Non-equilibrium crystallization in freezing porous media: Numerical solution

Abstract

Abstract The boundary value problem which arises during heat and moisture transfer in freezing fine-grained porous media under phase transition conditions is solved. It is assumed that the phase transition process occurs with finite rate of the water crystallization. So, the non-instantaneous kinetics is considered. Since the problem is significantly nonlinear the numerical method for the solution is applied. For the approximation of the system of differential equations the implicit two-level finite-difference scheme with central differences for space coordinate and one-side differences for time is used. The finite-difference system of equations is solved by “double sweep method.” It was shown the stability of “double sweep method” and solvability of the problem. Based on the correlation analysis, the dimensionless form for the diffusion coefficient as a function of moisture is obtained and used for the modeling. It is shown that the results for the characteristic distributions — temperature and total moisture, obtained in numerical solution, are in a good agreement with experimental investigations. The effect of the main criteria for the considered process — Lewis and Stefan numbers on the temperature, moisture, ice content and total moisture distributions is discussed. Especial attention was paid on the formation of the kinetic zone and its transformation in the course of non-equilibrium freezing. It was shown that the kinetic zone has a width of about 20–40% of the overall dimension of the system. Therefore the simulation of the phase transition zone as an infinitely thin front in freezing process, which is an approach incorporated in most theoretical models, is not suitable for the non-equilibrium water crystallization processes in fine-grained soils, and thereby conforms the validity of the kinetic approach.