🚿 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

Fluid Mechanics

📊 Solver Telemetry ● ACTIVE

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⚡ Solves 25

💾 Downloads 301 📦 Fortran Code 4.5 KB

📅 Released Aug 2026

⏱️ Latency < 1 ms

🚿 Spray Jet & Droplet Atomization Dynamics

Real-time particle & wave breakup simulation

📝 Configuration & Presets

🚗 Diesel Direct Injector ✈️ Gas Turbine Swirl 🌾 Agricultural Fan ❄️ HP Mist Cooling

📐 Nozzle Geometry & Flow Conditions

Nozzle Orifice Diameter d₀ [mm]:

Injection ΔP = P_inj − P_amb [bar]:

Discharge Coefficient C_d: Typical: 0.65 (swirl) to 0.85 (plain orifice)

💧 Injected Liquid Properties

Liquid Density ρ_L [kg/m³]:

Liquid Dynamic Viscosity μ_L [Pa·s]:

Surface Tension σ [N/m]: Water: 0.0728 N/m, Diesel/Fuel: ~0.028 N/m

💨 Ambient Gas Properties

Ambient Gas Density ρ_g [kg/m³]: Air 1 bar: 1.2 kg/m³, Diesel cylinder: 15–40 kg/m³

Key Formulations:
• Velocity: V_inj = C_d √(2ΔP/ρ_L)
• Sauter Mean Diameter: D₃₂ = 2.25 σ^0.25 μ_L^0.16 ρ_L^0.20 ṁ^0.22 ΔP^−0.43
• Weber Number: We_g = ρ_g V_inj² d₀ / σ
• Ohnesorge Number: Oh = μ_L / √(ρ_L σ d₀)

📊 Atomization & Spray Results

Configure inputs and click Calculate to view results.

📘 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, We_L < 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 (We_g > 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 μ_L).
Pressure-swirl / plain orifice discharge correlation valid for Re_L > 500.
Secondary droplet coalescence and wall impingement are not modeled.

ThermoFluidCalc Engineering Report