💧 Droplet Evaporation & d²-Law
Calculate single droplet lifetime, Godsave/Spalding evaporation constant K, convective Ranz-Marshall correction, and mass history.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
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📦 Code Fortran
4.5 KB
📅 Mise en service
Jun 2026
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< 1 ms
💧 Droplet Shrinkage, Thermal Halo & Vapor Plume Dynamics
Real-time d²-Law Godsave/Spalding evaporation simulation📝 Configuration & Presets
💧 Water Mist (150°C Air)
🔥 Diesel Combustion (850°C)
🥛 Spray Drying (200°C)
❄️ Cryogenic LN₂ Droplet
Key Formulations:
• d²-Law: d²(t) = d₀² − K · t
• Lifetime: τlife = d₀² / K
• Spalding Number: BT = Cp,g (T∞ − Ts) / Lv
• Constant: K = [8 kg / (ρL Cp,g)] ln(1 + BT) (1 + 0.3 Re1/2 Pr1/3)
• d²-Law: d²(t) = d₀² − K · t
• Lifetime: τlife = d₀² / K
• Spalding Number: BT = Cp,g (T∞ − Ts) / Lv
• Constant: K = [8 kg / (ρL Cp,g)] ln(1 + BT) (1 + 0.3 Re1/2 Pr1/3)
📊 Evaporation Results
Configure inputs and click Compute to view results.
📘 Calculation Methodology & Engineering Theory
The Classical $d^2$-Law
Diffusion-controlled droplet evaporation under quasi-steady conditions follows Godsave and Spalding's classic linear diameter-squared relation:
d²(t) = d₀² − K · t, τlife = d₀² / K
Where the evaporation constant $K$ depends on gas thermal conductivity and the thermodynamic driving force $\ln(1 + B_T)$.
Convective Enhancement (Ranz-Marshall)
When relative motion exists between droplet and surrounding gas ($U_{rel} > 0$), forced convection thins the boundary layer:
Nu = 2.0 + 0.6 · Red1/2 · Pr1/3
This accelerates heat transfer and mass evaporation rate by a convective multiplier $F_{conv}$.
Key Engineering Assumptions
- Spherically symmetric liquid core throughout evaporation lifetime.
- Droplet temperature remains near equilibrium wet-bulb/saturation value $T_s$.
- Gas phase quasi-steady state assumption ($\tau_{gas} \ll \tau_{droplet}$).
- Ideal gas mixture behavior in ambient gas film.