EXPERIMENTAL STUDY OF MULTICELLULAR NATURAL CONVECTION IN A TALL AIR LAYER

Transcription

1 EXPERIMENTAL STUDY OF MULTICELLULAR NATURAL CONVECTION IN A TALL AIR LAYER R. SAGARA 1, Y. SHIMIZU 1, K. INOUE 1 and T. MASUOKA 2 1 Department of Mechanical Systems Engineering, The University of Kitakyushu 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, , Japan 2 Professor Emeritus, Kyushu University 744, Motooka, Nishi-ku, Fukuoka, , Japan ABSTRACT This paper reports on the three-dimensional characteristics of multicellular air natural convection in a tall rectangular cavity with isothermal side s of different temperatures. The vertical aspect ratio of the rectangular cavity A h (=h/s) is 50. Convective flow motions on the two cross-sectional vertical planes were observed simultaneously by laser sheet lights and synchronized digital video cameras. The changes in flow patterns with time were analyzed by Particle Image Velocimetry (PIV) technique. When the Rayleigh number Ra s exceeds the critical value Ra s,c, multicellular secondary cells appear at the interior region of the primary circulatory flow. The present visual observations revealed the time-dependent and three-dimensional behaviors of the multicellular flows in a tall air layer at relatively low Ra s. INTRODUCTION Natural convection in enclosed rectangular tall air cavities occurs in various building elements, electric appliances, mechanical devices, etc. Thus, extensive studies have been made so far (1)-(15). According to the previous studies, natural convection in a tall rectangular cavity could be specified by the aspect ratio of the cavity A h, the Rayleigh number Ra s and the Prandtl number Pr. In the case of lower Ra s, a primary circulatory flow (unicellular flow) occurs in the entire cavity. When Ra s exceeds the critical Rayleigh number Ra s,c ; Ra s,c /Pr=(1+5/A h )/( ), (1) the flow pattern changed to the multicellular flow yielding secondary co-rotating cells (7, 12). Recently, some experimental and 3D (three-dimensional) numerical studies 15) suggested that the secondary cells of multicellular flow (12, 14, are stable only in a narrow range of Ra s. The secondary cells become unstable and 3D motions occur by the increase of Ra s. Gao et al. (14) reported that this transition processes evaluated by the 3D direct numerical simulation are different from those by the 2D (two-dimensional) simulation. To our knowledge, 3D multicellular air flow behaviors have not been clarified. In the present study, the time-dependent 3D natural convective flow behaviors in a tall rectangular air cavity have been investigated by the flow visualization with PIV technique. EXPERIMENTAL SETUP Apparatus Figure 1 schematically shows the test section of an internal air layer and coodinate system. The air layer was realized by two temperature-controlled copper plates (isothermal s) and four transparent polycarbonate plates (adiabatic s). Dimensions of the air layer were 1500 mm high (h), 500 mm wide (w) and 30mm thick (s), such that the vertical aspect ratio A h (=h/s) was 50, and the horizontal aspect ratio A w (=w/s) was Figure 2 shows the detailed configuration of the test section. The hot consisted of copper plate, aluminum plate, electric film heaters and insulating Bakelite plates. All materials were tightly fastened each other by bolts and thermal grease. The inner surface temperature of the copper plate was maintained at the uniform temperature by five electric film heaters controlled independently and ten thermocouples embedded in the copper plate. The temperature monitoring positions by these thermocouples are shown in Fig.3. The electric film heaters were installed side by side in the height direction. To reduce the heat loss from the test section to environment, 5mm thick Bakelite plates were installed on the rear side of the electric film heaters. The structure of the cold was similar to those of the hot as shown in Fig.2. The inner surface temperature of copper plate was maintained at the uniform temperature by adjusting the cooling capacity of five aluminum water cooling jackets installed side by side in the height direction. Cooling water was supplied from the water bath whose temperature was precisely controlled by chiller units and its flow rate to each cooling jacket was controlled independently. The cold was also monitored by ten thermocouples embedded in the copper plate. Thermocouples used for the measurement of the surface temperatures of the copper plates were K-type and had been calibrated in advance with the calibration bath. Temperatures were measured through the data acquisition system. The maximum temperature variation over the copper plates was within ±0.15K at the maximum temperature difference across the air layer. Average air temperature was ºC in the present experiments. Thus, the critical Rayleigh number was estimated by eq. (1) as Ra s,c = Experimental data were taken after the thermal condition had been reached a steady state for the range of <Ra s <

2 w polycarbonate (t30) copper plate (t2) h g aluminum water cooling jacket Air aluminum plate (t5) aluminum plate (t5) s=30 film heater x z copper plate (t2) Bakelite Plate (t5) s y Fig. 1 Diagram of internal air layer of test section and the coodinate system: h=1500mm, s=30mm, w=500mm. Fig. 2 Cross-sectional structure of the test section (unit: mm). Flow visualization In order to examine the time-dependent and 3D flow patterns in the tall air cavity, a smoke-tracer flowvisualization was performed using two sheet lasers and synchronizing two CMOS digital video cameras, as shown in Fig.4. The 2D flow patterns on the cross-sectional x-y plane irradiated by the sheet laser could be observed by the video camera. As the view area of the video camera was limited, the flow observations were conducted for 11- divided sections in a vertical direction. The 2D flow motions in two different x-y planes (z=125mm, 375mm) at the same height position were recorded simultaneously. Thus, relatively large scale 3D flow structures can be examined by the comparisons of two synchronized movies. The 2D velocity fields and streamlines were evaluated by Particle Image Velocimetry (PIV) technique. In this paper, the flow images at z=375mm were laterally inverted so that the left- and right-side of all flow images were the cold and hot vertical sides respectively. Both lateral ends of all flow images correspond approximately to the surfaces of the vertical isothermal s. Fig. 3 Temperature measurement positions on the hot and cold vertical side s (unit: mm).

3 cold hot cold hot (a) top: x mm (b) bottom: x 0-100mm Fig. 6 Flow patterns near top and bottom corners of air layer (z=125mm). Dotted area is observational error. Fig. 4 Flow visualization by lasers and video cameras. cold hot Fig. 5 Parallel flow in the x-y plane evaluated by PIV technique for Ra s (x mm, z=125mm). EXPERIMENTAL RESULTS AND DISCUSSION (a) Ra s In the case of Ra s , which was slightly below the critical Rayleigh number, steady flow with no unstable motions was observed. Figure 5 shows an example of the streamlines evaluated by the PIV technique. Stable upward and downward parallel flows along the isothermal vertical plates occupied the air layer, where no secondary cells were observed. It can be judged that the flow pattern was not multicellular flow for Ra s x mm x mm x mm Fig. 7 Typical flow patterns at middle sections of air layer (z=125mm). Dotted areas are observational error. (b) Ra s Figures 6 to 8 show examples of evaluated streamlines for Ra s , where Ra s slightly exceeded Ra s,c. As shown in Fig.6, flow turned at the top and bottom corners of the cavity. The upward flow area at the top was larger than that of downward flow. At the bottom, the situation is opposite. The flows near the corners were considerably stable. At the middle sections, the secondary co-rotating cells were clearly observed, as shown in Fig.7. Secondary cells

4 Vertical position from bottom Vertical position from bottom Vertical position from bottom Vertical position from bottom The 28 th International Symposium on Transport Phenomena (a) (b) (a) (b) (a) (b) (a) (b) (a) (b) =0 sec =30 sec =60 sec =90 sec =120 sec Fig.8 Time changes in secondary cells in two different s cross-sectional x-y planes at x mm, (a) z=125mm, (b) z=375mm. Dotted areas are observational error (a) x mm (b) x mm (c) x mm (d) x mm Fig.9 Time changes in height position of secondary cells ( : z=125mm, : z=375mm).

5 0 sec 4 sec 8 sec 12 sec 16 sec 0 sec Fig.10 Coalescence of secondary cells observed at x mm, z=375mm. Dotted areas are observational error. formed a line vertically in the tall air layer. All the secondary cells rotated in the same direction of primary circulating flow. The shape of the secondary cells was longwise elliptical with the aspect ratio in the range of 4 to 13. The distances between the neighboring secondary cells changed with time and position, such that the number of the secondary cells was reduced near the top and the bottom corners of the cavity. Figure 8 shows an example of time changes in secondary cells. Secondary cells were observed not to remain in fixed positions and to move in both upward and downward directions with slow velocities, whereas Lartigue et al. (10) and Wright et al. (12) observed the case of the secondary cells moving downward in their experiments of A h 40, which might be attributed to the end effects of different aspect ratio. To clarify the 3D flow structure of the secondary cells in detail, the trajectories of the center of the particular secondary cells on the two cross-sectional x-y planes (z=125, 375mm), recorded simultaneously, are plotted in Fig. 9. It is seen in Fig.9 that the speeds and the travelling directions of the neighboring secondary cells were basically similar. But the neighboring cells sometimes approached each other and yielded their coalescence. Typical coalescence of the secondary cells observed during = sec for x-y planes at z=375mm (Fig. 9(d)). Corresponding flow images during the coalescence are also shown in Fig.10. The interference due to the local counter flows at the boundary of the two neighboring co-rotating cells seemed to induce a flow change, where the two secondary cells gradually merged and coalesced into one secondary cell. The comparison of the observations on two different x- y planes as in Fig. 8 reveals that the secondary cells were not necessarily positioned at the same height and that they did not necessarily travel in the same direction. These behaviors can be confirmed also in the comparisons of streamlines shown in Fig. 9, which means that the secondary cells are not the transverse rolls with straight horizontal axis. We can interpret the transverse rolls to be accompanied by the meandering axis. The meandering secondary cells seem to be similar to wavy Taylor vortices (16) which appears at the transition from steady Taylor vortices to time-dependent Taylor vortices in the flow between concentric cylinders. CONCLUSION Multicellular natural convection in a tall air layer in the transition from the laminar to turbulent regime has been studied experimentally. Time-dependent and threedimensional secondary cellular flow behaviors were observed in detail by the smoke tracer flow visualization and PIV technique. The followings have been obtained. (1) In the case of lower Ra s, the stable unicellular flow is observed. When Ra s exceeds the critical Rayleigh number Ra s,c = , the longwise elliptical secondary co-rotating cells appear.

6 (2) The secondary cells exhibit time-dependent behaviors and move slowly upward and downward along the center line of the cavity. Although the speeds and direction of neighboring secondary cells moving on a vertical x-y plane are basically similar, the distances between the neighboring cells are found to vary with time, where their merging and coalescences can occur. (3) The vertical positions and moving directions of the secondary cells on a vertical x-y plane are observed not to coincide with those on another vertical x-y plane. These results suggest that the secondary cells become unsteady and three-dimensional flow structure even at the relatively low Ra s slightly above Ra s,c, which are considered to be meandering in the vertical direction and to be different from the horizontal transverse rolls such as postulated in many previous 2D numerical studies. (4) As for the effects of the dimensions of the enclosure, the secondary cells are observed to become unsteady and three-dimensional even in the range of relatively low Rayleigh number Ra s slightly above Ra s,c for such high tall air layer of aspect ratio of A h =50. NOMENCLATURE A h vertical aspect ratio (=h/s) A w horizontal aspect ratio (=w/s) g gravitational acceleration, m/s 2 h height of air layer, m Pr Prandtl number (= / ) Ra s Rayleigh number (=g Ts 3 / ) Ra s,c critical Rayleigh number due to first flow instability s thickness of air layer, m T temperature, C w width of air layer, m x, y, z coodinates, defined in Fig. 1 thermal diffusivity, m 2 /s coefficient of expansion, K -1 kinematic viscosity, m 2 /s time, s T temperature difference, K REFERENCES (1) Batchelor, G. K., (1954): Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Quarterly of Applied Mathematics, Vol. XII, No.3, pp (2) Eckert, E. R. G., Carlson, W. O., (1961): Natural convection in an air layer enclosed between two vertical plates with different temperatures, International Journal of Heat and Mass Transfer, Vol. 2, pp (3) Vest, C. M., Arpaci, V. S., (1969): Stability of natural convection in a vertical slot, Journal of Fluid Mechanics, Vol. 36, part 1, pp (4) Bergholtz, R. F. (1978): Instability of steady natural convection in a vertical fluid layer, Journal of Fluid Mechanics, Vol. 84, part 4, pp (5) Yin, S. H., Wung, T. Y., Chen, K., (1978): Natural convection in an air layer enclosed within rectangular cavities, International Journal of Heat and Mass Transfer, Vol. 21, pp (6) Korpela, S. A., Lee, Y., Drummond, J. E., (1982): Heat transfer through a double pane window, Journal of Heat Transfer, Vol. 104, pp (7) Chikhaoui, A., Marcillat, J. F., Sani, R. L., (1988): Successive Transitions in thermal convection within a vertical enclosure, ASME HTD-vol.99, pp (8) Zhao, Y., Curcija, D., Goss, W. P., (1997): Prediction of multicellular flow regime of natural convection in fenestration glazing cavities, ASHRAE Transactions Symposia, pp (9) Wakitani, S. (1997): Development of multicellular solutions in natural convection in an air-filled vertical cavity, Journal of Heat Transfer, Vol. 119, pp (10) Lartigue, B., Lorente, S., Bourret, B., (2000): Multicellular natural convection in a high aspect ratio cavity: experimental and numerical results, International Journal of Heat and Mass Transfer, Vol. 43, pp (11) Manz, H. (2003): Numerical simulation of heat transfer by natural convection in cavities of façade elements, Energy and Buildings, Vol. 35, pp (12) Wright, J. L., Jin, H., Hollands, K. G. T., Naylor, D., (2006): Flow visualization of natural convection in a tall, air-filled vertical cavity, International Journal of Heat and Mass Transfer, Vol. 49, pp (13) Ganguli, A. A., Pandit, A. B., Joshi, J. B., (2009): CFD simulation of heat transfer in a twodimensional vertical enclosure, Chemical Engineering Research and Design, Vol. 87, pp (14) Gao, Z., Segent, A., Podvin, B., Xin, S., Le Quere, P., Tuckerman, L. S., (2013): Transition to chaos of natural convection between two infinite differentially heated vertical plates, Physical Review E 88, (15) Honda, N., Sadamoto, H., Inoue, K., Masuoka, T., (2016): Experimental Investigation on Natural Convection in Vertical Air Layers with PIV, Proceedings of the 27th International Symposium on Transport Phenomena. (16) Davidson, P. A., (2015): Turbulence 2 nd ed., Oxford University Press.