y+ Calculator (First Cell Height for CFD)
Estimate the wall distance of the first mesh node needed to reach a target y+ — for wall-resolved (y+ ≈ 1) or wall-function (y+ ≈ 30–300) meshes.
Formula and correlation used
By default this calculator uses the Schlichting turbulent flat-plate skin-friction correlation, the same relation used by the widely cited Pointwise/Cadence y+ calculator. You can switch to the simpler 0.026 / Re1/7 power law; the two typically differ by 5–15% in y, which is well inside the uncertainty of the estimate. The friction velocity uτ comes from the wall shear stress, and the wall distance y follows from the definition y⁺ = ρ uτ y / μ.
Node vs cell height: the result y is the distance from the wall to the first grid point. In a cell-centred finite-volume solver (Fluent, STAR-CCM+, OpenFOAM) the y+ is evaluated at the cell centroid, so the first cell height should be about 2y. The calculator shows both.
Worked example
Air at 15 °C (ρ = 1.225 kg/m³, μ = 1.789×10⁻⁵ Pa·s) flows at U = 10 m/s over a 1 m plate. Re = 1.225 × 10 × 1 / 1.789×10⁻⁵ = 6.85×10⁵. Schlichting gives Cf = (2 × 5.8355 − 0.65)^−2.3 = 0.00401. Then τw = 0.5 × 0.00401 × 1.225 × 10² = 0.245 Pa, uτ = √(0.245 / 1.225) = 0.448 m/s, and for y⁺ = 1: y = 1.789×10⁻⁵ / (1.225 × 0.448) = 3.26×10⁻⁵ m (32.6 µm). A cell-centred mesh would use a first cell height of about 65 µm.
Reference table (Schlichting, L = 1 m)
| Fluid | U (m/s) | Re (L = 1 m) | Cf | y for y+ = 1 | y for y+ = 30 |
|---|---|---|---|---|---|
| Air | 5 | 3.424e+05 | 0.00456 | 61.17 µm | 1.835 mm |
| Air | 10 | 6.847e+05 | 0.00401 | 32.62 µm | 0.979 mm |
| Air | 30 | 2.054e+06 | 0.00331 | 11.96 µm | 0.359 mm |
| Air | 100 | 6.847e+06 | 0.00273 | 3.95 µm | 0.119 mm |
| Water | 0.5 | 4.981e+05 | 0.00425 | 43.56 µm | 1.307 mm |
| Water | 2 | 1.992e+06 | 0.00333 | 12.30 µm | 0.369 mm |
| Water | 5 | 4.981e+06 | 0.00287 | 5.30 µm | 0.159 mm |
Choosing a target y+
- y⁺ ≈ 1 — wall-resolved low-Reynolds models (k-ω SST, Spalart-Allmaras without wall functions), needed for separation, heat transfer and transition. Use 10–20 inflation layers with a growth ratio of 1.1–1.2.
- y⁺ ≈ 30–300 — standard wall functions with k-ε. Keep the first cell inside the log-law region; avoid y⁺ between 5 and 30 (buffer layer).
- All-y⁺ treatments — modern solvers blend the two, but y⁺ ≈ 1 remains the safest choice for accuracy.
Limitations
The correlation assumes a zero-pressure-gradient, fully turbulent flat plate. Real geometries have stagnation points, acceleration and separation where local y⁺ varies widely, so treat the result as a starting estimate and check the y⁺ contour after the first solution. Choose L as the characteristic length of the body (chord, plate length, pipe diameter for internal flow).
Frequently asked questions
Which skin friction formula does this y+ calculator use?
By default the Schlichting turbulent flat-plate correlation Cf = (2 log10 Re − 0.65)^−2.3, valid for Re below 10^9. You can switch to the power law Cf = 0.026 / Re^(1/7).
What y+ should I use for k-omega SST?
Aim for y+ ≈ 1 at the first cell centre for wall-resolved SST. SST tolerates higher values with automatic wall treatment, but accuracy for separation and heat transfer drops.
Is the result the first cell height or the cell centre distance?
The result y is the wall distance at which y+ reaches the target. For cell-centred solvers the first cell height should be roughly 2y, which the calculator also displays.
What reference length should I use?
Use the length over which the boundary layer develops: plate length, airfoil chord, or vehicle length. For pipes, the hydraulic diameter is a common choice.
Why is my actual y+ different from the estimate?
The correlation is for a flat plate. Pressure gradients, curvature, and local velocity changes alter wall shear, so check the computed y+ field and refine locally.