Vibrational Instabilities in Supercritical Fluids

ABSTRACT

Near-critical fluids have shown great interest in many applications because of their low-viscosity and high mass diffusion. The critical point is thermally unstable due to the divergence (compressibility, heat capacities, conductivity) and to the evanescence (thermal diffusivity) of their physical properties. Some experiments under zero-gravity conditions have shown that, when a cylindrical cell is cooled at its lateral boundaries and is submitted at the same time to a vibration of certain amplitude of acceleration, the boundary layer exhibits a Rayleigh-Bénard type of instability. Thermal plumes appear perpendicular to the acceleration direction and grow towards the center of the cell. Numerical simulations have been performed with regards to this problem in a square cavity. The critical Rayleigh number and wavelength showed a power law type curve as a function of the proximity to the critical point. In this paper, we consider this problem with a variable acceleration of vibration in order to determine the variation of the wavelength as a function of the acceleration with different proximities to the critical point. The Navier-Stokes equations coupled with the energy and the linear equation of state are solved by the finite volume method in the real configuration of a cylindrical cell as in the experiment.

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