Theory

The model solves two transport equations, one for the turbulent kinetic energy $k$ , equation (1), and one for its specific dissipation rate $\omega$ , equation (2) (Menter, 1994). A blending function $F_1$ switches the model from the k-ω form near walls, which needs no damping functions and works down to the wall, to a k-ε-like form in the free stream, which removes the k-ω model's sensitivity to the free-stream $\omega$ . The eddy viscosity is limited by the strain rate, equation (3) (the "shear-stress transport" limiter), which improves separated flows: the jets and recirculation zones of a muffler.

At walls the program uses wall functions or a resolved wall (Wall treatment): Spalding's law for $\nu_t$ with the log-law constants $\kappa = 0.41$ and $E = e^{\kappa B} = 8.43$ ( $B = 5.2$ ) (Spalding, 1961). The inlet values of $k$ and $\omega$ come from the turbulence intensity and length scale of the inlet (Turbulence intensity).

The model constants are OpenFOAM's defaults, which are Menter's standard set; the program does not change them.

Equations

\frac{\partial (\rho k)}{\partial t} + \nabla\cdot(\rho \mathbf{U} k) = \nabla\cdot\left(\rho D_k \nabla k\right) + \rho \tilde{P}_k - \beta^* \rho \omega k

(1)

\frac{\partial (\rho \omega)}{\partial t} + \nabla\cdot(\rho \mathbf{U} \omega) = \nabla\cdot\left(\rho D_\omega \nabla \omega\right) + \rho \gamma \frac{\tilde{P}_k}{\nu_t} - \rho \beta \omega^2 + 2(1 - F_1)\frac{\rho\,\alpha_{\omega 2}}{\omega}\nabla k\cdot\nabla\omega

(2)

\nu_t = \frac{a_1 k}{\max(a_1 \omega,\ b_1 F_2 S)}, \qquad \tilde{P}_k = \min(P_k,\ c_1 \beta^* k \omega)

(3)

where	meaning	unit
$k$	Turbulent kinetic energy	m²/s²
$\omega$	Specific dissipation rate	1/s
$\rho$	Density (constant for incompressible)	kg/m³
$\mathbf{U}$	Mean velocity	m/s
$D_k, D_\omega$	Effective diffusivities, $\nu + \alpha_k \nu_t$ and $\nu + \alpha_\omega \nu_t$	m²/s
$P_k$	Production of $k$ by the mean shear	m²/s³
$\nu_t$	Eddy viscosity	m²/s
$S$	Strain-rate magnitude	1/s
$F_1, F_2$	Blending functions (1 near walls, 0 far away)	-
$\alpha_k, \alpha_\omega, \beta, \gamma$	Blended constants: 0.85 / 1.0, 0.5 / 0.856, 0.075 / 0.0828, 5/9 / 0.44 (inner / outer)	-
$\beta^*, a_1, b_1, c_1$	0.09, 0.31, 1, 10	-

Default and rule

Default: k-ω SST
Rule: k-ω SST with OpenFOAM's default constants.
Source: Menter's SST model (Menter, 1994) as implemented in OpenFOAM (OpenFOAM user guide, 2026). The production limiter with $c_1 = 10$ and the form of the cross-diffusion term follow OpenFOAM's implementation, which is based on a later revision of the model by Menter and co-workers. Wall-function constants: see Wall treatment.

Valid range k-ω SST only

Fixed

No other turbulence model is offered. Laminar flow is not modelled: the setup check warns when an inlet Reynolds number is below 2300, where the model adds an eddy viscosity a laminar flow does not have.

Turbulence model

Theory

Equations

Default and rule

Valid range k-ω SST only

References 3

Theory

Equations

Default and rule

Valid range k-ω SST only

Related 6

References 3