便攜式動(dòng)物手術(shù)床的設(shè)計(jì)【說明書+CAD+SOLIDWORKS】,說明書+CAD+SOLIDWORKS,便攜式動(dòng)物手術(shù)床的設(shè)計(jì)【說明書+CAD+SOLIDWORKS】,便攜式,動(dòng)物,手術(shù)床,設(shè)計(jì),說明書,仿單,cad,solidworks Shrinkage of carrots during drying in an inert medium uidized bed M.S. Hatamipour * , D. Mowla Department of Chemical Engineering, Shiraz University, Shiraz, I.R. Iran Received 3 November 2001; accepted 4 March 2002 Abstract Agricultural food products and specially root vegetables undergo several physical and structural modications during the drying process. Shrinkage of root vegetables during drying is important not only from the viewpoint of material end-use but also for simulation problems. In this paper the shrinkage of root vegetables is studied in a pilot-scale, inert medium uidized bed dryer. Cylindrical carrot samples wereutilized as thetest media, providing simulantsfor high moisture contentfoodsystems. The eects of various parameters such as air temperature, air humidity, sample diameter, sample initial moisture content, existence of inert particles and air velocity were investigated. It was found that the shrinkage of root vegetables during drying in a uidized bed could be well correlated with moisture content of the sample during drying. Air velocity, temperature and presence of inerts did not show signicant eects on shrinkage in this system. C211 2002 Elsevier Science Ltd. All rights reserved. Keywords: Shrinkage; Fluidized bed drying; Inert medium uidized bed; Heat carrier 1. Introduction The drying process is one of the most important processes in food engineering. In most industrial pro- cesses at least one drying step exists, which means the removal of relatively small amounts of water or other liquid from the solid material to reduce the content of residual liquid to an acceptable low value. Simultaneous transfer of mass from the surface and heat to the surface and into the material, hydrodynamics of the movement of particles in the dryer, dierent mechanisms of mois- ture transport within the solid material, and shrinkage are some of problems associated with drying of foods. Various methods of drying have been developed for solids, and each method has its own characteristics. Considering the thermal eciencies of the equipment, uidized bed dryers are among the most ecient and are suitable for a variety of drying applications (Strumillo uni- form drying, core drying and semicore drying. In the uniform drying model, shrinkage is assumed to be equal to the volume of the water lost by evaporation, during all stages of drying. This model results in two equations, the rst requires equilibrium moisture content and bulk density, while the second requires the initial moisture Journal of Food Engineering 55 (2002) 247252 * Corresponding author. E-mail addresses: hatamishirazu.ac.ir (M.S. Hatamipour), dmowlashirazu.ac.ir (D. Mowla). 0260-8774/02/$ - see front matter C211 2002 Elsevier Science Ltd. All rights reserved. PII: S0260-8774(02)00082-1 content and the bulk density of the material. The core and semicore models both require the initial and equi- librium values for moisture content and bulk density. Lozano, Rotstein, and Urbicain (1983) developed two generalized correlations for prediction of water loss based on the bulk shrinkage coeeicient of fruits and vegetables. The rst correlation was established on the basis of foodstu composition and the second correla- tion, which was a modication of the rst one, was es- tablished for prediction of the nal bulk shrinkage coecient with only a knowledge of the initial moisture content of the sample. The latter model provided an adequate evaluation of their experimental data. Lang, Sokhansanj, and Rohani (1994) and Mulet (1994) used linear functions to relate shrinkage with the moisture content. Ratti (1994) proposed that the shrinkage charac- teristics of potatoes, apples and carrots are not only a function of moisture content, but also depend on the operating conditions and sample geometry. He reported that increasing of air velocity reduces the extent of apple and potato shrinkage signicantly; but air temperature, air humidity, and sample conguration render a negli- gible inuence. Madamba, Driscoll, and Buckle (1994) found that shrinkage of garlic during drying is ber oriented and dierent from the reported isotropic shrinkage of fruits and vegetables. They reported the power of the volume ratio as 0.448 instead of 2/3, which was reported earlier by Suzuki et al. (1976). Zogzas, Maroulis, and Marinous-Kouris (1994) re- ported independence of shrinkage characteristics on the temperature and humidity of drying air. Wang and Brennan (1995) reported a greater degree of potato shrinkage during low temperature air-drying. Sjoholm and Gekas (1995) correlated the volume changeofappleupondryinglinearlywithwatercontent. Achanta, Okos, Cushman, and Kessler (1997), based on a thermomechanical theory, studied the transport of moisture in shrinking food gels during drying. They concluded that for a long cylindrical gel, r=r 0 2 is a linear function of moisture content. McMinn and Magee (1997) reported a linear cor- relation for shrinkage with moisture content and air temperature during drying of cylindrical potato samples in a tunnel dryer. Park (1998) reported that shrinkage of material dur- ing drying is a linear function of linear dimension and moisture content. Zhou, Mowla, Wang, and Rudolph (1998) reported a linear relation for axial contraction and volume change of cylindrical carrots during the drying in a uidized bed with energy carriers. Hernandez, Pavon, and Garcia (2000) proposed a linear relation for shrinkage of foods as a function of moisture content. It is evident from the foregoing surveys that there is a strong relation between moisture content and physi- cal properties. However, it is recognized that the asso- ciated volume reduction does not always present a direct correlation with the amount of water evaporated. Rather, the shrinkage behaviour is dierent for various systems, dependent on the material type, the charac- teristic cell and tissue structure, and also operating conditions. This paper, which represents some of the results of an experimental investigation on drying of carrots in an inert medium uidized bed dryer, presents detailsfor the prediction of shrinkage behaviour of root vegetables during drying in uidized bed dryers. 2. Present work In this wok, which was designed for drying of agro- food products in a uidized bed dryer with some inert particles, carrot was chosen as the drying product to avoid seasonal availability problems; it is harvested throughout all the year, and its production and con- sumption are high. Samples were cut into cylinders with 86D612:5mmandL=DP5 fordrying. Thisvegetable has a natural moisture content about 90% and during drying it maintains its shape; although the size change originated by the great water loss during the process, cannot be ignored. A pilot-scale dryer was used for performing the dry- ing experiments. The schematic diagram of the experi- mental apparatus is shown in Fig. 1. The dryer was a Nomenclature A, A 0 , A 00 constants in Eqs. (1)(3) B, B 0 , B 00 constants in Eqs. (1)(3) D diameter of cylindrical carrot sample (mm) d diameter of inert material (mm) D 0 initial diameter of cylindrical carrot sample (mm) L length of cylindrical carrot sample (mm) L 0 initial length of cylindrical carrot sample (mm) V volume of cylindrical carrot sample (mm 3 ) V 0 initial volume of cylindrical carrot sample (mm 3 ) 248 M.S. Hatamipour, D. Mowla / Journal of Food Engineering 55 (2002) 247252 cylindrical Pyrex column equipped with a porous plate as air distributor. Drying air was supplied from a high- pressure air source. The pressure of drying air was reduced to a suitable pressure by using a pressure reg- ulator. Air was passed through a rotameter and then heated by a controlled electrical heater. A temperature controller was used for regulating the temperature of drying air; and the humidity was determined by mea- suring the dry and wet bulb temperatures of the drying air. Experiments were performed to obtain data for dry- ing curves with time. The operating variables were temperature and velocity of drying air, size and type of heat carrier, diameter of the drying sample, mass ratio of inert to drying sample, and drying time. The sample was suspended in the uidized bed. The rate of water loss from the sample was determined o- line. This was done by weighing the sample, with the holding string, on an electric balance placed next to the dryer. The accuracy of the weighing was C60.005 g. Temperature, weight loss, and dimension measurements were recorded simultaneously. 3. Results and discussion In order to show the eects of various parameters on the shrinkage of the carrot, several experiments were carried out under dierent operating conditions. These operating conditions are summarized in Table 1. For each experiment, the changes in V =V 0 , D=D 0 2 and L=L 0 were determined at various moisture contents (X). Analysis of experimental data revealed that changes in V =V 0 and D=D 0 2 during the drying of cylindrical carrotsamples,inauidizedbedwithinertheatcarriers, could be well correlated as linear functions of moisture content of the samples. Although the axial contraction, L=L 0 could be represented as a linear function of X,it can be better correlated as a logarithmic function of X. V =V 0 AX B 1 D=D 0 2 A 0 X B 0 2 L=L 0 A 00 lnXB 00 3 Dierent constants in the above equations were de- termined for various operating conditions and are summarizedinTable2alongwiththe R 2 parameter.The eects of various parameters on the shrinkage are out- lined as follows. 3.1. The eect of air temperature Referring to Table 1, the results of experiments nos. 2, 68 were used to analyse the eect of inlet air Table 1 Operating conditions for drying of carrots in a uidized bed of inert particles Exp. no. Air ow rate (l/min) Diameter of sample (mm) Length of sample (mm) Inlet air tem- perature (C176C) Diameter of inerts (mm) Type of inert Amount of inert (kg) 1 650 12.5 64.4 60 2.7 Glass 0.500 2 500 12.5 60 48 2.7 Glass 0.850 3 600 12.5 61.5 48 2.7 Glass 0.850 4 600 12.5 61.1 58 2.7 Glass 0.850 5 600 12.5 62.2 48 2.7 Glass 0.850 6 500 12.5 62.7 60 2.7 Glass 0.850 7 500 12.5 62.6 70 2.7 Glass 0.850 8 500 12.5 60.7 40 2.7 Glass 0.850 9 600 12.5 61 70 2.7 Glass 0.400 10 600 12.5 61.3 70 No inert 11 600 12.5 63.1 70 2.7 Glass 0.850 12 600 12.5 60.3 70 5 Glass 0.600 13 680 12.5 61.2 70 5 Glass 0.600 14 680 12.5 59.5 70 6.5 Glass 0.600 15 600 12.5 61.7 70 6.5 Glass 0.600 16 660 12.5 63.7 70 2.7 Glass 0.400 17 660 8 38.5 70 2.7 Glass 0.400 18 660 10.5 55.9 70 2.7 Glass 0.400 Fig. 1. Schematic diagram of the experimental apparatus. M.S. Hatamipour, D. Mowla / Journal of Food Engineering 55 (2002) 247252 249 temperature on V =V 0 . As can be seen from Table 2, there is no meaningful relation between the constants of Eq. (1) with temperature. Fig. 2 shows that air temper- ature does not aect the shrinkage of carrots. 3.2. The eect of sample diameter The results obtained in experiments nos. 1618 were used to analyse the eect of sample diameter on V =V 0 . As it can be seen, A is fairly constant and B decreases slightly with decreasing sample diameter, but Fig. 3 shows that samplediameter doesnothaveapronounced eect on shrinkage of cylindrical carrot samples. 3.3. The eect of presence of inert material For studying the eect of presence of inert mate- rial and also the eect of inert material diameter on V =V 0 , the results of experiments nos. 1012 and 15 were used. As can be seen in Fig. 4, the presence of inerts does not have any appreciable eect on shrinkage of carrots. The above discussion can also be extended for vari- ations of D=D 0 2 and L=L 0 with temperature, sample diameter and presence of inerts. The above analysis of the experimental data showed that shrinkage of carrots could be represented only as a linear function of X, without any dependency of the parameters on temperature, sample diameter, or inert material. In fact, the moisture content and its variation during drying, that is rate of drying, is the basic pa- rameter for determination of shrinkage. It was found in another part of this research that, the rate of drying increases with decreasing sample diameter, increasing the inert material thermal conductivity, and increasing air temperature, but the inert material diameter and air velocity have no signicant eects on the rate of drying. Also, it was found that the presence of inert particles enhances the rate of drying (Hatamipour & Mowla, in press). Figs. 5 and 6 show the eects of air velocity and sample diameter on drying rate, and Fig. 7 represents Table 2 Calculated values of constants for Eqs. (1)(3) Exp. no. V =V 0 (Eq. (1) D=D 0 2 (Eq. (2) L=L 0 (Eq. (3) ABR 2 A 0 B 0 R 2 A 00 B 00 R 2 6 0.0912 0.0858 0.9948 0.0841 0.1488 0.9927 0.0839 0.8170 0.9780 7 0.0934 0.0722 0.9962 0.0889 0.1232 0.9917 0.0848 0.8052 0.9861 8 0.0954 0.0567 0.9969 0.0906 0.1126 0.9945 0.1007 0.7719 0.9974 10 0.0969 0.0610 0.9954 0.0940 0.0971 0.9934 0.0777 0.8226 0.9913 11 0.0924 0.0438 0.9981 0.0867 0.0977 0.9963 0.1094 0.7653 0.9652 12 0.0947 0.0612 0.9982 0.0909 0.1059 0.9961 0.0776 0.8177 0.9678 15 0.0922 0.0820 0.9973 0.0875 0.1278 0.9961 0.0667 0.8503 0.9825 16 0.0891 0.1081 0.9975 0.0839 0.1582 0.9962 0.0755 0.8329 0.9897 17 0.0907 0.0987 0.9955 0.0829 0.1676 0.9945 0.0686 0.8458 0.9839 18 0.0910 0.1057 0.9947 0.0846 0.1702 0.9915 0.0969 0.8384 0.9908 Fig. 2. Eect of inlet air temperature on shrinkage of carrots. Fig. 3. Eect of sample diameter on shrinkage of carrots. Fig. 4. Eect of presence of inerts and inert material diameter on shrinkage of carrots. 250 M.S. Hatamipour, D. Mowla / Journal of Food Engineering 55 (2002) 247252 drying curve for 12.5 mm carrots, showing the eects of presence of inert material and inert type. Therefore, it can be concluded that the eects of air temperature, sample diameter and presence of inerts have been reected in drying rate. Fig. 8 shows the eect of drying rate on shrinkage at various temperatures. It must be noted that air humidity has a decisive in- uence on the rate of drying, that is, the velocity at which water leaves the solid matrix. Should it be rela- tively high at the beginning, it should provoke the so called case hardening, that is the hardening of the outer surface, reducing in turn the further rate of drying and consequently the volume reduction. Oppositely, a soft drying would lead to a more light deformation. In general, the whole cellular structure behaves dierent according to the velocity at which water leaves the cell. 4. Conclusion BasedonEq.(1)andthegiven valuesinTable2for A and B, several equations were obtained for V =V 0 .By plotting all of the equations on a single graph and comparing the values of constants in Table 2, it can be seen that the calculated values of the constants are close to each other and thus the average value of each con- stant can be used. Similarly, average constants can be used for equations obtained for D=D 0 2 and L=L 0 . Therefore, the following correlations can be used for the calculation of V =V 0 , D=D 0 2 and L=L 0 : V =V 0 0:0927X 0:07752 4 D=D 0 2 0:08741X 0:13091 5 L=L 0 0:08145lnX0:81671 6 Fig. 5. Eect of air velocity on drying rate (exp. 7, 11, 12, 13, 14, 15). Fig. 6. The eect of sample diameter on drying rate (exp. 16, 17, 18). Fig. 7. Drying curve for carrot (d p 2:7 mm, glass, T air 70 C176C, D s 12:5 mm, U air 2:36 m/s). Fig. 8. The eect of drying rate and air temperature on shrinkage. Fig. 9. Comparison of proposed correlation for V =V 0 with experi- mental data. M.S. Hatamipour, D. Mowla / Journal of Food Engineering 55 (2002) 247252 251 Figs 911 show a comparison of correlations (4)(6) with another sets of experimental data. The good agree- ments show the validity of the proposed correlations. Table 3 shows the maximum and average percent errors originated from the use of the correlations (4)(6), in- stead of the original correlations with values given in Table 2. References Achanta, S., Okos, M. R., Cushman, J. H., & Kessler, D. P. (1997). Moisture transport in shrinking gels during saturated drying. AIChE J., 43, 21122122. Hatamipour,M.S.,&Mowla,D.Experimentalinvestigationofdrying of carrots in a uidized bed with energy carrier, in press. Hernandez, J. A., Pavon, G., & Garcia, M. A. (2000). Analytical so- lutionofmasstransferequationconsideringshrinkageformodeling food-drying kinetics. J. Food Eng., 45, 110. Kilpatrick, P. W., Lowe, E., & Van Arsdel, W. B. (1955). Tunnel dehydrators for fruit and vegetables. In W. B. Van Arsdel (Ed.), Advances in Food Research, Vol. 6 (pp. 313372). New York: Academic Press. Lang, W., Sokhansanj, S., & Rohani, S. (1994). Dynamic shrinkage and variable parameters in BakkerArkemas mathematical simu- lationsofwheatandcanoladrying. Drying Tech., 12(7),16871708. Lozano, J. E., Rotstein, E., & Urbicain, M. J. (1983). Shrinkage, porosity and bulk density of foodstus at changing moisture contents. J. Food Sci., 48, 14971502. Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1994). Shrinkage, density and porosity of garlic during drying. J. Food Eng., 23, 309 319. McMinn,W.A.M.,&Magee,T. R.A.(1997).Physicalcharacteristics of dehydrated potatoes-Part I. J. Food Eng., 33, 3748. Mulet, A. (1994). Drying modeling and water diusivity in carrots and potatoes. J. Food Eng., 22, 329348. Park, K. J. (1998). Diusion model with and without shrinkage during salted sh muscle drying. Drying Tech., 16(35), 889905. Ratti, C. (1994). Shrinkage during drying of foodstus. J. Food Eng., 23, 91105. Sjoholm,I., & Gekas,V. (1995).Appleshrinkageupondrying. J. Food Eng., 25, 123130. Strumillo, C., & Kudra, T. (1996). Drying: principles, applications, and design. USA: Gordon & Breach Science Publishers. Suzuki, K., Kiyoshi, K., Hasegawa, T., & Hosaka, H. (1976). Shrinkage in dehydration of root vegetables. J. Food Sci., 41, 11891193. Wang, N., & Brennan, J. G. (1995). Changes in structure, density and porosity of potato during dehydration. J. Food Eng., 24, 6176. Zhou, S.J., Mowla, D., Wang, F.Y., & Rudolph, V. (1998). Experi- mental investigation of food drying processes in dense phase uidized bed with energy carrier. CHEMECA 98, port Doulas, North Queenslands, Australia. Zogzas, N. P., Maroulis, Z. B., & Marinous-Kouris, D. (1994). Densities, shrinkage and porosity of some vegetables during air drying. Drying Technol., 12(7), 16531666. Fig. 10. Comparison of proposed correlation for D=D 0 2 with experi- mental data. Fig. 11. Comparison of proposed correlation for L=L 0 with experi- mental data. Table 3 Maximum absolute error of Eqs. (4)(6) Error Exp. no. 6781011215161718 Absolute error of Eq. (4) (%) Max 0.798 0.518 2.0028 2.548 3.672 1.592 0.438 2.986 2.078 2.784 Avg. 0.395 0.228 0.895 1.140 3.52 0.713 0.205 1.36 1.11 1.97 Absolute error of Eq. (5) (%) Max 1.72 0.7412 1.76 3.25 4.031 2.43 0.309 2.66 3.58 3.87 Avg. 0.87 0.39 0.85 1.72 3.67 1.06 0.266 1.017 1.60 2.52 Absolute error of Eq. (6) (%) Max 0.593 1.69 7.58 1.19 9.64 0.787 5.73 2.57 4.98 4.07 Avg. 0.39 0.722 2.02 0.27 2.12 0.506 1.47 0.858 1.27 0.897 252 M.S. Hatamipour, D. Mowla / Journal of Food Engineering 55 (2002) 247252