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A shear instability mechanism for the pulsations of Rayleigh–Taylor unstable model flames

Published online by Cambridge University Press:  06 May 2014

E. P. Hicks
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Abstract

Previous studies have shown that the behaviour of Rayleigh–Taylor (RT) unstable flames depends on the boundary conditions. If the boundary conditions at the domain walls are impermeable/adiabatic or reflecting then the flame assumes a stable parabolic shape. On the other hand, periodic boundary conditions can produce unstable pulsating solutions. In this paper, we explore why periodic boundary conditions allow unstable solutions by showing the results of two-dimensional direct numerical simulations of model flames. We show that RT unstable premixed model flames pulsate at low gravity because of a shear instability of the vorticity layers behind the flame front. The resulting vortex shedding is controlled by a region of absolute-like instability which moves closer to the flame front as gravity is increased, ultimately disturbing the flame and leading to pulsations. We demonstrate that this region is ‘absolutely unstable’ by showing that the wake is dominated by pure frequency oscillations. In addition, the shear instability can be described by the Landau equation and can be represented dynamically by a Hopf bifurcation. The applicability of the Landau equation allows the apparently complex spatio-temporal behaviour of the vortex shedding to be described by a simple temporal model with only a secondary spatial dependence. We show that the flame behaviour is analogous to the initial instability downstream of a circular cylinder, which leads to the von Kármán vortex street for large enough values of the Reynolds number.

JFM classification

Instability: Absolute/convective instability Reacting Flows: Flames Wakes/Jets: Shear layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 618 - 640
Copyright
© 2014 Cambridge University Press 

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