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Ice crystallization mechanism in a SSHE
Schwartzberg and Liu (1990) proposed a model for the ice crystallization mechanism in SSHEs. Based on observations of dendritic growth during the quiescent freezing of sucrose solutions on a chilled surface, these authors suggested that due to the high rate of subcooling at the heat exchange cylinder wall, dendrites are likely to grow there, then are cut off and dispersed into the bulk flow by the scraper blades of the dasher. The dendrites are then ripened and become round shape ice crystals in the bulk warm region of the SSHE. Schwartzberg (1990) reported that the space between dendrites was proportional to the freezing rate to the -1/2 power, which means that high subcooling rates lead to a faster growth of more dendrites, with closely spaced branches and a thinner structure.
Sodawala and Garside (1997) used video microscopy to examine the freezing of a 10% sucrose solution on a cold surface with a rotating scraper blade. These authors observed the formation of ice in flocs which grew parallel to the surface after each scrape, then merged and grew vertically. They also observed that at low scraping speeds the ice flow were removed from the freezing surface and transported into the bulk solution. They also reported that an increase in the scraping frequency of the blade led to more frictional heat and to smaller flocs being cut off from the surface.
Cebula and Russell (1998) distinguished two different zones in which the freezing of ice cream occurs in a SSHE: a wall zone and a bulk zone. The freezing at the wall zone was simulated by a cold plate upon which a thin layer of ice cream mix was spread, and frozen at temperatures close to the temperatures of the heat exchanger wall. Based on observations of a cross section by scanning electron micrographs, these authors reported in the region adjacent to the cold surface the formation of small globular ice crystals, the effect of which was attributed to heterogeneous nucleation due to the sufficient subcooling in this zone. Further away from the surface, they also observed the formation of columnar ice crystals which do not attached themselves to the wall, but that grow out from the small nuclei near the cold surface. Visualization experiments on the crystallization of sucrose solutions on a cooled surface with a rotating scraper blade, showed that immediately after the surface was scraped, fragments of ice remained attached to the surface and served as points of growth for ‘islands’ of new ice that subsequently came together into a solid layer depending on the scraping frequency of the blades. For the simulation of the bulk zone, Cebula and Russell (1998) used a two stage freezer: in the first freezer the ice crystals were formed, and in the second freezer no cooling was employed so that there was no new ice crystals formed. Experiments at constant residence time and different dasher speeds to vary the mechanical energy dissipated into the system showed that the increase in the amount of mechanical heat reduced significantly the number of ice crystals and increase the ice crystal size. This effect was attributed to the melting of the smaller ice crystals with the increase in the energy input.
More recently, on the basis of thermal conductivity measurements of a sucrose solution in a flowcell equipped with a scraper blade and a chilled surface, Zheng (2006) concluded that the ice layer formed at the freezer wall was in fact a slush layer composed of both ice and concentrated sucrose solution. Zheng (2006) also observed that after each scrape of the blade, many ice nuclei grew rapidly from the ice debris remaining from previous scraping, and continued to grow along the chilled surface before merging and growing vertically. It was then concluded that the main effect of the scraper blades was to induce the secondary nucleation at the surface.
Influence of the operating conditions on ice crystallization in SSHEs
The temperature of the refrigerant fluid determines the heat removal rate of the system and provides the driving force for ice nucleation and growth. Lower refrigerant fluid temperatures result in a faster freezing and consequently lead to the formation of smaller ice crystals. Koxholt et al. (2000) as well as Drewett and Hartel (2007) reported ice creams with smaller ice crystals by using low refrigerant fluid temperatures, the effect of which was attributed to the higher subcooling applied to the product which enhanced the nucleation rate.
The scraping action of the dasher improves the heat transfer rate between the freezer wall and the product (Ben Lakhdar et al., 2005). Higher dasher speeds would thus be expected to give lower draw temperatures and smaller ice crystals. However, an increase in dasher speed would also increase the amount of frictional heat generated by the blades and the viscous dissipation, producing warmer draw temperatures. This effect will cause the melting of the small ice nuclei, and consequently, the reduction in the effective ice nucleation rate (Cebula and Russell, 1998). Furthermore, an increase in dasher speed may also lead to the attrition of the larger ice crystals (Haddad, 2009; Windhab and Bolliger, 1995). The scraping action of the blades would also be expected to produce new smaller ice nuclei from the ice debris remaining of previous scrapings at the cooling surface by secondary nucleation (Sodawala and Garside, 1997; Zheng, 2006). It has been demonstrated that the dasher speed has an effect on the ice crystal size. However, not all the studies available in literature are in agreement as to its effects. An increase in dasher speed has been found to increase (Russell et al., 1999; Drewett and Hartel, 2007), to decrease (Inoue et al., 2008) and not to affect (Koxholt et al., 2000) the ice crystal size.
The mix flow rate determines the residence time of the product, affecting the time available to remove heat from the product, and consequently, the ice nucleation and growth mechanisms of ice crystals. A number of studies in the literature have observed that high mix flow rates (short residence times) for a given draw temperature (by adjusting the temperature of the refrigerant fluid) and dasher speed produced smaller ice crystals due to the reduction in recrystallization phenomena in the bulk region of the product (Drewett and Hartel, 2007; Koxholt et al., 2000; Russell et al., 1999). For a given refrigerant fluid temperature (varying exit temperature) and dasher speed, Russell et al. (1999) also found smaller ice crystals produced at higher mix flow rates, the effect of which was attributed to the reduction in ice crystal coarsening. During the freezing of 30% sucrose/water solutions in an SSHE, Ben Lakhdar et al. (2005) reported that low product flow rates (long residence times) led to a reduction in the exit temperature of the product, and therefore to an increase of the ice mass fraction in the product.
Temperature profile and heat transfer in SSHEs
The temperature distribution inside the SSHE is highly heterogeneous. The heat transfer at the wall creates a radial temperature gradient, with the lowest temperature at the wall. Temperatures at the wall vary within a range between -15 to -30 °C, then the temperature of the product rises from the wall to the core of the heat exchange cylinder. The axial temperature profile in the SSHE also varies significantly. Russell et al. (1999) measured the axial temperature profile at the wall region by means of thermocouples mounted on a scraper blade. These authors found that during the first 15% of the axial fraction length of the SSHE, the temperature of ice cream decreases rapidly to a temperature range between -5 to -7 °C. Then the product temperature decreases more slowly to reach a temperature range between -6 to -10 °C within the axial fraction length from 15 to 65% of the SSHE. Finally the temperature of the product increases at the outlet pipe of the SSHE. It was also reported that the increase in dasher speed led to the increase in the axial temperature profile of the product, the effect of which was attributed to the increase in the rate of mechanical dissipation.
The mechanism of heat transfer in a SSHE can be explained by the penetration theory, which describes the heat transfer mechanism in two steps: firstly, heat penetrates by molecular conduction into an immobile thin product layer along the heat exchanger wall during the time interval between two scraping blades. Secondly, a heat transfer convection stage, in which the thin product layer is detached from the wall by the scraper blades and assumed to be perfectly mixed within the rest of the product, and simultaneously, new product enters into contact with the cold surface of the heat exchange cylinder (Maingonnat and Corrieu, 1983).
Residence time distribution in SSHEs
Sorbet behaves as a non-Newtonian shear-thinning fluid. Thus, this section will only review the available RTD studies for shear-thinning fluids. A number of studies in the literature have determined the RTD of non-Newtonian shear-thinning fluids flowing through SSHEs under isothermal conditions (Benezech and Maingonnat, 1989; Alcairo and Zuritz, 1990; Lee and Singh, 1991; Russell et al., 1997). However, there is a paucity of information available on the RTD of food products when crystallization occurs under cooling conditions (Russell et al., 1997; Belhamri, et al., 2009). At isothermal conditions, it has been demonstrated that the operating conditions, such as the product flow rate, the rotational speed and the apparent viscosity of the product, have an effect on the RTD of non-Newtonian fluids. Not all authors agree as to their effects, however. An increase in product flow rate has been found to narrow (Alcairo and Zuritz, 1990; Lee and Singh, 1991), or not to affect the RTD (Benezech and Maingonnat, 1989). An increase in rotational speed has been found to broaden (Benezech and Maingonnat, 1989; Russell et al., 1997), to narrow (Alcairo and Zuritz, 1990) or not to affect the RTD (Lee and Singh, 1991). An increase in the apparent viscosity of the product has been found to broaden (Lee and Singh 1991) or not to affect the RTD (Benezech and Maingonnat, 1989; Alcairo and Zuritz, 1990). At cooling conditions, during the crystallization of water in ice cream, Belhamri et al. (2009) found that an increase in product flow rate and in rotational speed led to a narrowing of the RTD. Furthermore, in the case of ice cream freezing, Russell, et al. (1997) found that ice cream exhibited a broader RTD, as compared to a less shear-thinning fluid, Carbopol. Table 2.1 shows a summary of the observed effects by various authors on RTD studies of non-Newtonian shear-thinning fluids in SSHEs under isothermal and cooling conditions.
Crystallization modelling approaches for SSHEs
Lian et al. (2006) reported a combined computational fluid dynamics (CFD) and PBE to simulate the ice crystallization of 25% sucrose solution in a SSHE. In order to simplify the fluid flow conditions, the flow field was solved at steady state for a 2D geometry, in which a constant viscosity and negligible ice crystal dispersion were assumed. The PBE was solved by the method of classes by discretizing the size domain in 14 granulometric classes. The comparison between experimental and modelling data showed that the predicted ice CSD overestimated the number of small ice crystal and underestimated the number of large ice crystals. The discrepancies between the model predictions and the experimental data were attributed in part to the lack of accuracy of the measurement technique of the ice crystal size, and to the assumptions made to simplify the fluid flow.
Dorneanu et al. (2010) proposed a reduced model for the freezing process of ice cream in a SSHE. The model considers two layers of fluid: a thin frozen ice layer adjacent to the wall of the SSHE, and a bulk layer located between the rotor and the frozen ice layer. It was considered that within the frozen ice layer the ice crystals form and grow into an ice layer of variable thickness, which is periodically removed into the bulk of the fluid by the rotation of the scraper blades. Within the bulk region the ice crystals are dispersed into the bulk fluid and only ice melting was considered. The fluid flow within the SSHE was simplified by considering a plug flow at steady state and the product to be well mixed within a cross-sectional area, perpendicular to the axial direction. Heat transfer and population balance equations were solved for 12 size classes. Simulation results predicted well the expected trends; nevertheless parameter estimation using experimental data was still required to assure more accurate results.
More recently Freireich et al. (2011) reported the incorporation of particle flow information from discrete element simulation in the PB modelling of mixed-coaters. This modelling approach made it possible to account for flow heterogeneity in the mixer-coater. In this approach a discrete element model simulates the trajectory of the particles within each region of the reactor; then it determines the residence time of the particle and generates sub-compartments in order to reproduce the measured residence time of the particle in each region. Subsequently, a system of PBE is written based on the sub-compartments and simulate the population density of particles. Simulation results predicted well the experimental trends and provided accurate results for the behavior of the system.
The mathematical models available in the literature for the simulation of the ice crystallization process in SSHEs use simplified fluid flow conditions and do not consider the influence of the RTD on the final ice crystal size. Furthermore, the effect of the apparent viscosity on the viscous dissipation and its repercussion on heat transfer and consequently ice crystal size and product temperature are rarely taken into account for the modelling of ice crystallization in SSHEs.
Bibliographical review conclusions
The aim of the initial freezing process is to deliver a product with the smallest possible ice crystal size, so as to produce a high quality sorbet. The optimization of the freezing process requires a good control of the operating conditions and the understanding of the development of the ice crystals inside the scraped surface heat exchanger (SSHE).
The literature available has made it possible to elucidate some basics of the ice crystallization mechanism in SSHEs; however, more research is still needed to confirm the existing theories. In particular, experimental studies to examine the influence of the operating conditions on ice crystal size and product temperature are still pertinent, since they not only make it possible to confirm the proposed ice crystallization mechanism models, but also these studies can orient sorbet manufacturers in the possible ways in which the initial freezing process can be improved.
The temperature and flow profiles in SSHEs are highly heterogeneous. The bibliographic review showed that there is little information about the effect of the operating conditions on the axial temperature profile. This information would be highly valuable from an industrial point of view, since it makes it possible to identify the operating conditions that will induce a faster freezing and therefore a small ice crystal size in the final product.
Residence time distribution studies when ice crystallization occurs under cooling conditions are very rare. Information is still needed to have a better understanding of the effect of the freezing operating conditions on the fluid flow behaviour of sorbet within the SSHE. The experimental characterization and modelling of the RTD can provide valuable information to improve the understanding of the fluid flow behaviour that make it possible to assess the degree of thermal treatment applied to the product. This information may aid to identify the operating conditions that improve product quality.
Table of contents :
Chapitre 1 – Introduction
1.1. Introduction générale
1.2. Méthodologie
1.3. Structure de la thèse
Chapter 2 – Background
2.1. Sorbet manufacturing process
2.1.1. Ice crystallization mechanism in a SSHE
2.1.2. Influence of the operating conditions on ice crystallization in SSHEs
2.2. Flow behaviour in SSHEs
2.3. Temperature profile and heat transfer in SSHEs
2.4. Residence time distribution (RTD)
2.4.1. Residence time distribution in SSHEs
2.5. Residence time distribution modelling
2.5.1. Plug-flow with axial dispersion model (ADM)
2.5.2. Tanks-in-series model (TSM)
2.5.3. The gamma distribution model (GDM)
2.5.4. RTD models used for the flow behaviour description in SSHEs
2.6. Rheological properties of sorbet
2.6.1. Rheological models
2.7. Modelling of the freezing process
2.7.1. Population balance approach
2.7.2. Crystallization modelling approaches for SSHEs
2.8. Bibliographical review conclusions
2.9. Aim of this work
References of bibliographic review
Chapter 3 – Materials and methods
3.1. Working fluid – Lemon sorbet mix
3.2. Description of the experimental platform
3.2.1. Control of process conditions and data acquisition in Labview®
3.3. Online sensors
3.3.1. Draw temperature measurements and ice volume fraction calculations
3.3.2 Ice crystal chord length distribution (CLD) measurements by the FBRM probe
3.3.3. Temperature profile measurement
3.4. Apparent viscosity measurements
3.5. Residence time distribution measurements
Chapter 4 – Articulation of the scientific papers
4.1. Online ice crystal size measurements during sorbet freezing by means of the focused beam reflectance measurement (FBRM) technology. Influence of operating conditions
4.2. Experimental study and modelling of the residence time distribution in a scraped surface heat exchanger during sorbet freezing
4.3. Rheological characterization of sorbet using pipe rheometry during the freezing process
4.4. Influence of ice and air volume fractions on the rheological properties of sorbet
5.5. Coupling population balance and residence time distribution for the ice crystallization modelling in a scraped surface heat exchanger
Chapter 5 – Results and discussion
5.1. Online ice crystal size measurements during sorbet freezing by means of the focused beam reflectance measurement (FBRM) technology. Influence of operating conditions
Abstract
1. Introduction
2. Materials and methods
2.1. Sorbet freezing
2.2. Experimental design and statistical analysis
2.3. Draw temperature measurements and ice mass fraction calculations
2.4. Ice crystal CLD measurements by the FBRM probe
3. Results and discussion
3.1. Freezer operating conditions and global ANOVA analysis
3.2. Influence of refrigerant fluid temperature and mix flow rate on draw temperature
3.3. Influence of refrigerant fluid temperature and mix flow rate on mean chord length
3.4. Influence of dasher speed on draw temperature
3.5. Influence of dasher speed on mean chord length
4. Conclusions
5.2. Experimental study and modelling of the residence time distribution in a scraped surface heat exchanger during sorbet freezing
Abstract
1. Introduction
2. Materials and methods
2.1. Working fluid
2.2. Crystallization process equipment and operating conditions
2.3. Temperature profile measurement
2.4. Residence time distribution measurement
2.5. Residence time distribution data treatment
3. Residence time distribution models
3.1. Plug-flow with axial dispersion model
3.2. Tanks-in-series model
3.3. The gamma distribution model
3.4. RTD model fitting to experimental RTD data
4. Results and discussion
4.1. Influence of refrigerant fluid temperature on axial temperature profile and RTD
4.2. Influence of mix flow rate on axial temperature profile and RTD
4.3. Influence of rotational speed on axial temperature profile and RTD
5. Conclusions
5.3. Rheological characterization of sorbet using pipe rheometry during the freezing process
1. Introduction
2. Materials and methods
2.1. Sorbet freezing and operating conditions
2.2. Pipe rheometry measurements
2.3. Ice volume fraction calculations
3. Results and discussion
3.1. Wall slip and viscous dissipation effects on the apparent viscosity of sorbet
3.2. Effect of draw temperature and ice volume fraction on the apparent viscosity.
3.3. Experimental uncertainty
4. Rheological model
4.1. Model description
5. Conclusions
5.4. Influence of ice and air volume fractions on the rheological properties of sorbet
Abstract
1. Introduction
2. Materials and methods
2.1. Sorbet freezing and operating conditions
2.2. Pipe rheometry measurements
2.3. Ice volume fraction calculations
3. Results and discussion
3.1. Influence of ice and air volume fraction on the flow behaviour index
3.2. Influence of ice and air volume fractions on the apparent viscosity
4. Conclusions
5.5. Coupling population balance and residence time distribution for the ice
crystallization modelling in a scraped surface heat exchanger
Abstract
1. Introduction
2. Experimental
2.1. Ice crystallization process equipment and operating conditions
2.2 Residence time distribution measurement and modelling
3. PBE and plug flow modelling approach
3.1. Fluid flow
3.2. Energy balance
3.3. Population balance
4. Modelling approach coupling PBE and RTD
5. Numerical solution of the models
6. Results and discussion
6.1. PBE and plug flow modelling approach
6.2 Coupling of PBE and RTD modelling approach
7. Conclusions
Chapitre 6 – Conclusions et perspectives
Publications and communications
Appendix
Abstract
Résumé
