_flow*(PI/4*d_hyd^2)/A_cross 
    "Mass flow rate for turbulent calculation";
  SI.Velocity velocity=m_flow/(IN_var.rho*A_cross) "Velocity of internal flow";
  SI.ReynoldsNumber Re=IN_var.rho*abs(velocity)*d_hyd/IN_var.eta;

protected 
  Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_overall_IN_con
    IN_2_con(
    final roughness=IN_con.roughness,
    final d_hyd=d_hyd,
    final K=IN_con.K,
    final L=IN_con.L) "Input record for turbulent regime";
  Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_overall_IN_var
    IN_2_var(                                                                     final eta=
          IN_var.eta, final rho=IN_var.rho) "Input record for turbulent regime";

  //Documentation

algorithm 
  DP := SMOOTH(
          Re_lam_min,
          Re_lam_max,
          Re)*(CF_lam/2)*IN_con.L/d_hyd^2*velocity*IN_var.eta + SMOOTH(
          Re_lam_max,
          Re_lam_min,
          Re)*Dissipation.PressureLoss.StraightPipe.dp_turbulent_DP(
          IN_2_con,
          IN_2_var,
          m_flow_turb);
end dp_internalFlowOverall_DP;

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_MFLOW

Pressure loss of internal flow | calculate mass flow rate | overall flow regime | surface roughness | several geometries

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_MFLOW

Information

Calculation of pressure loss for an internal flow through different geometries at overall flow regime for incompressible and single-phase fluid flow considering surface roughness.

Generally this function is numerically best used for the compressible case if the pressure loss (dp) is known (out of pressures as state variable) and the mass flow rate (M_FLOW) has to be calculated. On the other hand the function dp_internalFlowOverall_DP is numerically best used for the incompressible case , where the mass flow rate (m_flow) is known (as state variable) in the used model and the corresponding pressure loss (DP) has to be calculated.

The pressure loss calculation for internal fluid flow in different geometries is further documented here.

Extends from Modelica.Fluid.Dissipation.Utilities.Icons.PressureLoss.Channel_d (Geometry figure for channel).

Inputs

Type Name Default Description

Constant inputs

dp_internalFlowOverall_IN_con IN_con Input record for function dp_internalFlowOverall_MFLOW

Variable inputs

dp_internalFlowOverall_IN_var IN_var Input record for function dp_internalFlowOverall_MFLOW

Input

Pressure dp Pressure loss [Pa]

Type	Name	Description
Constant inputs
dp_internalFlowOverall_IN_con	IN_con	Input record for function dp_internalFlowOverall_MFLOW
Variable inputs
dp_internalFlowOverall_IN_var	IN_var	Input record for function dp_internalFlowOverall_MFLOW
Input
Pressure	dp	Pressure loss [Pa]

Outputs

Type Name Description

MassFlowRate M_FLOW Output of function dp_overall_MFLOW [kg/s]

Type	Name	Description
MassFlowRate	M_FLOW	Output of function dp_overall_MFLOW [kg/s]

Modelica definition

function dp_internalFlowOverall_MFLOW 
  "Pressure loss of internal flow | calculate mass flow rate | overall flow regime | surface roughness | several geometries"
  import FD = Modelica.Fluid.Dissipation.PressureLoss.Channel;
  import SMOOTH = Modelica.Fluid.Dissipation.Utilities.Functions.General.Stepsmoother;

  //icon
  extends Modelica.Fluid.Dissipation.Utilities.Icons.PressureLoss.Channel_d;

  //input records
  input Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_con
    IN_con "Input record for function dp_internalFlowOverall_MFLOW";
  input Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_var
    IN_var "Input record for function dp_internalFlowOverall_MFLOW";
  input SI.Pressure dp "Pressure loss";

  //output variables
  output SI.MassFlowRate M_FLOW "Output of function dp_overall_MFLOW";

protected 
  type TYP1 =
      Modelica.Fluid.Dissipation.Utilities.Types.GeometryOfInternalFlow;
  type TYP2 = Modelica.Fluid.Dissipation.Utilities.Types.Roughness;

  Real MIN=Modelica.Constants.eps;

  SI.Area A_cross=max(MIN, if IN_con.geometry == TYP1.Annular then (PI/4)*((
      IN_con.D_ann)^2 - (IN_con.d_ann)^2) else if IN_con.geometry == TYP1.Circular then 
            PI/4*(IN_con.d_cir)^2 else if IN_con.geometry == TYP1.Elliptical then 
            PI*IN_con.a_ell*IN_con.b_ell else if IN_con.geometry == TYP1.Rectangular then 
            IN_con.a_rec*IN_con.b_rec else if IN_con.geometry == TYP1.Isosceles then 
            0.5*(IN_con.a_tri*IN_con.h_tri) else 0) "Cross sectional area";
  SI.Length perimeter=max(MIN, if IN_con.geometry == TYP1.Annular then PI*(
      IN_con.D_ann + IN_con.d_ann) else if IN_con.geometry == TYP1.Circular then 
            PI*IN_con.d_cir else if IN_con.geometry == TYP1.Elliptical then PI*
      (IN_con.a_ell + IN_con.b_ell) else if IN_con.geometry == TYP1.Rectangular then 
            2*(IN_con.a_rec + IN_con.b_rec) else if IN_con.geometry == TYP1.Isosceles then 
            IN_con.a_tri + 2*((IN_con.h_tri)^2 + (IN_con.a_tri/2)^2)^0.5 else 0) 
    "Perimeter";
  SI.Diameter d_hyd=4*A_cross/perimeter "Hydraulic diameter";
  Real beta=IN_con.beta*180/PI "Top angle";

  //SOURCE_2: p.138, sec 8.5
  Real Dd_ann=min(max(MIN, IN_con.d_ann), IN_con.D_ann)/max(MIN, max(IN_con.d_ann,
      IN_con.D_ann)) "Ratio of small to large diameter of annular geometry";
  Real CF_ann=98.7378*Dd_ann^0.0589 "Correction factor for annular geometry";
  Real ab_rec=min(IN_con.a_rec, IN_con.b_rec)/max(MIN, max(IN_con.a_rec, IN_con.b_rec)) 
    "Aspect ratio of rectangular geometry";
  Real CF_rec=-59.85*(ab_rec)^3 + 148.67*(ab_rec)^2 - 128.1*(ab_rec) + 96.1 
    "Correction factor for rectangular geometry";
  Real ab_ell=min(IN_con.a_ell, IN_con.b_ell)/max(MIN, max(IN_con.a_ell, IN_con.b_ell)) 
    "Ratio of small to large length of annular geometry";
  Real CF_ell=-169.2211*(ab_ell)^4 + 260.9028*(ab_ell)^3 - 113.7890*(ab_ell)^2
       + 9.2588*(ab_ell)^1 + 78.7124 
    "Correction factor for elliptical geometry";
  Real CF_tri=-0.0013*(min(90, beta))^2 + 0.1577*(min(90, beta)) + 48.5575 
    "Correction factor for triangular geometry";
  Real CF_lam=if IN_con.geometry == TYP1.Annular then CF_ann else if IN_con.geometry
       == TYP1.Circular then 64 else if IN_con.geometry == TYP1.Elliptical then 
            CF_ell else if IN_con.geometry == TYP1.Rectangular then CF_rec else 
            if IN_con.geometry == TYP1.Isosceles then CF_tri else 0 
    "Correction factor for laminar flow";

  //SOURCE_1: p.81, fig. 2-3, sec 21-22: definition of flow regime boundaries
  Real k=max(MIN, abs(IN_con.K)/d_hyd) "Relative roughness";
  SI.ReynoldsNumber Re_lam_min=1e3 "Minimum Reynolds number for laminar regime";
  SI.ReynoldsNumber Re_lam_max=2090*(1/max(0.007, k))^0.0635 
    "Maximum Reynolds number for laminar regime";
  SI.ReynoldsNumber Re_turb_min=4e3 
    "Minimum Reynolds number for turbulent regime";

  SI.ReynoldsNumber Re_lam_leave=min(Re_lam_max, max(Re_lam_min, 754*
      Modelica.Math.exp(if k <= 0.007 then 0.0065/0.007 else 0.0065/k))) 
    "Start of transition regime for increasing Reynolds number (leaving laminar regime)";

  //determining darcy friction factor out of pressure loss calulation for straight pipe:
  //dp = lambda_FRI*L/d_hyd*(rho/2)*velocity^2 and assuming lambda_FRI == lambda_FRI_calc/Re^2
  TYP.DarcyFrictionFactor lambda_FRI_calc=2*abs(dp)*d_hyd^3*IN_var.rho/(IN_con.L
      *IN_var.eta^2) "Adapted Darcy friction factor";

  //SOURCE_3: p.Lab 1, eq. 5: determine Re assuming laminar regime
  SI.ReynoldsNumber Re_lam=lambda_FRI_calc/CF_lam 
    "Reynolds number assuming laminar regime";

  //SOURCE_3: p.Lab 2, eq. 10: determine Re assuming turbulent regime (Colebrook-White)
  SI.ReynoldsNumber Re_turb=if IN_con.roughness == TYP2.Neglected then (max(MIN,
      lambda_FRI_calc)/0.3164)^(1/1.75) else -2*sqrt(max(lambda_FRI_calc, MIN))
      *Modelica.Math.log10(2.51/sqrt(max(lambda_FRI_calc, MIN)) + k/3.7) 
    "Reynolds number assuming turbulent regime";

  //determine actual flow regime
  SI.ReynoldsNumber Re_check=if Re_lam < Re_lam_leave then Re_lam else Re_turb;
  //determine Re for transition regime
  SI.ReynoldsNumber Re_trans=if Re_lam >= Re_lam_leave then 
      Modelica.Fluid.Dissipation.Utilities.Functions.General.CubicInterpolation_DP(
      Re_check,
      Re_lam_leave,
      Re_turb_min,
      k,
      lambda_FRI_calc) else 0;
  //determine actual Re
  SI.ReynoldsNumber Re=if Re_lam < Re_lam_leave then Re_lam else if Re_turb >
      Re_turb_min then Re_turb else Re_trans;

  Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_overall_IN_con
    IN_2_con(
    final roughness=IN_con.roughness,
    final d_hyd=d_hyd,
    final K=IN_con.K,
    final L=IN_con.L) "Input record for turbulent regime";
  Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_overall_IN_var
    IN_2_var(                                                                     final eta=
          IN_var.eta, final rho=IN_var.rho) "Input record for turbulent regime";

  //Documentation

algorithm 
  M_FLOW := SMOOTH(
          Re_lam_min,
          Re_turb,
          Re)*IN_var.rho*A_cross*(dp*(2/CF_lam)*(d_hyd^2/IN_con.L)*(1/
    IN_var.eta)) + SMOOTH(
          Re_turb,
          Re_lam_min,
          Re)*(A_cross/((PI/4)*d_hyd^2))*
    Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_turbulent_MFLOW(
          IN_2_con,
          IN_2_var,
          dp);
end dp_internalFlowOverall_MFLOW;

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_con

Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW

Information

This record is used as input record for the pressure loss function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW.

Extends from Modelica.Fluid.Dissipation.Utilities.Records.PressureLoss.Geometry (Input for several geometries of internal flow).

Parameters

Type Name Default Description

Channel

Roughness roughness Dissipation.Utilities.Types.... Choice of considering surface roughness

GeometryOfInternalFlow geometry Modelica.Fluid.Dissipation.U... Choice of geometry for internal flow

Length K 0 Roughness (average height of surface asperities) [m]

Length L 1 Length [m]

Annular cross sectional area

Diameter d_ann d_cir Small diameter [m]

Diameter D_ann 2*d_ann Large diameter [m]

Circular cross sectional area

Diameter d_cir 0.1 Internal diameter [m]

Elliptical cross sectional area

Length a_ell (3/4)*d_cir Half length of long base line [m]

Length b_ell 0.5*a_ell Half length of short base line [m]

Rectangular cross sectional area

Length a_rec d_cir Horizontal length [m]

Length b_rec a_rec Vertical length [m]

Length a_tri d_cir*(1 + 2^0.5) Length of base line [m]

Triangle cross sectional area

Length h_tri 0.5*a_tri Heigth to top angle perpendicular to base line [m]

Angle beta 90*PI/180 Top angle [rad]

Type	Name	Default	Description
Channel
Roughness	roughness	Dissipation.Utilities.Types....	Choice of considering surface roughness
GeometryOfInternalFlow	geometry	Modelica.Fluid.Dissipation.U...	Choice of geometry for internal flow
Length	K	0	Roughness (average height of surface asperities) [m]
Length	L	1	Length [m]
Annular cross sectional area
Diameter	d_ann	d_cir	Small diameter [m]
Diameter	D_ann	2*d_ann	Large diameter [m]
Circular cross sectional area
Diameter	d_cir	0.1	Internal diameter [m]
Elliptical cross sectional area
Length	a_ell	(3/4)*d_cir	Half length of long base line [m]
Length	b_ell	0.5*a_ell	Half length of short base line [m]
Rectangular cross sectional area
Length	a_rec	d_cir	Horizontal length [m]
Length	b_rec	a_rec	Vertical length [m]
Length	a_tri	d_cir*(1 + 2^0.5)	Length of base line [m]
Triangle cross sectional area
Length	h_tri	0.5*a_tri	Heigth to top angle perpendicular to base line [m]
Angle	beta	90*PI/180	Top angle [rad]

Modelica definition

record dp_internalFlowOverall_IN_con 
  "Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW"

  //channel variables
  Modelica.Fluid.Dissipation.Utilities.Types.Roughness roughness=Dissipation.Utilities.Types.Roughness.Considered 
    "Choice of considering surface roughness";
  extends Modelica.Fluid.Dissipation.Utilities.Records.PressureLoss.Geometry;

end dp_internalFlowOverall_IN_con;

Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_IN_var

Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW

Information

This record is used as input record for the pressure loss function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW.

Extends from Modelica.Fluid.Dissipation.Utilities.Records.General.PressureLoss (Base record for fluid properties for pressure loss).

Parameters

Type Name Default Description

Fluid properties

DynamicViscosity eta Dynamic viscosity of fluid [Pa.s]

Density rho Density of fluid [kg/m3]

Type	Name	Description
Fluid properties
DynamicViscosity	eta	Dynamic viscosity of fluid [Pa.s]
Density	rho	Density of fluid [kg/m3]

Modelica definition

record dp_internalFlowOverall_IN_var 
  "Input record for function dp_internalFlowOverall_DP and dp_internalFlowOverall_MFLOW"

  //fluid property variables
  extends Modelica.Fluid.Dissipation.Utilities.Records.General.PressureLoss;

end dp_internalFlowOverall_IN_var;

Automatically generated Fri Nov 12 16:31:21 2010.