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In order to understand the effect of the Rayleigh number, the density inversion phenomenon and the aspect ratio on the flow patterns and the heat transfer characteristics of Rayleigh-Bénard convection of cold water in the neighborhood of the maximum density, a series of large eddy simulations are conducted by using the finite volume method. The Rayleigh number ranges between 10 6 and 10 9 , the density inversion parameter and the aspect ratio are varied from 0 to 0.9 and from 0.4 to 2.5, respectively. The results indicate that the reversal of the large scale circulation (LSC) occurs with the increase of the Rayleigh number. When there exists a density inversion phenomenon, the key driver for the LSC is hot plumes. When the density inversion parameter is large enough, a stagnant region is found near the top of the container as the hot plumes cannot move to the top wall. The flow pattern structures depend mainly on the aspect ratio. When the aspect ratio is small, the rolls are vertically stacked and the flow keeps on switching among different flow states. For a moderate aspect ratio, different long-lived roll states coexist at a fixed aspect ratio. For a larger aspect ratio, the flow state is everlasting. The number of rolls increases with the increase of the aspect ratio. Furthermore, the aspect ratio has only slight influence on the time averaged Nusselt number for all density inversion parameters.

The aim of this research is to understand the effect of the aspect ratio on the heat transfer ability and hydrodynamics characteristics of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers. The Rayleigh number is fixed at 109, density inversion parameters are 0.3, 0.5 and 0.7, and the aspect ratio ranges from 1/60 to 1. Results indicate that the average Nusselt number presents a weak dependence on the aspect ratio at the large aspect ratio (A > 0.3). However, it reaches the maximum and then drops when the aspect ratio decreases from A = 0.3. Large scale circulations are observed for containers at the large aspect ratio, and the confinement of sidewalls weakens the large-scale circulation and eventually destructs it. At the large aspect ratio, the velocity fluctuation near the sidewalls is stronger than that in the center zone, because plumes primarily move along the sidewalls of the container. At a small aspect ratio, more plumes appear in the center of the container, where the fluctuation is stronger than that near sidewalls. The effect of cold plumes on the flow is reduced as the density inversion parameter increases. Therefore, the flow is mainly driven by hot plumes, and the velocity magnitude and fluctuation decrease significantly.

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