Numerical simulation will play an increasing role in explosion safety. A hierarchy of models with increasing complexity can be developed, but in most realistic situations, drastic simplifications must be made to contain the simulation within a manageable size. In this context, two main issues dominate: turbulence and combustion chemistry. The work presented here focuses upon the latter. The range of models used goes from empirical propagation models with no connection with actual kinetics, to

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... duction length models, to single step Arrhenius, to two or a few steps, to reduced schemes, and finally to full kinetics. It is clear that kinetics play an important role. As the results below show, what behavior kinetics dictate at the initial conditions (pressure, temperature, mixture composition) under consideration can be crucial, especially with hydrogen. Thus an ability to yield accurate predictions that are not overly conservative may well require proper consideration of the effect of kinetics. Yet, dealing with complete kinetics, or even reasonable reduced schemes remains typically out of reach as a practical matter. Simulation of complex kinetics is plagued by the numerical stiffness problem, which is fundamental. Worse, even for the simplest hence best-known case, namely, hydrogen-air, considerable uncertainties remain about the detailed kinetics; the best predictions so far of the detonation cell size appear to be off by an order of magnitude compared with experimental results. 1 High-resolution multi-dimensional simulation of explosions and detonations rapidly become more expensive as more reactions are considered; using a competitive reduced scheme with say ten to fifteen species instead of a single step will typically increase the size of a computation by a factor 10. Given that computational resources such as CPU time are necessarily limited, often, the tradeoff is then to compromise on resolution. Yet as shown by Quirk 2 for the detonation wave structure, accurate results cannot be obtained without proper resolution of hot spots, where chemistry can be faster by orders of magnitude. Clearly, accurate modeling of ignition and detonation initiation or transition will also require well-resolved hot spots. As a result, simple kinetics often provide for a better tradeoff. However, as demonstrated by the results below, real mixtures, even hydrogen-oxygen, which this study is primarily concerned with, cannot realistically be represented using a single step reaction. Hydrogenoxygen chemistry features a very specific chain-branching mechanism. Short and Quirk 3 performed a linear stability study using a three-step chain-branching model, consisting of a chain-initiation step and a chainbranching step, both governed by Arrhenius kinetics, followed by a pressure and temperature-independent chain-termination step. While that model contains the essential dynamics of real chain-branching, unlike one-step Arrhenius kinetics, it only yields one explosion limit, similar to the first or third limit for hydrogen. Based upon chain-branching theory of Dainton, 4 Liang and Bauwens 5 considered a four-step model with the the same initiation and chain-branching steps as in, 3 but with two termination steps that feature pressuredependent rates. Their model yields the explosion peninsula between first and second limit characteristic of hydrogen. Experimental observations in hydrogen-oxygen-argon/nitrogen mixtures 6 show keystone features behind the shock front on Schlieren images. These are not obvious in numerical simulations with singlestep chemical model, but they are very clear on computations with four-step chain-branching kinetics. 5 The keystone figures are bounded by the shear layers that emanate from the triple points across which a discontinuity in reactivity occurs, and, behind Mach stems, by the layer where chain-branching occurs. These figures are clearly associated with the substantial differences in reactivity that occur across the slip lines, which are very large because of chain-branching. Although perhaps still not realistic, these three/four step chain-branching mechanisms go in the right direction. In this paper, a slighted revised four step chain-branching is now proposed. In contrast with the previous model 5 the current two termination steps yield not only the explosion peninsula between first and second limit characteristic of hydrogen, but also the third limit. Results from numerical simulation are shown that clearly relate keystone figures with chain-branching. Results from analysis are also presented, showing the detailed structure of the planar wave under the various kinetic steps and in the explosion and no-explosion regimes. Buckmaster and Ludford 8 analytically derive the complete structure of a steady square-wave detonation for sufficiently high activation energies, characterized by an irreversible one-step Arrhenius reaction, using matched asymptotic techniques. In this paper we adopt the similar technique and derive the steady wave structure for both post-shock states in the explosion region and non-explosion region. The reaction lengths predicted by the theory are close to numerical results. Corresponding two dimensional numerical simulations show different cell structures and differences in regularity in different zones.