The design and operation of the analog computers for normal freezing have been introduced to simulate the solute concentration in the freezing solid by the heights of liquid level in an array of vertical ingot tubes. Each tube represents a discrete length of the freezing ingot. The simulation was confirmed pretty well with the analytical solution. The main contribution of present paper is to introduce the method of adjusting (decreasing) the cross-section area of the liquid-zone tube during operation for simulating the decreasing in unfrozen zone. This simulation can further be applied to the problems in which the distribution coefficient varies with the solute concentration, or to the zone-refining problems with variable zone length, if the cross-section area of the liquid-zone tube is adjusted (decreased) appropriately during the simulation operation, while the analytical solutions to the problems of variable distribution coefficient and variable zone length are difficult to achieve.
Journal of the Chinese Institute of Chemical Engineers 32(2), pp.187-192