The Smagorinsky model typically over-predicts the mean SGS dissipation when the grid scale
Δ approaches the limits of the inertial range. The same problem is observed in the viscous sub-layer, and tends to delay the transition to turbulence. In addition, the assumption that the Smagorinsky coefficient
CΔs is scale independent leads to unreliable results, unless the grid scale
Δ is located within an inertial range of homogeneous and locally isotropic turbulence. Despite its admitted defficiencies, the Smagorinsky model has been used extensively in the literature, mostly due to its simplicity and robustness. However, LES based on more advanced models (the dynamic model for example) provides very good results. The computational cost is lower than for DNS, but remains far larger than typical RANS modeling. Spalart (2000) estimates that LES on a full aircraft configuration would require over
1011 grid points and
107 time steps. Such calculation should be possible in approximately 2045
[8].
Detached-Eddy Simulation (DES)
Detached-eddy simulation is a modern technique (Spalart (1997)
[10]) designed for tackling high Reynolds number, massively separated flows. DES uses LES where the grid is fine enough (compared to the turbulence length scale), and RANS modeling where it is not. Effectively, the boundary layer is treated with RANS and separated regions with LES. This approach provides a way for predicting the flow over complete geometries with good accuracy, while significantly reducing the computational cost associated with LES. However, DES still faces some issues. In CFD, increasing the mesh resolution typically improves monotonically the accuracy of the results. This is not the case in Detached-Eddy Simulation. If the mesh is refined excessively, the accuracy of DES can decrease and even fall below the accuracy of simple RANS modeling. For a complete survey of Detached-Eddy Simulation, the review written by Spalart (2009)
[9] is recommended.
Hybrid RANS / LES (HRLES)
Similarly to DES, HRLES aims at reducing the computer cost associated with LES while maintaining a high level of accuracy. The whole flow field is computed using both RANS modeling and LES. Blending functions (
fLES and
fLES) combine these two solutions into one.
The computational cost does not increase significantly compared to RANS simulation, since the grid and equations solved are very similar. In regions close to the wall, where the grid scale is far larger than the turbulence length scale, the LES predictions based on SGS modeling are unreliable. The blending functions
fLES and
fLES are defined to ensure that these LES predictions are mostly ignored, and that the RANS solution is retained. There are numerous ways to implement an Hybrid RANS/LES model. These methods are described in details by Frohlich (2008)
[1].
References
[1] J. Fröhlich and D. von Terzi. Hybrid LES/RANS methods for the simulation of turbulent flows. Progress in Aerospace Sciences, 44(5):349--377, 2008.
[2] M. Germano, U. Piomelli, P. Moin, and W.H. Cabot. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A: Fluid Dynamics, 3:1760, 1991.
[3] D.K. Lilly. The representation of small scale turbulence in numerical simulation experiments. IBM Scientific Computing Symposium on environmental sciences, pages 195--210, 1967.
[4] C. Meneveau and J. Katz. Scale-invariance and turbulence models for large-eddy simulation. Annual Review of Fluid Mechanics, 32(1):1--32, 2000.
[5] S.B. Pope. Turbulent flows. Cambridge university press, 2000.
[6] U. Schumann. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. Journal of computational physics, 18(4):376--404, 1975.
[7] J. Smagorinsky. General circulation experiments with the primitive equations. Monthly weather review, 91(3):99--164, 1963.
[8] P.R. Spalart. Strategies for turbulence modelling and simulations. International Journal of Heat and Fluid Flow, 21(3):252--263, 2000.
[9] P.R. Spalart. Detached-eddy simulation. Annual Review of Fluid Mechanics, 41:181--202, 2009.
[10] P.R. Spalart, W. Jou, M. Strelets, and S. Allmaras. Comments of feasibility of LES for wings, and on a hybrid RANS/LES approach. International Conference on DNS/LES, Ruston, Louisiana, Aug. 4-8, 1997.
[11] C.G. Speziale. A review of Reynolds stress models for turbulent shear flows. Citeseer, 1995.
[12] K.R. Sreenivasan. On the universality of the kolmogorov constant. Physics of Fluids, 7(11):2778--2784, 1995.
[13] S. Wallin and A.V. Johansson. An explicit algebraic reynolds stress model for incompressible and compressible turbulent flows. Journal of Fluid Mechanics, 403(1):89--132, 2000.
