, Volume 23, Issue 3, pp 221-231
Date: 28 Aug 2012

A comparison between constant volume induction times and results from spatially resolved simulation of ignition behind reflected shocks: implications for shock tube experiments

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The induction time measured in shock tube experiments is typically converted into kinetic data assuming that the reaction takes place in a constant volume process, thus neglecting spatial gradients. The actual process of shock ignition is, however, both time- and space-dependent; ignition takes place at a well-defined location, and subsequently a front travels, which may couple with the pressure wave that it created and forms a detonation wave behind the shock that reflects off the wall. To assess how different the actual processes are compared with the constant volume assumption, a numerical study was performed using a simplified three step chain-branching kinetic scheme. To overcome the difficulties that arise when simulating shock-induced ignition due to the initial absence of a domain filled with shocked reactive mixture, the problem is solved in a transformed frame of reference. Furthermore, initial conditions are derived from short-time asymptotics, which resolves the initial singularity. The induction times obtained using the full unsteady formulation with those of the homogeneous explosion are compared for various values of the heat release. Results for the spatially dependent formulation show that the evolution of the post-shock flow is complex, and that it leads to a gradient in induction times, after the passage of the reflected shock. For all cases simulated, thermal explosion initially occurs very close to the wall, and the corresponding induction time is found to be larger than that predicted under the constant volume assumption. As the measurement is made further away however, the actual time interval between passage of the reflected shock, and the specified pressure increase denoting ignition, decreases to a value close to zero, corresponding to that obtained along a Rayleigh line matching that of a steady ZND process (assuming a long enough tube). In situations where the constant volume assumption is expected to be weak, more accurate kinetic data will be obtained using a spatially resolved computation such as the one used in the current comparison.

Communicated by S. Dorofeev.
This paper is based on work that was presented at the 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine, California, USA, July 24–29, 2011.