🚿 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.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
📊 Solver Telemetry
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📦 Code Fortran
4.5 KB
📅 Mise en service
Aug 2026
⏱️ Latence
< 1 ms
🚿 Spray Jet & Droplet Atomization Dynamics
Real-time particle & wave breakup simulation📝 Configuration & Presets
Key Formulations:
• Velocity: Vinj = Cd √(2ΔP/ρL)
• Sauter Mean Diameter: D32 = 2.25 σ0.25 μL0.16 ρL0.20 ṁ0.22 ΔP−0.43
• Weber Number: Weg = ρg Vinj² d0 / σ
• Ohnesorge Number: Oh = μL / √(ρL σ d0)
• Velocity: Vinj = Cd √(2ΔP/ρL)
• Sauter Mean Diameter: D32 = 2.25 σ0.25 μL0.16 ρL0.20 ṁ0.22 ΔP−0.43
• Weber Number: Weg = ρg Vinj² d0 / σ
• Ohnesorge Number: Oh = μL / √(ρL σ d0)
📊 Atomization & Spray Results
📊 Output Summary
Identified Breakup Regime
Second Wind-Induced Regime
Turbulent shearing and short-wavelength wave stripping; droplets smaller than nozzle diameter.
Sauter Mean Diameter (D32)
519.3 µm
MMD (Dv50) = 612.8 µm
Spray Cone Angle (θ)
35.7°
Liquid Core Length = 50.6 mm
Injection Velocity (Vinj)
80.54 m/s
Flow = 3.946e-3 kg/s (0.24 L/min)
Dimensionless Numbers
Weg = 26.7 | Oh = 0.0074
ReL = 2.01e+4 | WeL = 2.22e+4
📈 Rosin-Rammler Droplet Size Distribution
📉 Sauter Mean Diameter D32 vs Injection ΔP
================================================================= THERMOFLUIDCALC — SPRAY & DROPLET ATOMIZATION REPORT ================================================================= Case Title : High-Pressure Misting & Evaporative Cooling Nozzle Nozzle Orifice Diameter : 0.250 mm (2.5000e-4 m) Injection Pressure Drop : 70.00 bar (7.000e+6 Pa) Discharge Coefficient Cd : 0.680 ----------------------------------------------------------------- Liquid Velocity (V_inj) : 80.539 m/s Mass Flow Rate (mdot) : 3.9456e-3 kg/s (3.946 g/s) Volumetric Flow Rate (Q) : 3.9535e-6 m3/s (0.237 L/min) ----------------------------------------------------------------- Liquid Reynolds Number ReL : 2.005e+4 Liquid Weber Number WeL : 2.223e+4 Gas Weber Number Weg : 2.673e+1 Ohnesorge Number Oh : 0.00743 Breakup Regime : Second Wind-Induced Regime ----------------------------------------------------------------- Sauter Mean Diameter (D32) : 519.32 microns (µm) Arithmetic Mean (D10) : 337.56 microns (µm) Mass Median Diameter (Dv50): 612.79 microns (µm) Spray Cone Angle : 35.71 deg Liquid Core Breakup Length : 50.62 mm =================================================================
📘 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 = ∑ di³ / ∑ di² = 2.25 · σ0.25 · μL0.16 · ρL0.20 · ṁL0.22 · ΔP−0.43
The cumulative volumetric distribution follows the Rosin-Rammler distribution with dispersion parameter q ≈ 2.85.
Key Engineering Assumptions
- Single-component liquid atomizing in a stagnant or co-flowing gas.
- Newtonian liquid behavior (constant dynamic viscosity μL).
- Pressure-swirl / plain orifice discharge correlation valid for ReL > 500.
- Secondary droplet coalescence and wall impingement are not modeled.