Y+ Calculator

The y+ value is a dimensionless distance used in CFD to define how close the first mesh node is to a solid boundary. The calculation begins by determining the Reynolds number using fluid density, freestream velocity, characteristic length, and dynamic viscosity. Next, the skin friction coefficient ($C_f$) is evaluated via empirical correlations based on the chosen model (such as flat plate or pipe flows). This leads to the calculation of wall shear stress and friction velocity, ultimately allowing the tool to compute the optimal physical wall distance for your target y+ value.

Consider an external aerodynamic simulation with air flowing over a flat plate. Assume a fluid density ($ ho$) of 1.225 kg/m³, a dynamic viscosity ($\mu$) of 1.789 x 10⁻⁵ Pa·s, and a freestream velocity ($u$) of 25 m/s over a characteristic length ($L$) of 1.0 meter. First, calculate the Reynolds number: Re = (1.225 * 25 * 1.0) / (1.789 x 10⁻⁵) = 1,710,397. Using a standard flat plate turbulent correlation, the skin friction coefficient ($C_f$) evaluates to approximately 0.0031. The wall shear stress ($ au_w$) is then 0.5 * 0.0031 * 1.225 * 25² = 1.187 Pa. The friction velocity ($u_ au$) becomes √(1.187 / 1.225) = 0.985 m/s. If your turbulence model requires a target y+ of 1.0, the required wall distance ($y$) is (1.0 * 1.789 x 10⁻⁵) / (1.225 * 0.985) = 1.48 x 10⁻⁵ meters, or about 14.8 micrometers.

Always align your target y+ value with the specific turbulence model requirements of your solver; for instance, resolving the viscous sublayer with standard k-epsilon models typically demands a y+ of approximately 1, whereas wall-function approaches generally require y+ values between 30 and 300. Verify your fluid property inputs at operating temperatures to prevent severe meshing errors, and always perform a mesh sensitivity study to ensure simulation results remain independent of grid resolution.