Chemical Engineering Science 61 (2006) 7819 – 7826 www.elsevier.com/locate/ces Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer Guoping Lian ∗ , Steve Moore, Luke Heeney Unilever Corporate Research, Colworth House, Sharnbrook, Bedford MK44 1LQ, UK Received 26 May 2006; received in revised form 23 August 2006; accepted 23 August 2006 Available online 16 September 2006 Abstract Ice crystallisation in a scraped surface freezer is exceedingly complex and there is very limited fundamental understanding of the influences of fluid flow and heat transfer on ice crystal size, number and shape. This paper presents a computer modelling study that combines population balance method and computational fluid dynamics method. Ice crystal nucleation and growth kinetics has been described by discrete population balance equation. Algorithms for solving the coupled equations of fluid flow, heat transfer and discrete population balance of ice crystallisation have been developed and implemented into a commercial code. Demonstrated is a 2-D computer simulation of ice crystallisation in a scraped surface freezer. Although the simulation makes several assumptions including simplified fluid flow conditions, the predicted ice crystal size distribution is comparable to the experimental data. It is shown that with combined computational fluid dynamics and population balance modelling much insight into the interaction of fluid flow, heat transfer and ice crystallisation in the scraped surface freezer can be obtained.  2006 Elsevier Ltd. All rights reserved. Keywords: Computer simulation; Coupled heat and mass transfer; Ice crystallisation; Nucleation; Particle size distribution 1. Introduction Ice crystallisation in a scraped surface freezer or heat ex- changer is an important process for making ice cream and/or frozen dissert (Hartel, 1996). The process can be also used for fruit juice concentration (Braddock and Marcy, 1985; Bayindirli et al., 1993). In order to achieve desired texture and sensory property, it is necessary to control the size, shape and distri- bution of ice crystals. The process of ice crystallisation is ex- ceedingly complex and involves many coupled interactions of fluid flow, heat transfer and ice crystal nucleation and growth. There is very limited understanding on the influence of freez- ing temperature and other process conditions on the kinetics of ice crystal nucleation and growth. Both the design and control of ice crystallisation process are essentially empirical. Studies on ice crystallisation in scraped surface freezer are limited. Most studies have considered the general mecha- nisms and kinetics of ice crystallisation under well-controlled ∗ Corresponding author. Tel.: +44 1234 222741; fax: +44 1234 248010. E-mail address: guoping.lian@unilever.com (G. Lian). 0009-2509/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.08.075 experimental conditions (e.g. Adapa et al., 2000; Flores and Goff, 1999; Hartel, 1996). Few studies have been reported on modelling the kinetics of ice crystal nucleation and growth (Hey and MacFarlane, 1998; Margolis et al., 1971; Omran and King, 1974; Shirai et al., 1986). Those studies considered relatively simple process conditions of mixed suspension mixed product removal (MSMPR) using the population balance (PB) equation of Randolph and Larson (1988). The MSMPR model has been mostly applied to modelling industrial crystallisation processes (e.g. Jancic and Garside, 1975; Jones et al., 1996; Mydlarz, 1996; Shirai et al., 1986). One of the main limitations of the MSMPR model is that the dispersed particles are assumed to be well-mixed and the process fields of temperature and flow are considered to be homogeneously distributed. In particular, the coupling of fluid flow, heat transfer and ice crystal nucleation and growth has been neglected. Recently, combined computational fluid dynamics (CFD) and PB modelling have been reported. The technique has been applied to various processes including soot formation during combustion (Zucca et al., 2006), droplet formation in liquid–liquid extraction (Schmidt et al., 2006; Vikhansky and Kraft, 2004; Vikhansky et al., 2006), air–water flow in bubble