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Research Papers: Fundamental Issues and Canonical Flows

# Analysis of Coherent Structures in the Far-Field Region of an Axisymmetric Free Jet Identified Using Particle Image Velocimetry and Proper Orthogonal Decomposition

[+] Author and Article Information
A.-M. Shinneeb

Department of Civil and Environmental Engineering,  University of Windsor, 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canadashinneeb@uwindsor.ca

R. Balachandar

Department of Civil and Environmental Engineering,  University of Windsor, 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canadarambala@uwindsor.ca

J. D. Bugg

J. Fluids Eng 130(1), 011202 (Dec 19, 2007) (9 pages) doi:10.1115/1.2813137 History: Received December 19, 2006; Revised July 10, 2007; Published December 19, 2007

## Abstract

This paper investigates an isothermal free water jet discharging horizontally from a circular nozzle $(9mm)$ into a stationary body of water. The jet exit velocity was $2.5m∕s$ and the exit Reynolds number was 22,500. The large-scale structures in the far field were investigated by performing a proper orthogonal decomposition (POD) analysis of the velocity field obtained using a particle image velocimetry system. The number of modes used for the POD reconstruction of the velocity fields was selected to recover 40% of the turbulent kinetic energy. A vortex identification algorithm was then employed to quantify the size, circulation, and direction of rotation of the exposed vortices. A statistical analysis of the distribution of number, size, and strength of the identified vortices was carried out to explore the characteristics of the coherent structures. The results clearly reveal that a substantial number of vortical structures of both rotational directions exist in the far-field region of the jet. The number of vortices decreases in the axial direction, while their size increases. The mean circulation magnitude is preserved in the axial direction. The results also indicate that the circulation magnitude is directly proportional to the square of the vortex radius and the constant of proportionality is a function of the axial location.

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## Figures

Figure 1

Schematic description of the apparatus

Figure 2

Axial mean velocity and turbulence intensity profiles near the jet exit (x∕D=0.2). Velocities are normalized by the exit velocity (2.5m∕s) and distances by the jet exit diameter (9mm).

Figure 3

((a)–(c)) Examples of POD reconstructed velocity fluctuation fields for the free jet representing three adjacent FOVs. The circles represent the size of identified vortices. Dark and light circles represent positive and negative rotational senses, respectively.

Figure 4

Variation of the normalized number of vortices Nv∕Nf in the axial direction x∕D

Figure 5

((a)–(c)) The distribution of vortex size R in the axial direction x at three adjacent locations. Each plot represents data extracted from 2000 velocity fields. Note that positive R∕D represents positive rotational sense and the gray lines represent the half-width of the jet.

Figure 6

Percentage of vortices for the free jet at axial locations: (a) 14<x∕D<25, (b) 34<x∕D<42, and (c) 52<x∕D<58

Figure 7

((a)–(c)) Distribution of vortex circulation Γ of the free jet in the axial direction x extracted from 2000 velocity fields of three adjacent FOVs. Note that positive Γ∕DUe represents positive rotational sense.

Figure 8

Variation of the normalized mean radius R∕D and circulation Γmean∕DUe of vortices in the normalized axial direction x∕D

Figure 9

Distribution of normalized circulation Γ∕DUe associated with the identified vortices of different sizes in the range 52<x∕D<58. The gray line represents the model values.

Figure 10

Variation of the K value in Eq. 2 with the axial location x∕D. Each point on this curve represents the K value obtained from a range of 2D to 3D in x.

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