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Research Papers: Fundamental Issues and Canonical Flows

Circulation Generation and Vortex Ring Formation by Conic Nozzles

[+] Author and Article Information
Moshe Rosenfeld

School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel

Kakani Katija, John O. Dabiri

Graduate Aeronautical Laboratories and Bioengineering, California Institute of Technology, Pasadena, CA 91125

J. Fluids Eng 131(9), 091204 (Aug 18, 2009) (8 pages) doi:10.1115/1.3203207 History: Received April 14, 2009; Revised July 08, 2009; Published August 18, 2009

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of the domain of computation

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Figure 2

Comparison of the circulation evolution of the numerical (solid line) and experimental (symbols) results (De/Dp=0.6)

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Figure 3

The evolution of the axial velocity profile at the nozzle exit (velocity program no. 1)

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Figure 4

The scaled vorticity (contour lines between 0 to 20 with an increment of 1) for velocity program no. 2. The spatial coordinates are scaled by De.

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Figure 5

The evolution of the total circulation, (a) normalization by piston parameters, and (b) normalization by exit parameters

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Figure 6

The evolution of the double-star normalized circulation

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Figure 7

The evolution of (a) the normalized circulation flux versus the formation time t∗∗, and (b) the centerline exit pressure versus te∗

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Figure 8

The asymptotic two-dimensional contribution to the total circulation generation (%)

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Figure 9

The evolutions of the total (lines) and vortex ring (lines with symbols) circulations

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Figure 10

The evolutions of the total (lines) and vortex ring (lines with symbols) normalized energies

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Figure 11

Geometry of the limiting cases (a) orifice and (b) straight tube vortex generators (De=1.5 cm, H=10 cm, Ls=45.1 cm, and L=80 cm)

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Figure 12

The evolution of the exit centerline velocity for the cases with an equal exit diameter (De=1.5 cm)

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Figure 13

Evolution of the (a) circulation and (b) circulation flux for the cases with an equal exit diameter (De=1.5 cm)

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