Y+ Calculator
Calculate dimensionless wall distance for CFD analysis and boundary layer modeling
Calculate Y+ Wall Distance
Fluid velocity far from the boundary
Default: 1.205 kg/m³ (air at 15°C)
Default: 0.01805 mPa·s (air at 15°C)
Characteristic length of the surface
Target dimensionless wall distance
Approximation method for skin friction coefficient
Y+ Calculation Results
Y+ Formula: y+ = y × ρ × u* / μ
Wall Distance: y = y+ × μ / (ρ × u*)
Friction Model: Schlichting: [2log₁₀(Re) - 0.65]^(-2.3)
Y+ Category: Buffer Layer
Buffer Layer: Transition region between viscous and log-law regions
Y+ Range Guidelines
Example Calculation
Air Flow Over Flat Plate
Freestream Velocity: 10 m/s
Fluid: Air (ρ = 1.205 kg/m³)
Dynamic Viscosity: 0.01805 mPa·s
Boundary Layer Length: 1 m
Target y+: 1
Step-by-Step Solution
1. Re = (1.205 × 10 × 1) / 0.01805 = 667,590
2. Cf = [2log₁₀(667,590) - 0.65]^(-2.3) = 0.004026
3. τw = 0.004026 × 0.5 × 1.205 × 10² = 0.2426 Pa
4. u* = √(0.2426 / 1.205) = 0.4487 m/s
5. y = 1 × 0.01805 / (1.205 × 0.4487) = 0.033 mm
Friction Models
Schlichting
[2log₁₀(Re) - 0.65]^(-2.3)
Prandtl (1927)
0.074 × Re^(-0.2)
Granville (1977)
Complex function with log terms
Kempf-Karman
0.055 × Re^(-0.182)
Boundary Layer Regions
Viscous Sublayer
Linear velocity profile
Buffer Layer
Transition region
Log-Law Region
Logarithmic profile
Outer Layer
Wake region
CFD Applications
Mesh sizing for boundary layer
Wall function implementation
Turbulence model selection
Heat transfer calculations
Understanding Y+ and Boundary Layer Theory
What is Y+?
Y+ (y-plus) is a dimensionless wall distance parameter crucial in CFD analysis. It represents the distance from the wall normalized by viscous length scale, helping determine appropriate mesh sizing and turbulence modeling strategies.
Boundary Layer Structure
- •Viscous Sublayer: Dominated by viscous forces
- •Buffer Layer: Transition between viscous and inertial
- •Log-Law Region: Turbulent shear stress dominates
- •Outer Layer: Wake region with reduced gradients
Mathematical Formulation
y+ = y × ρ × u* / μ
u* = √(τw / ρ)
τw = Cf × 0.5 × ρ × U²
- y: Physical distance from wall (m)
- ρ: Fluid density (kg/m³)
- u*: Friction velocity (m/s)
- μ: Dynamic viscosity (Pa·s)
- τw: Wall shear stress (Pa)
- Cf: Skin friction coefficient (-)
CFD Best Practice: Use y+ < 1 for near-wall modeling or 30 < y+ < 300 for wall functions.