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A numerical study of the vorticity field generated by the baroclinic effect due to the propagation of a planar pressure wave through a cylindrical premixed laminar flame

Published online by Cambridge University Press:  26 April 2006

G. A. Batley ,
A. C. McIntosh ,
J. Brindley  and
S. A. E. G. Falle
G. A. Batley
Affiliation:
Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, UK Department of Applied Mathematics, Leeds University, Leeds LS2 9JT, UK
A. C. McIntosh
Affiliation:
Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, UK
J. Brindley
Affiliation:
Department of Applied Mathematics, Leeds University, Leeds LS2 9JT, UK
S. A. E. G. Falle
Affiliation:
Department of Applied Mathematics, Leeds University, Leeds LS2 9JT, UK
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Abstract

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 279 , 25 November 1994 , pp. 217 - 237
Copyright
© 1994 Cambridge University Press

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