On the three-dimensional effect for natural convection in horizontal enclosure with an adiabatic body: Review from the 2D results and visualization of 3D flow structure

In this study, effect of three-dimensionality of natural convection in horizontal enclosure was discussed. Geometry which was taken into account was horizontal enclosure with radially unit aspect ratio and π of longitudinal direction. The enclosure was heated from the bottom wall, and then was cooled down from above. In addition, obstacle was located in middle of the enclosure to examine an effect of the existence of it. A two-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from steady state to chaotic pattern. As the geometry was elongated in conjunction with periodic boundary conditions to allow lateral freedom for the convection cells, longitudinal direction was discretized through a Fourier serious expansion with a uniform mesh configuration. Prior to investigate thermal behavior of fluid layer in three-dimensional simulation, two-dimensional results were reviewed with respect to spatial resolution. Whereas coarse resolution provoked thermal instability at intermediate Rayleigh number to have subharmonic solution, fine spatial resolution yielded stably steady convection mode. Thermal behavior in three-dimensional enclosure at low Rayleigh number showed two-dimensional pattern invariant to longitudinal direction. As increasing of buoyant force, longitudinal invariance was collapsed and onset of three-dimensional thermal plume occurred. At high Rayleigh number, three-dimensional thermal plume oscillates freely in elongated geometry and consequently yields higher heat transfer rate. In addition, thermal flow field was captured by visualizing the three-dimensional vortical structure. The chaotic three-dimensional flow behavior was quantitatively examined by obtaining turbulent statistics and compared with those from two-dimensional simulation.