Coupling population balance and residence time distribution for the ice crystallization modeling in a scraped surface heat exchanger

Abstract

This paper presents the mathematical modeling of the ice crystallization process occurring during the freezing of sorbet in a continuous scraped surface heat exchanger (SSHE). Two different modeling approaches have been used, both of which include the nucleation, growth and breakage phenomena of the ice crystals. For both models, the rate of ice crystal nucleation and growth were determined by the subcooling degree. The first model combines heat transfer and population balance equations (PBE), assuming plug flow. The evolution of the values of product temperature, mean chord length, ice volume fraction and apparent viscosity were determined as a function of the residence time. The second model is a coupled model of heat transfer and PBE combined with an empirical model of residence time distribution (RTD), which makes it possible to take into account the fact that the fluid fractions flowing throughout the SSHE do not have the same time–temperature history. The values of the variables (product temperature and mean chord length) were determined for each fraction of fluid exiting the SSHE, and the bulk values were then calculated using the RTD. Simulation results were compared to a set of experimental data obtained during the ice crystallization process of sorbet in a continuous SSHE at the laboratory pilot scale. With a first estimated set of model parameters, it has been shown that the experimental tendencies are represented very satisfactorily by the two models within a 10% error limit. These modeling approaches can then be considered as a promising tool for the understanding and the prediction of the ice crystallization process in SSHEs so as to identify new ways to improve the performance of the process.