Numerical simulation of two-dimensional gas flows through granular phase change materials
The perspective way of energy storage is using compressed-air energy storage plants with thermal energy storage systems based on phase change materials (PSM). In granular or capsular PCMs, particles can melt or solidify without loss of integrity. The present paper numerically models a two-dimensional flow of ideal gas through such materials; this flow is accompanied by phase transition inside PCM particles. The mathematical description of the process is based on the model of interacting interpenetrating continua and contains the equations of energy for the gas and the PCM, the equation of continuity for the gas, a generalization of Darcy's law and Sutherland correlation for the gas viscosity. As the phase transition is smooth, it is impossible to describe it by a classical Stefan problem. Instead, a parameter \(f\) is introduced in the equations, which stands for the liquid phase fraction in the PCM (\(f=0\) corresponds to the solid phase and \(f=1\) to liquid, respectively). So, a nonlinear mixed hyperbolic-parabolic system of equations is obtained, which cannot be solved analytically. The authors propose a numerical method combining explicit and implicit finite-difference schemes to solve it. The method's convergence cannot be proved analytically, but it is illustrated on some examples. The authors show that the total rate of convergence is close to 1 but it may be higher at the interior points of the domain under study. Calculations made for domains of several different shapes show that heating near domain walls occurs more slowly than in its central part.
scientific article; zbMATH DE number 7346778