🥞 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 12 Layers
4.3502 mm
= 4.3502e-3 m | First layer $h_1 = 150\ \mu\text{m}$ | Last layer $h_N = 0.6979\ \text{mm}$
Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.0872}$)
First Layer ($h_1$)150 μm
Growth Ratio ($r$)1.15
Layer Count ($N$)12
Last Layer ($h_N$)0.698 mm
Bulk Mesh ($\Delta x$)8 mm
Transition Ratio0.0872
📈 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 | 0.15 | 150 | 0.15 | 1 |
| 2 | 0.1725 | 172.5 | 0.3225 | 1.15 |
| 3 | 0.1984 | 198.4 | 0.5209 | 1.15 |
| 4 | 0.2281 | 228.1 | 0.749 | 1.15 |
| 5 | 0.2624 | 262.4 | 1.011 | 1.15 |
| 6 | 0.3017 | 301.7 | 1.313 | 1.15 |
| 7 | 0.347 | 347 | 1.66 | 1.15 |
| 8 | 0.399 | 399 | 2.059 | 1.15 |
| 9 | 0.4589 | 458.9 | 2.518 | 1.15 |
| 10 | 0.5277 | 527.7 | 3.046 | 1.15 |
| 11 | 0.6068 | 606.8 | 3.652 | 1.15 |
| 12 | 0.6979 | 697.9 | 4.35 | 1.15 |
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER =============================================================== Calculation Mode = 1 First Layer h1 [m] = 1.500000E-04 First Layer h1 [mm] = 1.500000E-01 First Layer h1 [um] = 1.500000E+02 Growth Ratio (r) = 1.1500 Number of Layers (N)= 12 Total Height H [m] = 4.350250E-03 Total Height H [mm] = 4.350250E+00 Last Layer h_N [m] = 6.978587E-04 Last Layer h_N [mm] = 6.978587E-01 Bulk Cell Size [m] = 8.000000E-03 Transition Ratio = 8.723234E-02 --------------------------------------------------------------- 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 1.500000E-04 1.500000E-01 1.500000E-04 1.500000E-01 1.0000 2 1.725000E-04 1.725000E-01 3.225000E-04 3.225000E-01 1.1500 3 1.983750E-04 1.983750E-01 5.208750E-04 5.208750E-01 1.1500 4 2.281312E-04 2.281312E-01 7.490062E-04 7.490062E-01 1.1500 5 2.623509E-04 2.623509E-01 1.011357E-03 1.011357E+00 1.1500 6 3.017036E-04 3.017036E-01 1.313061E-03 1.313061E+00 1.1500 7 3.469591E-04 3.469591E-01 1.660020E-03 1.660020E+00 1.1500 8 3.990030E-04 3.990030E-01 2.059023E-03 2.059023E+00 1.1500 9 4.588534E-04 4.588534E-01 2.517876E-03 2.517876E+00 1.1500 10 5.276814E-04 5.276814E-01 3.045558E-03 3.045558E+00 1.1500 11 6.068337E-04 6.068337E-01 3.652391E-03 3.652391E+00 1.1500 12 6.978587E-04 6.978587E-01 4.350250E-03 4.350250E+00 1.1500 --- END PRISM DISTRIBUTION ---