y⁺ wall distance calculator

When meshing geometry for a CFD analysis, it is often useful to estimate the wall distance to obtain a certain y+. With the calculator below you can calculate this wall distance.

Formulas used to calculate the wall distance from y⁺

The Reynolds number for a given free stream velocity U_∞ is:

$${Re = \frac{\rho \cdot U_{\infty} \cdot L_{boundary\,layer}}{\mu}}$$

The Schlichting formula to obtain the skin friction coefficient C_f is used in this calculator and is valid for Re_x < 10⁹:

$${C_f = [ 2 \cdot log_{10}(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{voor} \quad Re_x < \; 10^9}$$

The wall shear stress is calculated from the skin friction coefficient C_f:

$${\tau_w = C_f \cdot \frac{1}{2} \, \rho \, U_{\infty}^2}$$

The friction velocity u^* is a function of the fluid density and the wall shear stress:

$${u^* = \sqrt{\frac{\tau_w}{\rho}}}$$

And eventually the wall distance for a desired y⁺ is:

$${y = \frac{y^+ \mu}{\rho \, u^*}}$$

y⁺ wall distance calculator

The predefined values for density and dynamic viscosity in the calculator are for air at p = 1 atm and T = 20°C.
The density and dynamic viscosity for water at the same conditions are respectively 998.21 kg/m³ and 1.002e-3 Pa.s.

Input

Free stream velocity U:

[ m/s ]

Fluid density ρ:

[ kg/m³ ]

Dynamic viscosity μ:

[ Pa.s ]

Reference length L:

[ m ]

Desired y⁺:

Output

Reynolds number Re:

C_f:

τ_w:

[ N/m² ]

u^*:

[ m/s ]

Wall distance y:

[ mm ]

Calculate