Buoyancy driven convection in near-critical and supercritical fluids

Buoyancy driven thermal transport in a pure fluid (carbon dioxide) near its gas–liquid critical point is investigated using a two-dimensional numerical model. A square enclosure is considered with side heating. For all cases considered, the initial pressure and temperature of carbon dioxide is pi (>pc) and Ti (>Tc) respectively. The two side-walls of the enclosure are initially at temperature Ti and the left wall temperature is temporally raised to TL∞. The model considers the strong variable property effects (functions of both temperature and pressure) near the critical point, including the bulk viscosity variations. As thermal diffusivity approaches zero near the critical point, the divergence of thermo-physical properties near the critical point gives rise to large Rayleigh number flows even for very small temperature differences. The steady-state convective heat transfer coefficient near the critical point is investigated and a correlation for the steady state, spatially averaged Nusselt number along the vertical walls is developed as a function of the Rayleigh number and the ratios (pi − pc)/pc, (Tm − Tc)/Tc and image = (Tpc − Tc)/Tc, where Tm = (Ti + TL∞)/2. The subscripts ‘i’, ‘m’, ‘c’, ‘pc’ and refer to the initial, mean, critical, pseudo-critical conditions respectively while the subscript ‘L∞’ refers to the final value of the left (heated) wall temperature. The effect of critically diverging bulk viscosity on the flow field and heat transport induced by buoyancy in near-critical fluids is also investigated.