NATURAL-CONVECTION OF WATER NEAR THE DENSITY EXTREMUM FOR A WIDE-RANGE OF RAYLEIGH NUMBERS

A time-dependent penalty finite element model was used to investigate natural convection of pure water in a rectangular enclosure with verti cal end walls differentially heated near the temperature of maximum de nsity. Attention was focused on the main features of the flow at high Rayleigh numbers not considered previously (Ra = 10(5)-10(8)). Water i n a rectangular enclosure for the aspect ratio of 1.25 was initially k ept at 4 degrees C. The enclosure was then suddenly heated and cooled on the opposing vertical walls, i.e., 8 degrees C and 0 degrees C. The Rayleigh number was varied by the size of the enclosure. In the Rayle igh number range considered here, steady state was reached within a ti me of the order of 2t(f), where t(f) is the time to steady state sugge sted by Patterson and Imberger [1]. The steady state flow field and te mperature structure were symmetric at about the enclosure's midpoint, and a stable sinking jet was formed in the interior of the enclosure a s a result of density inversion. The velocity profile near the vertica l walls agreed well with Gill's approximation of the laminar boundary layer solution, but the temperature profile disagreed because of the d iscrepancy in the core temperature.