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Computer simulation of high pressure cooling of pork
Journal of Food Engineering 79 (2007) 401–409 www.elsevier.com/locate/jfoodeng
Computer simulation of high pressure cooling of pork C.R. Chen a, S.M. Zhu a, H.S. Ramaswamy
a,*
, M. Marcotte b, A. Le Bail
c
a
b
Department of Food Science and Agricultural Chemistry, Macdonald Campus of McGill University, 21111 Lakeshore, Ste. Anne de Bellevue, Que., Canada H9X 3V9 Food Research and Development Centre, Agriculture and Agri-Food Canada, 3600 Casavant Blvd West, St. Hyacinthe, Que., Canada J2S 8E3 c GEPEA-ENITIAA, (UA CNRS 6144), Rue de la Ge´raudie`re BP 82225, F-44322 Nantes Cedex 03, France Received 13 August 2005; accepted 1 February 2006 Available online 18 April 2006
Abstract A computer simulation was used to develop and evaluate two-dimensional axi-symmetrical of cooling of pork under high pressure (HP) processing conditions. The whole cooling process was divided into three stages of cooling: a preloading stage, a pressure buildup stage (compression) and a pressure hold stage (constant pressure), and the modeling domain covered the pressurization fluid, the sample holder and the pork sample. Modeling performance was evaluated by comparing the predicted and experimental temperatures at four locations: three within the pork sample and one for the high pressure fluid medium. Model generated images were used for visual observations of temperature distribution and movement of the pressure fluid, and transient temperature curves were generated for the four specified locations. Results indicated that the developed model well matched experimental results, especially for temperatures at the central area. The thermal conductivities of pork under pressure conditions: 100, 150 and 200 MPa were estimated by the model using error trials. The model provides a valuable tool for studying the pressure cooling behavior of test samples and for designing the pressure shift freezing process. 2006 Elsevier Ltd. All rights reserved. Keywords: High pressure; Simulation; Modeling; CFD; Temperature; Cooling; Pork
1. Introduction High pressure (HP) processes are currently receiving considerable attention because of its advantages and potential benefits in the preservation and modification of functionality of foods (Knorr, 1999; Le Bail, Chevalier, Mussa, & Ghoul, 2002). HP has interesting effects on the solid–liquid phase transition of water and offers possibilities for novel processes, such as pressure shift freezing (PSF), HP thawing, super-cooled storage without freezing, and so on (Bridgman, 1912; Cheftel, Thiebaud, & Dumay, 2002; Knorr, Schlueter, & Heinz, 1998). PSF is an interesting technique to achieve massive ice-nucleation showing potential benefits for improved quality of frozen foods *
Corresponding author. Tel.: +1 514 398 7919; fax: +1 514 398 7977. E-mail address: [email protected] (H.S. Ramaswamy). 0260-8774/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.02.034
(Chevalier, Sequeira-Munoz, Le Bail, Simpson, & Ghoul, 2001; Le Bail et al., 2002; Levy, Dumay, Kolodziejczyk, & Cheftel, 1999; Martino, Otero, Sanz, & Zaritzky, 1998). Elevation of pressure depresses the freezing point of water from 0 C at atmospheric pressure to 21 C at about 210 MPa (Bridgman, 1912). This phenomenon allows food samples to be super-cooled significantly resulting in a rapid and uniform ice nucleation and growth of ice crystals immediately upon the pressure release. The PSF process generally involves cooling the sample under pressure (usually up to 200 MPa) to just above the freezing point (20 C) and quickly releasing the pressure to form nuclei of ice crystals; ice crystals are then allowed to grow at atmospheric pressure in a conventional freezer. The PSF process can produce small ice crystals throughout the sample, rather than a stress-inducing ice front moving through the sample (Kalichevsky, Knorr, & Lillford, 1995; Martino et al., 1998; Otero, Martino, Zaritzky, Solas, & Sanz, 2000). Therefore,
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this concept can be specifically useful for freezing of large size foods in which a uniform distribution of fine ice crystals is required. For these foods, conventional freezing techniques would result in large thermal gradients and hence, low rate of freezing with considerable freeze-thaw damage and freeze cracking (Cheftel, Levy, & Dumay, 2000; Martino et al., 1998). Although PSF has potential benefits, existing knowledge in this area is still very limited (Cheftel et al., 2000; Le Bail et al., 2002). The thermal behavior as related to phase transition, heat transfer, ice-crystal formation and food quality changes during PSF processing are not fully understood (Knorr et al., 1998; Le Bail et al., 2002). PSF processes have unique characteristics different from those in conventional freezing methods. Modeling is considered a powerful approach for understanding systems involving complex heat and mass transfer applications. Only few studies have been reported on the modeling of PSF process Denys, Van Loey, Hendrickx, & Tobback, 1997; Denys, Van Loey, & Hendrickx, 2000; Sanz & Otero, 2000). Denys et al. (1997) proposed a twodimensional numerical model of heat transfer for pressure shift freezing and thawing to predict thawing and freezing times. The model was improved later (Denys et al., 2000) by taking into account the pressure dependence of the latent heat of the product used. Sanz and Otero (2000) established a model to simulate the whole procedure of PSF processing, but the use of the model is limited to cylindrical symmetry of samples and quick releases of pressure. On the other hand, several studies have been reported on computation of the percentage of ice instantaneously formed after a quick depressurization (Chevalier, Le Bail, & Ghoul, 2001; Le Bail, Chourot, Barillot, & Lebas, 1997; Otero & Sanz, 2000; Otero, Sanz, de Elvira, & Carrasco, 1997). The models of Otero et al. (1997) and Chevalier, Le Bail et al. (2001) are based on the phasechange curve of water (Bridgman, 1912) in the adiabatic expansion, although it has been proved that liquid water always enters metastable conditions in a real PSF process. Other calculation methods were based on the balance between the latent heat released by ice nucleation and the sensible heat absorbed by the super-cooled sample (Le Bail et al., 1997; Otero & Sanz, 2000). Most of studies on modeling of high pressure processes are limited to the product itself and assume the temperature of high pressure medium as the boundary condition to remain constant during the pressure cooling process. Preliminary experiments carried out in this study showed that the medium temperature was variable during whole process. During the cooling process, only the outside surface temperature of the vessel can be considered to be constant. The temperature on the sidewall is dependent on the cooling medium while that on the top or bottom is dependent on the conditions of the environment. In order to develop an accurate model, it is necessary to extent the boundary to the vessel, meaning that the modeling domain should include at least the pressure medium fluid, product
container/carrier and the product and its package materials. This makes it more complex especially while using conventional computer modeling techniques. Computation fluid dynamics (CFD) is a powerful tool that uses numerical techniques for simulation of fluid flow and heat transfer. It has been used in many areas but only recently for food processing applications (Scott & Richardson, 1997). More systematic modeling of various complex processes including the high pressure process can be carried out by use of CFD model. As a part of modeling PSF process, this study was focused on modeling of the cooling process under high pressure conditions which is the pre-requisite for the successful application of the PSF process. Specifically, the objectives of this study were to develop a CFD computer simulation model for evaluating the transient time and space dependent temperature in the system, and to validate the model using experimental data obtained from a pilot scale high pressure processing equipment. 2. Methodology 2.1. Cooling process and domain for modeling The whole cooling process was divided into three stages: pre-loading stage, pressure build-up stage (compression), and pressure holding stage (constant pressure). In the initial loading stage, the prepared product sample was moved from the storage room (4 C) to the pressure chamber immersed in the fluid medium; during the build-up stage, the pressure was increased from 0.1 MPa to the designed values (100, 150 or 200 MPa); and during pressure holding stage, the pressure was kept at a constant value until the center temperature of pork product reached its desired temperature. The system modeled included the pressure medium fluid, cylindrical sample holder and pork product. Since the high pressure vessel and the sample holder were of axi-symmetrical cylindrical shapes, one half of a vertical cross-section was taken as the modeling domain as shown in Fig. 1. In this figure, letters A, B, C, D represent the pressure fluid medium, the cylindrical sample holder, the cylinder caps at bottom and top of the holding cylinder, and the pork product, respectively, while numbers 1, 2, 3 and 4 were marked for different boundary conditions detailed in the next section. 2.2. Assumptions for modeling 1. The high pressure vessel was kept at a predetermined constant temperature during the cooling process by an efficient temperature controlled refrigeration system. 2. The adiabatic compression heat generated in the system linearly increased with pressure. 3. Convection heating could exist within the high pressure medium because of the motion caused by the temperature gradients and thermal expansion.
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403
q ¼ q20 ð1 bðT 20ÞÞ
ð4Þ
where q is the density, k, the thermal conductivity, CP, the specific heat, T, the temperature, u, v are velocity components in z and r directions, respectively; r, the coordinator in the radium and z, the coordinator in the height; p, the pressure. l, the viscosity. Eq. (1) was used for modeling of heat transfer within solid materials like pork and package, while the combination of Eqs. (1)–(4) was implemented for modeling of heat transfer and movement of the high pressure liquid medium. Convection was considered only for the HP liquid medium with a convective heat transfer coefficient at contact surfaces. 2.4. Initial and boundary conditions
Fig. 1. Modeling domain of high pressure cooling process [A is pressure medium fluid, B is cylindrical sample holder, C is bottom or top cap of the holder, and D is pork product. Numbers 1, 2, 3 and 4 are different boundary lines].
4. There was no slip for the pressure medium on the solid surfaces. 5. All the thermo-physical properties were isotropic for all the materials. 2.3. Governing equations
For the first stage, it was assumed that the medium was stationary and temperatures were uniform for each part as shown in the Table 1; for the second and final stages, temperature and velocity distribution at the end of the previous stage were used as the initial conditions. Boundary conditions marked by numbers as shown in Fig. 1 were given as below: at the boundary 1 oT ¼ U 1 ðT cool T a Þ or u¼v¼0
ka
at the boundary 2 oT ¼ U 2 ðT air T a Þ oz u¼v¼0
ka
There are two types of governing equations used for this modeling, as given as below:
at the boundary 3 (1) Energy conservation oT oT oT 1 1 o oT o oT þv þu ¼ rk k þ ot or ou qC P r or or oz oz ð1Þ (2) Momentum conservation In the vertical direction ou ou ou op 1 o ou o2 u q þv þu r ¼ þl þ 2 ot or oz oz r or or oz þ ðq q20 Þg
ð2Þ
In the radial direction ov ov ov op 1 o o2 v þv þu ðrvÞ þ 2 q ¼ þl ot or oz or r or oz
u¼v¼0
for the liquid part
at the boundaries 4 oT ¼0 or v ¼ 0 for the liquid part where Tcool is the temperature of the cooling medium, Tair, the temperature of environment air, u, the velocity component in z direction, v, the velocity component in r direction, ka, the thermal conductivity of the high pressure medium, Table 1 Initial temperature conditions for each part
ð3Þ where for liquid high pressure medium, the variable density with temperature was given below:
Pressure medium (C) Cylinder holder (C) Top and bottom cap (C) Pork (C)
100 MPa
150 MPa
200 MPa
15 4 4 4
19 4 4 4
20 3.3 3.3 3.3
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Ta, the transient temperature of the high pressure medium close to the vessel’s cylindrical surface or near the vessel’s inside top/bottom, U1 and U2 are the overall heat transfer coefficients for the vessel wall and ends (top and bottom), respectively, which are given below:
350
Enthalpy (J/g)
300
kv a kv U 1 U2 ¼ ðh þ U 1 Þ
U1 ¼
250 200 150 100 50
where h is the heat transfer between the vessel top or bottom and the environment air, a, the thickness of the vessel wall, kv was the thermal conductivity of the vessel. 2.5. Thermo-physical properties used for the computer modeling Thermo-physical properties used for the computer modeling are listed in Table 2. Only the thermal conductivity of the pork was estimated by the CFD model, others were gathered from different methods. A general calculation method was used for obtaining the properties of high pressure medium, a mixture (1:1) of water and ethanol as given below (Dennis, 2001; Harvey, Peskin, & Klein, 2000): X X ¼ wi xi where X is the property for the pressure medium, such as density, heat capacity or thermal conductivity; w, the mass fraction; x, the property of individual component such as water or ethanol; subscript i, the component. The variable heat capacity for the pork, obtained from enthalpy (Fig. 2) curves gathered using a differential scanning calorimeter (DSC-Q100, TA Instruments, New Castle, DE), was used during the pre-loading stage because the phase change
0 -40
-30
-20
-10 0 10 Temperature (oC)
20
30
Fig. 2. Pork enthalpy as a function of temperature obtained from a differential scanning calorimeter.
from liquid to ice was considered. For modeling of the compression stage, the pressure dependent properties including density and thermal conductivity for the pressure medium and density for the pork were the average values between 0.1 MPa and the target pressure. 2.6. Validation experiments Fresh pork (boneless rib portions) was purchased from market (Carrefour, Nantes, France). Cylindrical samples (50 mm diameter · 160 mm length) were cut along rib muscles using a cylindrical cutter. Each sample was vacuumsealed in a moisture-impermeable plastic pouch (80 lm thick multiplayer film) (La Bovida, France) and placed in a copper holder (50 mm diameter · 200 mm length) (Fig. 3). As shown in Fig. 3, three K-type thermocouples (0.3 mm diameter, Omega, Stamford, CT) were inserted
Table 2 Thermo-physical properties for each part materials Materials
Properties
Pressure medium
1
Pressure (MPa) 3
Density at 20 C (kg/m ) Thermal conductivity (W/m/C) 1 Heat capacity (J/kg/C) 1 Viscosity (lPa s) 1 Thermal expansion (C1) 2 Compression heat (J/MPa/m3) 1
Cylinder holder
0
100
150
200
900 0.375
940 0.42
960 0.44 3300 3360 8.7 · 104 1.89 · 105
980 0.46
3
Density (kg/m3) Heat capacity (J/kg/C) 3 Thermal conductivity (W/m/C)
8900 383 386
3
2700 840 0.45
3
Plastic cap
Density (kg/m3) Heat capacity (J/kg/C) 3 Thermal conductivity (W/m/C) 3
Pork
2
Density (kg/m3) Heat capacity (J/kg/C) 4 Thermal conductivity (W/m/C) 2 Compression heat (J/MPa/m3) 2
1024 Fig. 2
1074 1099 3350 Estimation by CFD model 1.03 · 105
1124
Note: 1 – from calculation, 2 – from separate experiments, 3 – from the reference (Harvey et al., 2000; Singh & Heldman, 2001), 4 – estimated from the CFD model.
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between the experimental and predicted transient temperatures at the given locations. The coefficient of variation, R2, and average relative error, Er, were also used for assessing the model performance: Pn ðy i y di Þ2 2 R ¼ 1 Pi¼1 n 2 ðy y m Þ Pn i¼1 i jðy y di Þj=n Er ¼ i¼1 i y d max y d min where yi is predicted by the CFD model, ydi, the experimental value, n, the number of data and ym, average of actual values, ydmax, the maximum of experimental values and ydmin, the minimum of experimental values. 3. Results and discussion 3.1. Temperature distribution images of cooling cycle for the whole system
Fig. 3. Schematic description of the sample package and thermocouple installation.
to the middle region of test sample with the tip located along different radial planes: center (To) (center), midway (Tm) between the center and the surface (midway) and near the surface (Tr) (surface). Another thermal couple was installed to measure the temperature close to the cylindrical holder surface (Ts). The packaged samples were stored in a cooler (4 C), no longer than 24 h, before freezing treatments. PSF treatments were performed using an experimental high pressure apparatus. The system is composed of a high pressure unit (ACIP-6500/5/12-VB, ACB Pressure Systems, Nantes, France), a refrigerating circulator (PrestoLH47, Julabo Labortechnik GMBH, Germany), and a data logger (SA-32, AOIP, France). The high pressure vessel was 120 mm in diameter and 310 mm in height. The medium used for pressure transmission in the system was ethanol/water solution (50%, v/v). Four thermocouple wires were installed through the top lid of the vessel with miniature connectors fixed on the inner face of the lid. These wires were connected to the four thermocouples in the prepared test sample placed in the center of the vessel (Figs. 1 and 3). 2.7. Evaluation of modeling performance The performance of the model was evaluated based on the prediction accuracy by computing the difference
Fig. 4(a)–(c) show the temperature distribution at the end of each of the three stages of pressure cooling at 100 MPa, in which the temperature values are represented by different colors.1 From Fig. 4(a), it can be seen that after pre-loading period (90 s), the temperature distribution in each section was altered from their initial values. Starting from the pork sample, the color of the central region appears red, meaning that it maintained the initial temperature (4 C) at the end of first phase. The area close to the sample holder wall appears yellow, indicating a change in the surface temperature of the test sample. For the high pressure medium, because of the convective heat transfer within the fluid, caused by the fluid natural movement, the temperature distribution became more complex. There were three temperature zones for the pressure medium. The first was near the sample holder surface indicated by light green color; the second zone on the top and central axis with green color; the third zone for the remaining part with a blue color. Especially, the bottom part showed the lowest temperature with indicated by the dark blue color. It can be observed that warmer area on the top was much larger than that in the bottom, in consistence with the natural convection phenomena. The fluid temperature close to the sidewall of the high pressure vessel did not change much because of the constant low temperature of the outside surface and high overall heat coefficient of associated with the side wall. The metal cylindrical sample holder, with small thickness and high thermal conductivity, was completely cooled down to the liquid temperature during the pre-loading period. But for the plastic plate on the top and bottom of the cylinder holder, the temperature for the inside surface was close to the initial temperature while that for the outside surface was closer to the temperature of the high pressure medium. 1 For interpretation of color in Fig. 4, the reader is referred to the web version of this article.
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Fig. 4. Temperature distribution generated from CFD model (100 MPa) at the end of each stage: (a) pre-loading (stage 1), (b) pressure build-up or compression (stage 2), and (c) pressure holding (stage 3).
Fig. 4(b) shows the temperature image of the modeling domain at the end of the compression period during which the pressure was increased from 0.1 to 100 MPa. It should be noted that in this graph, the maximum temperature reached (red color) is about 7 C while the minimum temperature (blue color) is about 11 C, different from the Fig. 4(a). Because of the compression generated heat within pork and medium fluid, their temperatures increased, even though during this period the product and medium were subjected to cooling from the surrounded refrigeration system. For example, the center temperature of pork reached to about 7 C from the initial temperature about 4 C, and the fluid temperature also increased to some extent, except for the small layer adjacent to vessel surface. It resulted that the area of the second zone defined for Fig. 4(a) was continuously enlarged and the difference between the first zone and the third zone was becoming hazy. After the pressurization (compression), the pressure cooling phase started until the product temperature is lowered to the target value at constant pressure. During this period, temperature at all locations decreased as shown in Fig. 4(c). As can be expected the coolest temperatures were next to the vessel surface. The product showed a small gradient in temperature and the process stopped once the final temperature at the center is reached. At the bottom and top of the vessel the temperatures were higher since there were no external cooling from these ends. 3.2. Movement of the pressure medium fluid Fig. 5(a)–(c) show velocity vector images generated by the CFD model for the case under 100 MPa, indicating
the movement of the medium fluid within the high pressure vessel during the different cooling stages. During the first stage, it can be seen that the fluid movement occurred mostly along the surface of the cylinder sample holder and reaching the top area of the high pressure vessel (Fig. 5(a)), because of the temperature difference between the high pressure medium fluid and the product. This can explain the result shown in the Fig. 4(a) with a high temperature area in the top zone of the vessel. The next stage (Fig. 5(b)) was similar, except for some difference near the bottom zone with an increased movement along the central line at the vessel bottom The compression results in elevating the temperature of medium (and product) and thus provides a temperature gradient along the vessel wall as well there by contributing to the fluid movement. During the final stage of pressure cooling (Fig. 5(c)), the system temperature is lowered, with the result the temperature differences that existed initially continue to decrease and there by gradually decreasing the fluid movement in the vessel. 3.3. Transient temperature profiles Fig. 6(a)–(c) show the temperature history at four typical locations in the system during different stages of pressure cooling at 100 MPa. Unlike Fig. 4 which shows the temperature snapshot of the system at different stages, Fig. 6 demonstrates the transient temperature changes at selected locations during the pressure cooling. Temperatures at the center and the middle locations of pork were not affected during the loading period and only the surface temperature close to the carrier was reduced linearly with
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Fig. 5. Velocity distribution generated from CFD model for 100 MPa at the end of each stage: (a) pre-loading (stage 1), (b) pressure build-up (stage 2), and (c) pressure holding (stage 3).
time (Fig. 6(a)). Temperature change in the high pressure medium was more complex due to existence of convection currents. At the beginning, the fluid temperature rose as the warmer pork sample was introduced. But then cooling resulted from the refrigeration system. Fig. 6(b) demonstrates that temperatures of both pork and pressure medium increased with the pressurization time, more prominent at the center of the pork sample. This was due to the heat generated by compression. During the final stage (Fig. 6(c)), temperatures decreased with time except for the fluid temperature which showed a slight increase at the start of the phase. As expected, the rate of decrease in temperature at each location decreased with time, meaning that the temperature distribution was continually narrowing. 3.4. Experimental validations In order to validate the performance of developed CFD computer model, a set of experiments were carried out to measure the transient temperature profiles at the four typical locations under three pressure cooling conditions as described previously. The results from experiments and the computer model under 150 MPa are shown in Fig. 7. The model predicted temperatures demonstrated a good match with the experimental values. However, it was apparent that the modeling performance varied with geometry locations, stages and pressure processing conditions.
Table 3 shows the statistical results for the comparison of transient temperature profiles at different stages for pressure cooling at 150 MPa. Based on the R2 values, it can be found that the model predicted temperature data for the central locations (To and Tm) much better than those near the surfaces (Tr and Ts); with respect to the stages, stage 3 temperatures were better predicted than the stage 1 or stage 2 temperatures. These results can be justified from three aspects. (1) The surface temperatures (Tr and Ts) were related to the convective heat transfer with the fluid medium which is much more complex than the conductive heat transfer within the pork sample (To and Tm). (2) Factors are less controllable during the pre-loading and compression stages, which would influence the heat convection in the pressure medium. (3) Surface locations of the thermocouples are less precise than the central ones and are generally influenced by the installation procedures. The statistical results for comparison of whole cooling cycle including the three stages under different pressure cooling conditions are summarized in Table 4. Again, there were better correlations for both To and Tm than for Ts and Tr. However, for the different pressure conditions, the average R2 value for 150 MPa were higher than for 100 MPa and for 200 MPa. This was because the conductivity of the pork under the high pressure condition, used for modeling of all cases, was first estimated based on the result from the 150 MPa, which might be affected by the pressure and temperature. Therefore, it is necessary to adjust the
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10
0 -5
To
Tr
Tm
Ts
5
Temperature (°C)
Temperature (°C)
15
5
-10 -15 -20 0
(a)
10 20 30 40 50 60 70 80 90 Time (s)
To
Tr
Tm
Ts
0 -5 -10 -15
10
-20
Temperature (°C)
5 -25
0
To Tm
-5
0
Tr Ts
1000
1500
2000
2500
3000
3500
Process time (s) Fig. 7. Comparison of transient temperature results from experiments and CFD model predicted (solid lines represent experimental results). To, Tm, Tr and Ts are temperatures at different locations of the sample package (see Fig. 3).
-10 -15 -20 0
5
(b)
10 15 Time (s)
20
25
30 Table 3 The correlation coefficient R2 and Er values for four typical temperature curves at different stages under 150 MPa
10 Temperature (°C)
500
To Tm
5
Tr Ts
To
0 Stage 1 Stage 2 Stage 3
-5
-10
Tm
Tr
Ts
R2
Er (%)
R2
Er
R2
Er
R2
Er
0.98 0.90 0.99
4.5 5.9 2.2
0.87 0.86 0.98
8.2 7.5 3.1
0.51 0.42 0.89
32.5 38.2 8.3
0.85 0.75 0.82
9.2 10.3 8.9
-15 0 (c)
500
1000
1500
2000
2500
Time (s)
Fig. 6. Transient temperature curves at different locations (To, Tm, Tr and Ts, see Fig. 3) generated from CFD model for 100 MPa at each stage: (a) pre-loading (stage 1), (b) pressure build-up (stage 2), and (c) pressure holding (stage 3).
Table 4 The correlation coefficient R2 values for four typical temperature curves under different pressure conditions To
Tm
Tr
2
Er (%)
R
2
Er
2
R
Er
R2
Er
5.5 2.9 6.2
0.83 0.93 0.88
9.2 3.9 7.1
0.57 0.65 0.53
25.5 18.2 29.8
0.85 0.75 0.82
7.2 10.3 6.9
R 100 MPa 150 MPa 200 MPa
0.90 0.97 0.81
Ts
input parameters in order to extend the developed CFD for different pressure conditions. 3.5. Estimation of thermal conductivity of pork under high pressure conditions Estimation of thermal properties by use of a computer model is one of important purposes for development of process models. In this study, the developed computer model was used for prediction of the thermal conductivity (kp) of pork under high pressure conditions. As shown in previous results, the temperature at the center of the pork sample is the most stable and best agreement between experimental and predicted results, thus the determination standard for the optimal thermal conductivity of the pork under different pressure conditions was to maximum the R2
value for the center point by adjusting the thermal conductivity value. The optimal values of thermal diffusivities for different pressure conditions were determined as shown in Fig. 8. It confirmed that the thermal conductivity of pork increased with the pressure value as that for water (Harvey et al., 2000), but the increase rate for pork was lower than that for water (Harvey et al., 2000). According to the results estimated by the model, the relationship between pressure and thermal conductivity can be described by a simple linear model as below: k p ¼ 0:00044P þ 0:447
R2 ¼ 0:96
where kp is the thermal conductivity, P, the pressure (MPa).
C.R. Chen et al. / Journal of Food Engineering 79 (2007) 401–409
Fig. 8. Thermal conductivity of pork estimated by the CFD model.
4. Conclusions A computer simulation of high pressure cooling process was developed by use of computational fluid dynamic software. It was used for analysis of temperature and velocity vector images at the end of different stages for the pressure cooling process. It was further used for investigation of transient temperature profiles at selected locations in both pork and fluid medium, to compare the temperature changes related to location and time. The performance of this CFD simulation was validated by a set of experiments carried out in the pilot scale high pressure equipment. The comparison of transient temperature profiles for the given locations confirmed that the developed CFD simulation well described the temperature changes in pork and fluid medium. The thermal conductivity of pork sample during different pressure conditions was estimated by the CFD model, indicating that it increased with pressure linearly during the range of pressure from 100 to 200 MPa. Acknowledgement This research was supported by a grant from the Strategic Grants Program of the Natural Sciences and Engineering Research Council of Canada. References Bridgman, P. W. (1912). Water in the liquid and five solid forms under pressure. Proceedings of the American Academy of Arts and Sciences, 47(13), 441–558. Cheftel, J. C., Levy, J., & Dumay, E. (2000). Pressure-assisted freezing and thawing: principles and potential applications. Food Reviews International, 16(4), 453–483. Cheftel, J. C., Thiebaud, M., & Dumay, E. (2002). Pressure-assisted freezing and thawing: a review of recent studies. High Pressure Research, 22, 601–611.
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Chevalier, D., Le Bail, A., & Ghoul, M. (2001). Evaluation of the ice ratio formed during quasi-adiabatic pressure shift freezing. High Pressure Research, 21, 227–235. Chevalier, D., Sequeira-Munoz, A., Le Bail, A., Simpson, B. K., & Ghoul, M. (2001). Effect of freezing conditio transfer during high-pressure freezing and thawing. Biotechnology Progress, 13(4), 416–423. Dennis, R. H. (2001). Predictions for thermophysical properties of foods. In Joseph Irudayaraj (Ed.), Food processing operations modeling (pp. 1–23). New York: Marcel Dekker Inc. Denys, S., Van Loey, A. M., & Hendrickx, M. E. (2000). Modeling conductive heat transfer during high-pressure thawing processes: determination of latent as a function of pressure. Biotechnology Progress, 16(3), 447–455. Denys, S., Van Loey, A. M., Hendrickx, M. E., & Tobback, P. P. (1997). Modeling heat transfer during high-pressure freezing and thawing. Biotechnology Progress, 13(4), 416–423. Harvey, A. H., Peskin, A. P., & Klein, S. A. (2000). NIST standard reference database 10: NIST/ASME steam properties (version 2.2). Standard reference data program, National Institute of Standards and Technology, U.S. Department of Commerce, Gaithersburg, Maryland. Kalichevsky, M. T., Knorr, D., & Lillford, P. J. (1995). Potential applications of high-pressure effects on ice–water transitions. Trends in Food Science and Technology, 6, 253–259. Knorr, D. (1999). Process assessment of high-pressure processing of foods: an overview. In F. A. R. Oliveira & J. C. Oliveira (Eds.), Processing foods: Quality optimization and process assessment (pp. 249–267). Boca Raton: CRC Press. Knorr, D., Schlueter, O., & Heinz, V. (1998). Impact of high hydrostatic pressure on phase transitions of foods. Food Technology, 52(9), 42–45. Le Bail, A., Chevalier, D., Mussa, D. M., & Ghoul, M. (2002). High pressure freezing and thawing of foods: a review. International Journal of Refrigeration, 25(5), 504–513. Le Bail, A., Chourot, J. M., Barillot, P., & Lebas, J. M. (1997). Conge´lation-de´conge´lation par haute pression. Revue Ge´ne´rale du Froid, 97(2), 51–56. Levy, J., Dumay, E., Kolodziejczyk, E., & Cheftel, J. C. (1999). Freezing kinetics of a model oil-in-water emulsion under high pressure or by pressure release, impact on ice crystals and oil droplets. LebensmittelWissenschaft und-Technologie, 32, 396–405. Martino, M. N., Otero, L., Sanz, P. D., & Zaritzky, N. E. (1998). Size and location of ice crystals in pork frozen by high-pressure-assisted freezing as compared to classical methods. Meat Science, 50(3), 303–313. Otero, L., Martino, M., Zaritzky, N., Solas, M., & Sanz, P. D. (2000). Preservation of microstructure in peach and mango during highpressure-shift freezing. Journal of Food Science, 65(3), 466–470. Otero, L., & Sanz, P. D. (2000). High-pressure shift freezing, part 1: amount of ice instantaneously formed in the process. Biotechnology Progress, 16, 1030–1036. Otero, L., Sanz, P. D., de Elvira, C., & Carrasco, J. A. (1997). Modelling thermodynamic properties of water in the high-pressure assisted freezing process. In K. Heremans (Ed.), High-pressure research in the biosciences and biotechnology (pp. 347–350). Leuven, Belgium: Leuven University Press. Sanz, P. D., & Otero, L. (2000). High-pressure freezing. Part 2. Modeling of freezing times for a finite cylindrical model. Biotechnology Progress, 16, 1037–1043. Scott, G., & Richardson, P. (1997). The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology, 8, 119–124. Singh, R. P., & Heldman, D. R. (2001). Introduction to food engineering (3rd ed., 659 pp). London: Academic Press.
Computer simulation of high pressure cooling of pork C.R. Chen a, S.M. Zhu a, H.S. Ramaswamy
a,*
, M. Marcotte b, A. Le Bail
c
a
b
Department of Food Science and Agricultural Chemistry, Macdonald Campus of McGill University, 21111 Lakeshore, Ste. Anne de Bellevue, Que., Canada H9X 3V9 Food Research and Development Centre, Agriculture and Agri-Food Canada, 3600 Casavant Blvd West, St. Hyacinthe, Que., Canada J2S 8E3 c GEPEA-ENITIAA, (UA CNRS 6144), Rue de la Ge´raudie`re BP 82225, F-44322 Nantes Cedex 03, France Received 13 August 2005; accepted 1 February 2006 Available online 18 April 2006
Abstract A computer simulation was used to develop and evaluate two-dimensional axi-symmetrical of cooling of pork under high pressure (HP) processing conditions. The whole cooling process was divided into three stages of cooling: a preloading stage, a pressure buildup stage (compression) and a pressure hold stage (constant pressure), and the modeling domain covered the pressurization fluid, the sample holder and the pork sample. Modeling performance was evaluated by comparing the predicted and experimental temperatures at four locations: three within the pork sample and one for the high pressure fluid medium. Model generated images were used for visual observations of temperature distribution and movement of the pressure fluid, and transient temperature curves were generated for the four specified locations. Results indicated that the developed model well matched experimental results, especially for temperatures at the central area. The thermal conductivities of pork under pressure conditions: 100, 150 and 200 MPa were estimated by the model using error trials. The model provides a valuable tool for studying the pressure cooling behavior of test samples and for designing the pressure shift freezing process. 2006 Elsevier Ltd. All rights reserved. Keywords: High pressure; Simulation; Modeling; CFD; Temperature; Cooling; Pork
1. Introduction High pressure (HP) processes are currently receiving considerable attention because of its advantages and potential benefits in the preservation and modification of functionality of foods (Knorr, 1999; Le Bail, Chevalier, Mussa, & Ghoul, 2002). HP has interesting effects on the solid–liquid phase transition of water and offers possibilities for novel processes, such as pressure shift freezing (PSF), HP thawing, super-cooled storage without freezing, and so on (Bridgman, 1912; Cheftel, Thiebaud, & Dumay, 2002; Knorr, Schlueter, & Heinz, 1998). PSF is an interesting technique to achieve massive ice-nucleation showing potential benefits for improved quality of frozen foods *
Corresponding author. Tel.: +1 514 398 7919; fax: +1 514 398 7977. E-mail address: [email protected] (H.S. Ramaswamy). 0260-8774/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.02.034
(Chevalier, Sequeira-Munoz, Le Bail, Simpson, & Ghoul, 2001; Le Bail et al., 2002; Levy, Dumay, Kolodziejczyk, & Cheftel, 1999; Martino, Otero, Sanz, & Zaritzky, 1998). Elevation of pressure depresses the freezing point of water from 0 C at atmospheric pressure to 21 C at about 210 MPa (Bridgman, 1912). This phenomenon allows food samples to be super-cooled significantly resulting in a rapid and uniform ice nucleation and growth of ice crystals immediately upon the pressure release. The PSF process generally involves cooling the sample under pressure (usually up to 200 MPa) to just above the freezing point (20 C) and quickly releasing the pressure to form nuclei of ice crystals; ice crystals are then allowed to grow at atmospheric pressure in a conventional freezer. The PSF process can produce small ice crystals throughout the sample, rather than a stress-inducing ice front moving through the sample (Kalichevsky, Knorr, & Lillford, 1995; Martino et al., 1998; Otero, Martino, Zaritzky, Solas, & Sanz, 2000). Therefore,
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this concept can be specifically useful for freezing of large size foods in which a uniform distribution of fine ice crystals is required. For these foods, conventional freezing techniques would result in large thermal gradients and hence, low rate of freezing with considerable freeze-thaw damage and freeze cracking (Cheftel, Levy, & Dumay, 2000; Martino et al., 1998). Although PSF has potential benefits, existing knowledge in this area is still very limited (Cheftel et al., 2000; Le Bail et al., 2002). The thermal behavior as related to phase transition, heat transfer, ice-crystal formation and food quality changes during PSF processing are not fully understood (Knorr et al., 1998; Le Bail et al., 2002). PSF processes have unique characteristics different from those in conventional freezing methods. Modeling is considered a powerful approach for understanding systems involving complex heat and mass transfer applications. Only few studies have been reported on the modeling of PSF process Denys, Van Loey, Hendrickx, & Tobback, 1997; Denys, Van Loey, & Hendrickx, 2000; Sanz & Otero, 2000). Denys et al. (1997) proposed a twodimensional numerical model of heat transfer for pressure shift freezing and thawing to predict thawing and freezing times. The model was improved later (Denys et al., 2000) by taking into account the pressure dependence of the latent heat of the product used. Sanz and Otero (2000) established a model to simulate the whole procedure of PSF processing, but the use of the model is limited to cylindrical symmetry of samples and quick releases of pressure. On the other hand, several studies have been reported on computation of the percentage of ice instantaneously formed after a quick depressurization (Chevalier, Le Bail, & Ghoul, 2001; Le Bail, Chourot, Barillot, & Lebas, 1997; Otero & Sanz, 2000; Otero, Sanz, de Elvira, & Carrasco, 1997). The models of Otero et al. (1997) and Chevalier, Le Bail et al. (2001) are based on the phasechange curve of water (Bridgman, 1912) in the adiabatic expansion, although it has been proved that liquid water always enters metastable conditions in a real PSF process. Other calculation methods were based on the balance between the latent heat released by ice nucleation and the sensible heat absorbed by the super-cooled sample (Le Bail et al., 1997; Otero & Sanz, 2000). Most of studies on modeling of high pressure processes are limited to the product itself and assume the temperature of high pressure medium as the boundary condition to remain constant during the pressure cooling process. Preliminary experiments carried out in this study showed that the medium temperature was variable during whole process. During the cooling process, only the outside surface temperature of the vessel can be considered to be constant. The temperature on the sidewall is dependent on the cooling medium while that on the top or bottom is dependent on the conditions of the environment. In order to develop an accurate model, it is necessary to extent the boundary to the vessel, meaning that the modeling domain should include at least the pressure medium fluid, product
container/carrier and the product and its package materials. This makes it more complex especially while using conventional computer modeling techniques. Computation fluid dynamics (CFD) is a powerful tool that uses numerical techniques for simulation of fluid flow and heat transfer. It has been used in many areas but only recently for food processing applications (Scott & Richardson, 1997). More systematic modeling of various complex processes including the high pressure process can be carried out by use of CFD model. As a part of modeling PSF process, this study was focused on modeling of the cooling process under high pressure conditions which is the pre-requisite for the successful application of the PSF process. Specifically, the objectives of this study were to develop a CFD computer simulation model for evaluating the transient time and space dependent temperature in the system, and to validate the model using experimental data obtained from a pilot scale high pressure processing equipment. 2. Methodology 2.1. Cooling process and domain for modeling The whole cooling process was divided into three stages: pre-loading stage, pressure build-up stage (compression), and pressure holding stage (constant pressure). In the initial loading stage, the prepared product sample was moved from the storage room (4 C) to the pressure chamber immersed in the fluid medium; during the build-up stage, the pressure was increased from 0.1 MPa to the designed values (100, 150 or 200 MPa); and during pressure holding stage, the pressure was kept at a constant value until the center temperature of pork product reached its desired temperature. The system modeled included the pressure medium fluid, cylindrical sample holder and pork product. Since the high pressure vessel and the sample holder were of axi-symmetrical cylindrical shapes, one half of a vertical cross-section was taken as the modeling domain as shown in Fig. 1. In this figure, letters A, B, C, D represent the pressure fluid medium, the cylindrical sample holder, the cylinder caps at bottom and top of the holding cylinder, and the pork product, respectively, while numbers 1, 2, 3 and 4 were marked for different boundary conditions detailed in the next section. 2.2. Assumptions for modeling 1. The high pressure vessel was kept at a predetermined constant temperature during the cooling process by an efficient temperature controlled refrigeration system. 2. The adiabatic compression heat generated in the system linearly increased with pressure. 3. Convection heating could exist within the high pressure medium because of the motion caused by the temperature gradients and thermal expansion.
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403
q ¼ q20 ð1 bðT 20ÞÞ
ð4Þ
where q is the density, k, the thermal conductivity, CP, the specific heat, T, the temperature, u, v are velocity components in z and r directions, respectively; r, the coordinator in the radium and z, the coordinator in the height; p, the pressure. l, the viscosity. Eq. (1) was used for modeling of heat transfer within solid materials like pork and package, while the combination of Eqs. (1)–(4) was implemented for modeling of heat transfer and movement of the high pressure liquid medium. Convection was considered only for the HP liquid medium with a convective heat transfer coefficient at contact surfaces. 2.4. Initial and boundary conditions
Fig. 1. Modeling domain of high pressure cooling process [A is pressure medium fluid, B is cylindrical sample holder, C is bottom or top cap of the holder, and D is pork product. Numbers 1, 2, 3 and 4 are different boundary lines].
4. There was no slip for the pressure medium on the solid surfaces. 5. All the thermo-physical properties were isotropic for all the materials. 2.3. Governing equations
For the first stage, it was assumed that the medium was stationary and temperatures were uniform for each part as shown in the Table 1; for the second and final stages, temperature and velocity distribution at the end of the previous stage were used as the initial conditions. Boundary conditions marked by numbers as shown in Fig. 1 were given as below: at the boundary 1 oT ¼ U 1 ðT cool T a Þ or u¼v¼0
ka
at the boundary 2 oT ¼ U 2 ðT air T a Þ oz u¼v¼0
ka
There are two types of governing equations used for this modeling, as given as below:
at the boundary 3 (1) Energy conservation oT oT oT 1 1 o oT o oT þv þu ¼ rk k þ ot or ou qC P r or or oz oz ð1Þ (2) Momentum conservation In the vertical direction ou ou ou op 1 o ou o2 u q þv þu r ¼ þl þ 2 ot or oz oz r or or oz þ ðq q20 Þg
ð2Þ
In the radial direction ov ov ov op 1 o o2 v þv þu ðrvÞ þ 2 q ¼ þl ot or oz or r or oz
u¼v¼0
for the liquid part
at the boundaries 4 oT ¼0 or v ¼ 0 for the liquid part where Tcool is the temperature of the cooling medium, Tair, the temperature of environment air, u, the velocity component in z direction, v, the velocity component in r direction, ka, the thermal conductivity of the high pressure medium, Table 1 Initial temperature conditions for each part
ð3Þ where for liquid high pressure medium, the variable density with temperature was given below:
Pressure medium (C) Cylinder holder (C) Top and bottom cap (C) Pork (C)
100 MPa
150 MPa
200 MPa
15 4 4 4
19 4 4 4
20 3.3 3.3 3.3
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Ta, the transient temperature of the high pressure medium close to the vessel’s cylindrical surface or near the vessel’s inside top/bottom, U1 and U2 are the overall heat transfer coefficients for the vessel wall and ends (top and bottom), respectively, which are given below:
350
Enthalpy (J/g)
300
kv a kv U 1 U2 ¼ ðh þ U 1 Þ
U1 ¼
250 200 150 100 50
where h is the heat transfer between the vessel top or bottom and the environment air, a, the thickness of the vessel wall, kv was the thermal conductivity of the vessel. 2.5. Thermo-physical properties used for the computer modeling Thermo-physical properties used for the computer modeling are listed in Table 2. Only the thermal conductivity of the pork was estimated by the CFD model, others were gathered from different methods. A general calculation method was used for obtaining the properties of high pressure medium, a mixture (1:1) of water and ethanol as given below (Dennis, 2001; Harvey, Peskin, & Klein, 2000): X X ¼ wi xi where X is the property for the pressure medium, such as density, heat capacity or thermal conductivity; w, the mass fraction; x, the property of individual component such as water or ethanol; subscript i, the component. The variable heat capacity for the pork, obtained from enthalpy (Fig. 2) curves gathered using a differential scanning calorimeter (DSC-Q100, TA Instruments, New Castle, DE), was used during the pre-loading stage because the phase change
0 -40
-30
-20
-10 0 10 Temperature (oC)
20
30
Fig. 2. Pork enthalpy as a function of temperature obtained from a differential scanning calorimeter.
from liquid to ice was considered. For modeling of the compression stage, the pressure dependent properties including density and thermal conductivity for the pressure medium and density for the pork were the average values between 0.1 MPa and the target pressure. 2.6. Validation experiments Fresh pork (boneless rib portions) was purchased from market (Carrefour, Nantes, France). Cylindrical samples (50 mm diameter · 160 mm length) were cut along rib muscles using a cylindrical cutter. Each sample was vacuumsealed in a moisture-impermeable plastic pouch (80 lm thick multiplayer film) (La Bovida, France) and placed in a copper holder (50 mm diameter · 200 mm length) (Fig. 3). As shown in Fig. 3, three K-type thermocouples (0.3 mm diameter, Omega, Stamford, CT) were inserted
Table 2 Thermo-physical properties for each part materials Materials
Properties
Pressure medium
1
Pressure (MPa) 3
Density at 20 C (kg/m ) Thermal conductivity (W/m/C) 1 Heat capacity (J/kg/C) 1 Viscosity (lPa s) 1 Thermal expansion (C1) 2 Compression heat (J/MPa/m3) 1
Cylinder holder
0
100
150
200
900 0.375
940 0.42
960 0.44 3300 3360 8.7 · 104 1.89 · 105
980 0.46
3
Density (kg/m3) Heat capacity (J/kg/C) 3 Thermal conductivity (W/m/C)
8900 383 386
3
2700 840 0.45
3
Plastic cap
Density (kg/m3) Heat capacity (J/kg/C) 3 Thermal conductivity (W/m/C) 3
Pork
2
Density (kg/m3) Heat capacity (J/kg/C) 4 Thermal conductivity (W/m/C) 2 Compression heat (J/MPa/m3) 2
1024 Fig. 2
1074 1099 3350 Estimation by CFD model 1.03 · 105
1124
Note: 1 – from calculation, 2 – from separate experiments, 3 – from the reference (Harvey et al., 2000; Singh & Heldman, 2001), 4 – estimated from the CFD model.
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between the experimental and predicted transient temperatures at the given locations. The coefficient of variation, R2, and average relative error, Er, were also used for assessing the model performance: Pn ðy i y di Þ2 2 R ¼ 1 Pi¼1 n 2 ðy y m Þ Pn i¼1 i jðy y di Þj=n Er ¼ i¼1 i y d max y d min where yi is predicted by the CFD model, ydi, the experimental value, n, the number of data and ym, average of actual values, ydmax, the maximum of experimental values and ydmin, the minimum of experimental values. 3. Results and discussion 3.1. Temperature distribution images of cooling cycle for the whole system
Fig. 3. Schematic description of the sample package and thermocouple installation.
to the middle region of test sample with the tip located along different radial planes: center (To) (center), midway (Tm) between the center and the surface (midway) and near the surface (Tr) (surface). Another thermal couple was installed to measure the temperature close to the cylindrical holder surface (Ts). The packaged samples were stored in a cooler (4 C), no longer than 24 h, before freezing treatments. PSF treatments were performed using an experimental high pressure apparatus. The system is composed of a high pressure unit (ACIP-6500/5/12-VB, ACB Pressure Systems, Nantes, France), a refrigerating circulator (PrestoLH47, Julabo Labortechnik GMBH, Germany), and a data logger (SA-32, AOIP, France). The high pressure vessel was 120 mm in diameter and 310 mm in height. The medium used for pressure transmission in the system was ethanol/water solution (50%, v/v). Four thermocouple wires were installed through the top lid of the vessel with miniature connectors fixed on the inner face of the lid. These wires were connected to the four thermocouples in the prepared test sample placed in the center of the vessel (Figs. 1 and 3). 2.7. Evaluation of modeling performance The performance of the model was evaluated based on the prediction accuracy by computing the difference
Fig. 4(a)–(c) show the temperature distribution at the end of each of the three stages of pressure cooling at 100 MPa, in which the temperature values are represented by different colors.1 From Fig. 4(a), it can be seen that after pre-loading period (90 s), the temperature distribution in each section was altered from their initial values. Starting from the pork sample, the color of the central region appears red, meaning that it maintained the initial temperature (4 C) at the end of first phase. The area close to the sample holder wall appears yellow, indicating a change in the surface temperature of the test sample. For the high pressure medium, because of the convective heat transfer within the fluid, caused by the fluid natural movement, the temperature distribution became more complex. There were three temperature zones for the pressure medium. The first was near the sample holder surface indicated by light green color; the second zone on the top and central axis with green color; the third zone for the remaining part with a blue color. Especially, the bottom part showed the lowest temperature with indicated by the dark blue color. It can be observed that warmer area on the top was much larger than that in the bottom, in consistence with the natural convection phenomena. The fluid temperature close to the sidewall of the high pressure vessel did not change much because of the constant low temperature of the outside surface and high overall heat coefficient of associated with the side wall. The metal cylindrical sample holder, with small thickness and high thermal conductivity, was completely cooled down to the liquid temperature during the pre-loading period. But for the plastic plate on the top and bottom of the cylinder holder, the temperature for the inside surface was close to the initial temperature while that for the outside surface was closer to the temperature of the high pressure medium. 1 For interpretation of color in Fig. 4, the reader is referred to the web version of this article.
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Fig. 4. Temperature distribution generated from CFD model (100 MPa) at the end of each stage: (a) pre-loading (stage 1), (b) pressure build-up or compression (stage 2), and (c) pressure holding (stage 3).
Fig. 4(b) shows the temperature image of the modeling domain at the end of the compression period during which the pressure was increased from 0.1 to 100 MPa. It should be noted that in this graph, the maximum temperature reached (red color) is about 7 C while the minimum temperature (blue color) is about 11 C, different from the Fig. 4(a). Because of the compression generated heat within pork and medium fluid, their temperatures increased, even though during this period the product and medium were subjected to cooling from the surrounded refrigeration system. For example, the center temperature of pork reached to about 7 C from the initial temperature about 4 C, and the fluid temperature also increased to some extent, except for the small layer adjacent to vessel surface. It resulted that the area of the second zone defined for Fig. 4(a) was continuously enlarged and the difference between the first zone and the third zone was becoming hazy. After the pressurization (compression), the pressure cooling phase started until the product temperature is lowered to the target value at constant pressure. During this period, temperature at all locations decreased as shown in Fig. 4(c). As can be expected the coolest temperatures were next to the vessel surface. The product showed a small gradient in temperature and the process stopped once the final temperature at the center is reached. At the bottom and top of the vessel the temperatures were higher since there were no external cooling from these ends. 3.2. Movement of the pressure medium fluid Fig. 5(a)–(c) show velocity vector images generated by the CFD model for the case under 100 MPa, indicating
the movement of the medium fluid within the high pressure vessel during the different cooling stages. During the first stage, it can be seen that the fluid movement occurred mostly along the surface of the cylinder sample holder and reaching the top area of the high pressure vessel (Fig. 5(a)), because of the temperature difference between the high pressure medium fluid and the product. This can explain the result shown in the Fig. 4(a) with a high temperature area in the top zone of the vessel. The next stage (Fig. 5(b)) was similar, except for some difference near the bottom zone with an increased movement along the central line at the vessel bottom The compression results in elevating the temperature of medium (and product) and thus provides a temperature gradient along the vessel wall as well there by contributing to the fluid movement. During the final stage of pressure cooling (Fig. 5(c)), the system temperature is lowered, with the result the temperature differences that existed initially continue to decrease and there by gradually decreasing the fluid movement in the vessel. 3.3. Transient temperature profiles Fig. 6(a)–(c) show the temperature history at four typical locations in the system during different stages of pressure cooling at 100 MPa. Unlike Fig. 4 which shows the temperature snapshot of the system at different stages, Fig. 6 demonstrates the transient temperature changes at selected locations during the pressure cooling. Temperatures at the center and the middle locations of pork were not affected during the loading period and only the surface temperature close to the carrier was reduced linearly with
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Fig. 5. Velocity distribution generated from CFD model for 100 MPa at the end of each stage: (a) pre-loading (stage 1), (b) pressure build-up (stage 2), and (c) pressure holding (stage 3).
time (Fig. 6(a)). Temperature change in the high pressure medium was more complex due to existence of convection currents. At the beginning, the fluid temperature rose as the warmer pork sample was introduced. But then cooling resulted from the refrigeration system. Fig. 6(b) demonstrates that temperatures of both pork and pressure medium increased with the pressurization time, more prominent at the center of the pork sample. This was due to the heat generated by compression. During the final stage (Fig. 6(c)), temperatures decreased with time except for the fluid temperature which showed a slight increase at the start of the phase. As expected, the rate of decrease in temperature at each location decreased with time, meaning that the temperature distribution was continually narrowing. 3.4. Experimental validations In order to validate the performance of developed CFD computer model, a set of experiments were carried out to measure the transient temperature profiles at the four typical locations under three pressure cooling conditions as described previously. The results from experiments and the computer model under 150 MPa are shown in Fig. 7. The model predicted temperatures demonstrated a good match with the experimental values. However, it was apparent that the modeling performance varied with geometry locations, stages and pressure processing conditions.
Table 3 shows the statistical results for the comparison of transient temperature profiles at different stages for pressure cooling at 150 MPa. Based on the R2 values, it can be found that the model predicted temperature data for the central locations (To and Tm) much better than those near the surfaces (Tr and Ts); with respect to the stages, stage 3 temperatures were better predicted than the stage 1 or stage 2 temperatures. These results can be justified from three aspects. (1) The surface temperatures (Tr and Ts) were related to the convective heat transfer with the fluid medium which is much more complex than the conductive heat transfer within the pork sample (To and Tm). (2) Factors are less controllable during the pre-loading and compression stages, which would influence the heat convection in the pressure medium. (3) Surface locations of the thermocouples are less precise than the central ones and are generally influenced by the installation procedures. The statistical results for comparison of whole cooling cycle including the three stages under different pressure cooling conditions are summarized in Table 4. Again, there were better correlations for both To and Tm than for Ts and Tr. However, for the different pressure conditions, the average R2 value for 150 MPa were higher than for 100 MPa and for 200 MPa. This was because the conductivity of the pork under the high pressure condition, used for modeling of all cases, was first estimated based on the result from the 150 MPa, which might be affected by the pressure and temperature. Therefore, it is necessary to adjust the
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10
0 -5
To
Tr
Tm
Ts
5
Temperature (°C)
Temperature (°C)
15
5
-10 -15 -20 0
(a)
10 20 30 40 50 60 70 80 90 Time (s)
To
Tr
Tm
Ts
0 -5 -10 -15
10
-20
Temperature (°C)
5 -25
0
To Tm
-5
0
Tr Ts
1000
1500
2000
2500
3000
3500
Process time (s) Fig. 7. Comparison of transient temperature results from experiments and CFD model predicted (solid lines represent experimental results). To, Tm, Tr and Ts are temperatures at different locations of the sample package (see Fig. 3).
-10 -15 -20 0
5
(b)
10 15 Time (s)
20
25
30 Table 3 The correlation coefficient R2 and Er values for four typical temperature curves at different stages under 150 MPa
10 Temperature (°C)
500
To Tm
5
Tr Ts
To
0 Stage 1 Stage 2 Stage 3
-5
-10
Tm
Tr
Ts
R2
Er (%)
R2
Er
R2
Er
R2
Er
0.98 0.90 0.99
4.5 5.9 2.2
0.87 0.86 0.98
8.2 7.5 3.1
0.51 0.42 0.89
32.5 38.2 8.3
0.85 0.75 0.82
9.2 10.3 8.9
-15 0 (c)
500
1000
1500
2000
2500
Time (s)
Fig. 6. Transient temperature curves at different locations (To, Tm, Tr and Ts, see Fig. 3) generated from CFD model for 100 MPa at each stage: (a) pre-loading (stage 1), (b) pressure build-up (stage 2), and (c) pressure holding (stage 3).
Table 4 The correlation coefficient R2 values for four typical temperature curves under different pressure conditions To
Tm
Tr
2
Er (%)
R
2
Er
2
R
Er
R2
Er
5.5 2.9 6.2
0.83 0.93 0.88
9.2 3.9 7.1
0.57 0.65 0.53
25.5 18.2 29.8
0.85 0.75 0.82
7.2 10.3 6.9
R 100 MPa 150 MPa 200 MPa
0.90 0.97 0.81
Ts
input parameters in order to extend the developed CFD for different pressure conditions. 3.5. Estimation of thermal conductivity of pork under high pressure conditions Estimation of thermal properties by use of a computer model is one of important purposes for development of process models. In this study, the developed computer model was used for prediction of the thermal conductivity (kp) of pork under high pressure conditions. As shown in previous results, the temperature at the center of the pork sample is the most stable and best agreement between experimental and predicted results, thus the determination standard for the optimal thermal conductivity of the pork under different pressure conditions was to maximum the R2
value for the center point by adjusting the thermal conductivity value. The optimal values of thermal diffusivities for different pressure conditions were determined as shown in Fig. 8. It confirmed that the thermal conductivity of pork increased with the pressure value as that for water (Harvey et al., 2000), but the increase rate for pork was lower than that for water (Harvey et al., 2000). According to the results estimated by the model, the relationship between pressure and thermal conductivity can be described by a simple linear model as below: k p ¼ 0:00044P þ 0:447
R2 ¼ 0:96
where kp is the thermal conductivity, P, the pressure (MPa).
C.R. Chen et al. / Journal of Food Engineering 79 (2007) 401–409
Fig. 8. Thermal conductivity of pork estimated by the CFD model.
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