๐ฟ Spray & Droplet Atomization
Calculate Sauter Mean Diameter (SMD, D32), liquid jet breakup regimes (Rayleigh, Wind-Induced, Atomization), spray cone angle, Rosin-Rammler droplet distribution, Weber and Ohnesorge numbers.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Fluid Mechanics
๐ Solver Telemetry
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โก Solves
25
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๐ฆ Fortran Code
4.5 KB
๐
Released
Aug 2026
โฑ๏ธ Latency
< 1 ms
๐ฟ Spray Jet & Droplet Atomization Dynamics
Real-time particle & wave breakup simulation๐ Configuration & Presets
Key Formulations:
โข Velocity: Vinj = Cd โ(2ฮP/ฯL)
โข Sauter Mean Diameter: D32 = 2.25 ฯ0.25 ฮผL0.16 ฯL0.20 mฬ0.22 ฮPโ0.43
โข Weber Number: Weg = ฯg Vinjยฒ d0 / ฯ
โข Ohnesorge Number: Oh = ฮผL / โ(ฯL ฯ d0)
โข Velocity: Vinj = Cd โ(2ฮP/ฯL)
โข Sauter Mean Diameter: D32 = 2.25 ฯ0.25 ฮผL0.16 ฯL0.20 mฬ0.22 ฮPโ0.43
โข Weber Number: Weg = ฯg Vinjยฒ d0 / ฯ
โข Ohnesorge Number: Oh = ฮผL / โ(ฯL ฯ d0)
๐ Atomization & Spray Results
๐ Output Summary
Identified Breakup Regime
Atomization / Catastrophic Shear Breakup
Complete instantaneous aerodynamic disintegration at nozzle exit forming a fine dense spray.
Sauter Mean Diameter (D32)
67.7 ยตm
MMD (Dv50) = 79.9 ยตm
Spray Cone Angle (ฮธ)
51.6ยฐ
Liquid Core Length = 7.4 mm
Injection Velocity (Vinj)
449.55 m/s
Flow = 9.552e-3 kg/s (0.69 L/min)
Dimensionless Numbers
Weg = 32479.7 | Oh = 0.0432
ReL = 2.41e+4 | WeL = 1.08e+6
๐ Rosin-Rammler Droplet Size Distribution
๐ Sauter Mean Diameter D32 vs Injection ฮP
================================================================= THERMOFLUIDCALC โ SPRAY & DROPLET ATOMIZATION REPORT ================================================================= Case Title : Common-Rail Diesel Direct Injector Nozzle Orifice Diameter : 0.180 mm (1.8000e-4 m) Injection Pressure Drop : 1500.00 bar (1.500e+8 Pa) Discharge Coefficient Cd : 0.750 ----------------------------------------------------------------- Liquid Velocity (V_inj) : 449.551 m/s Mass Flow Rate (mdot) : 9.5521e-3 kg/s (9.552 g/s) Volumetric Flow Rate (Q) : 1.1440e-5 m3/s (0.686 L/min) ----------------------------------------------------------------- Liquid Reynolds Number ReL : 2.413e+4 Liquid Weber Number WeL : 1.085e+6 Gas Weber Number Weg : 3.248e+4 Ohnesorge Number Oh : 0.04316 Breakup Regime : Atomization / Catastrophic Shear Breakup ----------------------------------------------------------------- Sauter Mean Diameter (D32) : 67.70 microns (ยตm) Arithmetic Mean (D10) : 44.01 microns (ยตm) Mass Median Diameter (Dv50): 79.89 microns (ยตm) Spray Cone Angle : 51.59 deg Liquid Core Breakup Length : 7.41 mm =================================================================
๐ Calculation Methodology & Engineering Theory
Breakup Regimes & Ohnesorge Diagram
The transition from a continuous liquid column to finely dispersed droplets is governed by the competing forces of inertia, surface tension, viscous shear, and aerodynamic drag:
- Rayleigh Regime (Oh < 0.1, WeL < 10): Capillary instabilities pinch off droplets larger than the nozzle.
- First & Second Wind-Induced: Aerodynamic interaction with surrounding gas causes surface wave shearing.
- Catastrophic Atomization (Weg > 40): Instantaneous chaotic stripping of ligaments into micro-droplets.
Sauter Mean Diameter (D32)
The Sauter Mean Diameter represents the ratio of droplet volume to surface area, critical for mass transfer, evaporation, and combustion:
D32 = โ diยณ / โ diยฒ = 2.25 ยท ฯ0.25 ยท ฮผL0.16 ยท ฯL0.20 ยท mฬL0.22 ยท ฮPโ0.43
The cumulative volumetric distribution follows the Rosin-Rammler distribution with dispersion parameter q โ 2.85.
Key Engineering Assumptions
- Single-component liquid atomizing in a stagnant or co-flowing gas.
- Newtonian liquid behavior (constant dynamic viscosity ฮผL).
- Pressure-swirl / plain orifice discharge correlation valid for ReL > 500.
- Secondary droplet coalescence and wall impingement are not modeled.