Numerical simulation of natural convection in a horizontal enclosure: Part I. On the effect of adiabatic obstacle in middle

Abstract

In this study, an effect of a three-dimensional obstacle of natural convection in a horizontal enclosure was discussed. Geometry which was taken into account was horizontal enclosure with unit aspect ratio and length of π along spanwise direction. The enclosure was heated from the bottom wall, and then was cooled down from above. An obstacle was located in the middle of the enclosure to examine its effect. A three-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from a steady state to a chaotic pattern. As the geometry was elongated in conjunction with periodic boundary conditions to allow lateral freedom for the convection cells, longitudinal geometry along spanwise direction was discretized through a Fourier series expansion with a uniform mesh configuration. An adiabatic obstacle played a different role in determining the thermal behavior: No-slip condition of the surface of the obstacle disturbed the overall plume behavior in terms of the momentum transfer, whereas the adiabatic boundary condition did not influence significantly in terms of energy transfer. At a low Rayleigh number, thermal behavior in three-dimensional enclosure showed steady invariant solution along spanwise direction which is identical to two-dimensional result. With increasing buoyant force, spanwise invariance of longitudinal roll cell was collapsed and three-dimensional mode was obtained following flow regime transition. After undergoing periodically oscillatory phase, a chaotic flow transition occurred. At a high Rayleigh number, three-dimensional thermal plume oscillates freely in elongated geometry and consequently yields higher heat transfer rate. In addition, the thermal flow field was captured by visualizing the three-dimensional vortical structure. The chaotic three-dimensional flow behavior was quantitatively examined by obtaining the turbulent statistics.