🥞 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 18 Layers

                        3.9601 mm
                    

= 3.9601e-3 m | First layer $h_1 = 25\ \mu\text{m}$ | Last layer $h_N = 0.7346\ \text{mm}$

Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.245}$)

First Layer ($h_1$)25 μm

Growth Ratio ($r$)1.22

Layer Count ($N$)18

Last Layer ($h_N$)0.735 mm

Bulk Mesh ($\Delta x$)3 mm

Transition Ratio0.245

📈 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	0.025	25	0.025	1
2	0.0305	30.5	0.0555	1.22
3	0.03721	37.21	0.09271	1.22
4	0.0454	45.4	0.1381	1.22
5	0.05538	55.38	0.1935	1.22
6	0.06757	67.57	0.2611	1.22
7	0.08243	82.43	0.3435	1.22
8	0.1006	100.6	0.4441	1.22
9	0.1227	122.7	0.5668	1.22
10	0.1497	149.7	0.7164	1.22
11	0.1826	182.6	0.8991	1.22
12	0.2228	222.8	1.122	1.22
13	0.2718	271.8	1.394	1.22
14	0.3316	331.6	1.725	1.22
15	0.4046	404.6	2.13	1.22
16	0.4936	493.6	2.623	1.22
17	0.6021	602.1	3.226	1.22
18	0.7346	734.6	3.96	1.22

Fortran Solver Raw Output:

===============================================================
  THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER
===============================================================
Calculation Mode    =  1
First Layer h1 [m]  =   2.500000E-05
First Layer h1 [mm] =   2.500000E-02
First Layer h1 [um] =   2.500000E+01
Growth Ratio (r)    =     1.2200
Number of Layers (N)=   18
Total Height H [m]  =   3.960113E-03
Total Height H [mm] =   3.960113E+00
Last Layer h_N [m]  =   7.346105E-04
Last Layer h_N [mm] =   7.346105E-01
Bulk Cell Size [m]  =   3.000000E-03
Transition Ratio    =   2.448702E-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    2.500000E-05    2.500000E-02    2.500000E-05    2.500000E-02    1.0000
   2    3.050000E-05    3.050000E-02    5.550000E-05    5.550000E-02    1.2200
   3    3.721000E-05    3.721000E-02    9.271000E-05    9.271000E-02    1.2200
   4    4.539620E-05    4.539620E-02    1.381062E-04    1.381062E-01    1.2200
   5    5.538336E-05    5.538336E-02    1.934896E-04    1.934896E-01    1.2200
   6    6.756770E-05    6.756770E-02    2.610573E-04    2.610573E-01    1.2200
   7    8.243260E-05    8.243260E-02    3.434899E-04    3.434899E-01    1.2200
   8    1.005678E-04    1.005678E-01    4.440576E-04    4.440576E-01    1.2200
   9    1.226927E-04    1.226927E-01    5.667503E-04    5.667503E-01    1.2200
  10    1.496851E-04    1.496851E-01    7.164354E-04    7.164354E-01    1.2200
  11    1.826158E-04    1.826158E-01    8.990512E-04    8.990512E-01    1.2200
  12    2.227913E-04    2.227913E-01    1.121842E-03    1.121842E+00    1.2200
  13    2.718053E-04    2.718053E-01    1.393648E-03    1.393648E+00    1.2200
  14    3.316025E-04    3.316025E-01    1.725250E-03    1.725250E+00    1.2200
  15    4.045551E-04    4.045551E-01    2.129805E-03    2.129805E+00    1.2200
  16    4.935572E-04    4.935572E-01    2.623363E-03    2.623363E+00    1.2200
  17    6.021398E-04    6.021398E-01    3.225502E-03    3.225502E+00    1.2200
  18    7.346105E-04    7.346105E-01    3.960113E-03    3.960113E+00    1.2200
--- 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