Y+ Calculator for CFD: Wall Distance, First Cell Height & Inflation Layers

y+ (y-plus) is the dimensionless wall distance, defined as y+ = u_tau * y / nu, where u_tau is the friction velocity, y is the distance from the wall to the first cell center, and nu is the kinematic viscosity. It tells you which region of the boundary layer your first mesh cell sits in: the viscous sublayer (y+ ~ 1), the buffer layer (y+ ~ 5-30), or the log-law region (y+ ~ 30-300). Turbulence models make assumptions about this placement, so getting y+ right is one of the most important meshing decisions in a CFD simulation.

Use y+ = u_tau * y / nu. For example, with friction velocity u_tau = 0.5 m/s, wall distance y = 1e-4 m (0.1 mm), and kinematic viscosity nu = 1.5e-5 m^2/s (air at about 20 C), y+ = 0.5 * 0.0001 / 0.000015 = 3.333. If you do not know u_tau directly, estimate it from wall shear stress as u_tau = sqrt(tau_w / rho), or use the correlation estimator on this page, which computes Reynolds number, skin friction coefficient, tau_w, and u_tau from velocity, density, viscosity, and a reference length.

As guidance (not an absolute rule): aim for y+ ~ 1 for k-omega SST, LES, or any wall-resolved simulation where the viscous sublayer is resolved directly. Use y+ between 30 and 300 for k-epsilon with standard wall functions, which assume the first cell lies in the log-law region. The buffer layer (roughly y+ 5-30) should be avoided when possible because neither the viscous-sublayer nor the log-law assumptions hold there. Always confirm with a mesh independence study on your actual case.

Rearrange the definition: y = y+ * nu / u_tau, equivalently y = y+ * mu / (rho * u_tau). With y+ = 1, air at 20 C (rho = 1.204 kg/m^3, mu = 1.8252e-5 Pa s), a freestream velocity of 10 m/s and a 1 m plate, the correlations give u_tau = 0.4505 m/s, so the first-cell-center distance is y = 1 * 1.8252e-5 / (1.204 * 0.4505) = 3.365e-5 m (0.03365 mm). Enter this value as the inflation-layer first height (or half the cell height in solvers that report cell centers, e.g. Fluent).

For external flat-plate flow: laminar Blasius cf_x = 0.664*Re_x^-1/2, the turbulent power-law Cf = 0.0592*Re_x^-1/5 (valid 5e5 < Re < 3e7), and the Schlichting correlation Cf = (2*log10(Re)-0.65)^-2.3 (valid Re < 1e9). For internal pipe flow: laminar Fanning Cf = 16/Re (exact) and the turbulent Blasius Cf = 0.079*Re^-1/4 (smooth pipe, 3e3 < Re < 1e5). Wall shear stress is tau_w = 0.5*Cf*rho*U^2 and friction velocity is u_tau = sqrt(tau_w/rho). All are zero-pressure-gradient, smooth-wall estimates; the page labels the exact correlation used.

A common setup is a growth ratio r of 1.1-1.3 (1.2 is typical). The stack height for n layers is total = y1*(r^n - 1)/(r - 1), and the layers needed to cover a target height H is n = ln(1 - H*(1-r)/y1)/ln(r), rounded up. Cover the boundary-layer thickness delta (estimated on this page, e.g. 0.37*L*Re^-1/5 for a turbulent flat plate) with at least 10-15 layers. The inflation layer calculator in section 3 does this math for you and lists every layer height.

The y+ formula uses y = distance from the wall to the first cell CENTER. In solvers such as ANSYS Fluent, when you specify a first-layer height in the mesher, the reported y+ is computed at the cell centroid, so set the first inflation layer height to 2*y (the full cell spans roughly 0 to 2*y). Other meshers and codes may differ, so check whether your solver reports wall distance at the centroid or at the face before applying the number.

No. This y+ tool is the near-wall specialist: it computes the dimensionless wall distance, estimates friction velocity, and sizes inflation layers. For Reynolds number, flow regime classification, and hydraulic diameter, use the Reynolds number calculator. For Darcy friction factor from the Colebrook equation in rough pipes, use the friction factor calculator. The three tools are complementary: y+ consumes Re and friction data produced by them.

No. All calculations run locally in your browser with JavaScript. There are no external requests, no accounts, and no data leaves your device.

Because correlations are estimates: they assume a smooth wall, zero pressure gradient, and fully developed or flat-plate flow. Real geometries have pressure gradients, separation, curvature, and roughness that shift the local wall shear. The standard workflow is: estimate with a tool like this, run the simulation, check the actual y+ field in the solver, and adjust the mesh (mesh independence study). Treat the correlation result as a starting point, not a guarantee.

Wall distance accepts m, mm, and micrometers; velocity in m/s; density in kg/m^3; viscosity as dynamic (Pa s) or kinematic (m^2/s); length in m or mm. All internal math is done in SI units, and results are shown in both metres and millimetres where it helps.

y+ uses the friction velocity u_tau = sqrt(tau_w/rho) and the kinematic viscosity, so it is tied to the actual wall shear stress. y* (y-star) is a scalable-wall-function quantity used by some solvers (e.g. CFX/Fluent scalable wall functions) that replaces u_tau with a velocity scale based on turbulent kinetic energy, u* = C_mu^1/4 * sqrt(k). For most practical meshing decisions, size your first cell with y+ as computed here.