Module 4: Interferometry
  Lecture 22: Three dimensional convection phenomenon
 

Lipps [127] has reported the appearance of a dominant flow pattern in the shape of a (semi) cross-roll followed by a disturbed flow regime, and the time scale for the switch-over was This result has a definite similarity with the experiments of the present study, in which the switching phenomenon has been reported. The time scale seen in the experiments (=0.25) is similar than1.3, but can be explained as being due to

  • A higher Rayleigh number which tends to lower the time scales, and
  • A higher aspect ratio which can active a whole range of wave numbers including small ones thus causing a lowering of

Results for the Nusselt number at a Rayleigh number of 4.02 x 104 are presented next. The numbers averaged over the entire surface are given in Table 11. These have been compared with the correlation of Gebhart et al. [89]. The agreement between the Nusselt numbers of the present work and the correlation can be seen to be close. Specifically, the Nusselt number computed from the present set of experiments is within 1.5% of the empirical correlation.

The variatrion of the line-of-sight averaged Nusselt number with distance closely reflects the flow pattern in the cavity. As in the case of tge lower Rayleigh number, these have been computed directly from the interferograms and are shown in Figure 4.60.Both projections have been presented. A roll-like structure can be seen from both view angles and so the Nusselt number variation is expected to be oppositely oriented for the two active surfaces. This result is clearly brought out in Figure 4.60. The line-of-sight averaged Nusselt numbers were also compute from the reconstructed (fully three-dimensional) temperature field. The comparison between the reconstructed and the original local Nusselt numbers is presented in Figure 4.61. For the and view angles that have been employed in reconstruction, the comparison for both surfaces is excellent. The Nusselt number surfaces over the two bounding planes are shown in Figure 4.62. These surfaces are clearly oppositely oriented at the hot and cold walls. This confirms that when visualized from any angle, the resulting fringe pattern will be a roll-like repeating structure. It strengthens the suggestion made that the flow field is in the form of a buoyant plume.

Table 11: Comparision of Average Nusslt number with [89], Ra=4.02 x 104

Projection angle in degree
Nu (cold surface)
Nu (Hot surface)
Nu (average) from all angles
Nu (reference)
0
3.22
3.30
3.32
3.28
90
3.48
3.30