Effect of volumetric expansion on shock-induced ignition of H2–NO2/N2O4 mixtures
Introduction
Under rich conditions, H2–NO2/N2O4 mixtures exhibit an unusual two-step energy release profile. The first step of oxidation is dominated by NO2 whereas the second one is dominated by NO [1], [2], [3]. This peculiar behavior results in very specific detonation features. For a large enough tube diameter, a propagating detonation demonstrates a cellular pattern characterized by two superimposed dominant length-scales of very different size which is referred to as “double cellular structure”. For a small enough tube diameter, low-velocity detonations with a single cellular structure and a stable propagation velocity can be observed [4], [5]. Such a behavior was attributed to the fact that the energy released by the second oxidation step does not significantly contribute to the detonation propagation because of various loss mechanisms. Multi-dimensional numerical simulation of the propagation of detonation in H2–NO2/N2O4 mixtures were performed by Guilly et al. [6], Sugiyama and Matsuo [7], Davidenko et al. [8], and Virot et al. [5], [9]. The diffraction of detonation with double cellular structure was investigated by Desbordes et al. [10] for Φ=0.4–1.3 and P1=30–130 kPa. They noted that (i) the extinction envelope was longer than expected from the behavior of diffraction in common mixtures; and (ii) the relationship between the critical tube diameter (dc) and the detonation cell width (λ) was different from that in common gases. Further details about detonation in H2–NO2/N2O4 mixtures are presented as a supplemental material.
From this literature review, it is concluded that, although the propagation and diffraction of detonation for mixtures with two-step energy release such as H2–NO2/N2O4 mixtures have received considerable attention, other detonation phenomena, such as direct detonation initiation, have not been studied. Direct detonation initiation can be achieved by releasing a large amount of energy within a small volume. The initially over-driven detonation wave progressively decays to a self-sustained detonation if the energy provided is high enough, i.e. the super-critical regime, or a non-reactive shock wave if the energy provided is too low, i.e. the sub-critical regime. At critical conditions, the shock wave and reaction first decouple and propagate at a sub-CJ quasi-constant velocity (referred to as “metastable period”) and an over-driven detonation emerges after local re-initiation eventually takes place. Eckett [11] and Eckett et al. [12] have shown, using the temperature gradient equation along the path of a Lagrangian particle, derived from the Euler equations, that direct detonation initiation was controlled by the competition between chemical energy release rate and the cooling induced by the volumetric expansion behind an unsteady decaying shock. Such a competition has been studied by several authors including Lundstrom and Oppenheim [13], Vazquez-Espi and Liñan [14], Radulescu and Maxwell [15], and Liu and Mevel [16]. In all these studies, one-step or two-step globalized chemical models were employed. It is noted that Liu and Mevel performed a comprehensive parametric study and considered the effect of both induction and excitation times. Using a detailed reaction model, Mevel et al. [17] investigated the effect of the mathematical form of the shock decay rate on the critical conditions for quenching ignition of a stoichiometric hydrogen-air mixture. They found that for initial pressures in the range 500–800 kPa, the ignition process was the most sensitive to the expansion-induced cooling whereas for initial pressures below 100 kPa, the ignition process was the least sensitive to quenching. They attributed this complex response to expansion to the extended second explosion limit of hydrogen-air mixtures.
To the best of the authors’ knowledge, the previous studies on the effect of volumetric expansion on the auto-ignition process have been limited to conditions for which monotonous energy release rate profiles are observed.
In the present study, we have investigated the ignition of H2–NO2/N2O4 mixtures which demonstrate either monotonous or non-monotonous energy release rate profiles under volumetric expansion conditions. Similar to Mevel et al. [17], we employed a variable-volume reactor to model certain fluid element behind the shock. In order to relate such a simple model to the direct detonation initiation phenomenon, we have employed the Taylor–Sedov similarity solution to link the rate of speed decay of a shock initiated by a point energy source to the rate of expansion of the mixture’s specific volume. We recognize that our approach cannot capture all the features of the direct detonation initiation phenomenon. Nevertheless, our simplified model contains the main physical processes which control the onset or failure of detonation, and presents the advantage of a much lower computational cost as compared to more realistic 1-D or 2-D simulations. This enabled us to use a full detailed reaction model and to study a wide parametric space.
The manuscript is structured as follows: a detailed description of the methodology and calculation procedure is presented in 2 Methodology and calculation procedure, 3 Results and discussion covers the results and discussion; and closing remarks are presented in Section 4.
Section snippets
Problem definition
Studying detonation dynamics along the path of a Lagrangian particle is a common approach [11], [18] because it enables to transform a time- and space-dependent problem into a time-dependent problem. We have adopted a similar approach in the present study. Figure 1 illustrates the configuration we have considered. A fluid element initially shocked by a decaying shock wave propagating at bDCJ with b ∈ [1, 0.7] is undergoing an isentropic volumetric expansion whose rate was imposed by the
Ignition and quenching under volumetric expansion
Our first interest was to examine the effect of the initiation energy and decay of shock speed on the ignition dynamics. Figure 2 shows the ignition behaviors of a lean H2-NO2/N2O4 mixture (Φ=0.5) for two different initiation energies (Ec=2 J and 300 mJ) and various initial shock speeds (D). As shown by Fig. 2(a), the largest shock speed of interest (D/DCJ=1) allows fastest ignition among all cases. Note that under this lean condition, a single-stage heat release is evidenced in the thermicity
Conclusion
In the present study, the ignition of H2–N2O/N2O4 mixtures under volumetric expansion has been studied using a 0-D variable-volume reactor model. Both a lean mixture (Φ=0.5), which demonstrates a single step of energy release, and a rich mixture (Φ=1.5), which demonstrates a two-step energy release, were investigated. The temporal rate of change of the specific volume was linked to the shock decay rate which was described using the Taylor–Sedov solution for blast wave initiation of a detonation
Declaration of Competing Interest
The authors declare having no conflict of interest.
Acknowledgments
RM and YCL were supported by a start-up fund of the Center for Combustion Energy of Tsinghua University, the Thousand Young Talents Program of China, and the 1000 Young Talents Matching Fund of Tsinghua University. YH was funded by China Postdoctoral Science Foundation (grant number 2019M650674).
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