A two–step kinetics model for numerical simulation of explosions and detonations in H ₂ –O ₂ mixtures

Abstract

A two-step chemical model for use in the numerical simulation of detonation phenomena in undiluted H 2 -O 2 mixtures is developed in this paper. The use of an induction-time parameter is examined, and its underlying assumptions are discussed. Various previously developed approximations for the induction time are compared with the results of numerical calculations using a detailed reaction mechanism, and on this basis, a new, more-accurate approximation is proposed. The heat-releasing reactions at the end of the induction period are replaced by a suitably calibrated chemical-transformation process. The results obtained using this approach in onedimensional unsteady detonation calculations agree well with theoretical predictions for Chapman-Jouguet detonations once the steady state has been attained. When the new model was applied to the diffraction of a detonation at the exit of a detonation tube, excellent agreement between simulation and experiment was obtained. Keywords: detonations; two-step H 2 -O 2 kinetics; H 2 -O 2 detonation diffraction; numerical simulation of detonations; H 2 -O 2 induction-time models; explosions

Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme

“…However, it requires too many computational resources even for 2D cases, not to mention three-dimensional computation. To achieve an acceptable compromise between the solution accuracy and the computational time, we choose an improved two-step kinetic model, [14] in which the complex chemical reactions are simplified to an induction reaction and an exothermic reaction. Neglecting the influences of thermal conduction, viscosity, and mass diffusion, the detonation propagation can be described in three-dimensional Cartesian coordinate system by the reactive Euler equation…”

“…Besides, one-step kinetics model [12] and other simplified models [13] were also put forward in previous work. Sichel et al [14] developed Taki's model by introducing a parameter which reflected changes in gas composition, and promoted the computational precision a lot. In the early study, two-dimensional (2D) simulations were usually used to study the detonation cellular structures and there were thousands of literatures available.…”

Numerical simulation of detonation structures using a thermodynamically consistent and fully conservative reactive flow model for multi-component computations

“…It becomes clear that the induction zone region cannot be approximated using single-step Arrhenius kinetics (Ng et al 2005b). Significant improvements can be obtained by using a two-step or three-step chain-branching kinetic model (Short & Quirk 1997;Clifford et al 1998;Sichel et al 2002;Ng & Lee 2003; Short & Sharpe 2003;Liang & Bauwens 2005). This is outside the scope of the present study.…”

Self-organized generation of transverse waves in diverging cylindrical detonations

“…Variables a and b specify the degree of chemical induction and heat release reaction of an improved two-step kinetics model proposed by Sichel et al [19]. In this model, the change of chemical components during reactions is included in the calculation of thermodynamic parameters and the reaction rates of the two-step chemical processes are expressed by…”