Y⁺ Calculator
Compute first cell height, friction velocity, wall shear stress, and full prism layer stack for any turbulence model. Flat-plate Cf correlations for laminar, transitional, and turbulent regimes.
5 turbulence models
Prism layer preview
Fluid presets
SI / Imperial toggle
Free to use
Flow Parameters
Freestream / reference velocity
Plate length, chord, pipe diameter…
Air @15°C: 1.225 · Water @20°C: 998
Air @15°C: 1.789e-5 · Water @20°C: 1.002e-3
Wall-resolved <1 · Wall-function 30–300
Auto-fills ρ and μ
Turbulence Model
k-ω SST
k-ε Realizable
Spalart-Allmaras
RSM
LES / DNS
k-ω SST: Best for adverse pressure gradients & separation. Requires y⁺ <1 for wall-resolved. Wall-function mode: 30–300.
SI (m)
Imperial
Key Results
First Cell Y⁺
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Press Calculate
Cell Height Δy₁
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Reynolds Number
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Total BL Stack
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Select parameters above and click Calculate.
Flow & Wall Properties
Wall Shear Stress τ_w
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Pa
Friction Velocity u*
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m/s
Skin Friction Cf
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Kinematic Viscosity ν
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m²/s
Growth Rate
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Prism Layers
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⚠ Flat-plate assumption: This calculator uses flat-plate Cf correlations. For curved surfaces, bluff bodies, or fully-developed internal flows, validate with a precursor simulation or apply appropriate corrections.
Y⁺ Zone Indicator
0530100300+
Your Y⁺
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Recommended — k-ω SST
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Prism Layer Stack
| Layer # | Cell Height | Y⁺ (this cell) | Cumulative Height | Zone |
|---|---|---|---|---|
| Press Calculate to generate layer table | ||||
Formula Reference
Re = ρ U∞ L / μReynolds number
Cf = f(Re)Skin friction coefficient
τ_w = ½ ρ U∞² CfWall shear stress
u* = √(τ_w / ρ)Friction velocity
Δy₁ = y⁺ ν / u*First cell height
Δy_n = Δy₁ · r^(n-1)Layer growth (geometric)
Cf correlations: Laminar (Re < 5×10⁵): 0.664 / √Re (Blasius) · Mixed (Re < 1×10⁷): 0.074/Re⁰·² − 1742/Re · Fully turbulent: 0.027/Re^(1/7)
Common Questions
What is Y⁺ and why does it matter in CFD?
Y⁺ is a dimensionless wall distance: y⁺ = u* Δy / ν. It tells the solver where the first mesh cell sits relative to the boundary layer. Wall-resolved models (k-ω SST, SA) need y⁺ < 1 to directly resolve the viscous sub-layer. Wall-function models (k-ε) need y⁺ = 30–300 to land in the log-law region. Incorrect y⁺ leads to inaccurate wall shear stress, heat transfer, and separation predictions.
What Y⁺ should I use for k-ω SST?
For wall-resolved k-ω SST, target y⁺ ≈ 0.5–1. Some solvers support automatic wall treatment that blends between y⁺ < 5 and wall-function mode (30–300), but for best accuracy with separation and adverse pressure gradients use y⁺ ≈ 1 with at least 10–15 prism layers at growth rate ≤ 1.2.
Wall-resolved vs wall-function — which should I use?
Wall-resolved (y⁺ < 5) directly resolves the steep velocity gradient — more accurate for separation, reattachment, and heat transfer, but requires many more cells. Wall-function (y⁺ = 30–300) uses analytical log-law bridging with far fewer cells, sufficient for attached high-Re flows. Avoid the buffer zone (y⁺ = 5–30) with either approach.
How many prism layers do I need?
A minimum of 10 layers is recommended for wall-resolved simulations; 15–20 is common for production CFD. The total prism stack should ideally cover the boundary layer thickness δ. Use a growth rate of 1.1–1.2 to maintain smooth aspect ratio transitions. Avoid growth rates above 1.3 as large cell size jumps introduce numerical diffusion.
Can I use this for internal flows (pipes, ducts)?
Yes, with care. Set the characteristic length to the hydraulic diameter D_h = 4A/P and use bulk mean velocity as U∞. The flat-plate Cf correlation is approximate — for fully developed pipe flow, a more accurate τ_w uses the Darcy-Weisbach friction factor: Cf = f/4, where f = 64/Re (laminar) or Colebrook (turbulent). The y⁺ sizing formula itself remains valid regardless of geometry.