cfd-turbulence

name	cfd-turbulence
description	CFD turbulence modeling — RANS (k-ε, k-ω SST, Spalart-Allmaras), LES, DES, DNS, turbulence model selection guide, near-wall modeling, free shear flows, heat transfer.
metadata	{"priority":7,"promptSignals":{"phrases":["turbulence model","k-epsilon","k-omega SST","SST","LES","Spalart-Allmaras","RANS","turbulent flow"],"minScore":4}}

CFD Turbulence Modeling — Complete Skill

Reynolds-Averaged Navier-Stokes (RANS)

Time-average the N-S equations → mean flow + Reynolds stress term: -ρ<u'_i u'_j> = Reynolds stress tensor (unknown — closure problem)

Boussinesq hypothesis: -ρ<u'u'> = μ_t(∂U_i/∂x_j + ∂U_j/∂x_i) - (2/3)ρkδ_ij μ_t = turbulent eddy viscosity [Pa·s] k = turbulent kinetic energy = ½<u'²+v'²+w'²>

Most industrial CFD uses RANS. Steady-state, fast, well-validated.

k-ε Models

Standard k-ε (Jones-Launder, 1972)

Transport equations for k and ε: ∂(ρk)/∂t + ∇·(ρUk) = ∇·(μ_t/σ_k × ∇k) + P_k - ρε ∂(ρε)/∂t + ∇·(ρUε) = ∇·(μ_t/σ_ε × ∇ε) + C₁ε/k × P_k - C₂ρε²/k

Constants: C_μ = 0.09, C₁ = 1.44, C₂ = 1.92, σ_k = 1.0, σ_ε = 1.3 μ_t = ρ C_μ k²/ε

Strengths: robust, fast, good for free shear flows (jets, wakes) Weaknesses: poor for adverse pressure gradients (over-predicts eddy viscosity), requires wall functions (y⁺ = 30-300)

Realizable k-ε

Modified C_μ (variable, satisfies realizability constraints) + modified ε equation Better for: round jets, recirculating flows, rotating flows Still needs wall functions (y⁺ = 30-300) Default choice for industrial flows without strong adverse pressure gradient

RNG k-ε

Derived from renormalization group theory; additional ε term Better for flows with high strain/streamline curvature Similar accuracy to realizable for most flows

k-ω Models

Standard k-ω (Wilcox)

Uses ω = ε/(C_μ k) (specific dissipation rate) Better near-wall behavior → integrates to wall (y⁺ < 1) Weakness: very sensitive to free-stream ω value (boundary condition sensitivity)

k-ω SST (Shear Stress Transport — Menter, 1994)

Gold standard for aerodynamics, most recommended. Blends k-ω (near wall) with k-ε (far field):

• k-ω in boundary layer: accurate for adverse pressure gradients, separation
• k-ε in free stream: insensitive to free-stream turbulence

Includes: production limiter (prevents excessive μ_t in stagnation), stress limiter Requires: y⁺ < 1 (low-Re mode) or wall functions (y⁺ 30-300)

Use SST for:

• Boundary layers with adverse pressure gradients
• Flows approaching separation (airfoils near stall)
• External aerodynamics, turbomachinery
• Heat transfer in boundary layers

Fluent: k-omega SST (tick "Low-Re Corrections" for y⁺ < 1) OpenFOAM: kOmegaSST

Spalart-Allmaras (SA)

One-equation model (ν_t transport equation) Developed for aerodynamics, low-Re effects Simple, robust, low computational cost Good for: attached boundary layers, airfoil/wing analysis Poor for: free shear flows, recirculation, heat transfer Used in: aerospace (legacy), some turbomachinery Requires: y⁺ < 1

Reynolds Stress Model (RSM)

Solves individual transport equation for each component of -ρ<u'_i u'_j> 7 equations (3D) instead of 2 Most physically complete RANS model Use for: strongly anisotropic turbulence (secondary flows in ducts, swirl, curved channels) Disadvantage: expensive, convergence difficult, rarely better than SST in practice

Large Eddy Simulation (LES)

Concept

Resolve large eddies (geometry-dependent) directly Filter small eddies (below filter width Δ) → model with subgrid scale (SGS) model Filter: Ū_i = resolved, u'_SGS = subgrid (modeled)

SGS Models: Smagorinsky: ν_SGS = (C_s Δ)² |S̃| (C_s = 0.1-0.2) Dynamic Smagorinsky: C_s computed locally (better, more accurate) WALE: better near walls (no damping function needed)

Requirements: y⁺ < 1 everywhere (wall-resolved LES) dx⁺ ≈ 50-150, dz⁺ ≈ 15-40 (streamwise, spanwise) Time step: CFL < 1 (Courant-Friedrichs-Lewy) Statistics: run for 5-10 flow-through times for convergence

Cost: 10-100× more expensive than RANS for same geometry Use for: combustion, acoustics, complex separation, when RANS fails

Detached Eddy Simulation (DES)

Hybrid: RANS near walls + LES in free shear regions Automatic switching: based on local mesh size vs. boundary layer thickness DES-SA, DDES (Delayed DES — avoids premature switch), IDDES Good balance of cost vs. accuracy for bluff bodies, separated flows

Direct Numerical Simulation (DNS)

No turbulence model — resolve ALL scales including Kolmogorov scale Grid: N³ ∝ Re^(9/4) — prohibitively expensive for Re > 10,000 Only used for: fundamental research, turbulence databases, model validation Not used in engineering practice

Model Selection Guide

Flow Type	Recommended Model
Attached boundary layers, aero	SST k-ω
Adverse pressure gradient, separation	SST k-ω
Free jets, mixing layers	Realizable k-ε
Recirculating flows	Realizable k-ε or SST
Rotating machinery (pump, fan, turbine)	SST or RSM
Strongly swirling flows	RSM
Combustion, reacting flows	k-ε + species transport
Acoustics, unsteady separation	LES or DES
Heat transfer in boundary layer	SST k-ω (y⁺ < 1)
Simple industrial internal flows	Realizable k-ε + wall functions

Turbulence Intensity and Length Scale at Inlet

Low turbulence (wind tunnel, clean inlet): I = 0.1-1%, L_t = 0.01×D Medium (typical industrial): I = 1-5%, L_t = 0.07×D_h High (after mixing/fans): I = 5-20%

k = 3/2 × (U × I)² ε = C_μ^(3/4) × k^(3/2) / L_t ω = k^(1/2) / (C_μ^(1/4) × L_t)

Heat Transfer with Turbulence

Turbulent Prandtl number: Pr_t = 0.85-0.9 (gases), 0.85-1.0 (liquids) q_t = -ρ c_p <u'T'> ≈ (μ_t / Pr_t) × ∂T/∂y Enhanced wall treatment (EWT) in Fluent: blends sublayer and log-law For accurate Nu: use SST with y⁺ < 1 and Pr_t appropriately set

Output

Provide: turbulence model selection with justification, y⁺ target, inlet turbulence I and L_t, expected accuracy ±%, wall treatment method, estimated cell count penalty vs. wall functions.