We use a Weighed Essentially Non-Oscillatory (WENO)scheme to perform very long-time two dimensional numerical simulations of detonation waves with a four-step reaction model.This model consists of a chain-initiation step and a chain-branching step,both temperature-dependent with Arrhenius kinetics,followed by two pressure-dependent termination steps.A chain-branching cross-over temperature (T_B)is introduced and its effect on the explosion limits,steady structure and detonation cellular structure are discussed.Increasing the chain-branching temperature decreases the chain-branching rate,thus increases the ratio of the initiation length to the length of the recombination zone,which leads to more unstable detonations according to linear stability analysis.As T_B increases,the ratio cell length over width increases and the cell sizes also increases.Chain-branching kinetics also results in distinctive keystone figures,observed in the instantaneous results.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.
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