Determination of thermophysical properties of foods ...

Innovative Food Science and Emerging Technologies 6 (2005) 318 – 326 www.elsevier.com/locate/ifset

Determination of thermophysical properties of foods under high hydrostatic pressure in combined experimental and theoretical approach W. Kowalczyka,T, C. Hartmanna, C. Luscherb, M. Pohlb, A. Delgadoa, D. Knorrb a Lehrstuhl fu¨r Fluidmechanik und Prozessautomation, Technische Universita¨t Mu¨nchen, Weihenstephaner Steig 23, D-85350 Freising, Germany Department of Food Biotechnology and Food Process Engineering, Technische Universita¨t Berlin, Ko¨nigin-Luise-Str. 22, D-14195 Berlin, Germany

b

Received 6 August 2004; accepted 25 March 2005

Abstract In the present contribution high pressure phase change of food in a 3.4 ml high pressure chamber is investigated by means of numerical simulation and experimental techniques. The researches of freezing and thawing in samples of potato, pork and cod at atmospheric pressure and two high pressure levels up to 200 MPa are carried out. In order to enable numerical simulations at high pressures the comparison with experimental results and determination of thermophysical properties of food were necessary. The numerical model is based on the enthalpy method. Additionally, a dimensional analysis of phase transition is carried out. The results indicate a strong influence of high pressure on the kinetics of phase transition. Thermophysical properties of food at high pressure are determined and discussed. D 2005 Elsevier Ltd. All rights reserved. Keywords: High hydrostatic pressure; Phase change; Numerical simulation; Thermophysical properties Industrial relevance: Knowledge about thermophysical properties and kinetics of freezing and thawing of food is of major importance for proper planning of industrial food processing and developing new technological processes. The proposed dimensional analysis enable the scale-up and transfer of explored in laboratories processes into the industrial scale.

1. Introduction High hydrostatic pressure (HHP) treatment of food in the range up to 600 MPa is already a real alternative to the conventional time – temperature processing in terms of pasteurization. High pressure is able to inactivate enzymes or microorganisms to achieve the pasteurization of food, but moreover, this technology allows the preservation of precious natural food properties like vitamins or natural aroma after treatment of food (Hendrickx & Knorr, 2002). In addition to the pasteurization applications high pressure also influences the phase transitions of water (freezing/thawing), which opens possibilities to optimize freezing and thawing processes of food. * Corresponding author. Tel.: +49 81 61 71 4003; fax: +49 81 61 71 4510. E-mail addresses: [email protected] (W. Kowalczyk), [email protected] (C. Luscher). 1466-8564/$ - see front matter D 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ifset.2005.03.007

The first investigations of influence of the high hydrostatic pressure on food were conducted at the end of the XIXth and at the beginning of the XXth century. In literature, first notes about the influence of high pressure on the preservation of milk were published by Hite (1899). Nobel Prize Laureate for Physics, Bridgman (1912, 1923) investigated the influence of pressure on phase transitions and thermophysical properties of water. After a period of lower research activity in this field, a dynamic development of this technology can be observed in the processing of food and biosubstances in the last twenty years. Nowadays, there are many studies in this research area describing in detail the principles and potential food applications of high pressure supported phase transitions in food technology. Knorr, Schlu¨ter, and Heinz (1998), Kalichevsky, Knorr, and Lillford (1995), Cheftel, Le´vy, and Dumay (2000), Cheftel, Thiebaud, and Dumay, (2002) and Denys, Schlu¨ter, Hendrickx, and Knorr (2002) indicate the effects of high pressure on ice –water transformation related

W. Kowalczyk et al. / Innovative Food Science and Emerging Technologies 6 (2005) 318 – 326

to food technology and also point out advantages of high pressure treatment. The latent heat of phase change decreases during increasing pressure between 0.1 and 200 MPa allowing faster freezing and thawing in comparison to these processes at atmospheric pressure. During pressure shift freezing (Fig. 1 — abcd) the aqueous food is pressurized and cooled under pressure to prevent ice crystallization at that stage. Freezing is then carried out by pressure release, leading to an instant formation of ice crystals throughout the piece of food. Not all water is immediately converted to ice, however the ice formation during pressure shift freezing is more homogeneous leading to a distribution of smaller crystals in a food matrix. Pressure shift freezing and its counterpart, the pressure induced thawing (Fig. 1 — dcba, respectively) are two processes in which freezing and thawing are triggered by pressure changes. Under pressure, another possibility is of course to achieve freezing and thawing by temperature changes, like it is done at atmospheric pressure conditions. These phase changes are the focus of this paper. For instance, freezing by cooling under high pressure is called high pressure assisted freezing (Fig. 1 — abcef), whereas thawing by raising the temperature under pressure is called pressure assisted thawing — Fig. 1 — fecba. Further high pressure supported phase change of water can be carried out at elevated temperatures (Fig. 1 — abg). Such processing leads to transformation of water into ice V or ice VI. The influence of high pressure on the increase in the freezing rate of potatoes at different pressure levels is presented by Knorr et al. (1998). The review of Le Bail, Chevalier, Mussa, and Ghoul (2002) presents contributions that consider high pressure supported phase changes both in animal and plant tissues, e.g., tofu, potatoes, beef, and pork.

293

a

b

g

283 273

T [K]

263

Ice VI d

c Ice V

253 Ice III 243

f

e Ice I Ice II

233 223 213 0.0

0.2

0.4

0.6

0.8

1.0

p [GPa] Fig. 1. Phase diagram of water up to 1.0 GPa (Kalichevsky et al., 1995). abcd—HP shift freezing/thawing, abcef — HP assisted freezing thawing and abg — HP freezing and thawing at elevated temperatures.

319

The properties like microstructure, texture, colour and drip loss are analysed after high pressure treatment and indicate many beneficial effects of high pressure treatment. The protein denaturation and structural damage of meat tissues caused by high pressure shift freezing describe FernańdezMartıń, Otero, Solas, and Sanz (2000). Molina-Garcıá et al., (2004) research the possibility of freezing of water and meat in the range of ice VI, i.e., with the temperature above 273 K and with the pressure up to 632.4 MPa. The authors could assert that tissues of meat are not damaged after the HP-processing contrary to conventional ice I freezing. The influence of the high pressure assisted thawing on quality of fillets of various fish species are investigated by Schubring, Meyer, Schlu¨ ter, Boguslawski, and Knorr (2003). The samples are tested with organoleptic methods and microbial analysis. Moreover, pH, colour, drip loss, water binding capacity, structure and denaturation of protein are studied. In conclusion, the optimal conditions for high pressure thawing of fish are suggested. Luscher, Schlu¨ter, and Knorr (2005) describe the influence of pressure supported phase transitions on structure of plant tissue in a wide range of pressure and characterise the positive influence of freezing to ice III and ice V on food cells. Kapranov, Pehl, Hartmann, Baars, and Delgado (2003) investigate the influence of high pressure on phase transition in edible oils. Changes in viscosity at high pressure conditions and phase diagram for several oils are described. Research of phase transition in liquids by means of numerical simulation is presented by Kowalczyk, Hartmann, and Delgado (2004). In this work both the mathematical modelling and the results of numerical simulation with its validation at normal and high pressure conditions are presented. It is shown that free and forced convection become significant as soon as the phase transition occurs in a low viscous medium. Water is chosen as a model liquidfood in this case. The main principle of pressure supported freezing and thawing in food with high water content can be seen on the phase diagram of water (Fig. 1). In the range of ice I the phase change temperature decreases to 251 K with increasing pressure up to 207 MPa. The phase change of water in other types of ice at high pressure occurs along the rising curves with increasing phase change temperature. The feature that food can be cooled down below 273 K without phase transition and the knowledge that different types of ice have diverse properties, e.g., crystal structure, provides some alternatives for food treatment. For example, storing of food without phase change at temperatures below 273 K can be realised under pressure, giving protection against microbiological infection (Cheftel et al., 2002). High pressure assisted or high pressure shift freezing in the range of ice III, V and VI, for which the density of these ice modifications is larger than that of water, might be of use for storage applications where special regard to damage of

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tissue structure must be taken into account. Furthermore, for pressure levels from approximately 650 MPa, it is possible to achieve the phase change of water at the temperatures higher than 273 K. The current paper addresses the high pressure assisted freezing and thawing of solid food with a focus on the determination of thermophysical properties of food at HHP conditions. Moreover, using both the experimental data and the numerical simulation enables an enhancement of knowledge about heat transfer in food during high pressure treatment.

2. Objectives In order to understand and to control thermal effects in food during high pressure treatment, thermophysical properties like density, conductivity, heat capacity and latent heat must be known. These data are available in literature for many food systems at atmospheric pressure. However, there is a lack of such data for processes under high pressure. In the review considering modelling of heat transfer in food under high pressure Otero and Sanz (2003) also confirm the absence of information about the properties of food under high pressure. Therefore, the principal objectives of this paper are: (i) the numerical simulation of phase change in food at normal pressure with thermophysical properties from literature; (ii) the determination of the thermophysical properties of food at elevated pressure; (iii) the numerical simulation of phase change at high pressure with determined thermophysical properties; (iv) the dimensional analysis of phase change at high hydrostatic pressure; (v) the analysis of the temperature and phase distributions in the food sample during freezing and thawing processes.

3. Material and methods In order to model the phase transitions in a liquid food the conservation equations of mass, momentum and energy with corresponding boundary conditions have to be solved (Kowalczyk et al., 2004). Furthermore, the equation of state and the dependence of thermophysical properties of pressurized medium or food on temperature and pressure should included in the system of equation. The equation of state and the values of the thermophysical properties at high pressure are available only for water (Saul & Wagner, 1989; Nagornov & Chizhov, 1990) and for many chemical substances generally not contained in food (Tonkov, 1992). The data for food are frequently given in a narrow pressure range or often only for temperatures above the freezing point. In this contribution previously unknown thermophysical properties of food at elevated pressure are determined. In this first approach the constant values of parameters are varied during numerical simulations in order

to obtain results in optimal agreement with experimental data. Freezing and thawing of food (potatoes, pork and cod) is investigated at three arbitrarily selected pressure levels: 0.1 MPa, 100 MPa (140 MPa for potatoes) and 200 MPa. The measurement set-up consists of a plug with three K-type thermocouples with a diameter of 0.5 mm. The central thermocouple is placed along the symmetry axis. The tips of two additional thermocouples at the outer edges of the sample are used as temperature controls. The cylindrical samples are cut with a cork borer from raw material and pricked to the thermocouples by the use of a steel sample holder (outer diameter — 13 mm, inner diameter — 9.8 mm). The whole set-up is then installed in the high pressure vessel. A laboratory system with a 3.4 ml high pressure unit, a tempering bath and the high pressure generator (Unipress, Warsaw, Poland) at the Department of Food Biotechnology and Food Process Engineering (TU Berlin) is used. Fig. 2 illustrates the geometry of the high pressure chamber. The temperatures on the outer pressure vessel wall and in the tempering bath are measured by additional thermocouples of type K with a diameter of 1 mm. The tempering bath is set to the temperature approx. 20 K above expected freezing temperature of the sample. The temperature in the system is controlled by immersing the whole vessel in the bath. The sample is pressurised and the equilibrium of temperature (DT < 1 K) after compression is awaited. Furthermore, the vessel is placed in a second tempering bath at a temperature 20 K below the expected freezing point to ensure comparable cooling rates for each freezing experiment (initial temperature gradient amounts 40 K). Because of changes in the density the pressure has to be kept constant during the experiments. In all investigated cases the density of frozen fraction is smaller than this of unfrozen fraction, according to the water – ice I transformations. After the phase change and complete equilibrium of the temperature, the vessel is immersed in the first bath again (temperature 20 -C above initial freezing temperature) and the thawing with a temperature gradient comparable to the freezing experiment is carried out. After thawing, the location of the central thermocouple is verified analysing the visible hole caused by the penetration of the thermocouple. Temperature and pressure values are digitally recorded. Because of the symmetry of the high pressure unit, 2D cross-sections with dimensions 40 9.8 mm (40 8.5 mm for cod) are used as a computational domain for the numerical simulation. In Fig. 3 D denotes the diameter, H the height, g the gravity, Tw the wall temperature, V 1 and V 2 the volume of the chamber before and after compression, respectively. The calculations are carried out with 185 25 (H D) grid points and time step interval of 0.2 s. The control point is situated in the symmetry axis of the high pressure chamber. The distance of the thermocouple from the top is 7.5 mm for cod and 10 mm for other food. For freezing and thawing of solid food mentioned above at constant pressure the system of governing equations, in


321

Fig. 2. Cross-section through the high pressure unit (Unipress, Poland).

comparison to the phase change in a compressible fluid, reduces to a single equation for transient heat transfer and can be written as B B ðqhÞ ¼ l&ðklT Þ ð qf1 DH Þ; Bt Bt

ð1Þ

where q describes the density, h the specific enthalpy, t the time, k the thermal conductivity, T the temperature, l the Nabla-operator, f l the volume fraction of unfrozen phase and DH the crystallisation enthalpy. The last term on the right hand side of the Eq. (1) describes the released during food

control point

Tw = f(t)

H

g

phase change enthalpy of crystallisation. It is defined as follow Z T2 DH ¼ cps cps dT þ Lf : ð2Þ T1

T 1 and T 2 are the temperatures at the beginning and at the end of the range of phase change, c Ps is the heat capacity of unfrozen food, c Ps is the heat capacity of frozen food and L f the latent heat of food. Comparing to the general case, liquid motion and internal stresses are not considered in current model. Furthermore, supercooling is not taken into account at present. For the analysis of similar processes and to investigate scale-up effects a dimensional analysis is very helpful. The energy equation can be converted in to the following dimensionless form B T T q h ¼ Fol4& kTlTT T Bt H B T 4 T q f1 DH ; Ste Bt T

ð3Þ

which is obtained after following substitutions V2

axis of cylinder

V1 D Fig. 3. Computational domain.

q ¼ qTq0 ; k ¼ kTk0 ; T ¼ T TT0 ; t ¼ t Ttp ; h ¼ hTcp T0 ; l ¼ lT fnf ¼ fnfT; DH ¼ DH TLf

1 ; D ð4Þ

322


in Eq. (1). The dimensionless thermal parameter is H¼

DT T0 T1 T1 ¼ ¼1 : T0 T0 T0

ð5Þ

In the mentioned terms DT is the difference between the phase change temperature T l and the initial temperature T 0, t p is the process time and D is the characteristic length of the high pressure unit. The terms marked with an asterisk are dimensionless values and those with index 0 are the initial values of variables. Eq. (3) shows that the investigated problem can be characterised with two dimensionless numbers. The Fourier number Fo ¼

k tp qcp D2

ð6Þ

that characterises the time scale of conductive heat transfer and the Stefan number Ste ¼

cp DT ; Lf

ð7Þ

comparison of the temperature characteristics from the experiment with the results from numerical simulation for freezing and thawing at different pressure levels can be seen in Figs. 4 and 5, respectively. The brighter lines on the diagrams represent the results from the experiment and the dark lines represent the temperature characteristics from numerical simulation. Because of higher phase change temperature the curves corresponding to the sample at normal pressure sit always above those obtained at elevated pressure. Since in the modelling the supercooling — cooling of the sample below the phase change temperature — is not taken into account, the major difference between experiment and numerical simulation can be seen especially at the beginning of phase transition. Additionally, it is known that close to the phase change temperature, significant changes in the structure and in the thermophysical properties of substance may occur. Otherwise, major parts of the temperature characteristics show very good agreement between both results.

which concerns phase transformation. Furthermore, the geometric ratio of the vessel comes into consideration as D PD ¼ ; ð8Þ H where D is diameter and H is height. Thus, investigated processes can be described by following relationship q k T t h DH f Fo; Ste;H; PD ; ; ; ; ; ;lD; fnf ; ¼ 0: q0 k0 T0 tp cp0 T0 Lf ð9Þ The advantage of non-dimensionalisation is used when scale-up of the process is considered. Some different processes have the same solution as long as the values of all dimensionless parameters (9) remain unchanged although the geometrical size of the vessel or the thermophysical properties of investigated substances are completely different. Thus, no further parameter modification will be necessary. The numerical simulations are carried out with the computational fluid dynamics software CFX-4.4 (Ansys, CFX). Additionally to the standard solver the source term with the enthalpy of crystallisation, the phase diagram of water with melting temperature of food in the range of ice I as well as the allocation of memory for time integration of Eq. (1) are implemented as Fortran code in several subroutines linked to the main code. The numerical simulation of the phase change in solid food takes approximately 15 min CPU time (Intel Pentium 4, 1.5GHz, 512 MB RAM).

4. Results The numerical simulations of phase transitions are carried out for potatoes, meat (pork) and fish (cod). The

Fig. 4. Temperature characteristics during freezing at 0.1 MPa, 100 MPa, (140 MPa for potatoes) and 200 MPa: a) potatoes, b) pork, c) cod.


a-1)

b-1)

323

c-1) 273 267

a-2)

262 258

b-2)

249 247

c-2)

Fig. 6. Temperature distribution in cod during freezing (5 min).

process. Figs. 8 and 9 illustrate temperature and phase distribution 3.33 min after beginning of thawing. Subnumbering used in Figs. 6 –9 has to be read in following

a-1) Fig. 5. Temperature characteristics during thawing at 0.1 MPa, 100 MPa (140 MPa for potatoes) and 200 MPa: a) potatoes, b) pork, c) cod.

b-1)

c-1) 0.0 0.8

a-2) The temperature characteristics reveal a significant influence of the pressure level on process time. With increasing pressure the initialisation of the phase change is shifted for both freezing and thawing. Generally, during freezing process the phase transition occurs later at high pressure than at atmospheric pressure. In thawing process this relation is inversed. The experimental data show larger supercooling rates for higher pressure levels. It can also be seen that high pressure acts on the reduction of phase change plateau, i.e., part of the curve which describe phase change at approximately constant temperature. The results from numerical simulation confirm mentioned phenomena for thawing perfectly. By freezing the time when supercooling occurs must be accounted for. It can be stated that high pressure supported freezing accelerates phase change process in the sample. However, the overall freezing time is longer under high pressure in our conditions. Temperature and phase distribution during freezing and thawing of cod are presented in Figs. 6 and 7 for 0.1, 100 and 200 MPa at 5 min after the beginning of the freezing

0.0 0.8

b-2)

0.6 0.8

c-2)

Fig. 7. Phase distribution in cod during freezing (5 min). The completely frozen state is indicated with the value 0.0 and the unfrozen state with 1.0.

324


a-1)

b-1)

c-1) 278 272

a-2)

270

261

b-2)

257

249

c-2)

are carried out with the thermophysical properties determined during HP freezing process. Table 1 shows the thermophysical properties of investigated food at three pressure levels. The thermophysical properties used for the simulation of freezing and thawing at normal pressure are chosen according to the values published by Rahman (1995). Since the literature does not deliver exact information about the temperature –pressure dependence of these parameters, the values of determined parameters can serve as trendsetting values for further experimental and numerical investigations. All numerical simulations are carried out with the thermophysical properties presented in Table 1. The latent heat Lis determined by use of the empirical relationship for pure water valid along the melting line as suggested by Hobbs (1974) and re-visited by Otero and Sanz (2000): L ¼ 3:114 103 Tp3 1:292Tp2 3:379 102 Tp þ 3:335 105 ½J=kg;

ð10Þ

where the pressure is used in MPa. The values achieved with Eq. (10) are corrected for real food systems: Fig. 8. Temperature distribution in cod during thawing (3.3 min).

manner: a-1), b-1) and c-1) indicate the temperature and phase distribution in the whole probe at different pressure levels; a-2), b-2) and c-2) indicate an enlarged view of the temperature and phase distribution at the top of the chamber. Figs. 6 and 7 illustrate the freezing process of cod both at normal and at high pressures. It can be observed that at normal pressure the freezing process is in a more advanced state comparing to elevated pressure. However, temperature gradients are smoother at high pressure (Fig. 6 — a-2, b-2, c-2). Similarly to the temperature the phase change front in Fig. 7 — a-2 is propagated much deeper into the centre of the chamber for normal pressure case. The phase change front for high pressure cases show Fig. 7 — b-2 and c-2. However, it can be seen both from the temperature and phase distributions of thawing process in Figs. 8 and 9 that thawing at high pressure conditions seems to be faster comparing to normal pressure. During high pressure treatment all thermophysical properties of food vary with pressure and temperature. In this first approach the properties are assumed to be independent of temperature. The determination of the thermophysical properties of food at high pressure is realised by means of curve fitting. At first the numerical simulation of HP freezing is carried out. In order to obtain a good agreement with the experiment the freezing curve is fitted to the experimental results via repeated changes of the density, the heat capacity and the conductivity. The numerical simulations of HP thawing

Lf ¼ LTX ;

ð11Þ

with X as the water content of food. Thus, it is assumed that the latent heat changes proportionally with water content in food. However, water content of the same food

a-1)

b-1)

c-1) 0.8 0.2

a-2)

0.8 0.2

b-2)

0.8 0.2

c-2)

Fig. 9. Phase distribution in cod during thawing (3.3 min). The completely frozen state is indicated with the value 0.0 and the unfrozen state with 1.0.


325

Table 1 Thermophysical properties of potatoes, pork and cod at different pressure levels

Potatoes

Pork

Cod

Pressure [MPa]

q l [kg/m3]

q s [kg/m3]

k l [W/mK]

k s [W/mK]

c pl [kJ/kgK]

L [kJ/kg]

0.1 140 200 0.1 100 200 0.1 100 200

1050 1107 1132 1070 1121 1165 1100 1160 1210

960 977 985 980 995 1010 954 969 984

0.54 0.60 0.63 0.52 0.57 0.60 0.55 0.60 0.63

1.70 1.77 1.79 1.47 1.52 1.56 1.40 1.46 1.50

3.64 3.33 3.22 3.45 3.15 3.03 3.73 3.43 3.38

275 221 198 242 209 174 267 229 192

species can vary in a wide range. After analyse of averaged values of water content presented by Rahman (1995) in the current paper following values are considered: potatoes (82.5%), pork (72.9%) and cod (80.1%). Because of possible significant discrepancies in homogeneity, structure and ratio of ingredients in food the values of thermophysical properties can vary in a wide range. Considering water content in investigated food mentioned above the accuracy of calculated data amounts about 5%. Table 2 illustrates the values of the dimensionless numbers in investigated cases. The Fourier number in Eq. (2), presented in Table 2, is a measure for the rate of conductive heat transport. The calculation of the Fourier number was carried out with the thermal properties of unfrozen food and the adequate process time read from the diagram with the temperature characteristics. The Stefan number in Eq. (7) is obtained with the specific heat of unfrozen food and with the corresponding latent heat. The temperature difference between the phase change temperature and the temperature of the cold wall is used. The Fourier number increases with increasing pressure. Higher Fourier numbers represent longer time scales of conductive heat transfer. The product of the inverse Stefan number and H of Eq. (3) decreases with increasing pressure what reveals one of the advantages of high pressure technology namely a decreasing amount of latent heat to be removed. Table 2 shows that during crystallisation the contribution of the latent heat in the energy balance (H / Ste) is one order of magnitude higher than the rate of conduction (Fo).

Table 2 Dimensional analysis

Potatoes

Pork

Cod

Pressure [MPa]

Fo (10 2)

Ste

H (10 1)

PD

0.1 140 200 0.1 100 200 0.1 100 200

0.267 0.380 0.356 0.311 0.377 0.606 0.321 0.427 0.590

0.341 0.424 0.466 0.247 0.292 0.351 0.246 0.333 0.399

0.867 0.990 1.030 0.616 0.750 0.811 0.606 0.790 0.836

0.245

0.213

5. Conclusions The purpose of this study is combining experimental and theoretical approaches in order to analyse the high pressure phase change process in solid food and determine the thermophysical properties of selected foods (cod, pork and potatoes). The temperature characteristics from the numerical simulation from the centre of the sample are compared to the experimental results. Except for differences in the supercooling region the excellent agreement between both results is obtained. All temperature characteristics show that the overall time of freezing increases slightly with increasing pressure. On the other hand, shorter plateau on the experimental curves for high pressure denotes faster phase transition in food. Although investigation on microstructure level and observation of obtained ice structure is not the aim of current contribution, it could be supposed that shorter freezing time at high pressure contributes to smaller ice crystals in frozen sample. The investigations confirming this supposition on microstructure level are not the aim of the current paper. For thawing both the overall process time and the time of the phase change shorten with increasing pressure. The changes observed in the temperature and phase distribution in the sample during freezing and thawing illustrate a strong influence of high pressure on these processes. It can be seen that the phase transition at high pressure occurs simultaneously in a major part of the volume. The dimensional analysis shows that the phase change process in solid food can be described mathematically with a set of dimensionless numbers: Fo, Ste, H and P D . The Fo number characterises the time scale of conductive heat transfer, the product of Ste number and H specifies the energy of crystallisation and P D is a geometry ratio of the high pressure chamber. It is found that the Fo number increases with the increasing pressure and indicates a longer overall duration of the freezing process as confirmed by experiments. The inverse Stefan number decreases with increasing pressure. It denotes smaller value of latent heat at high pressure than at normal pressure. These dimensionless numbers can be further applied for scale-up to industrial magnitudes. Fitting of numerical results to experimental data allows determination of thermophysical properties of food. Quan-

326


titative data about the thermophysical properties under high pressure for potatoes, pork and cod are obtained (Table 1). In this first approach, temperature dependency has not been taken into account. Because of increased pressure, the density and thermal conductivity of pressurizing food increase. Contrarily to this, the heat capacity decreases. Moreover, it is shown that the latent heat reduces at high hydrostatic pressure up to 200 MPa to approx. 72% of its amount at atmospheric pressure for all investigated food types. Further researches in this field would be appreciated in order to develop the relationships that describe thermophysical properties of food depending on temperature and pressure. It would certainly enhance an understanding of high pressure processing and an application of high pressure technology in food industry.

Acknowledgments This work is supported by Bundesministerium fu¨ r Bildung und Forschung within the project No. 0330098 and No. 0330089.

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