🥞 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 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 ---

📘 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