Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers

Functions to compute characteristic numbers

Information

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name Description

ReynoldsNumber Return Reynolds number from v, rho, mu, D

ReynoldsNumber_m_flow Return Reynolds number from m_flow, mu, D, A

NusseltNumber Return Nusselt number

Name	Description
ReynoldsNumber	Return Reynolds number from v, rho, mu, D
ReynoldsNumber_m_flow	Return Reynolds number from m_flow, mu, D, A
NusseltNumber	Return Nusselt number

Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber

Return Reynolds number from v, rho, mu, D

Information

Calculation of Reynolds Number

   Re = |v|ρD/μ

a measure of the relationship between inertial forces (vρ) and viscous forces (D/μ).

The following table gives examples for the characteristic dimension D and the velocity v for different fluid flow devices:

Device Type	Characteristic Dimension D	Velocity v
Circular Pipe	diameter	m_flow/ρ/crossArea
Rectangular Duct	4*crossArea/perimeter	m_flow/ρ/crossArea
Wide Duct	distance between narrow, parallel walls	m_flow/ρ/crossArea
Packed Bed	diameterOfSpericalParticles/(1-fluidFractionOfTotalVolume)	m_flow/ρ/crossArea (without particles)
Device with rotating agitator	diameterOfRotor	RotationalSpeed*diameterOfRotor

Inputs

Type Name Default Description

Velocity v Mean velocity of fluid flow [m/s]

Density rho Fluid density [kg/m3]

DynamicViscosity mu Dynamic (absolute) viscosity [Pa.s]

Length D Characteristic dimension (hydraulic diameter of pipes) [m]

Type	Name	Description
Velocity	v	Mean velocity of fluid flow [m/s]
Density	rho	Fluid density [kg/m3]
DynamicViscosity	mu	Dynamic (absolute) viscosity [Pa.s]
Length	D	Characteristic dimension (hydraulic diameter of pipes) [m]

Outputs

Type Name Description

ReynoldsNumber Re Reynolds number [1]

Type	Name	Description
ReynoldsNumber	Re	Reynolds number [1]

Modelica definition

function ReynoldsNumber "Return Reynolds number from v, rho, mu, D"
  input SI.Velocity v "Mean velocity of fluid flow";
  input SI.Density rho "Fluid density";
  input SI.DynamicViscosity mu "Dynamic (absolute) viscosity";
  input SI.Length D "Characteristic dimension (hydraulic diameter of pipes)";
  output SI.ReynoldsNumber Re "Reynolds number";
algorithm 
  Re := abs(v)*rho*D/mu;
end ReynoldsNumber;

Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber_m_flow

Return Reynolds number from m_flow, mu, D, A

Information

Simplified calculation of Reynolds Number for flow through pipes or orifices; using the mass flow rate m_flow instead of the velocity v to express inertial forces.

  Re = |m_flow|*diameter/A/μ
with
  m_flow = v*ρ*A

Inputs

Type Name Default Description

MassFlowRate m_flow Mass flow rate [kg/s]

DynamicViscosity mu Dynamic viscosity [Pa.s]

Length D Characteristic dimension (hydraulic diameter of pipes or orifices) [m]

Area A Modelica.Constants.pi/4*D*D Cross sectional area of fluid flow [m2]

Type	Name	Default	Description
MassFlowRate	m_flow		Mass flow rate [kg/s]
DynamicViscosity	mu		Dynamic viscosity [Pa.s]
Length	D		Characteristic dimension (hydraulic diameter of pipes or orifices) [m]
Area	A	Modelica.Constants.pi/4DD	Cross sectional area of fluid flow [m2]

Outputs

Type Name Description

ReynoldsNumber Re Reynolds number [1]

Type	Name	Description
ReynoldsNumber	Re	Reynolds number [1]

Modelica definition

function ReynoldsNumber_m_flow 
  "Return Reynolds number from m_flow, mu, D, A"
  input SI.MassFlowRate m_flow "Mass flow rate";
  input SI.DynamicViscosity mu "Dynamic viscosity";
  input SI.Length D 
    "Characteristic dimension (hydraulic diameter of pipes or orifices)";
  input SI.Area A = Modelica.Constants.pi/4*D*D 
    "Cross sectional area of fluid flow";
  output SI.ReynoldsNumber Re "Reynolds number";
algorithm 
  Re := abs(m_flow)*D/A/mu;
end ReynoldsNumber_m_flow;

Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.NusseltNumber

Return Nusselt number

Information

Nusselt number Nu = alpha*D/lambda

Inputs

Type Name Default Description

CoefficientOfHeatTransfer alpha Coefficient of heat transfer [W/(m2.K)]

Length D Characteristic dimension [m]

ThermalConductivity lambda Thermal conductivity [W/(m.K)]

Type	Name	Description
CoefficientOfHeatTransfer	alpha	Coefficient of heat transfer [W/(m2.K)]
Length	D	Characteristic dimension [m]
ThermalConductivity	lambda	Thermal conductivity [W/(m.K)]

Outputs

Type Name Description

NusseltNumber Nu Nusselt number [1]

Type	Name	Description
NusseltNumber	Nu	Nusselt number [1]

Modelica definition

function NusseltNumber "Return Nusselt number"
  input SI.CoefficientOfHeatTransfer alpha "Coefficient of heat transfer";
  input SI.Length D "Characteristic dimension";
  input SI.ThermalConductivity lambda "Thermal conductivity";
  output SI.NusseltNumber Nu "Nusselt number";
algorithm 
  Nu := alpha*D/lambda;
end NusseltNumber;

Automatically generated Fri Nov 12 16:31:14 2010.