🥞 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 15 Layers

                        3.6018 mm
                    

= 3.6018e-3 m | First layer $h_1 = 50\ \mu\text{m}$ | Last layer $h_N = 0.642\ \text{mm}$

Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.214}$)

First Layer ($h_1$)50 μm

Growth Ratio ($r$)1.2

Layer Count ($N$)15

Last Layer ($h_N$)0.642 mm

Bulk Mesh ($\Delta x$)3 mm

Transition Ratio0.214

📈 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	0.05	50	0.05	1
2	0.06	60	0.11	1.2
3	0.072	72	0.182	1.2
4	0.0864	86.4	0.2684	1.2
5	0.1037	103.7	0.3721	1.2
6	0.1244	124.4	0.4965	1.2
7	0.1493	149.3	0.6458	1.2
8	0.1792	179.2	0.825	1.2
9	0.215	215	1.04	1.2
10	0.258	258	1.298	1.2
11	0.3096	309.6	1.608	1.2
12	0.3715	371.5	1.979	1.2
13	0.4458	445.8	2.425	1.2
14	0.535	535	2.96	1.2
15	0.642	642	3.602	1.2

Fortran Solver Raw Output:

===============================================================
  THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER
===============================================================
Calculation Mode    =  1
First Layer h1 [m]  =   5.000000E-05
First Layer h1 [mm] =   5.000000E-02
First Layer h1 [um] =   5.000000E+01
Growth Ratio (r)    =     1.2000
Number of Layers (N)=   15
Total Height H [m]  =   3.601755E-03
Total Height H [mm] =   3.601755E+00
Last Layer h_N [m]  =   6.419592E-04
Last Layer h_N [mm] =   6.419592E-01
Bulk Cell Size [m]  =   3.000000E-03
Transition Ratio    =   2.139864E-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    5.000000E-05    5.000000E-02    5.000000E-05    5.000000E-02    1.0000
   2    6.000000E-05    6.000000E-02    1.100000E-04    1.100000E-01    1.2000
   3    7.200000E-05    7.200000E-02    1.820000E-04    1.820000E-01    1.2000
   4    8.640000E-05    8.640000E-02    2.684000E-04    2.684000E-01    1.2000
   5    1.036800E-04    1.036800E-01    3.720800E-04    3.720800E-01    1.2000
   6    1.244160E-04    1.244160E-01    4.964960E-04    4.964960E-01    1.2000
   7    1.492992E-04    1.492992E-01    6.457952E-04    6.457952E-01    1.2000
   8    1.791590E-04    1.791590E-01    8.249542E-04    8.249542E-01    1.2000
   9    2.149908E-04    2.149908E-01    1.039945E-03    1.039945E+00    1.2000
  10    2.579890E-04    2.579890E-01    1.297934E-03    1.297934E+00    1.2000
  11    3.095868E-04    3.095868E-01    1.607521E-03    1.607521E+00    1.2000
  12    3.715042E-04    3.715042E-01    1.979025E-03    1.979025E+00    1.2000
  13    4.458050E-04    4.458050E-01    2.424830E-03    2.424830E+00    1.2000
  14    5.349660E-04    5.349660E-01    2.959796E-03    2.959796E+00    1.2000
  15    6.419592E-04    6.419592E-01    3.601755E-03    3.601755E+00    1.2000
--- 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