- Email: [email protected]
Analysis of heterogeneous cooling of agricultural products inside bins
Journal of Food Engineering 39 (1999) 239±245
Analysis of heterogeneous cooling of agricultural products inside bins Part II: thermal study G. Alvarez *, D. Flick CEMAGREF Unit e de Recherche G enie des Proc ed es Frigori®ques, Parc de Tourvoie B.P. 44, 92185 Antony Cedex, France Received 15 September 1998; received in revised form 18 November 1998; accepted 18 November 1998
Abstract An experimental thermal study was performed in order to characterise heat transfer intensity for spherical objects packed in stacked bins and cooled by air forced convection. The heat transfer coecient was measured for each sphere in a test bin using spherical sensors. Large dierences in heat transfer coecient values, up to 40%, were observed. This heterogeneity could be explained by the fact that the air¯ow is not uniform (cf. Part I). Each object was exposed to local air¯ow conditions (mean velocity and turbulence). A correlation was established between the local heat transfer coecients and local air¯ow parameters. Cylindrical sensors were also constructed in order to measure the heat transfer coecient inside packed spheres. The measurements correlated well with the spherical sensors for the same positions in the bins. Ó 1999 Elsevier Science Ltd. All rights reserved. Keywords: Heat transfer coecient; Stacked bins; Chilling; Cooling; Agricultural products; Air forced convection; Local thermal heterogeneity; Heat transfer; Pallet
Symbols A Cp d e DHv h hr heff Tu L m Nu Nu0 Pa Ph Ps Pr q Re T t V v0 v *
area (m2 ) speci®c heat (J/kg K) diameter of object (m) emissivity latent heat of evaporation of water (J/kg) heat transfer coecient (W/m2 K) equivalent heat transfer coecient for radiation (W/ m2 K) q eective heat transfer coecient (W/m2 K) relative turbulence intensity Tu 100 v ÿ v2 =v length (m) slope of regression line for Eq. (1) Nusselt number hd=k Nusselt number when turbulence intensity present Tu 0 partial pressure of water vapour in air saturated water vapour pressure at wet bulb temperature Th (Pa ) water vapour pressure at product surface Prandtl number qCp=k heat power (W) Reynolds number qvd=l temperature (K) time (s) volume (m3 ) p instantaneous velocity Vx2 Vz2 mean air¯ow velocity
Corresponding author.; e-mail: [email protected]
x, y, z b e l q r
co-ordinates mass transfer coecient (kg/s m2 Pa) void fraction viscosity (Pa s) density (kg/m3 ) Stefan±Boltzmann constant (W/m2 /K4 )
Subscripts a c 0 r s t mean local
air convection initial radiation surface turbulent mean local
1. Introduction The temperature of agricultural products conditioned in bulk or in bins stacked on pallets is far from homogeneous for all the packed products during the cooling process. This can lead to a loss of quality in fresh fruits and vegetables. The heterogeneity of heat transfer is probably mainly due to the ¯ow heterogeneities described in Part I. The local velocity can be four times higher in one place than another at a given air¯ow rate. Local turbulence intensity varies from 20% to 50%. To
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 8 ) 0 0 1 6 6 - 6
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G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
understand heat transfer in stacked objects, three elements can be analysed: · the eect of velocity and turbulence on a single object; · local heat transfer in tubular exchangers; · local heat transfer in packed beds. Morgan (1975) and Kondjoyan (1993) have reviewed the eect of free stream velocity and turbulence on heat transfer for single cylinders and spheres. The correlations most commonly used in the absence of turbulence are those of Fr ossling for a sphere and Hilpert for cylinder. Fr ossling's correlation Nu0 2 0:6 Re0:5 Pr0:33 : Hilpert's correlation Nu0 0:615 Re0:466 ; Nu0 0:17 Re
0:618
;
40 < Re < 4000; 4000 < Re < 40 000:
The in¯uence of turbulence intensity cannot be neglected if it is above 1%. Comings et al. (1948), for instance, reported a rise of 25% in the Nusselt number when turbulence increased from 1% to 7%. Various corrections of the Nusselt number have been proposed, using either turbulence intensity (Tu) or a turbulent Reynolds number (Ret Re Tu). We will discuss only the correlations proposed by Lavender and Pei (1967) and Endho, Tsuruga, Hirano and Morihira (1972). The correlations proposed by Endho for single spheres and cylinders are similar, but the power factor of the turbulent Reynolds number is higher for the cylinder than for the sphere. The eect of turbulence thus appears to be slightly higher for single cylinders than for single spheres, as also reported by Maisel and Sherwood (1950). Spheres: Lavender and Pei Reÿ0:5 Pr0:33 ; Nu 2 0:145 Re0:25 t Nu 2 0:629
Reÿ0:5 Pr0:33 ; Re0:035 t
Ret > 1000; Ret < 1000:
Spheres: Endho Re0:5 Pr0:33 ; Nu Nu0 1 4:3 10ÿ6 Re0:78 t 400 < Ret < 8000; where Nu0 is calculated using the Fr ossling correlation Cylinders: Endho Nu Nu0 1 1:5 10ÿ6 Ret Re0:5 Pr0:33 400 < Ret < 8000; where Nu0 is calculated using the Hilpert correlation In our case there were important variations of local velocity and turbulence inside the bin, so we could expect heterogeneous heat transfer coecients. The results obtained for single objects could not be used directly, however, as heat transfer was in¯uenced by the proximity of the spheres inside the bin.
Pei and Hayward (1983) have shown that proximity between two spheres generates an interaction between their boundary layers and wakes. This phenomenon, called the blockage eect, strongly enhances heat transfer for two spheres next to one other. With tubular heat exchangers, the local heat transfer coecient depends on several parameters such as row position, arrangement, longitudinal pitch and transversal pitch. Sparrow and Yanezmoreno (1983) observed that the transfer coecient can fall to as low as 33% according to row position in the exchanger, while Stephan and Traub (1987) showed that the coecient could go up to 50% if free stream turbulence rose to 25%. With packed beds, heat transfer intensity also depends on position. Stanek and Vychodil (1987) and De Wasch and Froment (1972) observed that the heat transfer coecient also becomes lower in the air¯ow direction. Dixon, Dicostanzo and Soucy (1984) showed that the heat transfer coecient is low near container walls. This eect could be explained by a local variation of the void fraction in the bed, leading to variation of the interstitial velocity (Wakao & Kaguei, 1982). In the case of cooling or heating agricultural products piled in a deep layer (Abid & Laguerrie, 1998; Baird & Ganey, 1976; Beurkema & Bruin 1982; Daudin, 1982), local variations in the heat transfer coecient are always neglected. These authors nevertheless use a deep layer approach that takes variations of air temperature and air humidity through the product layer into account, so they partially explain the heterogeneity of the heat treatment. The objective of this study was to obtain a better understanding of heat transfer phenomena during the cooling of fruit and vegetables packed in bins. We measured the heat transfer coecient for each object in a bin as a function of its position and of the upstream air velocity, then established a relationship between this local heat transfer coecient and the local air¯ow parameters, i.e. velocity and turbulence intensity. 2. Materials and methods 2.1. Experimental material The products were represented by 75 mm diameter PVC spheres. An experimental pallet was used containing 15 bins ®lled with 70 spheres as described in Part I. The heat transfer coecients were measured for each spherical object and for cylindrical objects placed amongst the packed spheres. 2.2. Heat transfer coecient measurements 2.2.1. Spherical probes (amongst spherical products) The measurement method consisted of replacing 15 PVC spheres in a bin with 15 aluminium spheres of the
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
241
same diameter. Each had a thermocouple ®tted at its centre. The bin was then placed in an oven to obtain a thermal stability of 60°C for the aluminium spheres. Finally, the bin was removed from the oven, set on the pallet and cooled by forced convection using dierent upstream air velocities: 0.6, 0.8 and 1.2 m/s. The sphere core temperature was then monitored and the heat transfer coecient calculated by the ``non-stationary method'' mentioned by Arce and Sweat (1980). As aluminium has a high thermal conductivity, the Biot number is lower than 0.1 and the thermal gradients inside the aluminium object could be neglected. Using a simple thermal balance, we can write: dT : 1 dt The temperature of the air reaching each sphere was measured with a thermocouple placed upstream the sphere. Except during the ®rst 5 min, which were not considered, the air temperature, Ta , was quite constant (less than 0.3°C variation). The heat transfer coecient could then be evaluated by linear regression (Fig. 1) according to the equation
hA T ÿ Ta qCpV
ln
T ÿ Ta 6h t ÿ t0 : ÿ T0 ÿ Ta qCpd
2
The heat ¯ux leaves the sphere primarily by convection. Conduction between spheres could be neglected as the metallic probes were only in contact with plastic spheres and the area in contact with each probe was negligible (see Fig. 2). As far as radiation is concerned, the measured heat transfer coecient, h, could be compared with an equivalent radiation transfer coecient: hr 4erT3 . The h values ranged from 25 (low
Fig. 1. Measurement of heat transfer coecient by the ``non steady method'' (Arce & Sweat, 1980).
Fig. 2. Measurement of local heat transfer coecients inside packed spheres using spherical probes (Alvarez, 1992).
velocity) to 100 W/m2 /°C, with a maximum hr value of about 1.7 W/m2 /°C (T 60°C, e: emissivity of polished aluminium 0.2, Stefan±Boltzmann constant r 5.67 ´ 10ÿ8 W/m2 /K4 ). In the worst case, i.e. if the temperature around the probe was close to air temperature and just at the start of cooling, the maximum error due to radiation was about 8%. Overall, with the errors in measuring temperature ( 0.1°C) and heat ¯ux, the error for the convection heat transfer coecient was about 6% (mean temperature of probe 40°C). To apply these results to food products, which eventually evaporate water, one needs to use the Chilton±Colburn analogy between heat transfer and humidity transfer through the boundary layer around the sphere (Alvarez & Trystram, 1995). If there is free water evaporation, an eective heat transfer coecient, heff , can be de®ned (Kuitche, Daudin & Letang, 1996 ) hr bDHv Ps ÿ Ph : heff h 1 h h Ts ÿ Th
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G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
2.2.2. Cylindrical probes (amongst spherical products) Fruit and vegetables come in several shapes and sizes, so it is not always possible to construct metallic probes with the same shape as the product. We asked ourselves whether it was possible to estimate local heat transfer coecients inside a bin of a given product using a probe with a dierent shape from that of the product. We therefore studied the results obtained with cylindrical probes placed inside a bin of spherical products (the previous plastic spheres). Although the absolute values of the heat transfer coecient obtained in this way need to be corrected, we can hope that the ratio between the highest and the lowest heat transfer coecient is virtually correct. The cylindrical probes were made of aluminium and were 25 mm in diameter and 100 mm in length. Each was equipped with a thermal resistance, allowing a constant heat ¯ux (510 W/m2 ) to be delivered. Axial conduction was limited by the length/diameter ratio, L/ D, which was 4, and by Te¯on insulators, as shown in Fig. 3. The former condition made it possible to regard the cylinder as an in®nite one. Measurements were taken using the stationary method of Nakayama, Kuwahara and Shigeki (1988), Lazis (1986) and Arce and Sweat (1980). Surface temperature was measured with four Copper-Constantan thermocouples located 1 mm below the probe surface and at 90° intervals around the circumference. The heat transfer coecient is de®ned by the following equation, where Ts is the average value of the four surface thermocouples. As the dierence between any two of them was always less than 0.5°C, the surface temperature could be considered as uniform. h
Fifteen cylindrical probes were inserted in the bed of packed plastic spheres at the places previously occupied by the spherical probes. The void fraction is known to have a major eect on heat transfer for packed beds (Gupta & Thodos, 1962; Gibert, 1968; Gruda & Kaseiczka, 1991), so we kept it the same as for the spherical probes (one removed sphere was the equivalent of three inserted cylinders). Once the bin had been equipped in this way (Fig. 4), it was placed on the pallet. The measurements were taken using ®ve upstream air velocities: 0.6, 0.8, 1.2, 1.8 and 2.3 m/s. 3. Results and discussion 3.1. Heat transfer heterogeneity The results for heat transfer heterogeneity are presented in this section and correspond to 540 runs using spherical thermal probes. The eect of four factors was studied: · upstream velocity: 0.6, 0.8 and 1.2 m/s; · position in height: 2 layers;
q=A : Ts ÿ Ta
The maximum surface temperature was about 40°C, so hr (the equivalent heat transfer coecient for radiation) was under 1.4 W/m2 /°C. The error for the heat transfer coecient, which ranged from 35 to 120 W/m2 / °C) was about 4%.
Fig. 3. Cylindrical probe for heat transfer coecient measurements using ``steady state method'' (Arce & Sweat, 1980).
Fig. 4. Measurement of local heat transfer coecients inside packed spheres using cylindrical probes (Alvarez, 1992).
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
· position in depth: 7 rows (air¯ow direction); · position in width: 5 lines. Each experiment was repeated three times. As expected, upstream air velocity had an important in¯uence on the mean heat transfer coecient for the whole bin. Nevertheless, the ratio between the local and the mean heat transfer coecient remained practically constant. The results for all upstream velocities can therefore be represented by way of a relative local heat transfer coecient compared to the mean value of the bin (see Fig. 5). An ANOVA statistical analysis (analysis of variance) was performed with a 99% con®dence level in order to compare heat transfer heterogeneity in the three directions (in¯uence of each position factor). There is no signi®cant dierence between the two layers of spheres (Fisher value: 0.03 < critical value at 99%: 4.70); both layers were cooled in the same way. The greatest heat transfer heterogeneity was found in the depth position of spheres (axial heterogeneity) (Fisher value: 614 > critical value at 99%: 3.02). There was a dierence of up to 40% in the heat transfer coef®cient between the ®rst and the sixth row for the same upstream air velocity (Fig. 5). The heat transfer coecient became constant after the fourth row. This thermal behaviour (reduction of heat transfer coecient with depth or row position) has also been observed in packed beds (Stanek & Vychodil, 1987) and in tubular heat exchangers (Stephan & Traub, 1987). A second heat transfer heterogeneity was found in the width position (radial heterogeneity) (Fisher value: 8.25 > critical value at 99%: 3.32). For the ®rst rows we observed experimentally that the heat transfer coecient was 10% lower near the side walls of the bin than in the part away from the walls (Fig. 5). These results were comparable with those obtained for packed beds by Dixon et al. (1984). The latter found that the heat transfer coecient was lower near the wall than in the part away from the walls and that the eect was particularly pronounced when the ratio of container to particle diameter (dc /dp ) was under 10. Considering that the velocity ratio (centre/wall) is 2 (or above), we could expect the dierences in the heat
Fig. 5. Ratio of local heat transfer coecient to mean transfer coecient. Heat transfer heterogeneity inside the bin (Alvarez, 1992).
243
transfer coecient to be larger than the values found experimentally. The in¯uence of velocity can, in fact, be compensated for by that of turbulence. For instance, in the corner of the bin there was a low velocity zone but also intense turbulence because of the back-mixing effect. This example shows how the thermal results can be explained by the aerodynamic behaviour detailed in Part I and in Alvarez (1992). 3.2. Relationship between local heat transfer coecient and local air¯ow characteristics Aerodynamic measurements inside the bin (detailed in Part I) were used to calculate the mean upstream velocity and mean air¯ow turbulence values in front of each sphere in the ®rst, third and ®fth rows. Mean velocity and turbulence for a given sphere were obtained using a number of the 48 measurements taken for each row, as shown in Fig. 6. A relationship was established between the local heat transfer coecient and the local air¯ow conditions (velocity and turbulence intensity). Fig. 7 shows a relative good agreement between this correlation and the experimental data. Nu 2 3:78 Re0:44 Tu0:33 Pr0:33 ; < 15 000 0:2 < Tu < 0:49:
4000 < Ret
We also compared our results (obtained inside a packed bed) with correlations obtained for a single sphere with or without taking account of the turbulence eect. The classical Fr ossling correlation underestimates the heat transfer coecient by over 200% as it does not
Fig. 6. Measurements grid for aerodynamical study on 48 points (6 points in vertical direction and 8 across the bin).
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G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
drical probes. In our case (dsphere 75 mm, dcylinder 25 mm) hsphere 0.6 hcylinder: Fig. 8 also represents the heat transfer coecient for a single sphere (d 75 mm) vs. the heat transfer coecient for single cylinder (d 25 mm). The Fr ossling and Hilpert correlations were used for the sphere and the cylinder respectively. The relationship is in good agreement with the results obtained inside a packed bed. 4. Conclusions
Fig. 7. Experimental relationship between Nusselt number vs. local Reynolds number (local velocity) and local turbulence intensity. Comparison between our relationship and literature correlations.
take into account the in¯uence of turbulence (which can reach 50% inside the bin). The correlation proposed by Lavender and Pei (1967) is in better agreement with our results. Thus in our case, if turbulence is taken into account, it would appear that a correlation obtained for a single object can be a good approximation for the relationship between local heat transfer and local air¯ow conditions in a packed bed. 3.3. Extrapolation of measurements of the heat transfer coecient using cylindrical probes Fig. 8 represents the heat transfer coecients measured using cylindrical and spherical probes at the same positions in the bin. It would appear that the local heat transfer coecient inside a packed bed of spheres can be extrapolated from the measurements made using cylin-
The present experimental study shows that heterogeneity of cooling can be explained not only by the increase in air temperature when air passes around the products, but also by the heat transfer coecient as a function of position. The heat transfer coecient in packed spheres changes principally in the direction of the air¯ow. It decreases by 40% between the ®rst and fourth row of spheres, then remains constant from the fourth row onwards. These changes are explained by aerodynamic behaviour inside the bin, i.e. the local velocities and turbulence intensities observed in the aerodynamic study and described in Part I. A quantitative relationship was established between the heat transfer coecient for each object and the local air¯ow parameters. Fruit and vegetables come in very dierent shapes. It would be interesting to estimate the mean value and the heterogeneity of the heat transfer coecient inside a bin ®lled with dierent products, using only one kind of probe. This study shows that local heat transfer coef®cients for spherical products can be estimated using cylindrical probes. Further work would be required to con®rm such an extrapolation for other product shapes. The method used could be applied to improve refrigeration equipment and product packaging. It would appear, for example, that alternating the air¯ow direction though the product would homogenise not only the air temperature but also the local intensity of heat transfer.
References
Fig. 8. Comparison between heat transfer coecient measured using spherical probes vs heat transfer coecient measured using cylindrical probes.
Abid, M. G. H., & Laguerrie, C. (1988). Analyse Experimentale et theorique des mecanismes de transfert de matiere et de chaleur au cours du sechage d'un grain de maõs en lit ¯uidise. ENTROPIE (139), 3±12. Arce, J., & Sweat, V. (1980). Survey of published heat transfer coecients encountered in food refrigeration process. Paper No. 2602. Trans. ASRHAE, 86(2), 235±260. Alvarez, G. (1992). Etude de transferts de chaleur et de mati ere au sein d'un echangeur complexe de type palette. These de Doctorat de l'ENGREF specialite Genie des procedes Agro-Alimentaires, Paris.
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245 Alvarez, G., & Trystram, G. (1995). Design of a new strategy for the control of the refrigeration process: fruit and vegetables conditioned in a pallet. Food Control, 6(6), 347. Baird, C. D., & Ganey, J. J. (1976). A numerical procedure for calculating heat transfer in bulk loads of fruits and vegetables. Trans. ASHRAE, 86(2), 525±540. Beurkema, K. J., & Bruin, S. (1982). Heat and mass transfer during cooling and storage of agricultural products. Chem. Engrg. Sci., 37(2), 291±298. Comings, E. W., Clapp, J. T., & Taylor, J. F. (1948). Air turbulence and transfer processes. Industrial and Engineering Chemistry, 40(6), 1076±1082. Daudin, J. D. (1982). Modelisation dÕun sechoir a partir des cinetiques experimentales de sechange, These de Docteur±Ingenieur, ENSIA. Dixon, A. G., Dicostanzo, A. M., & Soucy, B. A. (1984)). Fluid-phase radial transport in packed-beds of ¯ow tube to particle diameter ratio. Internat. J. Heat and Mass Transfer, 27(9), 1659±1669. De Wasch, A. P., & Froment, G. F. (1972). Heat transfer in packed bed. Chem. Engrg. Sci., 27, 567±576. Endho, K., Tsuruga, H., Hirano, H., & Morihira, M. (1972). Eect of turbulence on heat and mass transfer. Japanese Res., 1, 113±115. Gibert, H. (1968). Contribution a lÕetude de lÕadsorption en lit ¯uidise heterogene. Analogies entre les transferts en Genie Chimique. These Doctor-Ingenieur, Universite Paul Sabatier, Toulouse, France. Gruda, Z., & Kaseiczka, W. (1991). Eect of the process parameter on particle to air heat transfer coecient in ¯uidized and ®xed beds freezing. XVIII eme Congr es Internationale du Froid, Montreal, Paper No. 377, pp. 1±13. Gupta, A. S., & Thodos, G. (1962). Mass and heat transfer in the ¯ow of ¯uids through ®xed and ¯uidized beds of spherical particles. AICHE Journal, 8(5), 608±610. Kondjoyan, A. (1993). Contribution a la connaissance des coecients de transfert de chaleur et de mati ere a l'interface air-surface. These de Docteur de lÕEcole Nationale Superieure des Industries Agricoles et Agroalimentaires.
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Kuitche, A., Daudin, J. D., & Letang, G. (1996). Modelling of temperature and weight Loss Kinetics during Meat chilling for time-variable conditions using an analytical-based Method ± I. The Model and its sensitivity to certain Parameters. J. Food Engrg., 28, 55±84. Lazis, J. (1986). In¯uence de l'incidence et de la turbulence de l' ecoulement amont sur le transfert de chaleur d'un faisceau de tubes a ailettes h elicoidales. These de Doctorat de Troisieme cycle de l'Universite de Poitiers, ENSMA. Lavender, W. J., & Pei, D. C. T. (1967). Eect of ¯uid turbulence and the rate of heat transfer from spheres. Internat. J. Heat and Mass Transfer, 10, 529±539. Masiel, D. S., & Sherwood, T. K. (1950). Eet de la turbulence sur la vitesse dÕevaporation de lÕeau. Chem. Engrg. Process, 46(4), 172± 175. Morgan, V. T. (1975). The overall convection heat transfer from smooth circular cylinders. In Advances in Heat Transfer, 11, 199± 225. Nakayama, W., Kuwahara, H., & Shigeki, H. (1988). Heat transfer from tube bank to air/water mist ¯ow. Internat. J. Heat and Mass Transfer, 31(2), 449±460. Pei, D. C. T., & Hayward, G. (1983). Local heat transfer rate from adjacent spheres in turbulent ¯ow. Internat. J. Heat and Mass Transfe, 6(10), 1547±1556. Sparrow, E. W., & Yanezmoreno, A. A. (1983). Heat transfer in a tube bank in the presence of upstream cross-sectional enlargement. Internat. J. Heat and Mass Transfer, 26(12), 1791±1803. Stanek, V., & Vychodil, P. (1987). Mathematical model and assessment of thermal induced gas ¯ow inhomogeneities in ®xed beds. Chem. Engrg. Process, 22, 107±115. Stephan, K., & Traub, D. (1987). Ein¯u (von Rohrreihenzahl und Anstromturbulenz auf die W armeleistung von quer angestr omten Rohrb undeln. W arme und Sto ubertragung, 21, 103±113. Wakao N., & Kaguei, S. (1982). Heat and mass transfer in packed beds. New York: Gordon and Breach.
Analysis of heterogeneous cooling of agricultural products inside bins Part II: thermal study G. Alvarez *, D. Flick CEMAGREF Unit e de Recherche G enie des Proc ed es Frigori®ques, Parc de Tourvoie B.P. 44, 92185 Antony Cedex, France Received 15 September 1998; received in revised form 18 November 1998; accepted 18 November 1998
Abstract An experimental thermal study was performed in order to characterise heat transfer intensity for spherical objects packed in stacked bins and cooled by air forced convection. The heat transfer coecient was measured for each sphere in a test bin using spherical sensors. Large dierences in heat transfer coecient values, up to 40%, were observed. This heterogeneity could be explained by the fact that the air¯ow is not uniform (cf. Part I). Each object was exposed to local air¯ow conditions (mean velocity and turbulence). A correlation was established between the local heat transfer coecients and local air¯ow parameters. Cylindrical sensors were also constructed in order to measure the heat transfer coecient inside packed spheres. The measurements correlated well with the spherical sensors for the same positions in the bins. Ó 1999 Elsevier Science Ltd. All rights reserved. Keywords: Heat transfer coecient; Stacked bins; Chilling; Cooling; Agricultural products; Air forced convection; Local thermal heterogeneity; Heat transfer; Pallet
Symbols A Cp d e DHv h hr heff Tu L m Nu Nu0 Pa Ph Ps Pr q Re T t V v0 v *
area (m2 ) speci®c heat (J/kg K) diameter of object (m) emissivity latent heat of evaporation of water (J/kg) heat transfer coecient (W/m2 K) equivalent heat transfer coecient for radiation (W/ m2 K) q eective heat transfer coecient (W/m2 K) relative turbulence intensity Tu 100 v ÿ v2 =v length (m) slope of regression line for Eq. (1) Nusselt number hd=k Nusselt number when turbulence intensity present Tu 0 partial pressure of water vapour in air saturated water vapour pressure at wet bulb temperature Th (Pa ) water vapour pressure at product surface Prandtl number qCp=k heat power (W) Reynolds number qvd=l temperature (K) time (s) volume (m3 ) p instantaneous velocity Vx2 Vz2 mean air¯ow velocity
Corresponding author.; e-mail: [email protected]
x, y, z b e l q r
co-ordinates mass transfer coecient (kg/s m2 Pa) void fraction viscosity (Pa s) density (kg/m3 ) Stefan±Boltzmann constant (W/m2 /K4 )
Subscripts a c 0 r s t mean local
air convection initial radiation surface turbulent mean local
1. Introduction The temperature of agricultural products conditioned in bulk or in bins stacked on pallets is far from homogeneous for all the packed products during the cooling process. This can lead to a loss of quality in fresh fruits and vegetables. The heterogeneity of heat transfer is probably mainly due to the ¯ow heterogeneities described in Part I. The local velocity can be four times higher in one place than another at a given air¯ow rate. Local turbulence intensity varies from 20% to 50%. To
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 8 ) 0 0 1 6 6 - 6
240
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
understand heat transfer in stacked objects, three elements can be analysed: · the eect of velocity and turbulence on a single object; · local heat transfer in tubular exchangers; · local heat transfer in packed beds. Morgan (1975) and Kondjoyan (1993) have reviewed the eect of free stream velocity and turbulence on heat transfer for single cylinders and spheres. The correlations most commonly used in the absence of turbulence are those of Fr ossling for a sphere and Hilpert for cylinder. Fr ossling's correlation Nu0 2 0:6 Re0:5 Pr0:33 : Hilpert's correlation Nu0 0:615 Re0:466 ; Nu0 0:17 Re
0:618
;
40 < Re < 4000; 4000 < Re < 40 000:
The in¯uence of turbulence intensity cannot be neglected if it is above 1%. Comings et al. (1948), for instance, reported a rise of 25% in the Nusselt number when turbulence increased from 1% to 7%. Various corrections of the Nusselt number have been proposed, using either turbulence intensity (Tu) or a turbulent Reynolds number (Ret Re Tu). We will discuss only the correlations proposed by Lavender and Pei (1967) and Endho, Tsuruga, Hirano and Morihira (1972). The correlations proposed by Endho for single spheres and cylinders are similar, but the power factor of the turbulent Reynolds number is higher for the cylinder than for the sphere. The eect of turbulence thus appears to be slightly higher for single cylinders than for single spheres, as also reported by Maisel and Sherwood (1950). Spheres: Lavender and Pei Reÿ0:5 Pr0:33 ; Nu 2 0:145 Re0:25 t Nu 2 0:629
Reÿ0:5 Pr0:33 ; Re0:035 t
Ret > 1000; Ret < 1000:
Spheres: Endho Re0:5 Pr0:33 ; Nu Nu0 1 4:3 10ÿ6 Re0:78 t 400 < Ret < 8000; where Nu0 is calculated using the Fr ossling correlation Cylinders: Endho Nu Nu0 1 1:5 10ÿ6 Ret Re0:5 Pr0:33 400 < Ret < 8000; where Nu0 is calculated using the Hilpert correlation In our case there were important variations of local velocity and turbulence inside the bin, so we could expect heterogeneous heat transfer coecients. The results obtained for single objects could not be used directly, however, as heat transfer was in¯uenced by the proximity of the spheres inside the bin.
Pei and Hayward (1983) have shown that proximity between two spheres generates an interaction between their boundary layers and wakes. This phenomenon, called the blockage eect, strongly enhances heat transfer for two spheres next to one other. With tubular heat exchangers, the local heat transfer coecient depends on several parameters such as row position, arrangement, longitudinal pitch and transversal pitch. Sparrow and Yanezmoreno (1983) observed that the transfer coecient can fall to as low as 33% according to row position in the exchanger, while Stephan and Traub (1987) showed that the coecient could go up to 50% if free stream turbulence rose to 25%. With packed beds, heat transfer intensity also depends on position. Stanek and Vychodil (1987) and De Wasch and Froment (1972) observed that the heat transfer coecient also becomes lower in the air¯ow direction. Dixon, Dicostanzo and Soucy (1984) showed that the heat transfer coecient is low near container walls. This eect could be explained by a local variation of the void fraction in the bed, leading to variation of the interstitial velocity (Wakao & Kaguei, 1982). In the case of cooling or heating agricultural products piled in a deep layer (Abid & Laguerrie, 1998; Baird & Ganey, 1976; Beurkema & Bruin 1982; Daudin, 1982), local variations in the heat transfer coecient are always neglected. These authors nevertheless use a deep layer approach that takes variations of air temperature and air humidity through the product layer into account, so they partially explain the heterogeneity of the heat treatment. The objective of this study was to obtain a better understanding of heat transfer phenomena during the cooling of fruit and vegetables packed in bins. We measured the heat transfer coecient for each object in a bin as a function of its position and of the upstream air velocity, then established a relationship between this local heat transfer coecient and the local air¯ow parameters, i.e. velocity and turbulence intensity. 2. Materials and methods 2.1. Experimental material The products were represented by 75 mm diameter PVC spheres. An experimental pallet was used containing 15 bins ®lled with 70 spheres as described in Part I. The heat transfer coecients were measured for each spherical object and for cylindrical objects placed amongst the packed spheres. 2.2. Heat transfer coecient measurements 2.2.1. Spherical probes (amongst spherical products) The measurement method consisted of replacing 15 PVC spheres in a bin with 15 aluminium spheres of the
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
241
same diameter. Each had a thermocouple ®tted at its centre. The bin was then placed in an oven to obtain a thermal stability of 60°C for the aluminium spheres. Finally, the bin was removed from the oven, set on the pallet and cooled by forced convection using dierent upstream air velocities: 0.6, 0.8 and 1.2 m/s. The sphere core temperature was then monitored and the heat transfer coecient calculated by the ``non-stationary method'' mentioned by Arce and Sweat (1980). As aluminium has a high thermal conductivity, the Biot number is lower than 0.1 and the thermal gradients inside the aluminium object could be neglected. Using a simple thermal balance, we can write: dT : 1 dt The temperature of the air reaching each sphere was measured with a thermocouple placed upstream the sphere. Except during the ®rst 5 min, which were not considered, the air temperature, Ta , was quite constant (less than 0.3°C variation). The heat transfer coecient could then be evaluated by linear regression (Fig. 1) according to the equation
hA T ÿ Ta qCpV
ln
T ÿ Ta 6h t ÿ t0 : ÿ T0 ÿ Ta qCpd
2
The heat ¯ux leaves the sphere primarily by convection. Conduction between spheres could be neglected as the metallic probes were only in contact with plastic spheres and the area in contact with each probe was negligible (see Fig. 2). As far as radiation is concerned, the measured heat transfer coecient, h, could be compared with an equivalent radiation transfer coecient: hr 4erT3 . The h values ranged from 25 (low
Fig. 1. Measurement of heat transfer coecient by the ``non steady method'' (Arce & Sweat, 1980).
Fig. 2. Measurement of local heat transfer coecients inside packed spheres using spherical probes (Alvarez, 1992).
velocity) to 100 W/m2 /°C, with a maximum hr value of about 1.7 W/m2 /°C (T 60°C, e: emissivity of polished aluminium 0.2, Stefan±Boltzmann constant r 5.67 ´ 10ÿ8 W/m2 /K4 ). In the worst case, i.e. if the temperature around the probe was close to air temperature and just at the start of cooling, the maximum error due to radiation was about 8%. Overall, with the errors in measuring temperature ( 0.1°C) and heat ¯ux, the error for the convection heat transfer coecient was about 6% (mean temperature of probe 40°C). To apply these results to food products, which eventually evaporate water, one needs to use the Chilton±Colburn analogy between heat transfer and humidity transfer through the boundary layer around the sphere (Alvarez & Trystram, 1995). If there is free water evaporation, an eective heat transfer coecient, heff , can be de®ned (Kuitche, Daudin & Letang, 1996 ) hr bDHv Ps ÿ Ph : heff h 1 h h Ts ÿ Th
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G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
2.2.2. Cylindrical probes (amongst spherical products) Fruit and vegetables come in several shapes and sizes, so it is not always possible to construct metallic probes with the same shape as the product. We asked ourselves whether it was possible to estimate local heat transfer coecients inside a bin of a given product using a probe with a dierent shape from that of the product. We therefore studied the results obtained with cylindrical probes placed inside a bin of spherical products (the previous plastic spheres). Although the absolute values of the heat transfer coecient obtained in this way need to be corrected, we can hope that the ratio between the highest and the lowest heat transfer coecient is virtually correct. The cylindrical probes were made of aluminium and were 25 mm in diameter and 100 mm in length. Each was equipped with a thermal resistance, allowing a constant heat ¯ux (510 W/m2 ) to be delivered. Axial conduction was limited by the length/diameter ratio, L/ D, which was 4, and by Te¯on insulators, as shown in Fig. 3. The former condition made it possible to regard the cylinder as an in®nite one. Measurements were taken using the stationary method of Nakayama, Kuwahara and Shigeki (1988), Lazis (1986) and Arce and Sweat (1980). Surface temperature was measured with four Copper-Constantan thermocouples located 1 mm below the probe surface and at 90° intervals around the circumference. The heat transfer coecient is de®ned by the following equation, where Ts is the average value of the four surface thermocouples. As the dierence between any two of them was always less than 0.5°C, the surface temperature could be considered as uniform. h
Fifteen cylindrical probes were inserted in the bed of packed plastic spheres at the places previously occupied by the spherical probes. The void fraction is known to have a major eect on heat transfer for packed beds (Gupta & Thodos, 1962; Gibert, 1968; Gruda & Kaseiczka, 1991), so we kept it the same as for the spherical probes (one removed sphere was the equivalent of three inserted cylinders). Once the bin had been equipped in this way (Fig. 4), it was placed on the pallet. The measurements were taken using ®ve upstream air velocities: 0.6, 0.8, 1.2, 1.8 and 2.3 m/s. 3. Results and discussion 3.1. Heat transfer heterogeneity The results for heat transfer heterogeneity are presented in this section and correspond to 540 runs using spherical thermal probes. The eect of four factors was studied: · upstream velocity: 0.6, 0.8 and 1.2 m/s; · position in height: 2 layers;
q=A : Ts ÿ Ta
The maximum surface temperature was about 40°C, so hr (the equivalent heat transfer coecient for radiation) was under 1.4 W/m2 /°C. The error for the heat transfer coecient, which ranged from 35 to 120 W/m2 / °C) was about 4%.
Fig. 3. Cylindrical probe for heat transfer coecient measurements using ``steady state method'' (Arce & Sweat, 1980).
Fig. 4. Measurement of local heat transfer coecients inside packed spheres using cylindrical probes (Alvarez, 1992).
G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
· position in depth: 7 rows (air¯ow direction); · position in width: 5 lines. Each experiment was repeated three times. As expected, upstream air velocity had an important in¯uence on the mean heat transfer coecient for the whole bin. Nevertheless, the ratio between the local and the mean heat transfer coecient remained practically constant. The results for all upstream velocities can therefore be represented by way of a relative local heat transfer coecient compared to the mean value of the bin (see Fig. 5). An ANOVA statistical analysis (analysis of variance) was performed with a 99% con®dence level in order to compare heat transfer heterogeneity in the three directions (in¯uence of each position factor). There is no signi®cant dierence between the two layers of spheres (Fisher value: 0.03 < critical value at 99%: 4.70); both layers were cooled in the same way. The greatest heat transfer heterogeneity was found in the depth position of spheres (axial heterogeneity) (Fisher value: 614 > critical value at 99%: 3.02). There was a dierence of up to 40% in the heat transfer coef®cient between the ®rst and the sixth row for the same upstream air velocity (Fig. 5). The heat transfer coecient became constant after the fourth row. This thermal behaviour (reduction of heat transfer coecient with depth or row position) has also been observed in packed beds (Stanek & Vychodil, 1987) and in tubular heat exchangers (Stephan & Traub, 1987). A second heat transfer heterogeneity was found in the width position (radial heterogeneity) (Fisher value: 8.25 > critical value at 99%: 3.32). For the ®rst rows we observed experimentally that the heat transfer coecient was 10% lower near the side walls of the bin than in the part away from the walls (Fig. 5). These results were comparable with those obtained for packed beds by Dixon et al. (1984). The latter found that the heat transfer coecient was lower near the wall than in the part away from the walls and that the eect was particularly pronounced when the ratio of container to particle diameter (dc /dp ) was under 10. Considering that the velocity ratio (centre/wall) is 2 (or above), we could expect the dierences in the heat
Fig. 5. Ratio of local heat transfer coecient to mean transfer coecient. Heat transfer heterogeneity inside the bin (Alvarez, 1992).
243
transfer coecient to be larger than the values found experimentally. The in¯uence of velocity can, in fact, be compensated for by that of turbulence. For instance, in the corner of the bin there was a low velocity zone but also intense turbulence because of the back-mixing effect. This example shows how the thermal results can be explained by the aerodynamic behaviour detailed in Part I and in Alvarez (1992). 3.2. Relationship between local heat transfer coecient and local air¯ow characteristics Aerodynamic measurements inside the bin (detailed in Part I) were used to calculate the mean upstream velocity and mean air¯ow turbulence values in front of each sphere in the ®rst, third and ®fth rows. Mean velocity and turbulence for a given sphere were obtained using a number of the 48 measurements taken for each row, as shown in Fig. 6. A relationship was established between the local heat transfer coecient and the local air¯ow conditions (velocity and turbulence intensity). Fig. 7 shows a relative good agreement between this correlation and the experimental data. Nu 2 3:78 Re0:44 Tu0:33 Pr0:33 ; < 15 000 0:2 < Tu < 0:49:
4000 < Ret
We also compared our results (obtained inside a packed bed) with correlations obtained for a single sphere with or without taking account of the turbulence eect. The classical Fr ossling correlation underestimates the heat transfer coecient by over 200% as it does not
Fig. 6. Measurements grid for aerodynamical study on 48 points (6 points in vertical direction and 8 across the bin).
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G. Alvarez, D. Flick / Journal of Food Engineering 39 (1999) 239±245
drical probes. In our case (dsphere 75 mm, dcylinder 25 mm) hsphere 0.6 hcylinder: Fig. 8 also represents the heat transfer coecient for a single sphere (d 75 mm) vs. the heat transfer coecient for single cylinder (d 25 mm). The Fr ossling and Hilpert correlations were used for the sphere and the cylinder respectively. The relationship is in good agreement with the results obtained inside a packed bed. 4. Conclusions
Fig. 7. Experimental relationship between Nusselt number vs. local Reynolds number (local velocity) and local turbulence intensity. Comparison between our relationship and literature correlations.
take into account the in¯uence of turbulence (which can reach 50% inside the bin). The correlation proposed by Lavender and Pei (1967) is in better agreement with our results. Thus in our case, if turbulence is taken into account, it would appear that a correlation obtained for a single object can be a good approximation for the relationship between local heat transfer and local air¯ow conditions in a packed bed. 3.3. Extrapolation of measurements of the heat transfer coecient using cylindrical probes Fig. 8 represents the heat transfer coecients measured using cylindrical and spherical probes at the same positions in the bin. It would appear that the local heat transfer coecient inside a packed bed of spheres can be extrapolated from the measurements made using cylin-
The present experimental study shows that heterogeneity of cooling can be explained not only by the increase in air temperature when air passes around the products, but also by the heat transfer coecient as a function of position. The heat transfer coecient in packed spheres changes principally in the direction of the air¯ow. It decreases by 40% between the ®rst and fourth row of spheres, then remains constant from the fourth row onwards. These changes are explained by aerodynamic behaviour inside the bin, i.e. the local velocities and turbulence intensities observed in the aerodynamic study and described in Part I. A quantitative relationship was established between the heat transfer coecient for each object and the local air¯ow parameters. Fruit and vegetables come in very dierent shapes. It would be interesting to estimate the mean value and the heterogeneity of the heat transfer coecient inside a bin ®lled with dierent products, using only one kind of probe. This study shows that local heat transfer coef®cients for spherical products can be estimated using cylindrical probes. Further work would be required to con®rm such an extrapolation for other product shapes. The method used could be applied to improve refrigeration equipment and product packaging. It would appear, for example, that alternating the air¯ow direction though the product would homogenise not only the air temperature but also the local intensity of heat transfer.
References
Fig. 8. Comparison between heat transfer coecient measured using spherical probes vs heat transfer coecient measured using cylindrical probes.
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