Particle transport in a small square enclosure in laminar natural convection

The transport of particles with diameters in the range of 50 nm to 1 μm in laminar free convection of air in square enclosures was numerically investigated by an Eulerian-Lagrangian method. Two-dimensional square enclosures with widths from 2.5 mm to 5 cm, with two adiabatic surfaces and 100 and 200 °C temperature difference between the other two surfaces, were considered. The Rayleigh numbers varied from 100 to 8×10⁵. The air flow was simulated in Eulerian frame using a commercial CFD software, whose predictions were compared with published benchmark results. Lagrangian particle transport calculations were carried out by tracking 1000 particles that were initially randomly distributed in the flow field, and assuming one-way coupling between the particles and the carrier gas. Particle motion mechanisms considered included gravity, drag, lift force, thermophoresis and Brownian dispersion. The results showed that at Rayleigh numbers lower than about 10 000 the entire flow field was dominated by a single recirculation pattern. For these low Rayleigh number cases most of the particles disperse towards the walls, while a fraction of particles were trapped in a quasi-steady recirculation zone. Inside this recirculation zone the particles were at quasi-equilibrium with respect to the hydrodynamic and dispersive forces that acted on them, and left the zone due to Brownian dispersion only at a very low rate. This quasi-equilibrium zone was not observed at the higher Rayleigh numbers where a single recirculation pattern no longer governed the entire flow field. The results also confirmed the important role of thermophoresis and Brownian dispersion, in particular for submicron size particles.