An Eulerian–Lagrangian approach for coupling fluid flow, heat transfer and liquid food product transformation

Numerical modeling of liquid food product transformation under thermo-mechanical treatment can often be achieved through computational fluid dynamics, but difficulties arise when the transformation cannot be reduced to a set of chemical reactions. Looking for a general strategy, a numerical approach is proposed by combining advantages of Eulerian and Lagrangian descriptions. Fluid flow and heat transfer are solved through the finite element method in the Eulerian frame, while the transformation is evaluated along representative Lagrangian trajectories. Any available model can be applied for assessing the transformation state, including population balance equations and stochastic models. The coupled problem is solved by iterating the Lagrangian and Eulerian steps. The approach is illustrated in studying the evolution of starch granules under hydrothermal treatment, where granule swelling is represented through a kinetic equation derived from experimental work. Results agree favorably with those obtained from a purely-Eulerian representation of the coupled processes.