Calculate first cell height for CFD mesh y⁺ requirements. Includes Reynolds number, friction velocity, boundary layer region guide, and y⁺ reference table.
Y-plus (y⁺) is a dimensionless wall distance used in computational fluid dynamics (CFD) to determine whether your near-wall mesh resolution is adequate for the chosen turbulence model. It's defined as y⁺ = yρu*/µ, where y is the distance from the wall, ρ is density, u* is the friction velocity, and µ is dynamic viscosity. Getting y⁺ right is arguably the most important step in CFD mesh generation.
Different turbulence models require different y⁺ ranges. Low-Reynolds-number models like k-ω SST need y⁺ ≈ 1 at the wall — the first cell must be entirely within the viscous sublayer. Wall-function models (standard k-ε) need y⁺ = 30-300 — the first cell should be in the log-law region. Using the wrong y⁺ range for your turbulence model produces incorrect wall shear stress, heat transfer, and separation predictions.
This calculator estimates the first cell height needed to achieve a target y⁺ using the flat-plate skin friction correlation. It also provides reverse calculation (y⁺ from given cell height), fluid property presets, and a full y⁺ range table showing which boundary layer region each value falls in.
Every CFD engineer calculates y⁺ before meshing. The wrong first cell height wastes computation (too fine) or gives wrong results (too coarse). This calculator replaces manual spreadsheets and provides instant results for any fluid and flow condition. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
y = y⁺µ/(ρu*). Friction velocity: u* = √(τw/ρ). Wall shear: τw = ½CfρU². Skin friction (Schlichting): Cf = 0.058Re⁻⁰·². Reynolds number: Re = ρUL/µ.
Result: First cell: 0.015 mm, Re = 3.4M, u* = 2.17 m/s
Air at 50 m/s over 1m plate: Re = 3.4M (turbulent). Cf = 0.058 × (3.4e6)^-0.2 = 0.0028. τw = 0.5 × 0.0028 × 1.225 × 50² = 4.3 Pa. u* = 1.87 m/s. y = 1 × 1.789e-5 / (1.225 × 1.87) = 7.8 µm.
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A dimensionless wall distance: y⁺ = yρu*/µ. It locates. the first mesh cell within the boundary layer structure: y⁺ < 5 is the viscous sublayer, 5-30 is the buffer layer, 30-300 is the log-law region.
Low-Re models resolve the viscous sublayer (need y⁺ ≈ 1). Wall-function models bridge the sublayer with empirical laws (need y⁺ = 30-300). Wrong y⁺ → wrong physics.
u* = √(τw/ρ) — a velocity scale derived from wall shear stress. It characterizes the turbulent boundary layer near the wall and is the key to the y⁺ definition.
Enough to span the boundary layer (~10-30 layers). With growth ratio 1.2 and first cell at y⁺=1, 15-20 layers typically cover the boundary layer for external flows.
This is normal — y⁺ varies with local velocity and geometry. Aim for average y⁺ in range, and accept some variation. Separation regions will have lower y⁺ than attached flow.
Yes — use pipe diameter as reference length and bulk velocity as U. The flat-plate analogy gives a reasonable initial estimate; check y⁺ after solving.