CAFE-project

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Case study of Structuring: ice-cream crystallization

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We know that the final quality of ice cream and specially its smooth texture depends on the ice crystal size distribution and on the viscosity of the ice cream. They are both related to the process conditions, such as the mix flow rate, the evaporation temperature, the cylinder pressure, the rotation speed and the air flow rate.

During ice cream process several steps are necessary such as pasteurization, homogenization and ripening of the ice cream mix. After those steps, the stage of pre-freezing and foaming of the ice cream, is performed inside a Scraped Surface Freezer.

The freezer is a tubular heat exchanger provided with a vessel jacket in which a refrigerant fluid is circulating continually. The freezer is also provided with scraper blades. Ice cream mix enters into the system at about 5°C in a liquid state, and comes out from the system at -5°C with an ice content of approximately 30-40%, depending on the formula.

 

Freezer scheme

 

Inside the freezer ice crystals are formed at the wall in contact with refrigerant R22 that evaporates. The action of the scraper blades remove the ice crystals which are being formed at the wall, this way ice crystals are mixed with the bulk and continue to decrease the temperature and to improve the heat exchange within the product.

Ice cream process is studied in a laboratory freezer pilot WCB 50. We study the effect of refrigerant evaporation temperature, the mix flow rate and the scraper rotation speed on the crystal chord length, outlet temperature of the product as well as the energy consumption.

The freezer is equipped with a very innovating device Focus Beam Reflectance Measurement called FBRM that allows to follow online the crystals chord length size. The FBRM probe works as follows: a laser beam is directed to a set of rotating optics that focuses it to a very small spot. A motor rotates the optics so the focused beam scans a circular path at the interface between the window of the probe and the process itself.

As particles flow past the probe window they intersect the scanning path, giving backscattered light from the individual particles and forms the basis for the FBRM measurement. Each pulse of backscattered light will correspond to a chord length.

 

 Chord-length measurement
 

The FBRM probe is inserted into the flow with an angle of 45°; this angle allows the renewal of slurry that is measured and maintains a clean window.

We equipped the freezer outlet also with a Pt100 probe for the product temperature measurements.

We use on-line fast imaging probe that allows us to visualize directly ice crystals. The probe is equipped with a CCD sensor and with an optical fiber that provides a retro diascopic lighting to the crystals in movement. The visualization depth equals 100 microns corresponding to several layers of depth.

To determine the viscosity we use the classic method of tubular viscometer in which the shear stress is proportional to the pressure drop, and the wall shear rate is proportional to the flow rate of the fluid according to the Rabinowitsch–Mooney equation. This viscometer is constructed by our technical team and is constituted of a succession of 4 tubes in PVC. Each tube has a different diameter in which the pressure drop within a defined tube length is measured.

 
We have developed a full model of ice crystallization. It considers that nucleation and growth of the crystals depends on the deviation to thermodynamic equilibrium. The deviation to thermodynamic equilibrium can be characterized by the difference between local temperature and local freezing point which depends on solute concentration in the solution. The crystals' breakage is also considered. This kind of model leads to population balance equations (PBE). As temperature and concentration are heterogeneous in the scraped surface freezer, the energy conservation equation is coupled to the PBE. This kind of approach leads to partial differential equations with at least one crystal size variable, up to three position variables and eventually the time variable. The next figure shows an example for one crystal size variable L, one position variable, radius r and the time variable t.
Schematic representation of crystals nucleation and growth in a SSHE

 
In order to limit computing time and memory, some simplifications were made for fluid flow by taking into account an effective radial diffusivity instead of the physical mixing of the scraping blades.The population balance equations are discretized using several size classes. These equations are solved by using the Volume Element Method in Matlab® with 200 crystal size classes. As crystals can grow near the scraped cold wall or melt far from it, a differencing method inspired from the upwind scheme was used to overcome numerical problems. Ice fraction and crystal size distribution and sorbet temperature are then obtained as a function of time and position in the scraped surface freezer.