Steady-state and stability analysis of a population balance based nonlinear ice cream crystallization model

Céline Casenave (1, 2) , Denis Dochain (2) , Graciela Alvarez (3) , Hayat Benkhelifa (4) , Denis Flick (4) , Denis Leducq (3, 5)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 UCL - Université Catholique de Louvain = Catholic University of Louvain
3 IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture
4 GENIAL - Ingénierie Procédés Aliments
5 CEMAGREF - Centre national du machinisme agricole, du génie rural, des eaux et forêts

The process of crystallization can be modelled by a population balance equation coupled with an energy balance equation. Such models are highly complex to study due to the infinite dimensional and nonlinear characteristics, specially when all the phenomena of nucleation, growth and breakage are considered. In the present paper, we have performed the stability analysis on a reduced order model obtained by the method of moments, which remains still highly complex. The considered model has been developed by the Cemagref and validated on experimental data. After computation, we get a scalar equation whose solutions correspond to the equilibrium points of the system. This equation is finally solved numerically for a concrete physical configuration of the crystallizer. We show that in most instances, there is only one steady state. The possibility of multiple steady-states is discussed.

Mots clés: crystallization; process; ice cream; equation

Domaines: Sciences du Vivant [q-bio]

Céline Casenave, Denis Dochain, Graciela Alvarez, Hayat Benkhelifa, Denis Flick, et al.. Steady-state and stability analysis of a population balance based nonlinear ice cream crystallization model. American Control Conference (ACC) 2012, Jun 2012, Montréal, Canada. 6 p., ⟨10.1109/ACC.2012.6314813⟩. ⟨hal-00854398v2⟩