The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier–Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases: (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in high-speed flows provokes an overheating of the upper wall; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO2 is found, in the form of a double-roll convective structure.
An analysis of the hydrodynamic stability of a fluid near its near critical point –
initially at rest and in thermodynamic equilibrium – is considered in the Rayleigh–Bénard
configuration, i.e. heated from below. The geometry is a two-dimensional
square cavity and the top and bottom walls are maintained at constant temperatures
while the sidewalls are insulated. Owing to the homogeneous thermo-acoustic heating
(piston effect), the thermal field exhibits a very specific structure in the vertical
direction. A very thin hot thermal boundary layer is formed at the bottom, then a
homogeneously heated bulk settles in the core at a lower temperature; at the top, a
cooler boundary layer forms in order to continuously match the bulk temperature
with the colder temperature of the upper wall. We analyse the stability of the two
boundary layers by numerically solving the Navier–Stokes equations appropriate for
a van der Waals' gas slightly above its critical point. A finite-volume method is used
together with an acoustic filtering procedure. The onset of the instabilities in the
two different layers is discussed with respect to the results of the theoretical stability
analyses available in the literature and stability diagrams are derived. By accounting
for the piston effect the present results can be put within the framework of the stability
analysis of Gitterman and Steinberg for a single layer subjected to a uniform, steady
temperature gradient.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.