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Numerical evaluation of the validity domain of Lorenz equations

Lindgren, Allison (2018) Numerical evaluation of the validity domain of Lorenz equations. Masters thesis, Northern Arizona University.

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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, Ra_cr, any disturbances will decay to a motionless solution and heat transfer will occur via conduction only. Above Ra_cr, natural convection develops in the domain. At some second critical Rayleigh number, Ra_t, 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.

Item Type: Thesis (Masters)
Publisher’s Statement: © Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords: Lorenz Equation; Method of manufactured solutions; Natural Convection; Porous media
NAU Depositing Author Academic Status: Student
Department/Unit: Graduate College > Theses and Dissertations
Date Deposited: 24 Apr 2019 22:25
URI: http://openknowledge.nau.edu/id/eprint/5449

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