Kemerovo, Kemerovo, Russian Federation
Methods that simulate the fast refrigeration of foods on the basis of a model of adjustable heat sink according to the principle of programmed freezing are considered. In this case, a fast freezer is seen as a system of modules, each of which can independently ensure the necessary heat-sink conditions for the fast refrigeration process. The focus is made on the analysis of physicochemical processes that form the water crystallization front at the first freezing stage, taking into account the thermophysical specifics of organizing a multizone combined system of refrigeration supply. Test-bench studies were conducted to obtain the main regularities of fast freezing of single-piece packaged dairy products by the nitrogen + air combined method in a wide range of heat-exchange conditions. The fast freezer has two freezing zones with various temperatures, allowing an efficient distribution of energy costs and creating the optimal conditions for freezing and for the continuity of the technological cycle. A mathematical model has been developed on the basis of experimental data analysis to determine the main technological parameter, the duration of food refrigeration in a nitrogen + air combined two-zone fast freezer with adjustable heat sink. The integral characteristics of the mathematical model have been determined. The model´s adequacy to the real freezing process has been proved.
combined method, refrigeration, dairy products, fast freezer, nitrogen, temperature, zone, duration, calcu-lations
INTRODUCTION
The simulation of refrigeration processes used for various foodstuffs and raw materials with precise goal setting and results obtained has been conducted by many authors, such as I.G. Alyamovskii, A.M. Brazh-nikov, K.P. Venger, D.G. Ryutov, G.B. Chizhov, I.G. Chumak, and A.P. Sheffer. These studies were based on the theories of Planck, Stefan, Lamé, and Clapeyron, and the solution of the problem was reduced to determining the duration of food freezing to a preset volume-averaged or final temperature in the middle of the body in a criterion, dimensionless, or classical form.
The simplest dependence for determining the duration of the refrigeration process was developed by Planck. This solution is considered classical, being notable for its simplicity and ease of use. It is built on the following assumptions:
- a homogeneous moisture-containing body is cooled to the cryoscopic temperature before refrigeration;
- ice formation occurs without overcooling and isothermally at the cryoscopic temperature, and the thermophysical properties of the frozen part of the body's total volume do not depend on temperature, the thermal capacity of the frozen part being equal to zero, and
- refrigeration occurs by removing heat from the body surface, the heat transfer coefficient and the temperature of the heat-sinking media being constant.
The first analytical solution to the problem of the duration of freezing a flat plate from the initial temperature, which is higher than the cryoscopic one, to the final temperature of the middle, which is below the cryoscopic one, was obtained by D.G. Ryutov and was widely recognized in refrigeration technology [1].
In order to take into account the duration of the plate's temperature decline after the convergence of phase boundaries, a linear temperature change is admissible along the thickness of the frozen layer. Further heat exchange in the plate is analyzed on the basis of the regularities of simple cooling. The time during which the temperature of the plate center decreases from the cryoscopic to the finial preset temperature is summed to the duration calculated by the Planck formula.
In order to take into account the influence of the initial temperature of the product plate on the duration of refrigeration to the heat amount removed from the mass unit during freezing, a binomial multiplier was introduced (1 + 0.0053 ti).
Alyamovskii adjusted Ryutov's formula by assuming that the temperature distributed parabolically at the initial moment of freezing [2].
V.E. Kutsakova proposed a model for calculating the duration of refrigeration of an infinite plate, characterized by a simple mathematical formula and reduced to the Planck formula, taking into account the period of further freezing and the process of crystallization front movement. The model assumes a linear approximation of the temperature field of the material along the axis of temperature front distribution at the stages of refrigeration and the period of relaxation of the temperature field [3].
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