🥞 CFD Prism Layer Growth & Inflation Mesh Calculator
Dimension boundary layer prism/inflation layers: compute cumulative thickness $H_{tot}$, layer count $N$, last cell height $h_N$, and transition ratio to the outer volume mesh.
🧱 2D Boundary Layer Prism Mesh Visualization
True-to-Scale Layer Inflation • Bulk Mesh Interface📝 Inflation Parameters
Geometric Progression Equations:
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
📊 Mesh Sizing Results
Boundary Layer Inflation Summary
Total Inflation Height ($H_{tot}$) across 15 Layers
3.6018 mm
= 3.6018e-3 m | First layer $h_1 = 50\ \mu\text{m}$ | Last layer $h_N = 0.642\ \text{mm}$
Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.214}$)
First Layer ($h_1$)50 μm
Growth Ratio ($r$)1.2
Layer Count ($N$)15
Last Layer ($h_N$)0.642 mm
Bulk Mesh ($\Delta x$)3 mm
Transition Ratio0.214
📈 Layer Thickness $h_i$ [mm]
📊 Cumulative Inflation Height $Y_i$ [mm]
📋 Detailed Layer-by-Layer Progression
| Layer # | Thickness [mm] | Thickness [μm] | Cumulative [mm] | Ratio |
|---|---|---|---|---|
| 1 | 0.05 | 50 | 0.05 | 1 |
| 2 | 0.06 | 60 | 0.11 | 1.2 |
| 3 | 0.072 | 72 | 0.182 | 1.2 |
| 4 | 0.0864 | 86.4 | 0.2684 | 1.2 |
| 5 | 0.1037 | 103.7 | 0.3721 | 1.2 |
| 6 | 0.1244 | 124.4 | 0.4965 | 1.2 |
| 7 | 0.1493 | 149.3 | 0.6458 | 1.2 |
| 8 | 0.1792 | 179.2 | 0.825 | 1.2 |
| 9 | 0.215 | 215 | 1.04 | 1.2 |
| 10 | 0.258 | 258 | 1.298 | 1.2 |
| 11 | 0.3096 | 309.6 | 1.608 | 1.2 |
| 12 | 0.3715 | 371.5 | 1.979 | 1.2 |
| 13 | 0.4458 | 445.8 | 2.425 | 1.2 |
| 14 | 0.535 | 535 | 2.96 | 1.2 |
| 15 | 0.642 | 642 | 3.602 | 1.2 |
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER =============================================================== Calculation Mode = 1 First Layer h1 [m] = 5.000000E-05 First Layer h1 [mm] = 5.000000E-02 First Layer h1 [um] = 5.000000E+01 Growth Ratio (r) = 1.2000 Number of Layers (N)= 15 Total Height H [m] = 3.601755E-03 Total Height H [mm] = 3.601755E+00 Last Layer h_N [m] = 6.419592E-04 Last Layer h_N [mm] = 6.419592E-01 Bulk Cell Size [m] = 3.000000E-03 Transition Ratio = 2.139864E-01 --------------------------------------------------------------- Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). =============================================================== --- PRISM LAYER DISTRIBUTION --- Layer Thickness[m] Thickness[mm] Cumulative[m] Cumulative[mm] Ratio 1 5.000000E-05 5.000000E-02 5.000000E-05 5.000000E-02 1.0000 2 6.000000E-05 6.000000E-02 1.100000E-04 1.100000E-01 1.2000 3 7.200000E-05 7.200000E-02 1.820000E-04 1.820000E-01 1.2000 4 8.640000E-05 8.640000E-02 2.684000E-04 2.684000E-01 1.2000 5 1.036800E-04 1.036800E-01 3.720800E-04 3.720800E-01 1.2000 6 1.244160E-04 1.244160E-01 4.964960E-04 4.964960E-01 1.2000 7 1.492992E-04 1.492992E-01 6.457952E-04 6.457952E-01 1.2000 8 1.791590E-04 1.791590E-01 8.249542E-04 8.249542E-01 1.2000 9 2.149908E-04 2.149908E-01 1.039945E-03 1.039945E+00 1.2000 10 2.579890E-04 2.579890E-01 1.297934E-03 1.297934E+00 1.2000 11 3.095868E-04 3.095868E-01 1.607521E-03 1.607521E+00 1.2000 12 3.715042E-04 3.715042E-01 1.979025E-03 1.979025E+00 1.2000 13 4.458050E-04 4.458050E-01 2.424830E-03 2.424830E+00 1.2000 14 5.349660E-04 5.349660E-01 2.959796E-03 2.959796E+00 1.2000 15 6.419592E-04 6.419592E-01 3.601755E-03 3.601755E+00 1.2000 --- END PRISM DISTRIBUTION ---