Friction Correlations

The friction in the FlowSimulator element can be calculated by the given equation where stands for calculated friction based on user selected friction mode (Abauf, Swamee), friction type (Fanning or Darcy) and Re (to determine whether it is in turbulent region, or in laminar region);

If ReDh < ReTurb, laminar friction calculations take place, otherwise, turbulent friction calculation routine is used.

Nomenclature: Subscripts:
f: friction F: fanning
Re: Reynolds number D: darcy
FMULT: friction multiplier turb: turbulent flow
ε: sand grain roughness lam: laminar flow
A: Cross sectional area Abuaf: Abuaf friction relation
L+: Inlet station + 1/9 of 2nd station Smooth: smooth surface
XMU: dynamic viscosity Rough: rough surface
W: mass flow rate SJ: Swamee-Jain approximation
X: station length Dh: hydraulic diameter
L: equivalent diameter

Laminar Friction

Calculates the friction coefficient for laminar flow in shaped ducts based on the references (Yunus A. Cengel, 2006) and (Bruce Munson, 2005).

Friction coefficient for hydrodynamically fully developed flow can be calculated as,

For Tube Element, Laminar Friction Inlets effects can be accounted. Friction coefficient for hydrodynamically developing flow with “Muzychka Yovanovich Laminar Inlet Effects” can be calculated as,

Friction coefficient for combination of developing flow and fully developed flow can be calculated as,

Darcy type friction then calculated as;

Fanning type friction then calculated as;

Turbulent Friction

Calculates the turbulent friction for smooth or rough walls.

Abuaf Friction Relation

The Abuaf friction relation should generally be used for smooth walled tubes.

Flow Simulator allows users to an option use the Abuaf friction relation together with wall roughness. The following adjustment equation is used:

Swamee-Jain approximation of the Colebrook-White equation (Moody diagram)

The Darcy and Fanning type frictions are calculated as:

User-specified friction factor

Roughness

Surface roughness values can be entered in four different measurement types. The roughness values are converted to sand grain roughness equivalents using the following equations from table 1 of reference 63.
ε=5.863∗Ra, Ra=Average Absolute Roughness
ε=3.100∗Rrms, Rrms=Root Mean Square Roughness
ε=0.978∗Rzd, Rzd=Peak to Valley Roughness