Choosing a turbulence model

Which turbulence model should close the equations?

This page applies when the equation set is rans or les; the choice of equation set is set out in Choosing an equation set.

For rans, name the turbulence model. To resolve eddies away from the wall while keeping RANS near it, add a hybrid on top of that model. For les, choose the sub-grid model.

The RANS turbulence models, selected by model:

`model`	Model	Reference
`sst`	Menter shear stress transport k-ω, in its 2003 form	Menter (1994); Menter et al. (2003)
`spalart-allmaras`	Spalart–Allmaras, solved in the negative form of `sa-neg`	Spalart and Allmaras (1994); Allmaras et al. (2012)
`sa-neg`	negative Spalart–Allmaras, without the $f_{t2}$ term	Allmaras et al. (2012)
`sst-transition`	Langtry–Menter four-equation transitional SST ( $\gamma$ – $Re_\theta$ )	Langtry and Menter (2009)
`sas`	scale-adaptive simulation, run as a standalone RANS model	Menter and Egorov (2010)

The incompressible solver solves sst and sa-neg only.

Hybrid RANS–LES

A hybrid of DES, DDES, IDDES or SAS layers an LES branch on the chosen model. On sst, DES follows Strelets (2001), and DDES and IDDES follow Gritskevich et al. (2012). On sa-neg, DES, DDES and IDDES follow Spalart et al. (1997), Spalart et al. (2006) and Shur et al. (2008) respectively. SAS follows Menter and Egorov (2010).

A hybrid model carries a transport-equation RANS model beneath its LES branch; SST-IDDES, for example, still solves the SST k and ω equations. It is configured through the rans equation set, with hybrid set alongside model, and never through les. Leave hybrid out to solve pure RANS.

The turbulence dictionary

Under rans, the turbulence dictionary holds model, hybrid and the model options below.

parameters["solver"]["equations"] = {
    "type": "rans",
    "precondition": True,
    "turbulence": {
        "model": "sa-neg",
        "hybrid": "IDDES",
    },
}

parameters["solver"]["equations"] = {
    "type": "rans",
    "precondition": True,
    "turbulence": {
        "model": "sst",
        "rotation_correction": False,
        "limit_gradient_k": 0.5,
        "qcr": 2020,
    },
}

qcr

qcr adds the non-linear quadratic constitutive relation (QCR) to the turbulent stress, for both SST and SA-neg. QCR has been shown to improve the prediction of separated corner flows, particularly on highly loaded wings. Three versions are available: QCR 2000, QCR 2020 and QCR 2021.

production

production selects the production term of the SST model: "vorticity" (SST-V), "strain-incompressible", "strain-compressible" or "kato-launder". The integers 0 to 3 are also accepted, and stand for the same four names in that order. Left out, the model chooses for itself: kato-launder for sst-transition and vorticity otherwise.

Advanced parameters for turbulence models

The constants in the turbulence dictionary tune the turbulence models: betastar, cdes_kw, cdes_keps, cd1, cd2, cw, a1, cdes, ca1, ca2, ce1, ce2, cthetat, sigmagamma, sigmathetat and separation_correction. They are advanced settings, and should not normally need adjusting.

LES sub-grid models

Under les, the turbulence dictionary is a much smaller, LES-specific one, unrelated to the RANS dictionary above. Its les key selects the sub-grid model: wale, deardorff or none. deardorff is implemented by the incompressible solver only. The whole dictionary is optional: leaving it out gives implicit LES, with no sub-grid model.

parameters["solver"]["equations"] = {
    "type": "les",
    "turbulence": {
        "les": "wale",
    },
}

Shielding the LES branch by CFL

les_cfl_limit is the CFL number at or below which the LES branch of a DES, DDES or IDDES model is left untouched. Left out, as it is by default, the CFL shield is disabled.

The LES branch replaces the modelled RANS stress with resolved eddies the size of the local filter width $\Delta$ . Those eddies are resolved only if the time step can follow them, that is if the cell CFL number is of order one. Where the CFL number is larger the model still drops the RANS stress, but the temporal discretisation cannot supply the resolved stress that should replace it. The shielding function $f_d$ gives no protection against this, because it is built from $r_d$ , a purely spatial ratio.

Setting a limit adds a second shield, built from the cell CFL number. The time step has to resolve two things: the transport of an eddy of size $\Delta$ across the cell, and that eddy's own turnover. The shield takes whichever of the two is binding,

\mathrm{CFL} = \max\left( \frac{\left| \mathbf{u} - \mathbf{u}_{grid} \right| \Delta t}{\Delta}, \; C_{turn} \left| S \right| \Delta t \right), \qquad f_{CFL} = \mathrm{smoothstep}\left( \mathrm{clamp}\left( \frac{\mathrm{CFL} - \mathrm{limit}}{\mathrm{width}}, 0, 1 \right) \right)

and is combined with $f_d$ so that the more protective of the two prevails.

The transport term uses the velocity relative to the mesh, so it is indifferent to the frame: a mesh and fluid in rigid-body motion together contribute nothing to it. On a rotating mesh, however, the solid-body term $\mathbf{\Omega} \times \mathbf{r}$ is a genuine relative speed and can dominate, so a fine rotating overset mesh is often shielded almost everywhere. That is the criterion reporting a real limitation of the mesh and time step, not an artefact; les_turnover_coefficient covers the opposite case. At $f_{CFL} = 1$ the hybrid length scale is exactly the RANS length scale, and the LES branch is fully suppressed. Because $f_{CFL}$ is exactly zero at or below the limit, a simulation whose CFL number is everywhere within the limit is unaffected.

The shield acts only in time-accurate runs, with time_settings of type "unsteady" under either dual or global time stepping, since a steady run has no meaningful real time step. It applies to the DES, DDES and IDDES settings only, not to SAS or to wale. Before enabling it, use the lescfl output variable to find where the CFL number exceeds the limit.

les_cfl_width is the width of the blend above les_cfl_limit: RANS is fully enforced at a CFL number of limit + width. A wider blend returns to RANS more gradually, which is usually preferable, since the shielded cells also revert to full upwind dissipation.

les_turnover_coefficient

les_turnover_coefficient is the weight $C_{turn}$ on the eddy-turnover term of the shielded CFL number. It has no effect unless les_cfl_limit is set. Setting it to 0.0 recovers the transport-only criterion.

Transport alone is a one-sided test. Where the flow is slow relative to the mesh it reports a CFL number near zero and permits the LES branch however large the time step, even though an energetic eddy in that cell may turn over many times per step. Stagnation regions, recirculation cores and the neighbourhood of a rotation axis, where $\Omega r \rightarrow 0$ , all fall in that blind spot.

The turnover term closes it. The velocity of an eddy at the filter width is $u'(\Delta) \sim \left| S \right| \Delta$ , so $\Delta$ cancels, and the measure is the shear-timescale Courant number $\left| S \right| \Delta t$ , with $\left| S \right| = \sqrt{2 S_{ij} S_{ij}}$ the resolved strain-rate magnitude.

The measure uses strain, not vorticity. Solid-body rotation carries $\left| \omega \right| = 2\Omega$ with no turnover at all, so a vorticity-based measure would shield every vortex core, which is exactly the content a DES run exists to resolve. The resolved strain is also preferred to the modelled $\sqrt{k}$ , which in a shielded cell is the full RANS turbulence kinetic energy rather than its sub-grid part, and would lock a cell into RANS once it got there.

Use the lesturnover output variable alongside lescfl to see which of the two mechanisms is binding in a given cell.

Literature

Allmaras, S. R., Johnson, F. T. and Spalart, P. R. (2012). Modifications and Clarifications for the Implementation of the Spalart–Allmaras Turbulence Model. Seventh International Conference on Computational Fluid Dynamics, paper ICCFD7-1902.
Gritskevich, M. S., Garbaruk, A. V., Schütze, J. and Menter, F. R. (2012). Development of DDES and IDDES Formulations for the k-ω Shear Stress Transport Model. Flow, Turbulence and Combustion, 88(3), 431–449. https://doi.org/10.1007/s10494-011-9378-4
Langtry, R. B. and Menter, F. R. (2009). Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes. AIAA Journal, 47(12), 2894–2906. https://doi.org/10.2514/1.42362
Menter, F. R. (1994). Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA Journal, 32(8), 1598–1605. https://doi.org/10.2514/3.12149
Menter, F. R. and Egorov, Y. (2010). The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description. Flow, Turbulence and Combustion, 85(1), 113–138. https://doi.org/10.1007/s10494-010-9264-5
Menter, F. R., Kuntz, M. and Langtry, R. (2003). Ten Years of Industrial Experience with the SST Turbulence Model. In K. Hanjalić, Y. Nagano and M. Tummers (editors), Turbulence, Heat and Mass Transfer 4, Begell House, 625–632.
Shur, M. L., Spalart, P. R., Strelets, M. and Travin, A. K. (2008). A Hybrid RANS-LES Approach with Delayed-DES and Wall-Modelled LES Capabilities. International Journal of Heat and Fluid Flow, 29(6), 1638–1649. https://doi.org/10.1016/j.ijheatfluidflow.2008.07.001
Spalart, P. R. and Allmaras, S. R. (1994). A One-Equation Turbulence Model for Aerodynamic Flows. La Recherche Aérospatiale, 1, 5–21.
Spalart, P. R., Deck, S., Shur, M. L., Squires, K. D., Strelets, M. and Travin, A. (2006). A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities. Theoretical and Computational Fluid Dynamics, 20(3), 181–195. https://doi.org/10.1007/s00162-006-0015-0
Spalart, P. R., Jou, W.-H., Strelets, M. and Allmaras, S. R. (1997). Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach. In C. Liu and Z. Liu (editors), Advances in DNS/LES, Greyden Press, 137–147.
Strelets, M. (2001). Detached Eddy Simulation of Massively Separated Flows. AIAA paper 2001-0879. https://doi.org/10.2514/6.2001-879

Reference entries

turbulence: model, hybrid, qcr, production
les
les_cfl_limit, les_cfl_width and les_turnover_coefficient