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Dissipation-scale fluctuations and mixing transition in turbulent flows

Published online by Cambridge University Press:  10 July 2008

VICTOR YAKHOT
VICTOR YAKHOT*
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
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Abstract

A small separation between reactants, not exceeding 10−8 − 10−7 cm, is the necessary condition for various chemical reactions. It is shown that random advection and stretching by turbulence leads to the formation of scalar-enriched sheets of strongly fluctuating thickness ηc. The molecular-level mixing is achieved by diffusion across these sheets (interfaces) separating the reactigants. Since the diffusion time scale is , knowledge of the probability density Q(ηc, Re) is crucial for evaluation of mixing times and chemical reaction rates. According to Kolmogorov–Batchelor phenomenology, the stretching time τeddy ≈ L/urms = O(1) is independent of large-scale Reynolds number Re = urmsL/ν and the diffusion time is very small. Therefore, in previous studies, molecular diffusion was frequently neglected as being too fast to contribute substantially to the reaction rates. In this paper, taking into account strong intermittent fluctuations of the scalar dissipation scales, this conclusion is re-examined. We derive the probability density Q(ηc, Re, Sc), calculate the mean scalar dissipation scale and predict transition in the reaction rate behaviour from to the high-Re asymptotics . These conclusions are compared with known experimental and numerical data.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 606 , 10 July 2008 , pp. 325 - 337
Copyright
Copyright © Cambridge University Press 2008

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