Y-Plus (y⁺) Calculator
Calculate CFD first cell height from y⁺ for turbulence-resolving meshes. Compute Reynolds number, skin friction, and wall distance for boundary layer meshing.
About This Calculator
The Y-Plus (y⁺) Calculator is an essential tool for computational fluid dynamics (CFD) engineers and researchers who need to determine the appropriate first cell height for turbulence-resolving meshes. The dimensionless wall distance y⁺ is the most critical parameter for ensuring accurate boundary layer resolution in CFD simulations, directly influencing the prediction of skin friction drag, heat transfer, and flow separation.
The calculator uses the Schlichting skin-friction correlation for turbulent flow over a smooth flat plate: Cf = 0.027 / Re1/7, valid for Reynolds numbers below 10⁹. From the skin friction coefficient, the wall shear stress τw = ½ρU²Cf is computed, followed by the friction velocity uτ = √(τw/ρ). The first cell height is then y = (y⁺ × μ) / (ρ × uτ). The bar chart visualizes the required wall distance across five standard y⁺ targets (1, 5, 30, 100, 300), helping you select the appropriate mesh resolution for your turbulence model.
The calculator provides fluid presets for air (ρ = 1.225 kg/m³, μ = 1.81×10⁻⁵ kg/(m·s)) and water (ρ = 998 kg/m³, μ = 1.002×10⁻³ kg/(m·s)) at 20°C, or you can enter custom fluid properties for other working fluids. The flow regime indicator classifies the flow as laminar (Re < 2300), transitional (2300 < Re < 4000), or turbulent (Re > 4000) based on the computed Reynolds number. For external aerodynamics, use the streamwise length from the leading edge as the characteristic length; for internal flows, use the hydraulic diameter.
Regional Notes
Global: The y⁺ calculation is independent of geographic region since it is based on universal fluid dynamics principles. The fluid properties presets use SI units (kg/m³, kg/(m·s), m/s, m) which are standard in CFD practice worldwide, including in India (IS:696), the US, and the UK. The Schlichting correlation and y⁺ definition follow the same formulation in all regions per the standard CFD literature (Schlichting & Gersten, "Boundary-Layer Theory"; Wilcox, "Turbulence Modeling for CFD").
Frequently Asked Questions
What is y⁺ (y-plus) in CFD?
Y⁺ (y-plus) is a dimensionless wall distance used in computational fluid dynamics (CFD) to describe the spacing of the first grid cell from a wall boundary. It is defined as y⁺ = (y × u_τ) / ν, where y is the absolute distance from the wall, u_τ is the friction velocity, and ν is the kinematic viscosity. A y⁺ value of approximately 1 is required for resolving the viscous sublayer in turbulence modeling, while values between 30 and 300 are acceptable for wall function approaches.
What y⁺ value should I use for my CFD simulation?
For low-Reynolds-number turbulence models (e.g., k-omega SST, Spalart-Allmaras), aim for y⁺ ≈ 1 to resolve the viscous sublayer. For high-Reynolds-number wall functions (e.g., standard k-epsilon), target y⁺ between 30 and 300 to place the first cell in the log-law region. For LES and DES simulations, y⁺ ≈ 1 is typically required for accurate wall-resolved results.
How is the first cell height calculated from y⁺?
The first cell height y is calculated as y = (y⁺ × μ) / (ρ × u_τ), where u_τ = √(τ_w/ρ) is the friction velocity. The wall shear stress τ_w is determined from the skin friction coefficient: τ_w = ½ × ρ × U² × C_f. For turbulent flat plate flow, the Schlichting correlation C_f = 0.027/Re^(1/7) is used, valid for Reynolds numbers below 10⁹.
What is the Schlichting skin-friction formula?
The Schlichting skin-friction formula for turbulent flow over a smooth flat plate is C_f = 0.027 / Re^(1/7), where Re is the Reynolds number based on the boundary layer length. This empirical correlation is valid for Reynolds numbers up to 10⁹ and is widely used in CFD y⁺ estimation tools. Alternative correlations include the Prandtl-Schlichting formula for higher Reynolds numbers.
What fluid properties do I need for y⁺ calculation?
You need the freestream velocity (U), fluid density (ρ), dynamic viscosity (μ), and the characteristic boundary layer length (L). For air at sea level and 20°C, density is 1.225 kg/m³ and dynamic viscosity is 1.81×10⁻⁵ kg/(m·s). For water at 20°C, density is 998 kg/m³ and viscosity is 1.002×10⁻³ kg/(m·s). The calculator provides presets for both fluids.
How does Reynolds number affect my mesh requirements?
Higher Reynolds numbers result in thinner boundary layers, requiring smaller first cell heights to achieve the same y⁺ value. For example, at Re = 10⁶, achieving y⁺ = 1 may require a first cell height on the order of 10⁻⁵ m, while at Re = 10⁸, the required height may be 100 times smaller. Always check your mesh growth rate (typically 1.1–1.2) and number of prism layers to ensure adequate boundary layer resolution.
What is the difference between y⁺ and y* in CFD?
Y⁺ (y-plus) and y* (y-star) are both dimensionless wall distances. Y⁺ is based on the friction velocity u_τ = √(τ_w/ρ) from the wall shear stress, while y* uses an alternative velocity scale based on the turbulent kinetic energy at the near-wall cell. In most practical cases, y⁺ and y* yield similar values, but y* is considered more robust for flows with separation or strong pressure gradients. Most commercial CFD codes report both values.
Can I use this calculator for external aerodynamics?
Yes, this calculator is ideal for external aerodynamics applications such as airfoil, wing, and vehicle body simulations. The flat plate boundary layer assumption provides a good first estimate for the first cell height. For internal flows like pipes and ducts, use the hydraulic diameter as the characteristic length. The calculator is suitable for aerospace, automotive, wind energy, and marine CFD applications.