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Fundamental Issues and Canonical Flows

Velocity Profiles in a Cylindrical Liquid Jet by Reconstructed Velocimetry

[+] Author and Article Information
J. R. Castrejón-Pita

Department of Engineering,  University of Cambridge, 17 Charles Babbage Road, Cambridge CB3 0FS, United Kingdomjrc64@cam.ac.uk

S. D. Hoath

Department of Engineering,  University of Cambridge, 17 Charles Babbage Road, Cambridge CB3 0FS, United Kingdomsdh35@cam.ac.uk

I. M. Hutchings

Department of Engineering,  University of Cambridge, 17 Charles Babbage Road, Cambridge CB3 0FS, United Kingdomimh2@cam.ac.uk

J. Fluids Eng. 134(1), 011201 (Feb 09, 2012) (13 pages) doi:10.1115/1.4005669 History: Received August 08, 2011; Accepted November 17, 2011; Published February 08, 2012; Online February 09, 2012

An experimental setup and a simple reconstruction method are presented to measure velocity fields inside slightly tapering cylindrical liquid jets traveling through still air. Particle image velocimetry algorithms are used to calculate velocity fields from high speed images of jets of transparent liquid containing seed particles. An inner central plane is illuminated by a laser sheet pointed at the center of the jet and visualized through the jet by a high speed camera. Optical distortions produced by the shape of the jet and the difference between the refractive index of the fluid and the surrounding air are corrected by using a ray tracing method. The effect of the jet speed on the velocity fields is investigated at four jet speeds. The relaxation rate for the velocity profile downstream of the nozzle exit is reasonably consistent with theoretical expectations for the low Reynolds numbers and the fluid used, although the velocity profiles are considerably flatter than expected.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic view of the experimental setup

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Figure 2

High speed images of a 0.59 m/s fluid jet (left image) and a 2.27 m/s fluid jet (right image) both captured with an exposure time of 60 μs. No mask has been applied to these images.

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Figure 3

Diagram showing the variables relevant to the axial reconstruction

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Figure 4

Diagram showing the methodology followed during the reconstruction process. The overlap of interrogation areas is not shown.

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Figure 5

Instantaneous velocity field inside a liquid jet with a terminal speed of 0.59 m/s: (a) radially distorted velocity field; (b) corrected field. The color scale shown on the right of (b) applies to (a) and (b).

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Figure 6

Instantaneous velocity field inside a liquid jet with a terminal speed of 1.00 m/s: (a) radially distorted velocity field; (b) corrected field. The color scale shown on the right of (b) applies to (a) and (b).

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Figure 7

Instantaneous velocity field inside a liquid jet with a terminal speed of 1.61 m/s: (a) radially distorted velocity field; (b) corrected field. The color scale shown on the right of (b) applies to (a) and (b).

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Figure 8

Instantaneous velocity field inside a liquid jet with a terminal speed of 2.27 m/s: (a) radially distorted velocity field; (b) corrected field. The color scale shown on the right of (b) applies to (a) and (b).

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Figure 9

Radially corrected velocity profiles for jet at 0.59 m/s from a wetted nozzle

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Figure 10

Radially corrected velocity profiles for jet at 1.00 m/s from a wetted nozzle

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Figure 11

Radially corrected velocity profiles for jet at 1.61 m/s from a wetted nozzle

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Figure 12

Radially corrected velocity profiles for jet at 2.27 m/s from a wetted nozzle

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Figure 13

Velocity range plotted against downstream distance (mm) for 0.59 m/s jet from a wetted nozzle. To highlight the differences, the inset graph shows the numerical and experimental results on a linear scale.

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Figure 14

Velocity range plotted against downstream distance (mm) for 1.00 m/s jet from a wetted nozzle. To highlight the differences, the inset graph shows the numerical and experimental results on a linear scale.

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Figure 15

Velocity range plotted against downstream distance (mm) for 1.61 m/s jet from a wetted nozzle. To highlight the differences, the inset graph shows the numerical and experimental results on a linear scale.

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Figure 16

Velocity range plotted against downstream distance (mm) for 2.27 m/s jet from a wetted nozzle. To highlight the differences, the inset graph shows the numerical and experimental results on a linear scale.

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Figure 17

The slope of the jet (dR/dz) as a function of downstream position (z/r0 )

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Figure 18

The shift of coordinates (1/R) as a function of radial coordinate (r/R). The axial shift has a maximum at r = 0, close to the approximate Eq. 2, while for the worst case slope (dR/dz = 0.5, corresponding to z = −0.25 mm in our experiments) the exact radial shift lies close to the zero slope approximation given by Eq. 3.

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