The critical tube diameter in a two reaction steps detonation: the H₂/NO₂ mixture case

Abstract

We present experimental results on the detonability of the H₂/NO₂ mixture whose detonation exhibits a single cellular structure (λ₁) for the lean mixtures and a double cellular structure (fine cells of size λ₁ inside larger cells of size λ₂) for stoichiometric and rich mixtures. Whatever the equivalence ratio ${\phi}$ , the chemical energy is released in two successive exothermic steps of heat of reaction Q ₁ and Q ₂ (Q ₁ + Q ₂ = Q, the total heat release) and characterised (for ${\phi > 1}$) by two chemical lengths. The detonability is evaluated on the basis of critical conditions of self-sustained detonations transmission from a cylindrical tube of i.d. d to free space. Results show that for the critical tube diameter relationship d/λ₁ = k, with respect to the equivalence ratio ${\phi}$ ranging from 0.5 to 1.3 at ambient temperature, k is higher than the classical value 13 and its variation is rather complex. Indeed, d/λ₁ increases with ${\phi}$ from 17–18 for ${\phi = 0.5}$ to 45–50 for ${\phi = 1}$ and to 90–100 for ${\phi = 1.3}$ . The highest detonability obtained for ${\phi = 0.6}$ is explained on the basis of the highest relative contribution of the first exothermic step to the total energy Q. We conclude that, as d/λ₁ drops with Q ₂ decreasing, it should tend to 13 with the vanishing second exothermic reaction.