In the directional solidification of concentrated alloys, the frozen solid region is separated from the melt region by a mushy zone consisting of dendrites immersed in the melt. Simultaneous occurrence of temperature and solute gradients through the melt and mushy zones may be conducive to the occurrence of salt-finger convection, which may in turn cause adverse effects such as channel segregation. We have considered the problem of the onset of finger convection in a porous layer underlying a fluid layer using linear stability analysis. The eigenvalue problem is solved by a shooting method. As a check on the method of solution and the associated computer program, we first consider the thermal convection problem. In this process, it is discovered that at low depth ratios dˆ (the ratio of the fluid layer depth to the porous layer depth), the marginal stability curve is bimodal. At small dˆ, the long-wave branch is the most unstable and the convection is dominated by the porous layer. At large dˆ, the short-wave branch is the most unstable and the convection is dominated by the fluid layer, with a convection pattern consisting of square cells in the fluid layer. In the salt-finger case with a given thermal Rayleigh number Ram = 50, as the depth ratio dˆ is increased from zero, the critical salt Rayleigh number Rasm first decreases, reaches a minimum, and then increases. The system is more stable at dˆ > 0.2 than at dˆ = 0. This rather unusual behavior is again due to the fact that at small dˆ, convection is dominated by the porous layer and, at large dˆ, convection is dominated by the fluid layer. However, in the latter case, the convection pattern in the fluid layer consists of a number of high aspect ratio cells.

Directional solidification experiments have been carried out using the analogue casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from - 31.5°C to + 11.9 °C. The NH4Cl concentration was 26% in all solutions, with a liquidus temperature of 15 °C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as + 11.0 °C. However, when the bottom temperature was raised to + 11.9 °C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

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.

An experimental study has been carried out to examine double-diffusive convection in a porous medium. The experiments were performed in a horizontal layer of porous medium consisting of 3 mm diameter glass beads contained in a box 24 cm × 12 cm × 4 cm high. The top and bottom walls were made of brass and were kept at different constant temperatures by separate baths, with the bottom temperature higher than that of the top. The onset of convection was detected by a heat flux sensor and by the temperature distribution in the porous medium. When the porous medium was saturated with distilled water, the onset of convection was marked by a change in slope of the heat flux curve. The temperature distribution in the longitudinal direction in the middle of the layer indicated a convection pattern consisting of two-dimensional rolls with axes parallel to the short side. This pattern was confirmed by flow visualization. When the porous medium was saturated with salinity gradients of 0.15% cm−1 and 0.225% cm−1, the onset of convection was marked by a dramatic increase in heat flux at the critical ΔT, and the convection pattern was three-dimensional. When the temperature difference was reduced from supercritical to subcritical values, the heat flux curve established a hysteresis loop. Results from linear stability theory, taking into account effects of temperature-dependent viscosity, volumetric expansion coefficients, and a nonlinear basic state salinity profile, are discussed.

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).