C. F. Chen

Experimental study of directional solidification of aqueous ammonium chloride solution

Directional solidification experiments have been carried out using the analogue casting system of NH 4 Cl-H 2 O solution by cooling it from below with a constant-temperature surface ranging from - 31.5°C to + 11.9 °C. The NH 4 Cl 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.

Double-diffusive convection in a porous medium

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 Δ T , 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.

Experimental study of convection in a mushy layer during directional solidification

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.

Double-Diffusive Convection: A report on an Engineering Foundation Conference

Under the auspices of the Engineering Foundation, financial support of the National Science Foundation, and the cochairmanship of the authors, a conference on ‘Double-Diffusive Convection’ was held from 14–18 March 1983 in Santa Barbara. The conference attracted more than seventy scientists and engineers working in various disciplines, and 45 talks were presented. There was an ad hoc film session which ended with a demonstration of a laboratory experiment on crystallization in a double-diffusive system.

Convection in superposed fluid and porous layers

A nonlinear computational investigation of thermal convection due to heating from below in a porous layer underlying a fluid layer has been carried out. The motion of the fluid in the porous layer is governed by Darcys equation with the Brinkman terms for viscous effects and the Forchheimer term for inertial effects included. The motion in the fluid layer is governed by the Navier-Stokes equation. The flow is assumed to be two-dimensional and periodic in the horizontal direction, with a wavelength equal to the critical value at onset as predicted by the linear stability theory. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios

Double-diffusive fingering convection in a porous medium

hat{d}=0, 0.1, 0.2, 0.5

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

and 1.0, where

Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model

hat{d}

Effect of gravity modulation on the stability of convection in a vertical slot

is the ratio of the thickness of the fluid layer to that of the porous layer. For

Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer

hat{d}=0.1