🥞 Prism Layer Growth & Inflation

Dimension CFD boundary layer inflation layers, geometric growth ratio, total height, and volume mesh transition ratio.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Cfd

📊 Solver Telemetry ● ACTIVE

👁️ Views 30

⚡ Solves 25

💾 Downloads 690 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

🧱 2D Boundary Layer Prism Mesh Visualization

True-to-Scale Layer Inflation • Bulk Mesh Interface

📝 Inflation Parameters

Presets: Automotive Aero HVAC Duct Turbine Blade Marine Hydrofoil

⚙️ Sizing Mode

Calculation Objective:

📐 Geometric Parameters

First Layer Height $h_1$ [m]:

Growth Ratio $r$ [-]:

Number of Layers $N$:

Total Inflation Height $H_{tot}$ [m]:

🌐 Outer Mesh & Boundary Layer

Outer Bulk Cell Size $\Delta x_{bulk}$ [m]:

Estimated BL Thickness $\delta$ [m]:

Geometric Progression Equations:

$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$

📊 Mesh Sizing Results

Boundary Layer Inflation Summary

Total Inflation Height ($H_{tot}$) across 25 Layers

                        3.426 mm
                    

= 3.4260e-3 m | First layer $h_1 = 10\ \mu\text{m}$ | Last layer $h_N = 0.5311\ \text{mm}$

Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.354}$)

First Layer ($h_1$)10 μm

Growth Ratio ($r$)1.18

Layer Count ($N$)25

Last Layer ($h_N$)0.531 mm

Bulk Mesh ($\Delta x$)1.5 mm

Transition Ratio0.354

📈 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	0.01	10	0.01	1
2	0.0118	11.8	0.0218	1.18
3	0.01392	13.92	0.03572	1.18
4	0.01643	16.43	0.05215	1.18
5	0.01939	19.39	0.07154	1.18
6	0.02288	22.88	0.09442	1.18
7	0.027	27	0.1214	1.18
8	0.03185	31.85	0.1533	1.18
9	0.03759	37.59	0.1909	1.18
10	0.04435	44.35	0.2352	1.18
11	0.05234	52.34	0.2876	1.18
12	0.06176	61.76	0.3493	1.18
13	0.07288	72.88	0.4222	1.18
14	0.08599	85.99	0.5082	1.18
15	0.1015	101.5	0.6097	1.18
16	0.1197	119.7	0.7294	1.18
17	0.1413	141.3	0.8707	1.18
18	0.1667	166.7	1.037	1.18
19	0.1967	196.7	1.234	1.18
20	0.2321	232.1	1.466	1.18
21	0.2739	273.9	1.74	1.18
22	0.3232	323.2	2.063	1.18
23	0.3814	381.4	2.445	1.18
24	0.4501	450.1	2.895	1.18
25	0.5311	531.1	3.426	1.18

Fortran Solver Raw Output:

===============================================================
  THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER
===============================================================
Calculation Mode    =  1
First Layer h1 [m]  =   1.000000E-05
First Layer h1 [mm] =   1.000000E-02
First Layer h1 [um] =   1.000000E+01
Growth Ratio (r)    =     1.1800
Number of Layers (N)=   25
Total Height H [m]  =   3.426035E-03
Total Height H [mm] =   3.426035E+00
Last Layer h_N [m]  =   5.310901E-04
Last Layer h_N [mm] =   5.310901E-01
Bulk Cell Size [m]  =   1.500000E-03
Transition Ratio    =   3.540600E-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    1.000000E-05    1.000000E-02    1.000000E-05    1.000000E-02    1.0000
   2    1.180000E-05    1.180000E-02    2.180000E-05    2.180000E-02    1.1800
   3    1.392400E-05    1.392400E-02    3.572400E-05    3.572400E-02    1.1800
   4    1.643032E-05    1.643032E-02    5.215432E-05    5.215432E-02    1.1800
   5    1.938778E-05    1.938778E-02    7.154210E-05    7.154210E-02    1.1800
   6    2.287758E-05    2.287758E-02    9.441968E-05    9.441968E-02    1.1800
   7    2.699554E-05    2.699554E-02    1.214152E-04    1.214152E-01    1.1800
   8    3.185474E-05    3.185474E-02    1.532700E-04    1.532700E-01    1.1800
   9    3.758859E-05    3.758859E-02    1.908585E-04    1.908585E-01    1.1800
  10    4.435454E-05    4.435454E-02    2.352131E-04    2.352131E-01    1.1800
  11    5.233836E-05    5.233836E-02    2.875514E-04    2.875514E-01    1.1800
  12    6.175926E-05    6.175926E-02    3.493107E-04    3.493107E-01    1.1800
  13    7.287593E-05    7.287593E-02    4.221866E-04    4.221866E-01    1.1800
  14    8.599359E-05    8.599359E-02    5.081802E-04    5.081802E-01    1.1800
  15    1.014724E-04    1.014724E-01    6.096527E-04    6.096527E-01    1.1800
  16    1.197375E-04    1.197375E-01    7.293901E-04    7.293901E-01    1.1800
  17    1.412902E-04    1.412902E-01    8.706804E-04    8.706804E-01    1.1800
  18    1.667225E-04    1.667225E-01    1.037403E-03    1.037403E+00    1.1800
  19    1.967325E-04    1.967325E-01    1.234135E-03    1.234135E+00    1.1800
  20    2.321444E-04    2.321444E-01    1.466280E-03    1.466280E+00    1.1800
  21    2.739303E-04    2.739303E-01    1.740210E-03    1.740210E+00    1.1800
  22    3.232378E-04    3.232378E-01    2.063448E-03    2.063448E+00    1.1800
  23    3.814206E-04    3.814206E-01    2.444868E-03    2.444868E+00    1.1800
  24    4.500763E-04    4.500763E-01    2.894945E-03    2.894945E+00    1.1800
  25    5.310901E-04    5.310901E-01    3.426035E-03    3.426035E+00    1.1800
--- END PRISM DISTRIBUTION ---

📘 Calculation Methodology: Prism Layer Mesh Inflation Progression

Mathematical Model & Theory

Boundary layer prism mesh inflation uses a geometric growth ratio $r$ to transition smoothly from first cell height $\Delta y_1$ to freestream grid size across $N$ layers:

$$\Delta y_j = \Delta y_1 \cdot r^{j-1}, \quad \text{Total Height } H = \Delta y_1 \frac{r^N - 1}{r - 1}$$

$$\text{Top Layer Height: } \Delta y_N = \Delta y_1 \cdot r^{N-1}$$

Assumptions

Smooth geometric progression along wall normals.
Growth ratio $r \le 1.20$ to maintain discretization accuracy.

Academic References

Wilcox, D. C.: Turbulence Modeling for CFD.
Schlichting, H., & Gersten, K.: Boundary-Layer Theory.

Worked Engineering Example

Problem Statement:
A turbine blade has $\Delta y_1 = 0.02\text{ mm}$, $N = 15$ layers, and $r = 1.20$. Calculate total stack height $H$ and top layer height $\Delta y_{15}$.

Step-by-step Solution:
1. $H = 0.02 \times (1.20^{15} - 1) / (1.20 - 1) = 0.02 \times 72.035 = 1.441\text{ mm}$.
2. $\Delta y_{15} = 0.02 \times 1.20^{14} = 0.2568\text{ mm}$.
Final Result:
Total stack thickness is 1.441 mm (top layer height 0.257 mm).

ThermoFluidCalc Report