Y+ (y-plus) Calculator - First Cell Wall Distance for CFD
Enter your flow conditions and desired y+ value to find the first cell height your CFD mesh needs near a wall. Or enter an existing cell height to see the y+ it produces. The calculator uses flat-plate boundary layer theory (Schlichting correlation) to estimate the friction velocity and wall shear stress, then converts between y+ and physical wall distance. Switch between air and water presets, or enter custom fluid properties.
Formula
Worked example
Air at 20 C (rho = 1.225 kg/m3, mu = 1.789e-5 Pa·s), U = 10 m/s, L = 1 m. Re = 1.225 x 10 x 1 / 1.789e-5 = 684,850 (turbulent). Cf = 0.0592 x 684850^(-0.2) = 0.00377. tau_w = 0.5 x 0.00377 x 1.225 x 100 = 0.231 Pa. u_tau = sqrt(0.231 / 1.225) = 0.434 m/s. For y+ = 1: y = 1 x 1.789e-5 / (1.225 x 0.434) = 3.36e-5 m (0.0336 mm).
What is y+ and why does it matter?
In computational fluid dynamics, y+ (y-plus) is the dimensionless distance from a solid wall to the centre of the first mesh cell. It is defined as y+ = (rho * u_tau * y) / mu, where rho is the fluid density, u_tau is the friction velocity at the wall, y is the physical distance, and mu is the dynamic viscosity. The value of y+ tells you which region of the turbulent boundary layer your first mesh cell sits in: the viscous sublayer (y+ < 5), the buffer layer (5 < y+ < 30), or the log-law region (y+ > 30). This matters enormously because most turbulence models are calibrated to one of these regions and will give unreliable results if the mesh does not match.
Viscous sublayer, buffer layer, and log-law region
The boundary layer near a wall is divided into three layers. The viscous sublayer (y+ < 5) is dominated by molecular viscosity and the velocity profile is linear: u+ = y+. Turbulence models designed for this region, such as SST k-omega and Spalart-Allmaras, need a very fine first cell (y+ close to 1). The buffer layer (5 < y+ < 30) is a transition zone where neither the linear nor the log-law profile is a good fit. Placing the first cell here is the worst choice: the viscous sublayer approximation overestimates shear, and the log-law is not yet valid. The log-law region (y+ 30-300) follows the law of the wall: u+ = (1/kappa) * ln(y+) + B. Standard wall functions (used with k-epsilon and RSM) assume the first cell sits in this region.
How the first cell height is calculated
This calculator uses flat-plate boundary layer theory to estimate the wall conditions. First it computes the Reynolds number Re = rho * U * L / mu. Then it applies the Schlichting skin-friction correlation to get the coefficient Cf (Blasius laminar formula below Re = 5e5, the 1/5-power turbulent law from Re = 5e5 to 1e7, and the 1/7-power formula above that). Wall shear stress follows as tau_w = 0.5 * Cf * rho * U^2, and friction velocity is u_tau = sqrt(tau_w / rho). Finally, the desired first cell height is back-calculated as y = (y+ * mu) / (rho * u_tau). These are estimates based on a canonical turbulent flat plate: actual near-wall conditions depend on your specific geometry, and CFD iteration is typically needed to verify the mesh.
Practical meshing tips
For wall-resolved approaches target y+ between 0.5 and 1 at the first cell. Use a geometric growth ratio of 1.1 to 1.3 for the inflation layers, and add enough layers to cover the entire boundary layer thickness (typically 15-30 layers). For wall-function approaches, keep y+ between 30 and 300 and avoid placing any cell in the buffer layer. After your first CFD run, visualize the y+ distribution across the wall: refine locally where y+ is too low or coarsen where it is unnecessarily fine. The SimScale, OpenFOAM, and ANSYS post-processors all have built-in y+ surface plots for this.
Y+ requirements by turbulence model
| Turbulence model | Wall treatment | Recommended y+ | Notes |
|---|---|---|---|
| SST k-omega | Low-Re / wall-resolved | ~1 | Most common choice for aerodynamics and external flow |
| Spalart-Allmaras | Wall-resolved | ~1 | Widely used for aerospace; requires y+ < 5 |
| k-epsilon (standard) | Standard wall functions | 30-300 | Avoid y+ < 11 and y+ > 300 |
| k-epsilon (realizable/RNG) | Standard wall functions | 30-300 | Better rotating flows than standard k-eps |
| Reynolds Stress Model | Standard wall functions | 30-300 | High-fidelity anisotropic turbulence |
| Enhanced Wall Treatment (EWT) | Blended | <5 or 30-300 | Fluent blended approach; avoids buffer layer issues |
| Scalable Wall Functions | Robust wall functions | >11.225 | OpenFOAM; clips to log-law when mesh is too fine |
| LES (wall-resolved) | No wall model | <1 | Requires extremely fine near-wall mesh |
| DES / DDES | RANS near wall | ~1 | LES away from walls, RANS in boundary layer |
Recommended y+ ranges for common RANS and LES turbulence models in ANSYS Fluent, OpenFOAM, and similar solvers.
Frequently asked questions
What y+ value should I use for SST k-omega?
The Shear Stress Transport (SST) k-omega model is wall-resolved, meaning it is designed to compute the flow all the way through the viscous sublayer rather than relying on a wall function. To do this correctly it needs y+ approximately equal to 1 (and no greater than about 5) at the first cell. If you use SST k-omega with y+ in the log-law region (30-300) you are forcing it to use a wall function hybrid mode, which reduces accuracy, especially for separated flows and adverse pressure gradients.
What is the buffer layer and why should I avoid it?
The buffer layer spans roughly 5 < y+ < 30. In this zone the flow transitions between the viscously dominated sublayer and the log-law region. Neither the linear sublayer model (u+ = y+) nor the log-law (u+ = (1/0.41) * ln(y+) + 5.2) accurately describes the velocity profile here. Placing your first cell in the buffer layer means neither the near-wall model nor the wall-function model is valid, which leads to errors in predicted wall shear stress, heat transfer, and skin friction. Always design your mesh to have y+ either below 5 or above 30.
Why does the calculator use flat-plate theory?
Flat-plate boundary layer theory (the Schlichting correlations) provides a geometry-independent estimate of friction velocity from only velocity, fluid properties, and a reference length. In reality, curvature, adverse pressure gradients, separation, and three-dimensional effects all alter the local y+ significantly from the flat-plate prediction. This is why the first-cell height computed here is a starting estimate, not a final answer. You will almost always need to inspect the y+ field after your first simulation run and adjust the mesh accordingly.
What is the difference between vertex-based and cell-centre solvers?
In vertex-based solvers (such as ANSYS CFX), the flow variable is stored at mesh nodes. The first mesh node sits at distance y from the wall. In cell-centred solvers (such as ANSYS Fluent and OpenFOAM), the variable is stored at the cell centre. If the first cell height (layer thickness) is delta, the cell centre is at y = delta / 2 from the wall. For a target y+ = 1 in a cell-centred solver you therefore need the first cell height to be twice the y that this calculator returns. This detail is important when setting up inflation layers in meshing tools.
How do I apply this to internal flow or a duct?
For internal flow, use the hydraulic diameter (Dh = 4 * cross-sectional area / wetted perimeter) as the reference length, and the bulk mean velocity as the freestream velocity. The Reynolds number and skin-friction estimate will then reflect duct flow conditions. For circular pipes, Dh equals the inner diameter. The recommended y+ ranges by turbulence model are the same as for external flow.
What growth ratio should I use for inflation layers?
A geometric growth ratio between 1.1 and 1.3 is standard for inflation layers. Smaller ratios (1.1-1.15) give smoother transitions and are preferable for high-accuracy RANS and LES. Larger ratios (1.2-1.3) reduce the total cell count and are acceptable when you only need moderate accuracy away from the wall. Add enough layers to cover the entire boundary layer: a rule of thumb is to stop the inflation when the layer thickness exceeds the boundary layer thickness estimated as delta ~ 0.37 * L * Re^(-1/5) for turbulent flow.