| In order to understand the nature of thermocapillary-buoyancy convection in a differentially heated annular pool with the outer heated container of radius ro = 40mm and the inner cooled cylinder ri that is variable (ri = (5-20)mm), and an adjustable depth d = 0.5–1.5mm. The top and bottom are assumed to be adiabatic. We conducted a series of unsteady two-dimensional numerical simulations with the finite-volume method. The pool was filled with the 0.65cSt silicone oil (Prandtl number Pr=6.7). Results showed that:1) The unicellular flow and steady multicellular flow appear when the small horizontal temperature difference is established between the lateral walls of the pool. The great mass of temperature drops is in the thermal boundary close to the lateral walls. With the temperature difference increased, the convection will become unstable and transform into different of the oscillatory flow.2) The steady flow is replaced by the hydrothermal wave when the temperature difference exceed the critical temperature difference. The hydrothermal wave itself looks as a succession of the cells moving from the cold side towards the hot side. The amplitude and frequency of the hydrothermal wave is various with the different temperature difference. If the temperature difference continues to increase, the flow will become very complex. And the hydrothermal wave will be replaced by a chaos flow that it looks ruleless and is different from hydrothermal wave.3) In the annular pool, with the increase of the depth of annular pool, the critical temperature difference reduces, the number of rolls in the pool and the frequency of the hydrothermal wave become small and the amplitude augments.4) The ratio of the inner and outer radius Cr=ri/ro effects the critical conditions of instability flow and the amplitude and frequency of the hydrothermal wave. With the increase of Cr, the flow in annular pool is close to the flow in rectangular pool.
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