THE EFFECT OF CHAIN INITIATION REACTION ON THE STABILITY OF GASEOUS DETONATIONS

Abstract

The present research is conducted to investigate the instability of gaseous detonations by emphasizing the role of the initiation step. To proceed with the study, two characteristic times are defined for the initiation and the branching steps (τ_I and τ_b, respectively). Depending on the values of these characteristic times, three different modes of detonation failure are observed. It is seen that the so-called cross over temperature detonability criterion is applicable only for high values of τ_b. The present work, in a systematic fashion, revealed the importance of two length scales that control the instability as well as the failure of gaseous detonation. These length scales are the induction length and the length of the main reaction layer. It appears that these two length scales may model a vast range of chemical kinetics.

For values of τ_b which are less than 0.033, the front propagates with a constant, non-oscillatory velocity. For high values of τ_I, an abrupt failure occurs. However, for values of τ_b larger than 0.033, the front propagates in an oscillatory manner. For values of τ_b between 0.033 and 0.053, the formation of unburned pockets of the reactant behind the shock is recognized as the reason of failure for high values of τ_I. Further varying of the two parameters cause the appearance of other modes of the front propagation.

Keywords:

• Chain-branching
• Chemical kinetics
• Detonation
• Initiation
• Instability
• Numerical

Notes

Case 1: Overdriven detonation, f = 1.4, stoichiometric H₂–O₂ mixture

Case 2: CJ detonation, f = 1.0, stoichiometric H₂–O₂ mixture

Case 3: CJ detonation, equivalence ratio = 0.6, H₂–O₂ mixture with 75% N₂ dilution Initial pressure and temperature in all cases are 1 atm and 300 ′K, respectively.

Reactions A (cm-mole-s) β Ea (kj/mole)

I1: H2 + M → 2H + M 6.99E18 −1. 436.08

I2: H2 + O2 → HO2 + H 6.84E13 0.0 243.10

b1: O2 + H → OH + O 2.00E14 0.0 70.30

b2: O + H2 → OH + H 5.06E4 2.67 26.30

C1: H + OH + M → H2O + M 2.20E22 −2.0 0.00

C2: H2O2 + OH → H2O + HO2 5.4E12 0.0 4.2

Additional information

Notes on contributors

S. A. HASHEMI

Current address: Department of Mechanical Engineering, Kashan University, Kashan, I. R. Iran.