Calculate y+ for CFD, or the first cell height (wall to cell center) for a target y+, from flow speed, wall shear, Cf or friction velocity.
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Y+ Formula
Where the friction velocity is:
And the first cell-center distance for a target y+ is:
- y+ โ dimensionless wall distance
- y โ distance from the wall to the first cell center (m)
- utau โ friction velocity (m/s)
- tauw โ wall shear stress (Pa)
- rho โ fluid density (kg/mยณ)
- nu โ kinematic viscosity (mยฒ/s)
- U โ freestream or reference flow speed (m/s)
- Cf โ local skin friction coefficient
For the first-layer estimate, Cf comes from smooth flat-plate correlations: local Cf = 0.664/โReโ for laminar flow and local Cf โ 0.0592/Reโ0.2 for turbulent flow, with Reโ = Ux/ฮฝ and x measured from the plate leading edge. The original laminar 1.328 coefficient was a plate-average drag coefficient, not a local wall-shear coefficient. These smooth, attached, incompressible, approximately zero-pressure-gradient correlations are not universal geometry models. The turbulent correlation has the stated range 5ร10โต < Reโ < 10โท; extrapolations are flagged. Auto assumes transition at Reโ = 500,000, rather than predicting it. These are first-cell estimates only. After running the simulation, recompute y+ from the solved wall shear stress and refine the mesh if needed.
Reference Values
Typical y+ guidance depends on the solver and wall treatment; these ranges are not mesh-quality pass/fail criteria:
| Approach | Target y+ | Notes |
|---|---|---|
| Wall-resolved (low-Re, SST k-ฯ, Spalart-Allmaras) | y+ < 1 | Often targets the viscous sublayer; also verify boundary-layer resolution and solver requirements. |
| Enhanced / blended wall treatment | Solver-specific | Blended/scalable methods differ; consult the selected solver treatment. |
| Standard wall functions | 30 โค y+ โค 300 | Log-law region. |
| Buffer layer | 5 < y+ < 30 | May be unsuitable for conventional wall functions; blended treatments can differ. |
Typical fluid properties, selectable under Fluid (air at 15 ยฐC; fresh water and seawater at 20 ยฐC; light oil is an example only). Use measured or specified properties for your simulation:
| Fluid | ฮฝ (mยฒ/s) | ฯ (kg/mยณ) |
|---|---|---|
| Air | 1.5 ร 10โปโต | 1.225 |
| Water | 1.004 ร 10โปโถ | 998 |
| Seawater | 1.05 ร 10โปโถ | 1025 |
| Light oil | 1.0 ร 10โปโด | 870 |
Example and FAQ
Example. A smooth flat plate at x = 1 m with U = 30 m/s, ฮฝ = 1.5e-5 mยฒ/s and target y+ = 1: Reโ = 2.0 ร 10โถ. Local turbulent Cf โ 0.00325174, utau โ 1.209662 m/s and y โ 1.240016 ร 10โปโต m = 0.012400 mm. Full orthogonal first-layer thickness is approximately 0.024800 mm. An airfoil pressure gradient can invalidate this flat-plate estimate.
Is y the first cell height or the cell-center distance? y is the distance from the wall to the first cell center. For an orthogonal near-wall prism with its center halfway through the thickness, the full first-layer thickness is about 2y. Check the mesherโs convention.
Should I divide by 2 for a half-channel? No. y is measured from the wall, regardless of channel symmetry.
My solved y+ differs from the estimate. Expected. Flat-plate Cf is a starting point. Choose Check y+ from friction velocity with solved utau = โ(|ฯw|/ฯ), or choose Cell-center distance from wall shear for a new target distance. Verify solved y+ and adjust the mesh.
What about pipe flow? Choose Cell-center distance from known Cf or from wall shear; the flat-plate estimate is not a pipe model. Use a pipe correlation appropriate to its Reynolds number, roughness and development. Cf is defined by ฯw/(ฯUยฒ/2), so a Darcy friction factor must be divided by four before entering it. The smooth turbulent Blasius example Cf โ 0.079ยทRe-0.25 is a conditional estimate, not a universal pipe formula.
