Statistical analysis of cellular detonation dynamics from numerical simulations: one-step chemistry

Abstract

In this paper, two methods are developed for statistically analysing the nonlinear cellular dynamics from numerical simulations of gaseous detonations, one use of which is the systematic determination of detonation cell sizes from such simulations. Both these methods rely on signed vorticity records in which the individual families of transverse waves are captured independently. The first method involves an automated extraction of the main triple-point tracks from the vorticity records, allowing statistical analysis of the spacings between neighbouring tracks. The second method uses the autocorrelation function to spectrally analyse the vorticity records. These methods are then employed for a preliminary analysis of the cellular dynamics of the standard, idealized one-step chemistry model. Evidence is found for ‘cell size doubling’ bifurcations in the one-step model as the cellular dynamics become more irregular (e.g. as the activation is increased). It is also shown that the statistical models converge slowly due to systematic ‘shot-to-shot’ variation in the cellular dynamics for fixed parameters with different initial perturbations. Instead, it appears that a range of equally probable cell sizes can be obtained for given parameters.

Keywords:

• gaseous detonation
• cellular instability
• numerical simulations
• nonlinear dynamics

Acknowledgments

We would like to thank James J. Quirk for much support with the AMRITA computational facility. GJS was in receipt of an EPSRC Advanced Fellowship during the course of this work and is also grateful to Rio Tinto Technology & Innovation for research sponsorship. MIR was supported by the Natural Science and Engineering Research Council of Canada (NSERC) under Discovery Grant 341897-07 and by the NSERC H2Can Network. The authors are grateful to Jeffrey Bergthorson, J.F. Haeck, Zouya Zarei, Graeme Watson, Gaby Ciccarelli, Daniel Szirti and Sergey Dorofeev for providing manual measurements of the cell size of the C₃H₈+5O₂ foil.