A finite difference solution for freezing brine on cold substrates of spongy ice

The process of rapid freezing of a thin layer of brine, suddenly in contact with a cold substrate of brine-spongy ice, is investigated. The mechanism of intermittent ice accretion on cold substrates, which occurs in a short period of time, is different from the slow freezing of salt water and must be evaluated using a differential analysis. Investigation of rapid freezing fills a gap of knowledge related to intermittent icing of superstructures, which has usually been studied using control volume methods. The equation of transient heat conduction through brine-spongy ice is developed. Rapid freezing causes complete solute trapping, which makes the salinity constant and stable at the phase interface. A finite difference method, using uniformly-spaced fixed-grid mesh, is employed as a numerical scheme for calculating the rate of ice accretion. A method is presented for discretization at nodes close to the phase interface for preventing the instability of numerical solutions when the phase interface passes the adjacent nodes. The discretization is based on the Method of Lines (MOL) which is a numerical-iterative method of solution. Numerical results show that higher salinities and lower initial temperatures of brine-spongy substrates have the potential to create a thicker layer of new ice. Experimental studies show that the model and numerical solutions accurately predict the rapid freezing of brine on a cold substrate of brine-spongy ice.