Reaction enhancement of initially distant scalars by Lagrangian coherent structures

Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatl...

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Bibliographic Details
Published in:Physics of fluids (1994) 2015-03, Vol.27 (3)
Main Authors: Pratt, Kenneth R., Meiss, James D., Crimaldi, John P.
Format: Article
Language:English
Subjects:
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COALESCENCE
Coalescing
Computational fluid dynamics
Cylinders
DILUTION
FILAMENTS
Fluid dynamics
Fluid flow
LAGRANGIAN FUNCTION
Liapunov exponents
LYAPUNOV METHOD
Mathematical models
PERIODICITY
Physics
REACTION KINETICS
Robustness (mathematics)
SCALARS
SHEAR
Shearing
STIRRING
TURBULENT FLOW
VORTICES
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Summary:Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4914467