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 checks y⁺ before meshing because the wrong first cell height either wastes computation or gives the wrong wall treatment. This calculator replaces manual spreadsheets and gives a fast first estimate for air, water, and other common flows, so you can set a wall-distance target before you build the prism layers.
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: 0.0078 mm, Re = 3.4M, u* = 1.87 m/s
Air at 50 m/s over a 1 m 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* = √(4.3 / 1.225) = 1.87 m/s. y = 1 × 1.789e-5 / (1.225 × 1.87) = 7.8 µm = 0.0078 mm.
Use y⁺ to decide whether the first cell sits in the viscous sublayer or in the wall-function region. That interpretation matters more than the number itself, because the same y⁺ target can imply very different physical cell heights in air, water, or high-speed flow.
The flat-plate estimate is a starting point, not a final mesh rule. Real geometries need local checks after the solver runs, especially around separation points, curvature, and changing Reynolds number.
If you are using k-ω SST, aim for y⁺ near 1. If you are using a wall-function approach, aim for the range your model expects and keep layer growth smooth enough that the near-wall grid does not collapse.
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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.