Turbulence Model Selection

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Flow & Geometry
Simulation Goals
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Regime Boundaries
Pipe laminar→turbulentRe ≈ 2300
Flat plate transition onsetRe_x ≈ 3×10⁵
Flat plate fully turbulentRe_x ≈ 5×10⁵
Cylinder drag crisisRe ≈ 2–5×10⁵
LES affordable (research)Re_L ≲ 10⁵
LES requires HPCRe_L ~ 10⁶
LES impractical (wall BL)Re_L ≳ 10⁷
Min Re for reliable DDESRe ≳ 10⁵
DDES preferred range10⁵–10⁸
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Model Re Ma/Compress. APG Rotation Tu Mesh Notes
How to Read
Sensitivity Scale
0 — NoneModel is insensitive to this parameter
1 — LowMinor effect, manageable
2 — ModerateNoticeable; review setup
3 — HighSignificant; requires care
4 — CriticalDominant; results strongly affected
Common Pitfalls
k-ω SST

Overestimates post-separation bubble length in massively separated flows. Use DES/DDES for post-stall. APG reattachment over-predicted.

k-ε Standard

Stagnation point anomaly overproduces TKE. Not suitable for APG or separation. Kato-Launder correction partially fixes stagnation issue.

Smagorinsky

Over-dissipative near walls due to non-zero νt in laminar regions. Cs must be tuned — default Cs=0.1 underestimates, Cs=0.2 over-dissipates bluff body wakes.

SST-DDES

Grey area at RANS-LES interface reduces eddy viscosity. Modelled Stress Depletion (MSD) possible near BL edge. Synthetic turbulence (SEM/STG) at inflow recommended.

γ-Reθ SST

Highly sensitive to freestream Tu and mesh. Empirical correlation limits generality outside validated Tu=0.1–10% range.

Model Type Cost Separation Heat Xfr Transition Acoustics Rotating y⁺ Range OpenFOAM Class
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y⁺ / First Cell Height Calculator
Turbulence Inlet BC Calculator
RANS Closure & Boussinesq
Boussinesq Approximation
τ_ij = 2μ_t S_ij − (2/3)ρk δ_ij S_ij = 0.5·(∂U_i/∂x_j + ∂U_j/∂x_i) — strain-rate tensor
When It Fails
  • Highly curved streamlines (Görtler vortices, swirl)
  • Strong adverse pressure gradient: turbulence ≠ proportional to mean strain
  • Secondary flows in non-circular ducts (requires RSM)
  • Impingement / stagnation (overpredicts k — use Kato-Launder)
RSM vs Two-Equation

RSM solves 6 Rij transport equations + ε (7 total). No eddy viscosity assumption. Captures anisotropy, secondary flows, streamline curvature. ~3× cost of k-ω SST; convergence is difficult. Use when: swirling combustion, turbomachinery secondary flow, non-circular duct, or strongly curved geometry.

DES / DDES Formulation
DES Length Scale
d̃ = min(d_wall, C_DES · Δ) Δ = max(Δx, Δy, Δz)
DDES Modification (Spalart 2006)
d̃ = d_wall − F_d · max(0, d_wall − C_DES·Δ) F_d = 1 − tanh((8·r_d)³) r_d = (ν_t + ν) / (κ² · d² · √(∂U_i/∂x_j · ∂U_i/∂x_j)) F_d ≈ 1 in log layer (shields RANS) F_d ≈ 0 in LES region
Grey Area Problem

At RANS-LES interface, neither well-resolved LES content nor full RANS modelling exists. Eddy viscosity drops, producing under-resolved turbulence. Mitigation: Synthetic Eddy Method (SEM) or Stochastic Turbulence Generator (STG) to inject resolved fluctuations at the interface.

Modelled Stress Depletion (MSD)

Near BL edge, grid refinement triggers early switch to LES mode before resolved content develops. Modelled stresses deplete but resolved stresses are not established. Fix: use DDES shielding and avoid grid refinement in BL interior.

Wall Treatment & y⁺ Physics
Three-Layer Turbulent BL Structure
Viscous sublayer y⁺ < 5u⁺ = y⁺ (linear)
Buffer layer 5 < y⁺ < 30⚠ Avoid — neither law valid
Log-law region y⁺ 30–300u⁺ = (1/κ)·ln(y⁺) + B, κ=0.41, B=5.1
Wall Function Approach (y⁺ 30–300)

First cell centroid in log-law region. Analytic wall functions bridge viscous sublayer. Cheap but inaccurate for strong APG, flow separation, heat transfer, and low Re.

Low-Re Resolved Approach (y⁺ ≤ 1)

First cell centroid at y⁺ ≈ 0.5–1. Viscous sublayer fully resolved by mesh. 15–30 prism layers spanning δ. Growth ratio 1.15–1.25. Required for: transition, accurate heat transfer, separation/reattachment, and LES/DES.

u_τ = √(τ_w / ρ_w) y⁺ = u_τ · Δy / ν_w Δy = y⁺_target · ν_w / u_τ
LES Mesh Requirements & Cost
Pope's 80% Criterion

Mesh must resolve ≥80% of total TKE. Check M(x) = k_resolved / (k_resolved + k_sgs) ≥ 0.8. Requires approximately Δx ≈ 12η near wall, where η = Kolmogorov scale.

Near-Wall LES Resolution (Wall-Resolved)
Δx⁺ (streamwise)≈ 50–150
Δz⁺ (spanwise)≈ 15–40
Δy⁺ (wall-normal, first cell)≤ 1
Cost scaling (channel)N_cells ~ Re^1.8, total ~ Re^2.4
Wall-Modelled LES (WMLES)

Relax Δx⁺/Δz⁺ to ~500/200. Use algebraic or ODE wall model to bridge inner layer. Enables LES at engineering Re. Supported in OpenFOAM via kOmegaSSTLowRe as wall model.

Time-Step Guidance
LES CFL≤ 0.5
LES Δt≈ Δx_min / U_ref
PIMPLE-DES CFL≤ 1–2, nCorrectors ≥ 2
Acoustics (aliasing)Δx ≤ c/(20·f_target)