Turbulence Model Selection

OpenFOAM Case Generator y+ Calculator ◈ Portfolio

Flow & Geometry

Reynolds Number Re

Mach Number Ma

Geometry

Wall Treatment

Simulation Goals

Primary Goal

Unsteadiness

Compute Budget

Configure inputs and press ▶ RUN SELECTOR.

Y-Axis Grouping

Highlight Type

Cursor Inspector (Click map to pin)

Hover map to see models at Re. Click to pin.

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

WMLES required (wall BL)Re_L ≳ 5×10⁶

DDES preferred range10⁵–10⁸

Click any model card to expand full profile. Includes exact equations, failure modes, validation history, and OpenFOAM tips.

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

Abbreviations & Full Forms

ReReynolds Number (ρUL/μ)

MaMach Number (U/c)

APGAdverse Pressure Gradient

FPGFavourable Pressure Grad.

ZPGZero Pressure Gradient

TuTurbulence Intensity (%)

y⁺Wall distance (u_τ·Δy/ν)

BLBoundary Layer

TKE / kTurbulent Kinetic Energy

ωSpecific dissipation rate

εTurbulent dissipation rate

RANSReynolds-Averaged N-S

LESLarge Eddy Simulation

DESDetached Eddy Simulation

DDESDelayed DES

IDDESImproved DDES

RSMReynolds Stress Model

SGSSubgrid-Scale (model)

SASScale Adaptive Simulation

SASpalart-Allmaras

SSTShear Stress Transport

WMLESWall-Modelled LES

Model	Type	Cost	Separation	Heat Xfr	Transition	Acoustics	Rotating	y⁺ Range	Anisotropy	Comp. Ready	Min Cells (Est.)	OF Class

Head-to-Head: k-ω SST vs Competitors

Canonical Flow	SST Result Quality	Competitor Model & Quality	Winner	Engineering Note
Flat Plate (ZPG)	Excellent (captures log-law perfectly)	SA: Excellent (designed for it)	Tie	SA is 20% cheaper computationally.
RAE2822 Airfoil (Transonic APG)	Excellent (predicts shock location well)	k-ε: Poor (shock too far aft, no sep)	SST	SST limits shear stress in APG via Bradshaw's assumption.
Backward Facing Step (Sep.)	Good (reattachment slightly late)	v2f / LRR: Excellent (exact reattachment)	RSM / v2f	SST overpredicts TKE in shear layer. RSM handles anisotropy.
Pipe Flow (Internal ZPG)	Good (requires fine mesh near wall)	k-ε Realizable: Excellent + cheap	k-ε Real.	k-ε with wall functions is vastly cheaper for bulk pipe flows.
Tandem Cylinder (Acoustics)	Poor (Steady RANS damps shedding)	SST-DDES: Excellent (resolves wake)	DDES	RANS cannot resolve broadband noise. Scale-resolving required.
Turbine Cascade (Curvature)	Moderate (blind to streamline curvature)	SARC / SSG: Good (captures curvature)	SARC / RSM	Standard eddy viscosity assumes turbulence is blind to rotation.

1. 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)

k-ω SST Exact Transport Equations

∂(ρk)/∂t + ∂(ρU_j k)/∂x_j = P_k - β*ρkω + ∂/∂x_j[(μ + σ_k μ_t) ∂k/∂x_j] ∂(ρω)/∂t + ∂(ρU_j ω)/∂x_j = (γ/ν_t)P_k - βρω² + ∂/∂x_j[(μ + σ_ω μ_t) ∂ω/∂x_j] + 2(1-F1)ρσ_{ω2}(1/ω) ∂k/∂x_j ∂ω/∂x_j

RSM (Reynolds Stress Model)

∂(ρR_ij)/∂t + C_ij = P_ij + D_ij + Φ_ij - ε_ij

Φ_ij (Pressure-Strain) is the critical closure. LRR uses a linear model; SSG uses a quadratic model (better for swirl). Realizability (Lumley triangle) ensures physical positive-definite turbulent normal stresses.

2. DES / DDES Formulation

DES Length Scale

d̃ = min(d_wall, C_DES · Δ) Δ = max(Δx, Δy, Δz)

DDES Shielding Function

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 · d_wall² · √|S_ij|²)

IDDES & SAS & WMLES

IDDES: Blends DDES shielding with WMLES formulation. Introduces elevating function to fix log-layer mismatch.
SAS-SST: Uses von Kármán length scale L_vK = κS / |∇²U|. Break RANS into LES structures without explicit grid dependence.
WMLES: Algebraic wall model imposes wall shear stress τ_w as a BC for the resolved outer layer.

3. Wall Treatment & y⁺ Physics

Spalding Unified Wall Law

y⁺ = u⁺ + e^{-κB} [ e^{κu⁺} - 1 - κu⁺ - 0.5(κu⁺)² - (1/6)(κu⁺)³ ]

Valid from y⁺=0 to y⁺=300 continuously. Used in OpenFOAM's nutUSpaldingWallFunction.

OpenFOAM Wall Function Mapping

Model	y+ < 1	y+ > 30
k-ε	nutLowReWallFn	nutkWallFunction
k-ω SST	nutLowReWallFn	nutkWallFunction
SA	nutLowReWallFn	nutUSpalding...

y⁺ Physics

y⁺ = u_τ·Δy / ν. First cell centroid dictates valid assumptions. Buffer layer (y⁺ 5–30) violates both viscous and log-law assumptions.

4. LES Cost & Scales

Cost Scaling vs Re

Model	Grid (N)	Timesteps	Total Cost
RANS	Re^0	Re^0 (steady)	O(1)
WMLES	Re^1.0	Re^0.5	O(Re^1.5)
WRLES	Re^1.8	Re^0.6	O(Re^2.4)
DNS	Re^2.25	Re^0.75	O(Re^3.0)

Turbulence Scales

Integral (L): Macro scale, contains most energy.
Taylor (λ): Inertial subrange. λ/L ~ Re_L^(-1/2)
Kolmogorov (η): Dissipation scale. η = (ν³/ε)^(1/4). η/L ~ Re_L^(-3/4). Resolved by DNS.

5. Transition Physics

Transition Mechanisms

Natural: TS waves → secondary instability → breakdown. Needs very low freestream Tu (< 0.1%).
Bypass: High freestream Tu (> 1%) penetrates BL, bypassing TS waves. Typical in turbomachinery.
Separation-induced: Laminar BL separates in APG, transitions in shear layer, reattaches as turbulent (LSB).

γ-Reθ Formulation

Uses empirical correlations (e.g. Mayle) linking local Tu to transition onset Re_θt. γ (intermittency) equation multiplies TKE production, switching it on smoothly.

6. Compressible Turbulence

Favre Averaging

ũ_i = \bar{ρ u_i} / \bar{ρ} u_i = ũ_i + u_i''

Density-weighted averaging eliminates complex density fluctuation terms in N-S equations.

Dilatation Dissipation (Sarkar)

ε_c = α M_t² ε_s M_t = √(2k) / c

As Mach increases, compressibility drains energy via shocks/dilatation. Reduces spreading rate of supersonic jets (comp. shear layer anomaly). Corrected via Sarkar/Wilcox modifiers.

Validation Databases

NASA Turbulence Modeling Resource

The gold standard for CFD turbulence model verification. Grid-convergence studies for canonical 2D/3D flows.
turbmodels.larc.nasa.gov

ERCOFTAC Classic Database

Extensive experimental data sets specifically for turbulence model validation. Flow geometries categorised by complexity.
cfd.mace.manchester.ac.uk/ercoftac

AGARD Advisory Reports

AGARD AR-345 and AR-291 are fundamental compilations of experimental data for aerospace fluid dynamics.

NPARC Alliance Verification & Validation

Provides test cases for WIND code validation, applicable universally.
www.grc.nasa.gov/www/wind/valid

Landmark Bibliography

Books

Wilcox, D.C. (2006). "Turbulence Modeling for CFD", 3rd ed. DCW Industries. [ISBN 978-1-928729-08-2]
Pope, S.B. (2000). "Turbulent Flows". Cambridge University Press. [ISBN 0-521-59886-9]
Durbin, P.A. & Pettersson Reif, B.A. (2010). "Statistical Theory and Modeling for Turbulent Flows", 2nd ed. Wiley.
Sagaut, P. (2006). "Large Eddy Simulation for Incompressible Flows", 3rd ed. Springer.

Key Papers

Menter (1994). Two-equation eddy-viscosity turbulence models...
Spalart & Allmaras (1992). A one-equation turbulence model for aerodynamic flows.
Shih et al. (1995). "A new k-ε eddy viscosity model..." Computers & Fluids.
Spalart et al. (1997). "Comments on the feasibility of LES for wings..."
Langtry & Menter (2009). Correlation-Based Transition Modeling...
Launder, Reece & Rodi (1975). Progress in the development of a Reynolds-stress turbulence closure.

Disclaimer

This tool compiles information from the above peer-reviewed sources. All recommendations should be validated against case-specific benchmark data before production use. The author assumes no liability for engineering decisions made solely on the basis of this tool.