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Research Papers: Fundamental Issues and Canonical Flows

On a New Passive Scalar Equation With Variable Mass Diffusivity: Flow Between Parallel Plates

[+] Author and Article Information
Fabio Gori1

Department of Mechanical Engineering, University of Rome “Tor Vergata,” 00133, Rome, Italyfammannati@yahoo.com,

Andrea Boghi

Department of Mechanical Engineering, University of Rome “Tor Vergata,” 00133, Rome, Italy

1

Corresponding author.

J. Fluids Eng 132(11), 111202 (Nov 09, 2010) (11 pages) doi:10.1115/1.4002743 History: Received October 19, 2008; Revised September 29, 2010; Published November 09, 2010; Online November 09, 2010

The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Details of scalar grid

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Figure 2

Mean concentration for constant mass diffusivity

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Figure 3

Root mean square of concentration fluctuation for constant mass diffusivity

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Figure 4

Normalized budget of concentration variance at Sc=3 for constant mass diffusivity

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Figure 5

Normalized budget of concentration variance at Sc=49 for constant mass diffusivity

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Figure 6

Time scale ratio for constant mass diffusivity

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Figure 7

Concentration variance time scale for constant mass diffusivity

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Figure 8

Production of concentration variance

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Figure 9

Dissipation of concentration variance

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Figure 10

Turbulent diffusion of concentration variance

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Figure 11

Molecular diffusion of concentration variance

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Figure 12

D-fluctuating diffusion of concentration variance

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Figure 13

Budget of concentration variance for Sc=49

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Figure 14

D-fluctuating mass flux

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Figure 15

Mass flux terms for Sc=49

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