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Research Papers: Fundamental Issues and Canonical Flows

Choking Phenomena in a Vortex Flow Passing a Laval Tube: An Analytical Treatment

[+] Author and Article Information
Theo Van Holten

Department of Design, Integration and Operation of Aircraft and Rotorcraft, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlandst.vanholten@tudelft.nl

Monique Heiligers, Annemie Jaeken

Department of Design, Integration and Operation of Aircraft and Rotorcraft, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands

J. Fluids Eng 131(4), 041201 (Mar 06, 2009) (7 pages) doi:10.1115/1.3089532 History: Received July 28, 2006; Revised January 31, 2008; Published March 06, 2009

The behavior of a vortex flow through a Laval nozzle was studied in connection with the purification of natural gas. By creating a vortex and passing it through a Laval nozzle, the gas will be cooled, and water droplets will form and will be centrifuged out of the gas. This system is named the Condi-Cyclone. An analytical theory is developed to reveal the most important phenomena of the flow, to first order accuracy. Experiments have been performed with a prototype of the Condi-Cyclone. A Euler numerical simulation was performed, using the geometry of the test channel. This paper presents an analytical theory for a vortex flow through a Laval nozzle. It will demonstrate that when a vortex is present the total velocity reaches sonic conditions upstream of the nozzle throat, that the axial component of the velocity in the nozzle throat is equal to the local speed of sound and that the mass flow through the Laval nozzle decreases with increasing vortex strength. The predictions of the analytical theory have been compared with the results of the experiments and the Euler numerical simulation, and it can be concluded that the analytical theory describes the main characteristics of the flow very well.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 7

Calculated back-flow at the end of the center-body

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Figure 8

Mass flow and vortex strength as a function of the blade deflection angle

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Figure 9

Temperature and Mach number at the end of the nozzle as a function of the blade deflection angle

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Figure 6

Tangential velocity (horizontal axis) as a function of radial distance (vertical axis) for several stations

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Figure 5

Axisymmetric mesh; zoomed in at the end of the center-body

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Figure 4

General geometry of the channel with axisymmetric mesh. The zero station is located at the end of the center-body; the throat is located at the 0.5 m station.

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Figure 3

Flow angle just downstream of the subsonic vortex generator and the resulting velocities

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Figure 2

Definition of annulus and corresponding velocities

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Figure 1

Schematic lay-out of the Condi-Cyclone

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