ALBERT

Description: The effect of surface tension on the onset of convection in a horizontal double-diffusive layer was studied both experimentally and by linear stability analysis. The experiments were conducted in a rectangular tank with base dimension of 25 x 13 cm and 5 cm in height. A stable solute (NaCl) stratification was first established in the tank, and then a vertical temperature gradient was imposed. Vertical temperature and concentration profiles were measured using a thermocouple and a conductivity probe and the flow patterns were visualized by a schlieren system. Two types of experiments were carried out which illustrate the effect of surface tension on the onset of convection. In the rigid-rigid experiments, when the critical thermal Rayleigh number, RT, is reached, large double-diffusive plumes were seen simultaneously to rise from the heated bottom and descend from the cooled top. In the rigid-free experiments, owing to surface-tension effects, the first instability onset was of the Marangoni type. Well-organized small plumes were seen to emerge and persist close to the top free surface at a relatively small RMT (where subscript M denotes ‘Marangoni’). At larger RbT 〉 RtT (where subscript t denotes ‘top’) these plumes evolved into larger double-diffusive plumes. The onset of double-diffusive instability at the bottom region occurred at a still higher RbT 〉 RtT (where subscript b denotes ‘bottom’), A series of stability experiments was conducted for a layer with an initial top concentration of 2wt% and different concentration gradients. The stability map shows that in the rigid-free case the early Marangoni instability in the top region reduces significantly the critical RT for the onset of double-diffusive convection. Compared with the rigid-rigid case, the critical RT in the top region is reduced by about 60 % and in the bottom region by about 30%. The results of the linear stability analysis, which takes into account both surface-tension and double-diffusive effects, are in general agreement with the experiments. The analysis is then applied to study the stability characteristics of such a layer as gravity is reduced to microgravity level. Results show that even at 10-4go, where g0is the gravity at sea level, the double-diffusive effect is of equal importance to the Marangoni effect. © 1995, Cambridge University Press. All rights reserved.

Description: Experiments are conducted to study the longitudinal vortices that develop in the boundary layer on the upper surface of an inclined, heated plate. An isothermal plate in water is inclined at angles ranging from 20 to 60 degrees (from the vertical) while the temperature difference is varied from 2 to 23°C. A double-pass Schlieren system is used to visualize the vortices and particle image velocimetry (PIV) is used to measure velocities. In addition, a unique method is developed such that both the Schlieren visualization and PIV can be performed simultaneously. The wavelengths of the vortices and the critical modified Reynolds numbers (R̃) for the onset, merging, and breakup of the vortices are determined from Schlieren images for Pr = 5.8. The critical values for R̃ and the critical wavelengths are compared to results of previous experiments and stability analyses. The spatial growth rates of vortices are determined by using the PIV measurements to determine how the circulation in the vortices grows with distance from the leading edge. This is the first time that the growth rate of the vortices have been found using velocity measurements. These spatial growth rates are compared to the results of Iyer & Kelly (1974) and found to be in general agreement. By defining a suitable circulation threshold, the critical R̃ for the onset of the vortices can be found from the growth curves.

Description: The nature of instability occurring in a differentially heated infinite slot under steady gravity depends only on the Prandtl number of the contained Boussinesq fluid. For fluids with Pr 〈 12.5, the instability is shear dominated and onsets in a steady convection mode; for fluids with Pr 〉 12.5, the instability is buoyancy dominated and onsets in an oscillatory mode. In this paper, we examine the effect of gravity modulation on the stability characteristics of convection in an infinite slot with both kinds of fluids, in particular, Pr = 1 and Pr = 25. Using the method of Sinha & Wu (1991), we are able to obtain accurate results without excessive numerical integration in the linear stability analysis by Floquet theory. Results show that, for Pr = 1, at a non-dimensional oscillation frequency ω = 20, the critical state alternates between the synchronous and subharmonic modes. At higher frequencies, ω 〉 100, all critical states occur in the synchronous mode. For Pr = 25, with a modulation amplitude ratio of 0.5, resonant interaction occurs in the neighbourhood of ω = 2σ c where σ c is the oscillation frequency of the instability at the critical state under steady gravity. This resonant interaction is destabilizing, with the critical Grashof number being reduced by approximately 20% from that at steady gravity. It is due to the presence of a detached subharmonic branch of the marginal stability curve. In frequency ranges where the detached subharmonic branch is absent, the critical state is in the quasi-periodic mode consisting of two waves of different oscillation frequencies whose sum is the forcing frequency. An analysis of the rate of change of the perturbation kinetic energy shows that, for Pr = 1, the instability is shear dominated regardless of the mode of oscillation, synchronous or subharmonic. Similarly, for Pr = 25, the instability is buoyancy dominated whether it is in the quasi-periodic or subharmonic mode. The mode switching is a response to the forcing and is independent of the dominant mechanisms of instability.

Description: Results of experiments using a number of techniques to study the nature of convection in a mushy layer generated by directional solidification of aqueous ammonium chloride solutions are reported. The techniques include flow visualization using a dye tracing method to study convection within the mushy layer before and after the onset of plume convection, and X-ray tomography to measure the solid fraction of a growing mush. The principal results are as follows, (i) Prior to the onset of chimneys, there is no convective motion in the mush, in spite of the vigorous finger convection at the mush-liquid interface, (ii) When the plume convection is fully developed, the flow of fluid in the mush consists of a nearly uniform downward motion toward the bottom of the tank, horizontal motion along the bottom toward the chimneys, then upward plume motion through the chimneys in the liquid region above the mush. (iii) The solid fraction of a growing mush as determined by X-ray tomography shows a significant decrease toward the bottom of the tank after the chimneys are fully developed. As a result, the concomitant increase in the local permeability can be as much as 50 %. Some of the results reported herein confirm theoretical predictions of Worster (1992) and Amberg & Homsey (1993). Others reveal phenomena not observed heretofore. © 1995, Cambridge University Press. All rights reserved.

Description: When a tank of fluid with a solute gradient is subjected to lateral heating, a series of horizontal convection cells is generated when the critical condition is exceeded. This phenomenon has been observed experimentally and simulated by two-dimensional numerical schemes by a number of previous investigators. In each of the convection cells, relatively warm and solute-rich fluid flows from the hot to the cold wall along the top of the cell while the return of the relatively cool and solute-poor fluid is along the bottom of the cell. This situation is conducive to the onset of salt fingers. We recently performed a series of such experiments with salt-water and ethanol-water solutions. By using flow visualization techniques, salt fingers in longitudinal rolls typical of those occurring in shear flows were observed. Salt fingers were observed as soon as convection was initiated, and they advanced with the convection front. Experiments with an ethanol-water solution showed that salt fingers can be generated by flows driven by a surface tension gradient and that the effect of solute concentration on surface tension plays an important role in the process.