Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers

Functions to compute characteristic numbers

Package Content

NameDescription
Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber ReynoldsNumber Return Reynolds number from v, rho, mu, D
Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber_m_flow ReynoldsNumber_m_flow Return Reynolds number from m_flow, mu, D, A
Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.NusseltNumber 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 TypeCharacteristic Dimension DVelocity v
Circular Pipediameter m_flow/ρ/crossArea
Rectangular Duct4*crossArea/perimeter m_flow/ρ/crossArea
Wide Ductdistance between narrow, parallel walls m_flow/ρ/crossArea
Packed BeddiameterOfSpericalParticles/(1-fluidFractionOfTotalVolume) m_flow/ρ/crossArea (without particles)
Device with rotating agitatordiameterOfRotor RotationalSpeed*diameterOfRotor

Inputs

TypeNameDefaultDescription
Velocityv Mean velocity of fluid flow [m/s]
Densityrho Fluid density [kg/m3]
DynamicViscositymu Dynamic (absolute) viscosity [Pa.s]
LengthD Characteristic dimension (hydraulic diameter of pipes) [m]

Outputs

TypeNameDescription
ReynoldsNumberReReynolds 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
See also Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber.

Inputs

TypeNameDefaultDescription
MassFlowRatem_flow Mass flow rate [kg/s]
DynamicViscositymu Dynamic viscosity [Pa.s]
LengthD Characteristic dimension (hydraulic diameter of pipes or orifices) [m]
AreaAModelica.Constants.pi/4*D*DCross sectional area of fluid flow [m2]

Outputs

TypeNameDescription
ReynoldsNumberReReynolds 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

TypeNameDefaultDescription
CoefficientOfHeatTransferalpha Coefficient of heat transfer [W/(m2.K)]
LengthD Characteristic dimension [m]
ThermalConductivitylambda Thermal conductivity [W/(m.K)]

Outputs

TypeNameDescription
NusseltNumberNuNusselt 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;

HTML-documentation generated by Dymola Sun Jan 17 21:12:14 2010.