Investigation of mean flow and vertical vorticity in turbulent convection using spectral simulations on massively parallel processors
Cortese, Thomas Anthony
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https://hdl.handle.net/2142/21009
Description
Title
Investigation of mean flow and vertical vorticity in turbulent convection using spectral simulations on massively parallel processors
Author(s)
Cortese, Thomas Anthony
Issue Date
1996
Doctoral Committee Chair(s)
Balachandar, S.
Department of Study
Mechanical Science and Engineering
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Computer Science
Language
eng
Abstract
Direct numerical simulations of Rayleigh-Benard convection are performed at several values of Rayleigh number (Ra). The computational domain consists of a square-planform rectangular box with horizontal-to-vertical aspect ratio equal to four. This domain is periodic in the horizontal directions, and the top and bottom boundaries are isothermal, no-slip, impermeable walls. The flow-fields considered here range from steady horizontally-oriented two-dimensional rolls to unsteady three-dimensional turbulence.
At lower values of Ra the convective flow exhibits regular spatial patterns that possess horizontal symmetry and therefore have zero instantaneous mean horizontal velocity. Also, when the flow is marginally supercritical the energy is primarily in the poloidal component and the flow does not exhibit any vertical vorticity. However, instantaneous mean horizontal motion and the spontaneous generation of concentrated vertical vorticity are observed at high Ra, indicating that turbulent Reynolds stresses have broken the horizontal symmetries.
Thermal plumes, which play an important role in the heat transfer at high Ra, can have significant vertical vorticity associated with them and thus are reminiscent of tornados in the atmosphere. The primary thrust of the present work is to investigate the three closely inter-related phenomena of mean horizontal motion, vertical vorticity, and thermal plumes.
The velocity field is decomposed into mean, toroidal, and poloidal components in order to investigate the physical mechanisms which drive these three phenomena. The poloidal motion is driven directly by the buoyancy that is induced by the temperature gradient. The mean flow is driven by the vertical gradients of the horizontally averaged Reynolds stresses, and the vertical vorticity is generated and maintained by vortex-tilting and vortex-stretching mechanisms, with the poloidal motion acting as catalyst.
Several important computational issues are also addressed. A library of kernel routines central to many different spectral method algorithms was successfully implemented on the Thinking Machines Corp. Connection Machine 5 (CM5), a massively parallel machine. The spectral-method algorithm performed beyond all expectations, at 26 Gflops on a 512-node CM5, in spite of the global data communication involved, thus demonstrating that spectral algorithms can be effectively implemented on massively parallel machines.
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