One question separates the turbulence approaches: are the eddies modelled or resolved?
Four levels
RANS. All turbulent scales are modelled; only the mean field is solved. The cheapest route and the most common in industry. Sufficient for mean quantities — pressure drop, efficiency, total heat flux. See the turbulence model note.
URANS. The same models, solved transiently. Meaningful when there is a periodic event clearly separated from turbulence (vortex shedding, blade passing). It does not resolve the turbulence itself.
DES / hybrid. Behaves as RANS in the boundary layer and as LES in the separated region. The proposal of Spalart and co-workers aims to avoid the cost of resolving the near-wall region while resolving the post-separation eddies [1]. A good balance where separation governs.
LES. Large eddies are resolved and only the small scales are modelled; Smagorinsky's sub-grid approach is the first example of this family [2]. Required for quantities such as mixing, noise and temperature fluctuation.
The decision criterion
| Quantity sought | Sufficient approach |
|---|---|
| Pressure drop, efficiency, mean temperature | RANS |
| Periodic force, blade passing load | URANS |
| Post-separation flow, vehicle wake, aerodynamic noise source | DES |
| Mixing quality, temperature fluctuation, acoustics | LES |
A cost warning
LES and DES are transient and must gather statistics: no result is available until several flow-through times have been run and averaged. The total cost can reach a hundred times that of RANS.
The mesh requirement is also different in kind: in LES the mesh is part of the model — it sets the boundary between resolved and modelled scales. For that reason "grid independence" is not defined in LES in the sense it has in RANS, and validation needs separate care. See the verification and validation note.
References
- Spalart, P. R., Jou, W.-H., Strelets, M. & Allmaras, S. R. (1997). Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In Advances in DNS/LES, Greyden Press, Columbus, OH.
- Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly Weather Review, 91(3), 99–164. DOI: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
- Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149