🥞 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 20 Layers
5.6006 mm
= 5.6006e-3 m | First layer $h_1 = 30\ \mu\text{m}$ | Last layer $h_N = 0.9584\ \text{mm}$
Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.24}$)
First Layer ($h_1$)30 μm
Growth Ratio ($r$)1.2
Layer Count ($N$)20
Last Layer ($h_N$)0.958 mm
Bulk Mesh ($\Delta x$)4 mm
Transition Ratio0.24
📈 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 | 0.03 | 30 | 0.03 | 1 |
| 2 | 0.036 | 36 | 0.066 | 1.2 |
| 3 | 0.0432 | 43.2 | 0.1092 | 1.2 |
| 4 | 0.05184 | 51.84 | 0.161 | 1.2 |
| 5 | 0.06221 | 62.21 | 0.2232 | 1.2 |
| 6 | 0.07465 | 74.65 | 0.2979 | 1.2 |
| 7 | 0.08958 | 89.58 | 0.3875 | 1.2 |
| 8 | 0.1075 | 107.5 | 0.495 | 1.2 |
| 9 | 0.129 | 129 | 0.624 | 1.2 |
| 10 | 0.1548 | 154.8 | 0.7788 | 1.2 |
| 11 | 0.1858 | 185.8 | 0.9645 | 1.2 |
| 12 | 0.2229 | 222.9 | 1.187 | 1.2 |
| 13 | 0.2675 | 267.5 | 1.455 | 1.2 |
| 14 | 0.321 | 321 | 1.776 | 1.2 |
| 15 | 0.3852 | 385.2 | 2.161 | 1.2 |
| 16 | 0.4622 | 462.2 | 2.623 | 1.2 |
| 17 | 0.5547 | 554.7 | 3.178 | 1.2 |
| 18 | 0.6656 | 665.6 | 3.844 | 1.2 |
| 19 | 0.7987 | 798.7 | 4.642 | 1.2 |
| 20 | 0.9584 | 958.4 | 5.601 | 1.2 |
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER =============================================================== Calculation Mode = 1 First Layer h1 [m] = 3.000000E-05 First Layer h1 [mm] = 3.000000E-02 First Layer h1 [um] = 3.000000E+01 Growth Ratio (r) = 1.2000 Number of Layers (N)= 20 Total Height H [m] = 5.600640E-03 Total Height H [mm] = 5.600640E+00 Last Layer h_N [m] = 9.584400E-04 Last Layer h_N [mm] = 9.584400E-01 Bulk Cell Size [m] = 4.000000E-03 Transition Ratio = 2.396100E-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 3.000000E-05 3.000000E-02 3.000000E-05 3.000000E-02 1.0000 2 3.600000E-05 3.600000E-02 6.600000E-05 6.600000E-02 1.2000 3 4.320000E-05 4.320000E-02 1.092000E-04 1.092000E-01 1.2000 4 5.184000E-05 5.184000E-02 1.610400E-04 1.610400E-01 1.2000 5 6.220800E-05 6.220800E-02 2.232480E-04 2.232480E-01 1.2000 6 7.464960E-05 7.464960E-02 2.978976E-04 2.978976E-01 1.2000 7 8.957952E-05 8.957952E-02 3.874771E-04 3.874771E-01 1.2000 8 1.074954E-04 1.074954E-01 4.949725E-04 4.949725E-01 1.2000 9 1.289945E-04 1.289945E-01 6.239671E-04 6.239671E-01 1.2000 10 1.547934E-04 1.547934E-01 7.787605E-04 7.787605E-01 1.2000 11 1.857521E-04 1.857521E-01 9.645126E-04 9.645126E-01 1.2000 12 2.229025E-04 2.229025E-01 1.187415E-03 1.187415E+00 1.2000 13 2.674830E-04 2.674830E-01 1.454898E-03 1.454898E+00 1.2000 14 3.209796E-04 3.209796E-01 1.775878E-03 1.775878E+00 1.2000 15 3.851755E-04 3.851755E-01 2.161053E-03 2.161053E+00 1.2000 16 4.622106E-04 4.622106E-01 2.623264E-03 2.623264E+00 1.2000 17 5.546528E-04 5.546528E-01 3.177917E-03 3.177917E+00 1.2000 18 6.655833E-04 6.655833E-01 3.843500E-03 3.843500E+00 1.2000 19 7.987000E-04 7.987000E-01 4.642200E-03 4.642200E+00 1.2000 20 9.584400E-04 9.584400E-01 5.600640E-03 5.600640E+00 1.2000 --- END PRISM DISTRIBUTION ---