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 ($\Delta y_1$)
23.929 μm
= 0.023929 mm | = 2.3929e-5 m (Centroid $y = 11.96\ \mu\text{m}$)
Turbulence Model Diagnostic: Optimal for Low-Re resolved models (SST k-omega, Spalart-Allmaras, LES/DNS).
Reynolds ($Re_L$)2.054e+6
Transitional
Transitional
Skin Friction ($C_f$)3.3109e-3
Wall Shear ($\tau_w$)1.825 Pa
Friction Vel ($u_\tau$)1.221 m/s
Viscous Length ($\ell^+$)12 μm
BL Thickness ($\delta$)20.2 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] = 3.000000E+01 L_ref [m] = 1.000000E+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= 2.054220E+06 Flow Regime = Transitional Skin Friction Cf = 3.310867E-03 Wall Shear Tau_w[Pa]= 1.825116E+00 Friction Vel u_tau = 1.220611E+00 Viscous Length l+ = 1.196457E-05 Wall Dist y [m] = 1.196457E-05 Cell Height Dy1 [m] = 2.392914E-05 Cell Height Dy1 [mm]= 2.392914E-02 Cell Height Dy1 [um]= 2.392914E+01 --------------------------------------------------------------- BL Thickness delta = 2.021493E-02 Displacement delta* = 2.526867E-03 Momentum theta = 1.965341E-03 Shape Factor H = 1.285714E+00 Viscous Sublayer [m]= 5.982285E-05 Buffer Layer Top [m]= 3.589371E-04 Log-law Region [m] = 3.589371E-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 1.220610E-01 1.196457E-06 1.165914E-01 1.165914E-01 1.423127E-01 1.394966E-06 1.359356E-01 1.359356E-01 1.659244E-01 1.626412E-06 1.584893E-01 1.584892E-01 1.934536E-01 1.896257E-06 1.847850E-01 1.847848E-01 2.255503E-01 2.210873E-06 2.154435E-01 2.154431E-01 2.629722E-01 2.577689E-06 2.511886E-01 2.511880E-01 3.066028E-01 3.005364E-06 2.928645E-01 2.928633E-01 3.574721E-01 3.503997E-06 3.414549E-01 3.414528E-01 4.167809E-01 4.085361E-06 3.981072E-01 3.981032E-01 4.859290E-01 4.763181E-06 4.641589E-01 4.641516E-01 5.665483E-01 5.553462E-06 5.411695E-01 5.411559E-01 6.605407E-01 6.474861E-06 6.309573E-01 6.309320E-01 7.701223E-01 7.549134E-06 7.356423E-01 7.355951E-01 8.978751E-01 8.801643E-06 8.576959E-01 8.576078E-01 1.046805E+00 1.026196E-05 1.000000E+00 9.998352E-01 1.220409E+00 1.196457E-05 1.165914E+00 1.165606E+00 1.422751E+00 1.394966E-05 1.359356E+00 1.358776E+00 1.658537E+00 1.626412E-05 1.584893E+00 1.583801E+00 1.933204E+00 1.896257E-05 1.847850E+00 1.845787E+00 2.252987E+00 2.210873E-05 2.154435E+00 2.150525E+00 2.624954E+00 2.577689E-05 2.511886E+00 2.504454E+00 3.056963E+00 3.005364E-05 2.928645E+00 2.914470E+00 3.557433E+00 3.503997E-05 3.414549E+00 3.387457E+00 4.134766E+00 4.085361E-05 3.981072E+00 3.929279E+00 4.796120E+00 4.763181E-05 4.641589E+00 4.542945E+00 5.545167E+00 5.553462E-05 5.411695E+00 5.225782E+00 6.378645E+00 6.474861E-05 6.309573E+00 5.966299E+00 7.282528E+00 7.549134E-05 7.356423E+00 6.742984E+00 8.230558E+00 8.801643E-05 8.576959E+00 7.527886E+00 9.188617E+00 1.026196E-04 1.000000E+01 8.294498E+00 1.012435E+01 1.196457E-04 1.165914E+01 9.024715E+00 1.101566E+01 1.394966E-04 1.359356E+01 9.710534E+00 1.185278E+01 1.626412E-04 1.584893E+01 1.035153E+01 1.263519E+01 1.896257E-04 1.847850E+01 1.095138E+01 1.336738E+01 2.210873E-04 2.154435E+01 1.151530E+01 1.405569E+01 2.577689E-04 2.511886E+01 1.204862E+01 1.470668E+01 3.005364E-04 2.928645E+01 1.255624E+01 1.532628E+01 3.503997E-04 3.414549E+01 1.304237E+01 1.591966E+01 4.085361E-04 3.981072E+01 1.351055E+01 1.649113E+01 4.763181E-04 4.641589E+01 1.396374E+01 1.704429E+01 5.553462E-04 5.411695E+01 1.440438E+01 1.758214E+01 6.474861E-04 6.309573E+01 1.483449E+01 1.810714E+01 7.549134E-04 7.356423E+01 1.525575E+01 1.862134E+01 8.801643E-04 8.576959E+01 1.566957E+01 1.912644E+01 1.026196E-03 1.000000E+02 1.607710E+01 1.962388E+01 1.196457E-03 1.165914E+02 1.647933E+01 2.011484E+01 1.394966E-03 1.359356E+02 1.687707E+01 2.060033E+01 1.626412E-03 1.584893E+02 1.727102E+01 2.108119E+01 1.896257E-03 1.847850E+02 1.766177E+01 2.155814E+01 2.210873E-03 2.154435E+02 1.804980E+01 2.203177E+01 2.577689E-03 2.511886E+02 1.843553E+01 2.250261E+01 3.005364E-03 2.928645E+02 1.881933E+01 2.297108E+01 3.503997E-03 3.414549E+02 1.920150E+01 2.343755E+01 4.085361E-03 3.981072E+02 1.958228E+01 2.390234E+01 4.763181E-03 4.641589E+02 1.996191E+01 2.436571E+01 5.553462E-03 5.411695E+02 2.034056E+01 2.482790E+01 6.474861E-03 6.309573E+02 2.071839E+01 2.528909E+01 7.549134E-03 7.356423E+02 2.109554E+01 2.574944E+01 8.801643E-03 8.576959E+02 2.147212E+01 2.620910E+01 1.026196E-02 1.000000E+03 2.184823E+01 2.666819E+01 1.196457E-02 --- END PROFILE ---