Institute of Fundamental Technological Research

Our aim is to explore, both experimentally and theoretically, the cumulative effects of small particle–liquid density difference, where the particles are used as tracers in recirculating flow. As an example we take a flow field generated in a differentially heated cavity. The main flow structure in such a cavity consists in one or two spiraling motions. Long‐term observations of such structures with the help of tracers (small particles) indicated that accumulation of the particles may set in at some flow regions. For theoretical insight into the phenomenon, a simple analytical model of recirculating (rotating) flow was studied. It was assumed that particles are spherical and rigid, and their presence does not affect the flow field. The particle Reynolds number is negligibly small, hence only the effects of particle–liquid density difference are of importance. Besides buoyancy, the effects of Saffman’s force and the inertial forces are also taken into account when calculating particle trajectories. Both cases were analyzed, particles with density slightly higher and lower than the fluid. It was found that in our case the inertial forces are egligible. In the numerical experiment trajectories of particles were investigated. The particles were allocated at random in the flow field obtained by numerical solution of the natural convection in the differentially heated cavity. In the experimental part, behavior of a dilute particle suspension in the convective cell was explored. In the model‐analytical study of a simple spiraling motion, it was found that due to the interaction of the recirculating convective flow field and the gravity‐buoyancy force, the particles may be trapped in some flow regions, whereas the rest of the flow field becomes particle‐free. This prediction agrees fairly well with the numerical and experimental findings.

The problem of transient natural convection in a cube-shaped cavity is investigated experimentally and numerically. The motion is driven by a sudden temperature difference applied to two opposite side walls of the vessel. The experiments are performed at a Rayleigh number of 1.66 × 105 and a Prandtl number of 1109, inside a 5 × 5 × 5 cm3 cavity made of Plexiglas, with two isothermal copper walls kept at a prescribed temperature. Numerical simulation has been performed using a finite difference vorticity-velocity model of the Navier-Stokes equation with the Boussinseq approximation. The theoretical predictions are found to be in good agreement with the experimental results.

The thermal convection in a cubic cavity, with two opposite vertical walls kept at prescribed temperatures, is investigated experimentally. The Rayleigh numbers ranged from 104 to 2 × 107 and the Prandtl numbers from 5.8 to 6 × 103. The velocity and vorticity fields are shown. The temperature fields were visualized with the help of liquid crystals suspended as small tracer particles in the medium. It is observed that convection in the cavity is strongly three-dimensional. The streamlines spiral from the foci on the walls toward the foci in the vertical midplane and vice versa. The disappearance of one of the vortices midway between the center and the front or back wall is observed for RA > 6 × 104. The topological structures are discussed. The experimental observations are compared with numerical calculations found in the literature.

natural convection, rectangular enclosures