Convection in a Horizontal Differentially Heated Fluid Layer 

Overview

An experimental study of Rayleigh-Benard convection in an intermediate aspect ratio box that is square in plan is reported. An intermediate range of Rayleigh numbers has been considered in the study. The fluid employed is air. A Mach-Zehnder interferometer is used to collect the line-of-sight projections of the temperature field in the form of interferometric fringes. Images have been recorded after a sufficient time has elapsed for the initial transients to have been eliminated. Interferograms have been collected from four to six view angles. These are used to obtain the three-dimensional temperature field inside the cavity by using tomography. The MART algorithm has been used for the inversion of the projection data. The convergence of the iterative inversion procedure was unambiguous and asymptotic. The reconstructed temperature field with a subset of the total data was found to be consistent with the remaining unused projections.

Result for two Rayleigh numbers, namely 1.39 x 10⁴ and 4.02 x 10⁴ have been reported. These were found to correspond to two distinct flow regimes. At these Rayleigh numbers, a well-defined steady state was not observed. At the lower Rayleigh number, the fringes away from the wall showed mild unsteadiness. At the higher Rayleigh number, the fringes were found to switch between two patterns. Result for the dominate mode alone have been presented for this problem. At a Rayleigh number of 1.39x10⁴ , three-dimensional flow structures, whose influence is equivalent to longitudinal rolls have been observed. At a Rayleigh number of 4.02 x 10⁴, cubic cells have been noted in the cavity. The associated flow pattern is inferred to be a plume rising from the heated plate. The local Nusselt number variation is seen to be consistent with the observed flow patterns.

Motivation

Rayleigh-Benard convection in horizontal fluid layers is a problem of fundamental as well as practical importance. The flow pattern associated with this configuration shows a sequence of transitions from steady laminar to unsteady flow and ultimately to turbulence. This configuration has been studied by analytical and computational techniques as well as by experiments to understand the physics involved in the transition phenomena. Although extensive work has been reported, many questions remain to be answered. Many of the global features observed by numerical solutions are supported by experimental observations. However, a closer comparison in terms of thermal field and convection patterns remains to be carried out. With renewed interest in understanding nonlinear systems and simultaneously the availability of powerful computers, there has been a revival of interest in Rayleigh-Benard convection. The experimental technique has also been strengthened by the availability of optical methods to visualize the flow phenomena and computers for data storage, processing, and analysis.

Interferometric study of Rayleigh-Benard convection for two Rayleigh numbers (1.39x10⁴ and 4.02 x 10⁴) is reported in the present work. The cavity is square in plan and aspect ratio employed leads to an intermediate aspect ratio box. The aspect ratio is defined as the ratio of the horizontal dimension to the height of the cavity. The fluid considered is air. Results have been presented for flow patterns that develop at long-time that are after the initial transients have been eliminated. Interferograms collected from several line-of-sight projections have been processed to reconstruct the complete three-dimensional temperature field. The multiplicative algebraic reconstruction technique in a modified form called AVMART has been used as the preferred tomographic algorithm (AVMART)