๐ CFD yโบ & First Layer Cell Height Calculator
Accurately estimate wall distance $y$, first prism layer thickness $\Delta y_1$, skin friction coefficient $C_f$, wall shear stress $\tau_w$, and boundary layer thickness $\delta$ for ANSYS Fluent, OpenFOAM, STAR-CCM+, and SU2.
๐ Boundary Layer & Near-Wall Mesh Structure
Interactive Canvas (Viscous sublayer • Buffer • Log-law • First cell centroid)๐ Flow & Mesh Parameters
Key Formulation:
$$Re_L = \frac{\rho U_\infty L}{\mu} = \frac{U_\infty L}{\nu}$$ $$\tau_w = \frac{1}{2} C_f \rho U_\infty^2 \quad \Longrightarrow \quad u_\tau = \sqrt{\frac{\tau_w}{\rho}}$$ $$y = \frac{y^+ \nu}{u_\tau} \quad \Longrightarrow \quad \Delta y_1 = 2 y \quad \text{(for cell-centered FVM)}$$
$$Re_L = \frac{\rho U_\infty L}{\mu} = \frac{U_\infty L}{\nu}$$ $$\tau_w = \frac{1}{2} C_f \rho U_\infty^2 \quad \Longrightarrow \quad u_\tau = \sqrt{\frac{\tau_w}{\rho}}$$ $$y = \frac{y^+ \nu}{u_\tau} \quad \Longrightarrow \quad \Delta y_1 = 2 y \quad \text{(for cell-centered FVM)}$$
๐ Results & Diagnostics
CFD Mesh Sizing Summary
Recommended First Layer Cell Height ($\Delta y_1$)
598.13 μm
= 0.59813 mm | = 5.9813e-4 m (Centroid $y = 299.1\ \mu\text{m}$)
Turbulence Model Diagnostic: Optimal for High-Re wall functions (Standard k-epsilon, Realizable k-epsilon).
Reynolds ($Re_L$)1.992e+5
Laminar
Laminar
Skin Friction ($C_f$)5.0716e-3
Wall Shear ($\tau_w$)10.12 Pa
Friction Vel ($u_\tau$)0.1007 m/s
Viscous Length ($\ell^+$)9.97 μm
BL Thickness ($\delta$)1.12 mm
๐ Universal Law of the Wall ($u^+$ vs $y^+$)
๐ Near-Wall Physical Velocity $u(y)$ [m/s]
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC โ CFD Y+ & FIRST LAYER HEIGHT SOLVER =============================================================== U_inf [m/s] = 2.000000E+00 L_ref [m] = 1.000000E-01 Density rho [kg/m3] = 9.980000E+02 Viscosity mu [Pa.s] = 1.002000E-03 Nu [m2/s] = 1.004008E-06 Target y+ = 3.000000E+01 Cf Model = Schlichting (Prandtl-Schlichting) Cell Definition Mode= 1 --------------------------------------------------------------- Reynolds Number Re_L= 1.992016E+05 Flow Regime = Laminar Skin Friction Cf = 5.071646E-03 Wall Shear Tau_w[Pa]= 1.012300E+01 Friction Vel u_tau = 1.007139E-01 Viscous Length l+ = 9.968911E-06 Wall Dist y [m] = 2.990673E-04 Cell Height Dy1 [m] = 5.981347E-04 Cell Height Dy1 [mm]= 5.981347E-01 Cell Height Dy1 [um]= 5.981347E+02 --------------------------------------------------------------- BL Thickness delta = 1.120272E-03 Displacement delta* = 3.853737E-04 Momentum theta = 1.487722E-04 Shape Factor H = 2.590361E+00 Viscous Sublayer [m]= 4.984456E-05 Buffer Layer Top [m]= 2.990673E-04 Log-law Region [m] = 2.990673E-03 =============================================================== CFD TURBULENCE MODEL RECOMMENDATION: STATUS: Optimal for High-Re wall functions (Standard k-epsilon, Realizable k-epsilon). --- LAW OF THE WALL PROFILE --- y_plus u_plus u_phys[m/s] y_phys[m] 1.000000E-01 9.999998E-02 1.007139E-02 9.968911E-07 1.165914E-01 1.165914E-01 1.174238E-02 1.162290E-06 1.359356E-01 1.359356E-01 1.369060E-02 1.355130E-06 1.584893E-01 1.584892E-01 1.596207E-02 1.579966E-06 1.847850E-01 1.847848E-01 1.861040E-02 1.842105E-06 2.154435E-01 2.154431E-01 2.169812E-02 2.147737E-06 2.511886E-01 2.511880E-01 2.529813E-02 2.504077E-06 2.928645E-01 2.928633E-01 2.949541E-02 2.919540E-06 3.414549E-01 3.414528E-01 3.438904E-02 3.403933E-06 3.981072E-01 3.981032E-01 4.009453E-02 3.968695E-06 4.641589E-01 4.641516E-01 4.674652E-02 4.627159E-06 5.411695E-01 5.411559E-01 5.450193E-02 5.394871E-06 6.309573E-01 6.309320E-01 6.354363E-02 6.289958E-06 7.356423E-01 7.355951E-01 7.408465E-02 7.333552E-06 8.576959E-01 8.576078E-01 8.637303E-02 8.550294E-06 1.000000E+00 9.998352E-01 1.006973E-01 9.968911E-06 1.165914E+00 1.165606E+00 1.173927E-01 1.162290E-05 1.359356E+00 1.358776E+00 1.368477E-01 1.355130E-05 1.584893E+00 1.583801E+00 1.595108E-01 1.579966E-05 1.847850E+00 1.845787E+00 1.858964E-01 1.842105E-05 2.154435E+00 2.150525E+00 2.165878E-01 2.147737E-05 2.511886E+00 2.504454E+00 2.522333E-01 2.504077E-05 2.928645E+00 2.914470E+00 2.935277E-01 2.919540E-05 3.414549E+00 3.387457E+00 3.411641E-01 3.403933E-05 3.981072E+00 3.929279E+00 3.957331E-01 3.968695E-05 4.641589E+00 4.542945E+00 4.575378E-01 4.627159E-05 5.411695E+00 5.225782E+00 5.263089E-01 5.394871E-05 6.309573E+00 5.966299E+00 6.008893E-01 6.289958E-05 7.356423E+00 6.742984E+00 6.791123E-01 7.333552E-05 8.576959E+00 7.527886E+00 7.581628E-01 8.550294E-05 1.000000E+01 8.294498E+00 8.353714E-01 9.968911E-05 1.165914E+01 9.024715E+00 9.089143E-01 1.162290E-04 1.359356E+01 9.710534E+00 9.779859E-01 1.355130E-04 1.584893E+01 1.035153E+01 1.042543E+00 1.579966E-04 1.847850E+01 1.095138E+01 1.102957E+00 1.842105E-04 2.154435E+01 1.151530E+01 1.159751E+00 2.147737E-04 2.511886E+01 1.204862E+01 1.213464E+00 2.504077E-04 2.928645E+01 1.255624E+01 1.264588E+00 2.919540E-04 3.414549E+01 1.304237E+01 1.313548E+00 3.403933E-04 3.981072E+01 1.351055E+01 1.360701E+00 3.968695E-04 4.641589E+01 1.396374E+01 1.406343E+00 4.627159E-04 5.411695E+01 1.440438E+01 1.450721E+00 5.394871E-04 6.309573E+01 1.483449E+01 1.494039E+00 6.289958E-04 7.356423E+01 1.525575E+01 1.536467E+00 7.333552E-04 8.576959E+01 1.566957E+01 1.578144E+00 8.550294E-04 1.000000E+02 1.607710E+01 1.619188E+00 9.968911E-04 1.165914E+02 1.647933E+01 1.659698E+00 1.162290E-03 1.359356E+02 1.687707E+01 1.699756E+00 1.355130E-03 1.584893E+02 1.727102E+01 1.739432E+00 1.579966E-03 1.847850E+02 1.766177E+01 1.778786E+00 1.842105E-03 2.154435E+02 1.804980E+01 1.817866E+00 2.147737E-03 2.511886E+02 1.843553E+01 1.856715E+00 2.504077E-03 2.928645E+02 1.881933E+01 1.895369E+00 2.919540E-03 3.414549E+02 1.920150E+01 1.933858E+00 3.403933E-03 3.981072E+02 1.958228E+01 1.972208E+00 3.968695E-03 4.641589E+02 1.996191E+01 2.010442E+00 4.627159E-03 5.411695E+02 2.034056E+01 2.048577E+00 5.394871E-03 6.309573E+02 2.071839E+01 2.086630E+00 6.289958E-03 7.356423E+02 2.109554E+01 2.124614E+00 7.333552E-03 8.576959E+02 2.147212E+01 2.162542E+00 8.550294E-03 1.000000E+03 2.184823E+01 2.200421E+00 9.968911E-03 --- END PROFILE ---