ANSYS Fluent Turbulence Modeling

#+CATEGORY: ansys

ANSYS Fluent Turbulence Modeling :: RANS, LES, DES, and Hybrid Approaches

ANSYS Fluent provides many turbulence models. They range from RANS (Reynolds-averaged) to DNS (direct numerical simulation). Hybrid RANS/LES (DES, SAS) bridges the gap between scale-resolving and scale-modeling approaches. This note catalogs all available turbulence models. It includes their governing equations, assumptions, recommended applications, and comparison with OpenFOAM equivalents.

RANS Turbulence Models

Spalart-Allmaras

The one-equation model targets external aerodynamics (aerofoil, aircraft). It solves a transport equation for a modified eddy viscosity ν̃ (related to actual turbulent viscosity νₜ):

where $P_{\tilde{\nu}}$ is production and $D_{\tilde{\nu}}$ is destruction/dissipation.

Turbulent viscosity comes from $\tilde{\nu}$:

with $f_{v1}$ a damping function. It vanishes near walls.

Fluent implementation: Spalart-Allmaras model. Skip low-Re correction. The model works on y₊ ≈ 1 walls. Users typically apply wall functions (y₊ ≈ 30–300).

RNG k-epsilon

The RNG $k$-$\epsilon$ model derives from Renormalization Group (RNG) theory. It modifies the standard $k$-$\epsilon$ equations. It incorporates small-scale turbulence effects analytically. Key differences from Standard $k$-$\epsilon$:

1. New term in the $\epsilon$-equation improves accuracy for high strain rates and moderate swirl 2. $C_\mu$ is no longer constant. It depends on the dimensionless strain rate:

Where $P_{ij}$ is production, $D_{ij}$ is diffusion, $\Pi_{ij}$ is pressure-strain correlation, and $\epsilon_{ij}$ is dissipation. A model handles the pressure-strain term (usually Rotta + Daly-Harlow closure).

Fluent RSM is the most complete RANS model (second-moment closure). It is also the most expensive (9 equations total: 7 transport + 2 for k and $\epsilon$). It converges significantly worse than two-equation models.

k-omega SST (Shear Stress Transport)

Use k-omega SST as the default RANS model for general engineering in Fluent. It blends the $k$-$\omega$ model near the wall with the $k$-$\epsilon$ model in the free stream. The $k$-$\omega$ model has correct near-wall asymptotic behavior. The $k$-$\epsilon$ model works better in the free stream (where $k$-$\omega$ is over-sensitive).

The blending function approaches 1 (pure $k$-$\omega$) near walls and 0 (pure $k$-$\epsilon$) in the free stream. The SST modification adds a limiter on eddy viscosity. This prevents over-prediction of turbulent shear stress:

where $\alpha$ is a blending function. This limiter makes k-omega SST superior to standard $k$-$\omega$ for adverse pressure gradient flows.

Fluent implementation: kOmegaSST model. Omega at walls defaults to $S\frac{\nu}{\beta_1 y^2}$, where $S$ is the specific rotation rate and $y$ is near-wall distance.

LES (Large Eddy Simulation)

Fluent's LES solves filtered Navier-Stokes equations with an SFS (SubFilter-Scale) model. Available SFS models:

LES in Fluent needs:

• Fine mesh (typically $10^7$–$10^9$ cells for engineering applications)
• Small time step (CFL ≤ 1)
• No wall functions unless using hybrid RANS/LES
• Prescribed inlet turbulence (synthetic turbulence, precursor simulation, or recycled data)

Use the WALE model for LES with Fluent. It provides correct near-wall scaling. It needs no damping functions:

where $S_{ij}^d$ is the symmetric part of the squared velocity gradient.

DES / DDES / SAS (Hybrid RANS/LES)

Fluent supports these hybrid RANS/LES approaches:

Summary (ANSYS vs OpenFOAM)

See Also

• ANSYS Fluent Overview
• Turbulence Models (CFD)
• OpenFOAM Solver Selection