Taylor dispersion in premixed combustion: Questions from turbulent combustion answered for laminar flames

Joel Daou, Philip Pearce, and Faisal Al-Malki
Phys. Rev. Fluids 3, 023201 – Published 14 February 2018

Abstract

We present a study of Taylor dispersion in premixed combustion and use it to clarify fundamental issues related to flame propagation in a flow field. In particular, simple analytical formulas are derived for variable density laminar flames with arbitrary Lewis number Le providing clear answers to important questions arising in turbulent combustion, when these questions are posed for the case of one-scale laminar parallel flows. Exploiting, in the context of a laminar Poiseuille flow model, a thick flame distinguished asymptotic limit for which the flow amplitude is large with the Reynolds number Re fixed, three main contributions are made. First, a link is established between Taylor dispersion [G. Taylor, Proc. R. Soc. London Ser. A 219, 186 (1953)] and Damköhler's second hypothesis [G. Damköhler, Ber. Bunsen. Phys. Chem. 46, 601 (1940)] by describing analytically the enhancement of the effective propagation speed UT due to small flow scales. More precisely, it is shown that Damköhler's hypothesis is only partially correct for one-scale parallel laminar flows. Specifically, while the increase in UT due to the flow is shown to be directly associated with the increase in the effective diffusivity as suggested by Damköhler, our results imply that UTRe (for Re1) rather than UTRe, as implied by Damköhler's hypothesis. Second, it is demonstrated analytically and confirmed numerically that, when UT is plotted versus the flow amplitude for fixed values of Re, the curve levels off to a constant value depending on Re. We may refer to this effect as the laminar bending effect as it mimics a similar bending effect known in turbulent combustion. Third, somewhat surprising implications associated with the dependence of UT and of the effective Lewis number Leeff on the flow are reported. For example, Leeff is found to vary from Le to Le1 as Re varies from small to large values. Also, UT is found to be a monotonically increasing function of Re if Le<2 and a nonmonotonic function if Le>2.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 16 October 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.023201

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Interdisciplinary Physics

Authors & Affiliations

Joel Daou*

  • School of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom

Philip Pearce

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA

Faisal Al-Malki

  • Department of Mathematics and Statistics, Taif University, Taif P.O. Box 88, Saudi Arabia

  • *joel.daou@manchester.ac.uk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 3, Iss. 2 — February 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Fluids

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×