Abstract
The birth, evolution and disappearance of quasiperiodic dynamics in buoyancy-driven flow arising from an enclosed horizontal cylinder are analysed here, by numerical means, in the limit of the 2D approximation. The governing equations are solved on orthogonal Cartesian grids, giving special treatment to the internal, non-aligned boundaries. Thanks to the adoption of a high level of refinement of the Rayleigh number range, quasiperiodicity was observed to emerge from a periodic limit cycle (P1), and to turn into its omologous orbit with doubled period (P2), eventually evolving into a classical period-doubling route to chaos, for further increases of the Rayleigh number. The present study gives a deeper insight to what appears to be an imperfect period doubling bifurcation through a quasiperiodic T2-torus. The approach used is based on the classical tools for time series analysis. The distribution of the power spectral densities is used to search for and characterise the existence of relations between the frequencies of the P1, T2 and P2 dynamics. The topology of the orbits, as well as their evolution within the quasiperiodic window, are analysed with the aid of phase space representation and Poincaré maps.
Highlights
The strong dependence on the system geometrical configuration and on the thermal boundary conditions is known to determine a great variety of complex buoyancy-driven flows in confined enclosures
In the present section, the dynamical behaviour of the system under investigation is described for the cavity of aspect ratio A = 2.5, characterized by a thermal plume whose swaying motion is dependent on the intensity of the buoyancy force, i.e. on the forcing term Ra [29]
Reported results refer to the system variables simulated at point (0; 0.5) and are representative of the dynamics observed in the other points
Summary
The strong dependence on the system geometrical configuration and on the thermal boundary conditions is known to determine a great variety of complex buoyancy-driven flows in confined enclosures. Great interest has been given to the non-linear dynamics of thermal convection in basic enclosure configurations, with the heat source either corresponding with the bottom or side walls of the cavity [1, 2]. Though most of the effort has been mainly focused on heat transfer performances [4,5,6,7], the use of optical techniques such as Particle Image Velocimetry (PIV), has recently allowed the experimental study of the flow field and of its influence on the overall heat transfer[8, 9].
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