(178g) Model Reduction of Phase-Field Models Describing Crystallisation Phenomena

Crystallisation determines both quality and function of a wide range of food products. For example, texture in ice cream is given by targeting a certain crystal size/distribution that enhances mouth feel, and the first stage of freeze-drying processes – i.e. freezing and thus crystal formation – is key to determine a well-interconnected porous structure that will allow for drying and further rehydration or dissolution of the dried product (e.g. instant coffee). In all these cases, a proper control of the conditions that lead to crystal formation and growth is critical.

Phase Field models have been increasingly used to simulate and predict the formation and evolution of material microstructure and phase change interfacial kinetics. However, these methods usually lead to computationally involved numerical schemes, revealing the need for more efficient computational solutions: i.e. industrial applications, like real-time control and optimisation, require the development and implementation of process models that are capable to operate at faster time scales than the process itself.

This work presents a reduced order Phase-field model for ice crystal formation in food model systems. The model couples heat and mass transfer phenomena, describing the evolution of the solid/liquid interface. We have considered two different model reduction techniques: (i) Proper Orthogonal Decomposition (ii) Laplacian Spectral Decomposition, and we have compared their performance using a range of undercooling and seeding conditions.

Results revealed an overall good reduction performance of both model reduction methods, with savings in computation times up to up to 40% for the POD reduced model and up to 30% for the LSD model. Both reduced models (LSD and POD) exhibited similar predictive capabilities. Simulations showed plate morphologies at high supercooling and more needle-like dendrite formation at low supercooling degrees. In terms of error analysis, RMSE values revealed that the reduced models (both LSD and POD) were able to predict better the temperature field dynamics rather than the more complex ones (i.e. interface kinetics) represented by the phase field.

Overall, this work demonstrates the potential of reduced order approaches for the modelling of phase change processes and also for the development of virtual tools that allow a “fast” (yet accurate) monitoring, design and optimisation of food manufacture operations.