Choosing a Turbulence Model Without Guessing

Why a model is needed at all

Resolving every turbulent scale directly — Direct Numerical Simulation — requires a cell count scaling roughly with Re^(9/4). For any engineering Reynolds number this is computationally impossible and will remain so.

Practical CFD therefore models turbulence rather than resolving it. The near-universal approach is Reynolds-Averaged Navier–Stokes (RANS): decompose each variable into a mean and a fluctuation, average the equations, and confront the term that does not close — the Reynolds stress. A turbulence model is a hypothesis about that term.

Every model is a hypothesis calibrated against a limited set of flows. Understanding which flows determines where it can be trusted.

The common RANS models

Spalart–Allmaras. A single transport equation, developed for external aerodynamics. Robust, cheap, and well behaved for attached flows with mild pressure gradients over aerofoils and airframes. Weak for free shear flows, jets and strongly separated flows.

k–ε. Two equations, historically the industrial default. Performs well for free shear flows and internal flows far from walls. Its notable weakness is adverse pressure gradients and separation, where it tends to be over-diffusive and delays or misses separation. Usually deployed with wall functions.

k–ω. Better near-wall behaviour than k–ε and superior in adverse pressure gradients, but sensitive to the freestream value of ω specified at the inlet — a sensitivity that has caused a great many irreproducible results.

k–ω SST. Menter's shear stress transport blends k–ω near the wall with k–ε in the freestream, capturing the strengths of each and removing the freestream sensitivity. It also limits eddy viscosity in adverse gradients, which improves separation prediction markedly. This is the sensible default for external aerodynamics with separation, and where a single choice must be defended, it is usually this one.

Reynolds Stress Models. Solve transport equations for each Reynolds stress component, abandoning the isotropic eddy-viscosity assumption. Necessary for strongly swirling flows, secondary flows in ducts and highly anisotropic turbulence — at substantially higher cost and with more fragile convergence.

Beyond RANS

LES resolves large eddies and models only the small ones. Far more accurate for unsteady and separated flows, and essential where turbulent mixing, acoustics or unsteady loads are the question — at a cost typically one to two orders of magnitude above RANS, plus the requirement to time-average over a long enough sample.

DES and hybrid RANS-LES apply RANS near walls and LES away from them, which is a pragmatic compromise for massively separated flows such as bluff bodies. Attention must be paid to the transition region, where the model switches and can misbehave.

The assumption that quietly fails

Most RANS models rest on the Boussinesq hypothesis — that Reynolds stress is proportional to the mean strain rate through a scalar eddy viscosity. This treats turbulence as isotropic.

It is reasonable for simple shear flows. It is poor for flows with strong streamline curvature, rotation, swirl, or rapid strain — precisely the cases where turbulence becomes strongly anisotropic. When a k–ω SST result looks wrong in a swirling flow, this assumption is usually the reason, and no amount of mesh refinement will address it.

A practical selection order

1. Is the flow attached with mild gradients? Spalart–Allmaras or k–ω SST. Either is defensible.
2. Is separation the question? k–ω SST, resolved to the wall with y⁺ ≈ 1.
3. Is there strong swirl or rotation? Consider an RSM, or accept that eddy-viscosity results will be indicative rather than quantitative.
4. Are unsteady loads, mixing or acoustics the deliverable? RANS cannot answer this. Budget for LES or DES.
5. Is transition significant? At low Reynolds number, add a transition model such as γ–Reθ. Fully turbulent assumptions will misplace separation on a small UAV wing.

Always state the choice

Report the model, the wall treatment, the achieved y⁺, and — where it exists — a validation comparison against experimental or published data for a similar configuration. A CFD result quoted without its turbulence model is not a result. It is a picture.