Simulation of normal-freezing processes

The design and operation of the analog computers for normal freezing have b een introduced to simulate the solute concentration in the freezing solid b y the heights of liquid level in an array of vertical ingot tubes. Each tub e represents a discrete length of the freezing ingot. The simulation was co nfirmed pretty well with the analytical solution. The main contribution of present paper is to introduce the method of adjusting (decreasing) the cros s-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 conce ntration, or to the zone-refining problems with variable zone length, if th e cross-section area of the liquid-zone tube is adjusted (decreased) approp riately during the simulation operation, while the analytical solutions to the problems of variable distribution coefficient and variable zone length are difficult to achieve.