The effects of forced boundary conditions on flow within a cubic cavity using digital particle image thermometry and velocimetry (DPITV)

Abstract

Buoyancy-driven convection within a cavity, whose sidewalls are heated and cooled, is a problem of great interest, because it has applications in heat transfer and mixing. Most studies to date have studied one of two cases: the steady-state case or the development of the transient flow as it approaches steady state. Our main concern was to study the response of the cavity to time-varying thermal boundary conditions. We therefore decided to observe the flow phenomena within a convection cavity under sinusoidal thermal forcing of the sidewalls. To map the flow properly, it is necessary to have simultaneous kinematic and thermal information. Therefore, the digital particle image thermometry and velocimetry (DPITV) is used to acquire data. Implementing this technique requires seeding the flow with encapsulated liquid crystal particles and illuminating a cross section of the flow with a sheet of white light. Extraction of the thermal and kinematic content is in two parts. For the first, the liquid crystals will reflect different colors of the visible spectrum, depending on the temperatures to which they are subjected. Therefore, calibrating their color reflection with temperature allows for the extraction of the thermal content. For the second part, the kinematic information is obtained through the use of a digital cross-correlation particle image velocimetry technique. With the use of DPITV, the flow within a convection cavity is mapped and studied under steady forcing and sinusoidally forced boundary conditions at the Brunt-Väisälä frequency. For the sinusoidally forced case, three cases are studied. In the first, the heating between the two walls is in phase. In the second, the heating between the two walls is 180° out of phase. In the third, the heating between the two walls is 90° out of phase. For steady forcing, the thermal plots show that the flow develops a linearly stratified profile within the center of the cell. At the sidewalls, however, owing to forcing, hot/cold thermal boundary layers develop at the left/right walls. These hot/cold thermal boundary layers then turn around the upper-left/lower-right corners and develop into intrusion layers that extend across the top and bottom walls. The vorticity and streamlines show that the bulk of the fluid motion is concentrated around the walls, whereas the fluid within the center of the cell remains stationary. For the sinusoidally forced cases, the thermal plots show the existence of many thermal "islands," or pockets of fluid where the temperature is different with respect to its surroundings. The vorticity plots show that the center of the cell is mostly devoid of vorticity and that the vorticity is mainly confined to the sidewalls, with some vorticity at the top and bottom walls. For the 0° forcing, the streamlines show the development of two counterrotating rollers. For the 180° forcing, the streamlines show the development of only one roller. Finally, for the 90° forcing, the streamlines show the development of both a two-roller and a one-roller system, depending on the position within the forcing cycle.

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