Turbulence Model Guide & y+ Calculator Back EN | ZH
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Turbulence Model Selection Guide & y⁺ Calculator

Compare k-ε, k-ω SST, Spalart-Allmaras, and LES. Calculate first-cell height Δy for target y⁺, friction velocity u*, and inlet k/ε/ω boundary conditions in real time.

y⁺ Calculator
Reynolds Number Re1.0×10⁶
Reference Velocity U [m/s]10.0 m/s
Density ρ [kg/m³]1.225 kg/m³
Kin. Viscosity ν [×10⁻⁶ m²/s]15.1 ×10⁻⁶
Target y⁺
Inlet Turbulence Conditions
Turbulence Intensity Tu [%]5.0 %
Length Scale L [m]0.100 m
k = — m²/s²   ε = — m²/s³   ω = — s⁻¹
Friction velocity u* [m/s]
Cell height Δy [μm]
Boundary layer δ [mm]
Recommended model
Law of the Wall — u⁺ vs y⁺

Law of the Wall & RANS Closure

Viscous sublayer ($y^+<5$):

$$u^+ = y^+$$

Log-law region ($y^+>30$):

$$u^+ = \frac{1}{\kappa}\ln(y^+) + B \quad (\kappa=0.41,\; B=5.2)$$

Friction velocity: $u^* = \sqrt{\tau_w/\rho}$,   $C_f \approx 0.027\,Re_L^{-1/7}$

Inlet turbulence: $k = \tfrac{3}{2}(T_u U)^2$,   $\varepsilon = C_\mu^{3/4} k^{3/2}/L$,   $\omega = k^{1/2}/(C_\mu^{1/4} L)$

Practice note: In OpenFOAM, SST + y⁺≈1 is the de facto standard for external aerodynamics. Fluent's standard wall function assumes y⁺=30–300; values below 11 degrade accuracy significantly.
Model Selection Guide
Model Performance Comparison
ModelFree ShearAdverse ∂P/∂xSeparationHeat TransferRotationCost
k-ε Std⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Low
k-ε RNG⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Low
k-ε Real.⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Low
k-ω Std⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Low
k-ω SST⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Low–Med
SA⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Lowest
LES⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Very High