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Research Papers

An Inviscid Solution for Modeling of Tornadolike Vortices

[+] Author and Article Information
Zhuyun Xu

 Vipac Engineers & Scientists Ltd., 279 Normanby Road, Port Melbourne VIC 3207, Austrailiazhuytunx@vipac.com.auThe Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, ON, N6A 5B9, Canadazhuytunx@vipac.com.au

Horia Hangan

 Vipac Engineers & Scientists Ltd., 279 Normanby Road, Port Melbourne VIC 3207, Austrailiahmh@blwtl.uwo.caThe Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, ON, N6A 5B9, Canadahmh@blwtl.uwo.ca

J. Appl. Mech 76(3), 031011 (Mar 11, 2009) (5 pages) doi:10.1115/1.3063632 History: Received September 25, 2007; Revised August 14, 2008; Published March 11, 2009

An inviscid tornadolike vortex is analytically modeled using a free narrow jet solution combined with a modified Rankine vortex. An empirical and simplified solution to existing models is defined for flows similar to the ones simulated in Ward-type vortex chambers. Velocity profiles are calculated for a particular swirl ratio Sr=0.28. The model shows reasonable agreement with existing experimental measurements by Baker (1981, “Boundary Layers in Laminar Vortex Flows,” Ph.D. thesis, Purdue University, West Lafayette, IN) and the numerical simulation by Wilson and Rotunno (1986, “Numerical Simulation of a Laminar End-Wall Vortex and Boundary Layer,” Phys. Fluids, 29(12), pp. 3993–4005).

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Copyright © 2009 by American Society of Mechanical Engineers
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Figure 8

Comparison of velocity variation versus r (modified model, Baker’s test and Wilson and Rotunno’s CFD): (a) z=0.075, (b) z=0.25, and (c) z=0.625

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Figure 7

Comparisons of velocity profiles versus height at r=0.75 (modified model, Baker’s test and Wilson and Rotunno’s numerical simulation): (a) r=0.0475, (b) r=0.1025, (c) r=0.2125, and (d) r=0.75

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Figure 6

Influx radial velocity profiles at r=1

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Figure 5

Contours of typical swirl velocities (Sr=0.28) (the values from the higher are 6, 5, 4, 3, 2, and 1)

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Figure 4

Contours of radial velocities (the values from the lower are −10, −5, −4, −3, −2, −1, −0.5, 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 1)

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Figure 3

Contours of axial velocities (the values are 64, 32, 8, 6, 5, 4, 3, 2, 1, and 0.5)

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Figure 2

Vorticity contours (the values from the core to outside are 1000, 100, 10, 1, and 0.1)

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Figure 1

Contours of Stokes’ stream function, which represent the modeled streamlines of the vortex (the values are −0.1, −0.2, −0.3, −0.4, −0.5, −0.6, −0.7, −0.8, −0.9, −1, −1.5, −2, and −2.5)

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