Effects of geometry on turbulent Rayleigh-Bénard convection
by Hao Song
xiv, 79 p. : ill. (some col.) ; 30 cm
A systematic study of turbulent thermal convection is carried out in horizontal cylindrical cells of different lengths filled with water. The aim of the thesis work is to study the geometry effect on the fluid dynamics of the large-scale circulation (LSC) and the scaling laws in turbulent Rayleigh-Bénard convection. The results obtained in the horizontal cylinders are compared with those obtained in the upright cylinders....[ Read more ]
A systematic study of turbulent thermal convection is carried out in horizontal cylindrical cells of different lengths filled with water. The aim of the thesis work is to study the geometry effect on the fluid dynamics of the large-scale circulation (LSC) and the scaling laws in turbulent Rayleigh-Bénard convection. The results obtained in the horizontal cylinders are compared with those obtained in the upright cylinders.
The large-scale flow shows interesting new dynamics in the horizontal cylindrical cells. Four different flow modes are found in the cells with varying aspect ratio Γ: two-dimensional rotation (2DR), small-Γ diagonal switching (SDS), large-Γ diagonal switching (LDS) and periodic reversals (PR). In the 2DR phase (Γ ≤ 0.16), the flow is quasi-two-dimensional and is confined in the circular plane of the horizontal cylinder. In this phase, a well-defined in-plane oscillation of LSC is observed, resulting from the periodical eruption of thermal plumes from the top and bottom thermal boundary layers. In the SDS phase (0.16 < Γ < 0.82), the rotation plane of LSC switches periodically between the two diagonals of the cell, spanning across the curved sidewalls. The switching period is found to be equal to the LSC turnover time. In the LDS phase (0.82 ≤ Γ ≤ 1.69), the periodic switching of the LSC orientation still remains, but the switching is now spanning across the flat end walls of the cell. The switching period has a large jump at the transition aspect ratio Γc = 0.82 and then exponentially decays with increasing Γ. For even larger aspect ratios (1.30 ≤ Γ ≤ 1.69), the bulk fluid as a whole rotates around the central axis of the horizontal cylinder with periodic reversals. The reversal period is found to change linearly with the length of the cell.
The scaling laws of turbulent convection are also investigated in the horizontal cylinders. The scaling behavior of the measured Nusselt number (total heat flux) Nu(Ra) and the Reynolds number Re(Ra) associated with the velocity of LSC, remains the same as that in the upright cylinders. These results suggest that the thermal boundary layer dynamics are insensitive to the geometry change and that the role of the buoyancy forces, which drive LSC, does not change with the cell geometry either.
The scaling exponent for the rms value of local temperature fluctuations, however, shows strong dependence on the aspect ratio Γ of the convection cell, indicating that small-scale fluctuations depend more sensitively on the detailed structures of LSC and are sensitive to the change of cell geometry.