Closure

A three-dimensional temperature field in a differentially heated horizontal fluid layer has been reconstructed from its interferometric projections. Two different Rayleigh numbers namely 1.39x10⁴ and 4.02 x 10⁴ have been considered. The tomographic reconstruction technique that has been employed AVMART. The algorithm converged without ambiguity to the final solution and did not display excessive sensitivity to the initial guess, relaxation factor, and noise in experimental data. The reconstructed field was seen to be fully consistent with the projection data. The reconstructed field was also seen to be in good agreement with the projection recorded, but not used in the tomographic algorithm. The three-dimensional field was seen to satisfy energy balance checks. the cavity-averaged Nusselt number computed from the interferometric projections was seen to be in reasonable agreement with published correlations.

Figure 4.61: Comparision of experimentally obtained line-integrals of Nusselt numbers with generated line-integrals of Nusselt numbers, Ra=4.02 x 10⁴, (a) (b) projections.

At a Rayleigh number of 1.39x10⁴, the fringes were seen to be steady near the bounding walls, but mild unsteadiness was observed in the central horizontal players. At the higher Rayleigh number of 4.02 x 10⁴, the unsteadiness was more pronounced, with flow switching between two well-defined states. The interfergrams corresponding to the dominant mode have been recorded and analyzed in the present work.

Figure 4.62: Nusselt number surfaces for top and bottom walls, Ra=4.02 x 10⁴

At a Rayleigh number of 1.39x10⁴ the flow field was seen to be organized in the form of a three-dimensional structure. A two-view tomographic calculation showed a set of longitudinal rolls as dominant pattern in the fluid layer. The rolls could be indentified from the projection data. The numbers of rolls was smaller than that based on the aspect ration consideration. The rolls also displayed three-dimensionality along its axis. At a Rayleigh number of 4.02 x 10⁴, the thermal field was determined by cube-like ells that were spread all over the cavity. A collection of four cubic-cells was found to reveal a centrally located buoyancy-driven thermal plume rising from the hot plate and descending around it from the cold wall. The variation of the line-of sight averaged Nusselt number as a function of a wall coordinate at each of the hot and cold surfaces was seen to be consistent with the proposed flow models.