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A reduced-order partial differential equation model for dynamics of the flow in athermosyphon

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/20180

A reduced-order partial differential equation model for dynamics of the flow in athermosyphon

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dc.contributor.author Coutsias, Evangelos A.
dc.contributor.author Burroughs, Elisabeth A.
dc.contributor.author Romero, L.
dc.date.accessioned 2012-03-22T19:04:45Z
dc.date.available 2012-03-22T19:04:45Z
dc.date.issued 2005-11-07
dc.identifier.citation Journal of Fluid Mechanics, 543: 203-237 en_US
dc.identifier.issn 0022-1120
dc.identifier.uri http://hdl.handle.net/1928/20180
dc.description.abstract Flow in a closed loop thermosyphon heated from below exhibits a sequence of bifurcations with increasing Grashof number. Using the Navier-Stokes equations in the Boussinesq approximation we have derived a model where, in the case of a slender circular loop, the first Fourier modes exactly decouple from all other Fourier modes, leaving a system of three coupled nonlinear partial differential equations that completely describes the flow in the thermosyphon. We have characterized the flow through two bifurcations, identifying stable periodic solutions for flows of Prandtl number greater than 18.5, a much lower value than predicted previously. Because of the quadratic nonlinearity in this system of equations, it is possible to find the global stability limit, and we have proved it is identical to the first bifurcation point. The numerical study of the model equations is based on a highly accurate Fourier-Chebyshev spectral method, combined with asymptotic analysis at the various bifurcation points. Three-dimensional computations with a finite element method computational fluid dynamics code (MPSalsa), are also pursued. All three approaches are in close agreement. en_US
dc.language.iso en_US en_US
dc.publisher Cambridge University Press en_US
dc.title A reduced-order partial differential equation model for dynamics of the flow in athermosyphon en_US
dc.type Article en_US


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