Abstract

A pseudospectral algorithm has been used to compute solutions u(x,t), Ax,t), B(x,t), and R(x,t) to one-dimensional equations of change incorporating the simple reaction A + B → R for statistically homogeneous random velocity and partially premixed reactant concentration fields. An initial turbulence Reynolds number of 400 has been used, together with Damkohler numbers of 102 and 103 for fast reactions and Schmidt numbers of 10-3, 1, and 102 to span a wide range of diffusivities. Evolving concentration profiles inform intuition in general and provide insight into the evolution of the single-point statistical measures in particular: (A), (B), (a2), (b2), (ab), (ab)/(A)(B), and (a2b). There is a pronounced effect of Da on all the statistical properties, but for a given value of Da, (A), (B), (ab)/(A)(B) (t), and (a2b) are identical for Sc = 1 and 102 and virtually so for Sc = 10-3 as well, whereas (a2), (b2), and (ab) evolve differently for Sc = 10-3 than for Sc = 1 and 102. Comparisons between different single-point closures for nonpremixed turbulent reactions and the present partially premixed results have been made. As was found by Leonard et al. in three dimensions for a slower nonpremixed reaction (Ind. Eng. Chem. Res. 1995, 34, 3640-3652), it is found that Toor's closure (Ind. Eng. Chem. Fundam. 1969, 8, 655-659) comes closest to agreement with our direct numerical simulations of (ab)(t) in one dimension for a faster partially premixed reaction. We propose a closure for partially premixed reactions that incorporates a reaction segregation effect which yields improved agreement with our simulations of (ab)(t).

Department(s)

Chemical and Biochemical Engineering

International Standard Serial Number (ISSN)

0888-5885

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 American Chemical Society, All rights reserved.

Publication Date

01 Jan 1998

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