Open Access

ARTICLE

ANALYSIS OF CHAOTIC NATURAL CONVECTION IN A TALL RECTANGULAR CAVITY WITH NON-ISOTHERMAL WALLS

Heather Dillon^a , Ashley Emery^b,† , Ann Mescher^b

a Dept of Mechanical Engineering, University of Portland, Portland, Oregon, 97203, USA
b Dept of Mechanical Engineering, University of Washington, Seattle, Washington, 98105, USA
† Corresponding author. Email: emery@u.washington.edu

Frontiers in Heat and Mass Transfer 2013, 4(2), 1-9. https://doi.org/10.5098/hmt.v4.2.3004

Abstract

A computational model is presented that extends prior work on unsteady natural convection in a tall rectangular cavity with aspect ratio 10 and applies Proper Orthogonal Decomposition to the results. The solution to the weakly compressible Navier-Stokes equation is computed for a range of Rayleigh numbers between 2 × 10⁷ and 2.2 × 10⁸ with Prandtl number 0.71. A detailed spectral analysis shows dynamic system behavior beyond the Hopf bifurcation that was not previously observed. The wider Rayleigh range reveals new dynamic system behavior for the rectangular geometry, specifically a return to a stable oscillatory behavior that was not predicted in prior work. Proper Orthogonal Decomposition (POD) has been used to analyze the computational results. Five eigenvalue modes were required to capture correctly the basic flow structure. The POD failed to capture subtle aspects of the flow structure at high Rayleigh numbers for the model, indicating that a POD and Galerkin projection for several Rayleigh numbers will be needed to reproduce the complex behavior of the system.

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