Taylor dispersion and flame propagation / 2015

In 1953, the British physicist G.I. Taylor published an influential paper describing the enhancement of diffusion processes by a (shear) flow, a phenomenon later termed Taylor dispersion. This has generated to date thousands of publications in various areas involving transport phenomena, none of which, surprisingly, in the field of combustion.

In 1940, the German chemist G. Damköhler postulated two hypotheses which have largely shaped current views on the propagation of premixed flames in turbulent flow fields. According to Damköhler’s first hypothesis, the large scales in the flow simply increase the flame surface area by wrinkling it, without affecting its local normal propagation speed. According to Damköhler’s second hypothesis, the small scales in the flow do not cause any significant flame wrinkling but do increase the normal propagation speed (and flame thickness). However, unlike the first hypothesis, the second one has received little support in the research literature, especially as far as analytical work is concerned.

In the talk, we shall present analytical and numerical studies which are the first on Taylor dispersion in the context of combustion. In particular, simple analytical formulas will be derived which establish the link between Taylor dispersion and Damköhler’s second hypothesis. The findings will be applied to provide explanations, within simple tractable analytical laminar-flow models, of the differing and often apparently contradictory results found in experimental and numerical studies concerned with flame propagation in more complex (turbulent) flows. One such explanation is related to the so-called bending-effect of the turbulent flame speed, which is observed experimentally under high intensity turbulent flows. Another explanation is related to clarifying the dependence of the apparent Lewis number on the flow.

The talk will start with an introduction to Taylor dispersion, before generalising the problem to account for flame propagation (including density variations). An attempt is made to make the talk instructive for a wide audience including applied mathematicians, physicists and engineers.

Lieu: Petit Amphi M2P2/ La Jetée 2ème étage / Ecole Centrale