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 ($\Delta y_1$)
24.454 μm
= 0.024454 mm | = 2.4454e-5 m (Centroid $y = 12.23\ \mu\text{m}$)
Turbulence Model Diagnostic: Optimal for Low-Re resolved models (SST k-omega, Spalart-Allmaras, LES/DNS).
Reynolds ($Re_L$)1.027e+7
Fully Turbulent
Fully Turbulent
Skin Friction ($C_f$)2.5684e-3
Wall Shear ($\tau_w$)1.748 Pa
Friction Vel ($u_\tau$)1.194 m/s
Viscous Length ($\ell^+$)12.2 μm
BL Thickness ($\delta$)65.9 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] = 3.333000E+01 L_ref [m] = 4.500000E+00 Density rho [kg/m3] = 1.225000E+00 Viscosity mu [Pa.s] = 1.789000E-05 Nu [m2/s] = 1.460408E-05 Target y+ = 1.000000E+00 Cf Model = Schlichting (Prandtl-Schlichting) Cell Definition Mode= 1 --------------------------------------------------------------- Reynolds Number Re_L= 1.027007E+07 Flow Regime = Fully Turbulent Skin Friction Cf = 2.568400E-03 Wall Shear Tau_w[Pa]= 1.747589E+00 Friction Vel u_tau = 1.194405E+00 Viscous Length l+ = 1.222708E-05 Wall Dist y [m] = 1.222708E-05 Cell Height Dy1 [m] = 2.445415E-05 Cell Height Dy1 [mm]= 2.445415E-02 Cell Height Dy1 [um]= 2.445415E+01 --------------------------------------------------------------- BL Thickness delta = 6.593250E-02 Displacement delta* = 8.241562E-03 Momentum theta = 6.410104E-03 Shape Factor H = 1.285714E+00 Viscous Sublayer [m]= 6.113538E-05 Buffer Layer Top [m]= 3.668123E-04 Log-law Region [m] = 3.668123E-03 =============================================================== CFD TURBULENCE MODEL RECOMMENDATION: STATUS: Optimal for Low-Re resolved models (SST k-omega, Spalart-Allmaras, LES/DNS). --- LAW OF THE WALL PROFILE --- y_plus u_plus u_phys[m/s] y_phys[m] 1.000000E-01 9.999998E-02 1.194405E-01 1.222708E-06 1.165914E-01 1.165914E-01 1.392574E-01 1.425572E-06 1.359356E-01 1.359356E-01 1.623622E-01 1.662095E-06 1.584893E-01 1.584892E-01 1.893003E-01 1.937861E-06 1.847850E-01 1.847848E-01 2.207079E-01 2.259380E-06 2.154435E-01 2.154431E-01 2.573264E-01 2.634244E-06 2.511886E-01 2.511880E-01 3.000203E-01 3.071303E-06 2.928645E-01 2.928633E-01 3.497974E-01 3.580876E-06 3.414549E-01 3.414528E-01 4.078329E-01 4.174995E-06 3.981072E-01 3.981032E-01 4.754965E-01 4.867687E-06 4.641589E-01 4.641516E-01 5.543850E-01 5.675306E-06 5.411695E-01 5.411559E-01 6.463594E-01 6.616921E-06 6.309573E-01 6.309320E-01 7.535884E-01 7.714763E-06 7.356423E-01 7.355951E-01 8.785985E-01 8.994754E-06 8.576959E-01 8.576078E-01 1.024331E+00 1.048711E-05 1.000000E+00 9.998352E-01 1.194208E+00 1.222708E-05 1.165914E+00 1.165606E+00 1.392205E+00 1.425572E-05 1.359356E+00 1.358776E+00 1.622929E+00 1.662095E-05 1.584893E+00 1.583801E+00 1.891700E+00 1.937861E-05 1.847850E+00 1.845787E+00 2.204617E+00 2.259380E-05 2.154435E+00 2.150525E+00 2.568598E+00 2.634244E-05 2.511886E+00 2.504454E+00 2.991333E+00 3.071303E-05 2.928645E+00 2.914470E+00 3.481058E+00 3.580876E-05 3.414549E+00 3.387457E+00 4.045996E+00 4.174995E-05 3.981072E+00 3.929279E+00 4.693151E+00 4.867687E-05 4.641589E+00 4.542945E+00 5.426117E+00 5.675306E-05 5.411695E+00 5.225782E+00 6.241701E+00 6.616921E-05 6.309573E+00 5.966299E+00 7.126178E+00 7.714763E-05 7.356423E+00 6.742984E+00 8.053854E+00 8.994754E-05 8.576959E+00 7.527886E+00 8.991345E+00 1.048711E-04 1.000000E+01 8.294498E+00 9.906991E+00 1.222708E-04 1.165914E+01 9.024715E+00 1.077917E+01 1.425572E-04 1.359356E+01 9.710534E+00 1.159831E+01 1.662095E-04 1.584893E+01 1.035153E+01 1.236392E+01 1.937861E-04 1.847850E+01 1.095138E+01 1.308039E+01 2.259380E-04 2.154435E+01 1.151530E+01 1.375393E+01 2.634244E-04 2.511886E+01 1.204862E+01 1.439094E+01 3.071303E-04 2.928645E+01 1.255624E+01 1.499724E+01 3.580876E-04 3.414549E+01 1.304237E+01 1.557788E+01 4.174995E-04 3.981072E+01 1.351055E+01 1.613707E+01 4.867687E-04 4.641589E+01 1.396374E+01 1.667836E+01 5.675306E-04 5.411695E+01 1.440438E+01 1.720466E+01 6.616921E-04 6.309573E+01 1.483449E+01 1.771839E+01 7.714763E-04 7.356423E+01 1.525575E+01 1.822155E+01 8.994754E-04 8.576959E+01 1.566957E+01 1.871581E+01 1.048711E-03 1.000000E+02 1.607710E+01 1.920257E+01 1.222708E-03 1.165914E+02 1.647933E+01 1.968299E+01 1.425572E-03 1.359356E+02 1.687707E+01 2.015806E+01 1.662095E-03 1.584893E+02 1.727102E+01 2.062860E+01 1.937861E-03 1.847850E+02 1.766177E+01 2.109530E+01 2.259380E-03 2.154435E+02 1.804980E+01 2.155877E+01 2.634244E-03 2.511886E+02 1.843553E+01 2.201950E+01 3.071303E-03 2.928645E+02 1.881933E+01 2.247791E+01 3.580876E-03 3.414549E+02 1.920150E+01 2.293437E+01 4.174995E-03 3.981072E+02 1.958228E+01 2.338918E+01 4.867687E-03 4.641589E+02 1.996191E+01 2.384260E+01 5.675306E-03 5.411695E+02 2.034056E+01 2.429486E+01 6.616921E-03 6.309573E+02 2.071839E+01 2.474615E+01 7.714763E-03 7.356423E+02 2.109554E+01 2.519662E+01 8.994754E-03 8.576959E+02 2.147212E+01 2.564641E+01 1.048711E-02 1.000000E+03 2.184823E+01 2.609564E+01 1.222708E-02 --- END PROFILE ---