1. Steady-state and stability analysis of a population balance based nonlinear ice cream crystallization model
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Centre for systems engineering and applied mechanics [Louvain] (CESAME) ; Université Catholique de Louvain (UCL), CESAME ; Centre for systems engineering and applied mechanics [Louvain] (CESAME) ; Université Catholique de Louvain (UCL) - Université Catholique de Louvain (UCL), Génie des procédés frigorifiques (UR GPAN) ; Irstea, SP2 ; Ingénierie Procédés Aliments (GENIAL) ; Institut national de la recherche agronomique (INRA) - Conservatoire National des Arts et Métiers [CNAM] - AgroParisTech - Institut national de la recherche agronomique (INRA) - Conservatoire National des Arts et Métiers [CNAM] - AgroParisTech, Génie des procédés frigorifiques (UR GPAN) ; CEMAGREF, European Project : 212754, KBBE, FP7-KBBE-2007-1, CAFE(2008), Casenave, Céline, Dochain, Denis, Alvarez, Graciela, Benkhelifa, Hayat, Flick, Denis, Leducq, Denis, Centre for systems engineering and applied mechanics [Louvain] (CESAME) ; Université Catholique de Louvain (UCL), CESAME ; Centre for systems engineering and applied mechanics [Louvain] (CESAME) ; Université Catholique de Louvain (UCL) - Université Catholique de Louvain (UCL), Génie des procédés frigorifiques (UR GPAN) ; Irstea, SP2 ; Ingénierie Procédés Aliments (GENIAL) ; Institut national de la recherche agronomique (INRA) - Conservatoire National des Arts et Métiers [CNAM] - AgroParisTech - Institut national de la recherche agronomique (INRA) - Conservatoire National des Arts et Métiers [CNAM] - AgroParisTech, Génie des procédés frigorifiques (UR GPAN) ; CEMAGREF, European Project : 212754, KBBE, FP7-KBBE-2007-1, CAFE(2008), Casenave, Céline, Dochain, Denis, Alvarez, Graciela, Benkhelifa, Hayat, Flick, Denis, and Leducq, Denis
- Abstract
International audience, 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, especially 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.