Hydrogen Explosion Safety Calculator
How It Works
This calculator estimates the overpressure generated by hydrogen-air explosions using a multi-step approach:
- Atmospheric Modeling: Calculates temperature, pressure, and air density at the specified altitude using standard atmosphere models.
- Oxygen Availability: Determines available oxygen based on the Air Mixing Ratio (AMR) - the proportion of air in the hydrogen-air mixture.
- Combustion Limits: Calculates how much hydrogen could theoretically combust based on stoichiometric limits and available oxygen.
- Energy Release: Computes the effective energy release using the Lower Heating Value (LHV) of hydrogen and efficiency factors.
- TNT Equivalence: Converts the energy release to TNT equivalent for blast modeling.
- Overpressure Prediction: Uses scaled distance correlations to estimate overpressure at various distances.
Technical Details & Equations
Key Acronyms
- LHV (Lower Heating Value): The heat released when a fuel is completely combusted, excluding the heat of vaporization of water formed. For hydrogen, LHV ≈ 120 MJ/kg.
- AMR (Air Mixing Ratio): The volume fraction of air in the hydrogen-air mixture. AMR = V_air / (V_air + V_H2), where V_air and V_H2 are the volumes of air and hydrogen respectively.
- TNT Equivalent: The mass of TNT that would release the same energy as the hydrogen explosion.
Atmospheric Model
Temperature: T = T₀ - L × h
Pressure: P = P₀ × (T/T₀)^(g/(L×R))
Air Density: ρ = P/(R×T)
Where: T₀ = 288.15 K, P₀ = 101325 Pa, L = 0.0065 K/m, g = 9.80665 m/s², R = 287.058 J/(kg·K)
Oxygen Availability
Volume Ratio: V_air/V_H2 = AMR/(1-AMR)
Available Oxygen: m_O2 = ρ_air × V_air × 0.2314
Where 0.2314 is the mass fraction of oxygen in dry air.
Combustion Limits
Stoichiometric Ratio: H₂ + ½O₂ → H₂O
Mass Ratio: m_O2/m_H2 = 31.998/(2×2.016) ≈ 7.936
Theoretically Combustible Hydrogen: m_H2_combustible = min(m_H2_initial, m_O2_available/7.936)
Energy Release
Effective Energy: E_effective = m_H2_combustible × LHV × η_overall × η_AMR
Where η_overall is the overall explosion efficiency and η_AMR is the AMR-specific efficiency factor.
TNT Equivalence
TNT Equivalent: m_TNT = E_effective / E_TNT
Where E_TNT = 4.184 MJ/kg is the energy content of TNT.
Scaled Distance
Scaled Distance: Z = r / (m_TNT)^(1/3)
Where r is the actual distance and m_TNT is the TNT equivalent mass.
Overpressure Model
Simplified Correlation: ΔP = 1000 / Z^1.5 (kPa)
Note: This is a simplified placeholder model. Validated correlations should be used for actual safety assessments.
Efficiency Factors
The calculator uses AMR-specific efficiency factors (η_AMR) based on experimental data:
- 10% AMR: η = 0.05
- 20% AMR: η = 0.10
- 30% AMR: η = 0.20
- 40% AMR: η = 0.30
- 50% AMR: η = 0.40
Disclaimer: This calculator estimates overpressure generated by hydrogen-air explosions at various distances and air mixing ratios. It is designed to help assess potential hazards and determine safe distances. The overpressure model is simplified and should be replaced with validated correlations for actual safety assessments. Use at your own risk.