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
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Friction velocity u* [m/s]
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Cell height Δy [μm]
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Boundary layer δ [mm]
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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
| Model | Free Shear | Adverse ∂P/∂x | Separation | Heat Transfer | Rotation | Cost |
|---|---|---|---|---|---|---|
| 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 |