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Numerical Evaluation of the Validity Domain of Lorenz Equations
Başlık:
Numerical Evaluation of the Validity Domain of Lorenz Equations
Yazar:
Lindgren, Allison, author.
ISBN:
9780438015401
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (83 pages)
Genel Not:
Source: Masters Abstracts International, Volume: 57-06M(E).
Advisors: Peter Vadasz Committee members: Tom Acker; James Swift.
Özet:
Natural convection in a two-dimensional rectangular domain heated at the bottom and cooled at the top with perfectly insulated sidewalls is the topic of interest for this research. For Rayleigh numbers less than the critical value, Racr, any disturbances will decay to a motionless solution and heat transfer will occur via conduction only. Above Racr, natural convection develops in the domain. At some second critical Rayleigh number, Rat, the steady convection cells lose stability and the solution transitions to a weakly turbulent (chaotic) state. The Lorenz system was previously derived from the governing equations using a truncated Galerkin expansion. This research investigates the validity domain of the Lorenz system as a model for natural convection in porous media. The temperature and velocity fields given by the Lorenz system are compared to a numerical solution for the temperature and velocity fields for increasing Rayleigh numbers. Results show that near Ra = 80 the number of convection cells predicted by the numerical solution increases from two to three as a result of the chosen wavenumber becoming unstable. The result is a significant difference between the Lorenz system and the numerical solution. To provide a comparison between the Lorenz solution and the numerical solution that is global in scale relative to the problem domain, we compared the Nusselt numbers resulting from each solution to experimental data.
Notlar:
School code: 0391
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(693194.1) | 693194-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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