Decay of Three-Dimensional Vortex Motion in an Enclosure

Deshpande, MD (2000) Decay of Three-Dimensional Vortex Motion in an Enclosure. Project Report. National Aerospace Laboratories, Bangalore, India.

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Abstract

Consider viscous, incompressible flow in a cubical container generated by the uniform,13; linear motion of the top wall. Depending on the Reynolds number Re the flow could be13; laminar, transitional or turbulent. If the motion of the top wall is now suddenly stopped13; the fluid motion will begin to decay. Direct numerical simulations show that no matter13; what the initial conditions are, the finalstages of decay follow an exponential law, i.e. the13; maximum of the Y-component of velocity V,,, is given by V, = V,,,ezp(-id/Re) where13; the decay constant d is aboilt 62. In order to explain this interesting behaviour of three-13; dimensional vortex motion, exact decaying, axisymmetric solutions of the Navier-Stokes13; equations were sought. It is shown that in cylindrical coordinates the field13; (urrue,uZ) - (-27rJ,(Xr)cos(2;rr), a J , ( X r ) sin(2;rz), XJ,(Xr) in(2irz)]e-quot;13; represents a swirling decaying vorkex and a corresponding field is found for the spherical13; case. These new exact solutions to the N-S equations are used to identify and quantify13; the different regimes of vortex decay and scaling in the cubical cavity. .The results may13; be of relevance to fluid mixing and geophysical Bows.

Item Type: Monograph (Project Report)
Uncontrolled Keywords: Vortex motion; viscous decay; closed streamlines; cavity13; torodial surface
Subjects: AERONAUTICS > Aerodynamics
Depositing User: Users 15 not found.
Date Deposited: 17 May 2005
Last Modified: 24 May 2010 04:09
URI: http://192.168.9.127/id/eprint/770

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