NeuralFlow Theory & User Reference Manual › GE k-omega Turbulence Model

14 GE Turbulence Model

NeuralFlow revision. This chapter has been rebuilt from the current GE-RANS formulation. The earlier placeholder compressibility expression has been removed. The equations below distinguish the active SST-like core, optional low-Reynolds modifications, Kato-Launder production, production limiting, curvature corrections, free-stream modification and axisymmetric terms.

14.1 Coupled transport equations

The turbulence model transports turbulent kinetic energy and specific dissipation rate :

(14.1)

(14.2)

unless the optional scale-adaptive extension is enabled; its exact formulation is documented in Chapter 15.

14.2 SST blending and local coefficients

(14.3)

The cross-diffusion sensor used by the first blending function is

(14.4)

(14.5)

(14.6)

The standard blended coefficients are and , with current constants .

(14.7)

14.2.1 Optional low-Reynolds coefficient modification

With the low-Reynolds option off, and because both blended endpoint values are equal. When it is on, the near-wall endpoint coefficients are modified using :

(14.8)

(14.9)

14.3 Turbulent time scale and eddy viscosity

NeuralFlow first evaluates the strain magnitude. In planar flow, . In axisymmetric flow, the radial contribution is added:

(14.10)

(14.11)

When the realizable time-scale option is enabled, an additional upper limit is used:

(14.12)

Otherwise . Eddy viscosity follows directly:

(14.13)

If the resulting viscosity ratio exceeds the configured maximum, the formulation raises the effective and reevaluates :

(14.14)

14.4 Turbulence production

Away from the wall-function cell treatment, the baseline production is

(14.15)

When Kato-Launder production is enabled, the strain-vorticity form is used instead:

(14.16)

where is the stored vorticity magnitude. If the SSTm production option is off, the dilatation correction is then applied:

(14.17)

For axisymmetric flow, the divergence in this expression is . The optional production limiter and nonnegativity enforcement give

(14.18)

If the production limiter is disabled, only the final nonnegative bound remains. Near walls, NeuralFlow uses the wall-function production based on wall shear rather than this cell-center strain formula.

14.5 Dissipation, omega production and free-stream modification

Without free-stream modification,

(14.19)

With free-stream modification, the stored ambient values shift the decay:

(14.20)

The specific-dissipation production is built from the already limited :

(14.21)

With low-Reynolds modification off, . With it on, the near-wall endpoint becomes

(14.22)

The omega dissipation coefficient is . Therefore

(14.23)

without free-stream modification, and

(14.24)

when it is enabled.

14.6 Cross diffusion

(14.25)

14.7 Curvature corrections

14.7.1 Smirnov-Menter production correction

The source forms strain and rotation tensors

(14.26)

(14.27)

Using the steady material strain derivative , the rotation sensor is

(14.28)

(14.29)

(14.30)

The current defaults are . Simulation note: the NeuralFlow formulation currently constructs a 2-by-2 internal velocity-gradient tensor for this correction; the manual therefore does not claim a separately verified full-3D Smirnov-Menter formulation.

14.7.2 Hellsten omega-dissipation correction

The alternative curvature option modifies omega dissipation through

(14.31)

14.8 Turbulent heat and species transport

The turbulence closure also supplies the turbulent conductivity and species diffusivity used by the carrier transport equations:

(14.32)

(14.33)

The viscous face operator uses harmonic interpolation of effective viscosity/conductivity between the two cells and retains the compact non-orthogonal correction plus the strong two-point implicit contribution.

14.9 Axisymmetric turbulence source terms

Besides the strain/divergence additions already shown, the radial momentum source includes modified-pressure and viscous-dilatation contributions. With cell volume , radius and ,

(14.34)

(14.35)

The circumferential viscous stress contribution used by the energy equation is

(14.36)

(14.37)

14.10 Turbulent viscous/thermal energy flux

The viscous face energy flux contains thermal conduction and, when viscous dissipation is enabled, viscous work. In compact continuum notation the corresponding energy contribution is

(14.38)

The used in NeuralFlow face discretization uses harmonic interpolation of the effective conductivity and the arithmetic face velocity in the viscous-work term. Viscous dissipation is enabled by default in the current solver options.

14.11 Inlet and initialization relations

At an inflow face the current NeuralFlow formulation uses the boundary-normal transport speed . If turbulent kinetic energy is not prescribed directly, the intensity route gives

(14.39)

The specific-dissipation variable can then be prescribed directly, inferred from a turbulence length scale, or inferred from a prescribed turbulent-viscosity ratio:

(14.40)

(14.41)

(14.42)

The inlet turbulence flux also contributes the isotropic turbulent pressure . For a far-field inlet, the energy flux includes the associated turbulent-pressure work in addition to turbulent-energy transport.