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Fundamental Issues and Canonical Flows

The Effect of Spanwise Width on Rectangular Jets With Sidewalls

[+] Author and Article Information
Deepak Rangarajan1

 University of Florida, Department of Chemical Engineering, Gainesville, FL 32611deepakrangarajan@ufl.edu

Jennifer S. Curtis

 University of Florida, Department of Chemical Engineering, Gainesville, FL 32611

1

Corresponding author.

J. Fluids Eng. 134(3), 031202 (Mar 19, 2012) (8 pages) doi:10.1115/1.4006019 History: Received June 24, 2011; Revised January 30, 2012; Published March 16, 2012; Online March 19, 2012

A CFD study on the effect of spanwise width on a rectangular jet with sidewalls is conducted using a standard k-ɛ model with wall functions. An order of magnitude analysis reveals the role played by spanwise turbulent shear terms, arising from the wall bounded flow, as the aspect ratio is decreased at high streamwise distances. A comparative study involving experimental data and other turbulence models is also presented to validate the k-ɛ model for this confined jet flow. It is found that the effect of bounding walls is negligible up to a streamwise distance of at least 105 jet diameters for an aspect ratio of 40, however this distance, within which the flow can be approximated as two-dimensional, decreases with decrease in aspect ratio.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Influence of initial conditions on the mean velocity decay along the centerline. (b) Influence of initial conditions on the turbulent kinetic energy intensity evolution along the centerline.

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Figure 2

An ideal planar jet

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Figure 3

Typical laboratory setup

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Figure 4

Simulation domain and boundary conditions

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Figure 5

(a) Validation of the k-ɛ model in predicting centerline decay in mean streamwise velocity. (b) Validation of the k-ɛ model in predicting the centerline turbulent intensity evolution. (c) Validation of the k-ɛ model in predicting the evolution of the half-width.

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Figure 6

(a) Centerline mean velocity decay. (b) Evolution of turbulent kinetic energy along the centerline. (c) Streamwise evolution of the jet half-width.

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Figure 7

(a) Momentum budget along the centerline (y=0,z=w/2) for AR=40. (b) Momentum budget along the centerline (y=0,z=w/2) for AR=2.

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Figure 8

(a) Momentum budget along the centerline (y=0,z=w/2) for AR=40. The spanwise turbulent diffusion term is absent. (b) Momentum budget along the centerline (y=0,z=w/2) for AR=2. The spanwise turbulent diffusion term plays a significant role.

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Figure 9

(a) Turbulent energy budget along the centerline (y=0,z=w/2) for AR=40. (b) Turbulent energy budget along the centerline (y=0,z=w/2) for AR=2.

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Figure 10

(a) Turbulent energy budget along the centerline (y=0,z=w/2) for AR=40. The spanwise turbulent diffusion term is absent. (b) Turbulent energy budget along the centerline (y=0,z=w/2) for AR=2. The spanwise turbulent diffusion term plays a significant role.

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Figure 11

(a) Momentum budget at x=71h and z=w/2 for AR=40. The spanwise diffusion term is absent. (b) Momentum budget at x=71h and z=w/2 for AR=2. The spanwise diffusion term plays a significant role.

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Figure 12

Plot showing the minimum value of AR, which can be considered unaffected by the bounding wall influence for a given x/h

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