Theory

The k-ω SST model (Menter, 1994) needs the turbulent kinetic energy $k$ and the specific dissipation rate $\omega$ on every inlet. The program writes OpenFOAM's turbulentIntensityKineticEnergyInlet for $k$ and turbulentMixingLengthFrequencyInlet for $\omega$ (OpenFOAM user guide, 2026), which compute them every iteration from the local velocity of the inlet faces, an intensity $I$ and a mixing length $\ell$ , equations (2) and (3).

"Fully developed" estimates $I$ and $\ell$ from the inlet, equation (1): the Reynolds number uses the equivalent uniform velocity of the inlet (the magnitude, for a velocity vector) and the hydraulic diameter of the inlet patch, $D_h = 4A/P$ from the exported surface. The typed intensity and length are then not used (they are kept in the case file). "Intensity and length" uses Turbulence intensity and Mixing length (blank length: $0.07\,D_h$ ).

The same formulas give the starting values written next to the boundary conditions. In a muffler the inlet turbulence usually matters little for the pressure drop: the jets and expansions inside generate far more turbulence than the inlet carries.

Equations

I = 0.16\,Re^{-1/8}, \qquad \ell = 0.07\,D_h, \qquad Re = \frac{U D_h}{\nu}, \qquad D_h = \frac{4A}{P}

(1)

where	meaning	unit
$I$	Turbulence intensity	-
$\ell$	Mixing length	m
$Re$	Inlet Reynolds number	-
$U$	Equivalent uniform inlet velocity	m/s
$D_h$	Hydraulic diameter of the inlet patch	m
$A, P$	Area and perimeter of the inlet patch	m², m
$\nu$	Kinematic viscosity of the gas	m²/s

k = \tfrac{3}{2}\left(I\,\lvert\mathbf{U}\rvert\right)^2

(2)

\omega = \frac{\sqrt{k}}{C_\mu^{1/4}\,\ell}, \qquad C_\mu = 0.09

(3)

where	meaning	unit
$k$	Turbulent kinetic energy at the inlet	m²/s²
$\omega$	Specific dissipation rate at the inlet	1/s
$\lvert\mathbf{U}\rvert$	Velocity magnitude on the inlet face	m/s

Default and rule

Default: Fully developed
Rule: Fully developed.
Source: Equations (2) and (3) are the definitions behind OpenFOAM's two inlet conditions (OpenFOAM user guide, 2026). The intensity estimate $0.16\,Re^{-1/8}$ and the mixing length $0.07\,D_h$ for fully developed pipe flow are widely used engineering estimates.

Valid range Fully developed | Intensity and length

When to type values

Use "Intensity and length" when the inlet turbulence is known (for example measured), or when the inlet is fed by something other than a long straight pipe.

Estimate

Equation (1) is a pipe-flow estimate; a short or disturbed inlet pipe has a different turbulence level.

Inlet turbulence

Theory

Equations

Default and rule

Valid range Fully developed | Intensity and length

References 2

Theory

Equations

Default and rule

Valid range Fully developed | Intensity and length

Related 5

References 2