Chaotic Natural Convection in an Annular Geometry

This work examines the natural convection flow of a Newtonian fluid (Pr = 0.71) in an annular differentially heated furnace. The annular geometry is defined by an outer heated wall and an inner polymer surface that has no temperature control.;To explore natural convection in the annulus, experiments were conducted to vary the Rayleigh number by adjusting the temperature of the upper boundary of the air cavity. A non-uniform vertical wall temperature is specified which creates a set of experiments not explored in existing work. A range of heating profiles was explored with Rayleigh numbers between 2.2e7 and 7.5e7. The experimental results show a supercritical Hopf bifurcation followed by a period halving route to chaos. The experimental results also indicate that the air flow in the system is three-dimensional and that the highest amplitude of the oscillations occurs in the upper half of the annulus.;A set of six CFD models was developed to provide a comprehensive view of the capabilities of the commercial code COMSOL for modeling natural convection. The models provide a broad transient natural convection benchmark for COMSOL which has never been attempted in prior work.;A benchmarking CFD model was developed using the commercial code COMSOL which indicates flow transitions for low driving force natural convection cannot be captured with COMSOL. Numerical diffusion coefficients were adjusted for the benchmark model to correctly predict experimental results reported in the literature for the Cartesian geometry. Benchmarking in the annular geometry was not successful in versions 3.5a or 4.0 of COMSOL.;A coupled two dimensional CFD model for the experimental system was also developed, including the air cavity and inner solid polymer using COMSOL. Experimental results are used to define most of the boundary conditions and the model solves a coupled conduction-convection problem for the interior air behavior and conduction within the polymer preform. The modeling results match the experimental results well for the steady state behavior but do not accurately predict the transition to oscillatory behavior.;A new radiation technique has been developed to use analytically determined viewfactors in COMSOL. This technique offers significant reductions in computation time for complex radiation problems and addresses a deficiency in the software. The new radiation method is used to develop a coupled radiation model which has fair agreement with experimental results in the stable region of the flow.;Based on software limitations for low driving force natural convection, a simplified computational model using linear variation in the vertical boundary conditions was developed to explore the capabilities of COMSOL with a stronger driving force. This computational model extended the Rayleigh range of a previous model, and exposed dynamic system behavior which has not been seen in prior work. Increasing the Rayleigh number revealed a transition to chaotic behavior which then becomes stable again at higher Rayleigh numbers. This type of dynamic system behavior has not been seen in the literature for this type of computational model.;Proper Orthogonal Decomposition (POD) has been used to analyze the computational model of the air cavity with linear temperature variations along the vertical boundaries. Five eigenvalue modes were required to capture correctly the basic flow structure in the annular geometry. The POD failed to capture the subtle fluid structures for the model, indicating that POD based reduced order models are very limited for this type of complex flow system.;POD was used to analyze the experimental results over two transitions in a way not previously examined in the literature. The POD captures the dynamics of a range of Rayleigh numbers and predicts the chaotic, oscillatory and stable regions of the flow observed experimentally with 8--10 modes.