Y+ Calculator

How to use the Y+ wall distance calculator

What this calculator does

This calculator estimates the physical wall distance required to place the first CFD cell center at a chosen dimensionless wall distance, y+. It starts from freestream velocity, fluid density, dynamic viscosity, a boundary-layer length, and one empirical skin-friction approximation. It then computes Reynolds number, skin-friction coefficient, wall shear stress, friction velocity, and finally the wall distance. The result is a mesh-planning estimate for a smooth-wall, turbulent flat-plate-style approximation; it is not a substitute for a mesh-independence study, solver-specific near-wall guidance, roughness modeling, or post-processing the achieved y+ field.

When to use it

• Estimate a first-layer height before generating inflation or prism layers around an aerodynamic surface.
• Compare how different accepted skin-friction correlations change a preliminary near-wall spacing target.
• Check whether a proposed mesh is in the scale expected for a low-y+ resolved-wall approach or a higher-y+ wall-function approach.
• Create a reproducible workbook containing the current assumptions, results, and correlation comparison for a CFD setup review.

How to calculate

1. The calculator opens with a complete air-flow demonstration: 10 m/s, 1.205 kg/m³ density, 1.805e-5 Pa·s viscosity, a 1 m boundary-layer length, target y+ of 1, and the Schlichting correlation. The example results and Excel workbook are ready immediately.
2. Replace each demonstration value with your case data. Use the adjacent unit selectors when needed; changing an input unit converts the value already in that field rather than merely relabeling it.
3. Select the skin-friction approximation used by your engineering method. Read the headline Wall distance, then review Reynolds number, Skin-friction coefficient, Wall shear stress, and Friction velocity.
4. Use the Correlation comparison table to gauge sensitivity. Change the Wall-distance display unit to present the result in metres, millimetres, micrometres, or inches.
5. Select Download Excel to generate a validated workbook from the current canonical model. Reset clears the demonstration and all calculated content; export then remains unavailable until a complete valid state is entered again.

For physical context, NASA explains how the no-slip condition creates a velocity gradient inside the boundary layer near a surface and gives the same density – velocity – length – viscosity structure used for Reynolds number.

Input guide

Freestream velocity is a required positive decimal in m/s, km/h, or ft/s; 10 m/s is the example. Higher velocity raises Reynolds number and shear stress and usually reduces the wall distance. Do not enter a Mach number or include a unit symbol in the text field. Fluid density is required in kg/m³ or lb/ft³; 1.205 kg/m³ is the example. Use a density at the actual temperature and pressure, because density changes both Reynolds number and shear stress. Dynamic viscosity is required in Pa·s or cP; the example 1.805e-5 Pa·s may be entered in scientific notation. Do not confuse dynamic viscosity with kinematic viscosity.

Boundary-layer length is the required positive streamwise distance from the leading edge to the location being sized; the example is 1 m. It may be entered in m, cm, mm, or ft. A longer length raises Reynolds number and changes the selected correlation. Target dimensionless y+ is required and may be zero or positive; the example is 1. Wall distance scales directly with this target, so changing y+ from 1 to 30 multiplies the computed distance by 30 while the flow-derived quantities stay unchanged. Skin-friction approximation is required; the Schlichting option drives the initial result, while the table shows Prandtl, Granville, Kempf – Kármán, and Schultz – Grunov alternatives. Wall-distance display unit affects only presentation and workbook formatting, not the SI calculation.

Output guide

Wall distance is the estimated first-cell-center distance from the wall in the selected display unit. Zero occurs only when target y+ is zero. Reynolds number is dimensionless and measures the relative importance of inertial and viscous effects; NASA provides a detailed derivation of the Reynolds number relationship. Skin-friction coefficient is the dimensionless value returned by the selected correlation. Wall shear stress is reported in pascals, and Friction velocity is reported in m/s; both are intermediate estimates that connect the external flow to y+.

The three summary pills repeat Reynolds number, skin friction, and wall distance from the same model. In the Correlation comparison table, Approximation names the empirical relation, C_f is its coefficient, Shear stress and Friction velocity are the resulting intermediates, and Wall distance is the resulting mesh spacing. Large differences among rows signal correlation sensitivity, not numerical uncertainty quantified by this tool.

Worked example

With U = 10 m/s, ρ = 1.205 kg/m³, μ = 1.805e-5 Pa·s, and L = 1 m, Reynolds number is 1.205 × 10 × 1 ÷ 1.805e-5 = 667,590. Using Schlichting gives C_f = 0.004026. Wall shear stress is then 0.004026 × 0.5 × 1.205 × 10² = 0.2426 Pa, and friction velocity is √(0.2426 ÷ 1.205) = 0.4487 m/s. For target y+ = 1, wall distance is 1 × 1.805e-5 ÷ (1.205 × 0.4487) = 3.3386e-5 m, displayed as 0.03339 mm. These values match the first-open controls, results, table, and workbook checkpoints.

Learn more

Use fluid properties at the modeled state rather than generic room-temperature values. The NIST Chemistry WebBook thermophysical-property interface provides density and viscosity data for supported fluids and unit systems. After meshing, verify the achieved y+ distribution in your solver; SimScale's documentation identifies dimensionless wall distance and wall shear stress as CFD output fields that can be requested or reviewed.