Population balance modeling for the charging process of a PCM cold energy storage tank

In this paper, a dynamic model is proposed for the charging process of a cold energy storage made of a fixed bed of spherical nodules containing a Phase Change Material (PCM). During the charging process, even if the temperature of the cooling liquid that flows through the storage is uniform, the solidification process does not begin at the same temperature among the nodules due to the supercooling phenomenon. A first number distribution can be defined according to the solid mass fraction among the nodules experiencing solidification. At the end of the solidification process, the temperature of the solid phase is not the same among the nodules population having completed the solidification. A second number distribution can be defined according to their mean temperature. In order to calculate the time evolution of these two number distributions, we propose to use the population balance equation approach coupled with nodules energy balance equations. The resulting partial differential equations are spatially discretized by the finite difference method. The supercooling phenomenon is taken into account as a boundary condition of the population balance equation associated with the solid mass fraction by using a nucleation kinetic model. The resulting set of ordinary differential equations is numerically solved. The model is applied for simulating the charge cycle of an ice storage system. Good agreement between simulation results and experimental data is achieved.