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Front speed in reactive compressible stirred media

Federico Bianco

Sergio Chibbaro

Davide Vergni

Angelo Vulpiani

  • Institut D’Alembert, University Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 5, France, CNRS UMR 7190, 4 place Jussieu, 75252 Paris, Cedex 5, France, and Dipartimento di Fisica, Università “La Sapienza,” Piazzale Aldo Moro 2, 00185 Rome, Italy

  • Institut D’Alembert, University Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 5, France and
  • CNRS UMR 7190, 4 place Jussieu, 75252 Paris Cedex 5, France

  • Istituto Applicazioni Calcolo, CNR, Viale Manzoni 30, 00185 Rome, Italy

  • Dipartimento di Fisica, Università “La Sapienza” and ISC-CNR, Piazzale Aldo Moro 2, I-00185 Rome, Italy

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Phys. Rev. E 87, 042924 – Published 29 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.042924

Abstract

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate vf in a shear flow increases with compressibility intensity ε, following the relation Δvf∼ε2. Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case. The effect has been quantitatively measured, and it turns out to be generally small. For the cellular flow, two extreme cases have been investigated, with the whole perturbation situated either in the center of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behavior in the two cases. The enhancing remains modest and is always less than 20%.

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Phys. Rev. E 87, 042924– Published 29 April, 2013
  • Received 21 January 2013

©2013 American Physical Society

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