Y+ Calculator

Y+ is a non-dimensional wall distance that describes how far the first mesh node sits from a solid wall, scaled by the local flow and fluid properties. It is defined as y⁺ = (ρ · U_fric · Δs) / μ. Y+ determines whether the boundary layer is resolved directly (low Y+) or modeled via wall functions (high Y+), and choosing the right value is critical for accurate turbulence predictions.

The appropriate Y+ depends on your turbulence modeling approach. For wall-resolving methods (e.g. Spalart-Allmaras or k-ω SST in low-Re mode), aim for Y+ ≤ 1. For wall-function approaches (standard k-ε, high-Re k-ω), a Y+ between 30 and 300 is typically recommended. Always check the guidelines of your specific solver and turbulence model.

The calculator uses the Schlichting flat-plate turbulent boundary layer correlation: Reₓ = ρ·U∞·L/μ, Cf = 0.026·Reₓ^(−1/7), τ_wall = Cf·ρ·U∞²/2, U_fric = √(τ_wall/ρ), and finally Δs = y⁺·μ/(U_fric·ρ). This correlation is valid for Reynolds numbers up to approximately 10⁹.

The first cell height controls how accurately the near-wall velocity gradient — and therefore wall shear stress, heat transfer, and separation — are captured. Too coarse a first cell will yield inaccurate wall fluxes; too fine can increase cell count dramatically and cause poor aspect ratios. Getting Δs right from the outset saves both compute time and post-simulation corrections.

The defaults correspond to dry air at sea level and room temperature (20°C): density ρ = 1.225 kg/m³ and dynamic viscosity μ = 1.81×10⁻⁵ kg/m·s. For other fluids or conditions, enter the appropriate values — for example, water at 20°C uses ρ ≈ 998 kg/m³ and μ ≈ 1.002×10⁻³ kg/m·s.

This calculator uses flat-plate theory to estimate the wall spacing, which provides a good starting approximation for most external aerodynamic and hydrodynamic cases. For highly curved surfaces, internal flows, or regions with strong pressure gradients and separation, the actual local skin friction may differ. Treat the result as an initial estimate and refine through mesh sensitivity studies.

Enter the characteristic dimension of your geometry relevant to the boundary layer development — for example, the chord length of an airfoil, the length of a flat plate, or the diameter of a cylinder. For a conservative estimate (smallest Δs), use the full body length; for a local estimate near the leading edge, use a shorter length.

Yes, with caution. For internal flows, set the reference length to the hydraulic diameter (or pipe diameter) and ensure the Reynolds number falls within a turbulent regime. The Schlichting flat-plate correlation is not strictly derived for internal flows, so the result should be used as a first approximation. Many CFD practitioners use it as a practical starting point before running a grid sensitivity study.