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Correlations for shrinkage, density and diffusivity for drying of maize and green peas in a fluidized bed with energy carrier
Journal of Food Engineering 59 (2003) 221–227 www.elsevier.com/locate/jfoodeng
Correlations for shrinkage, density and diffusivity for drying of maize and green peas in a fluidized bed with energy carrier M.S. Hatamipour a
a,*
, D. Mowla
b
Department of Chemical Engineering, Isfahan University, Isfahan, Iran Department of Chemical Engineering, Shiraz University, Shiraz, Iran
b
Received 2 September 2002; accepted 19 November 2002
Abstract Drying behavior of maize and green peas investigated in a pilot scale fluidized bed dryer with inert energy carriers. The variations of drying material density, size and mass diffusivity with change of moisture content were investigated. It was found that, air temperature, inert material, and air velocity had no significant effect on physical properties and therefore, shrinkage and density are only functions of moisture content, but diffusivity is a function of temperature and moisture content. Based on the experimental data obtained, some correlations were developed for variation of shrinkage, density and diffusivity of green peas and maize during drying in a fluidized bed with inert particles. The shrinkage, density and moisture diffusivity of green peas and maize could be predicted by an average accuracy of 98% by use of proposed correlations. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Fluidized drying; Diffusivity; Shrinkage; Inert material; Density; Green peas; Maize
1. Introduction Simulation of drying behavior of agricultural products is an important task in food engineering. Production of corns such as maize has a great economic importance due to the large quantity of starch, corn syrup, ethanol, oil, chemicals and other products which could be produced from it. Maize and some other corns are characterized by a high initial moisture content at harvest. Hence drying becomes an essential operation before storage. Drying is a difficult task due to the variation in harvest moisture, deterioration of corn quality, the environmental, health and safety regulations and the need of energy savings. In addition hydrodynamics of the movement of particles in the dryer, different mechanisms of moisture transport within the solid material, and shrinkage are some of other problems associated with drying of foodstuffs. Considering the thermal efficiencies of the equipment, fluidized bed dryers are among the most efficient (Strumillo & Kudra, 1996). Use of these dryers for drying of maize is very
*
Corresponding author. E-mail addresses: [email protected] [email protected] (D. Mowla).
(M.S.
Hatamipour),
common today. Improving the rate of heat transfer can provide significant benefits to the drying process. Use of inert particles is one of the proposed methods for improving the drying process. This subject has been of special interest during recent decades, from which the works of Abid, Gibert, and Laguerie (1990); Chancellor (1968); Cobbinah, Laguerie, and Gibert (1987); Grabowski, Mujumdar, Ramaswamy, and Strumillo (1994); Jariwara and Hoelscher (1970); Kirkwood and Olson (1986); Lee and Kim (1993, 1999); Taracatac, Flores, and Chaudhry (1985); Zhou, Mowla, Wang, and Rudolph (1998), are of interest. The objectives of this work were to determine the changes of density, shrinkage and mass diffusivity of green peas and maize in a fluidized bed with and without inert particles, and proposing correlations for them.
2. Materials and procedure 2.1. Materials In this work, green peas and maize were chosen as the drying materials. These vegetables have natural moisture contents about 75% and during drying they
0260-8774/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0260-8774(02)00461-2
222
M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227
Nomenclature A B a b d d0 D R t Ta
parameter in Eq. (1) constant in Eq. (1) parameter in Eq. (4) constant in Eq. (4) drying solid diameter (m) initial solid diameter (m) diffusivity (m2 /h) outer radius of solid to be dried (m) time (s) air temperature (K)
maintain their shape; although the size change deriving from the great water loss during the process, cannot be ignored. In order to ensure reproducible results, all peas and maize were obtained from a single region and kept in a refrigerator at 4 °C until required. Several measurements of the spherical dimensions were made using a micrometer and only samples within a 5% tolerance of the average dimensions were used. In each run, the final volume of dried sample was determined by immersing it in toluene and measuring the volume change. 2.2. Drying apparatus A pilot-scale fluidized bed dryer with inert particles was set up for performing the drying experiments. The schematic diagram of the experimental apparatus is shown in Fig. 1. The dryer was a 77 mm cylindrical Pyrex column equipped with a porous plate as an air distributor. Drying air was supplied from a high-pressure air source and a pressure regulator adjusted its pressure. Air was passed through a rotameter and then heated by a controlled electrical heater. A temperature controller was used for regulating the temperature of
X X0 X Xe qs
moisture content of drying solid (kg/kg, dry basis) initial moisture content of drying solid (kg/ kg, dry basis) average moisture content of drying solid (kg/ kg, dry basis) equilibrium moisture content (kg/kg, dry basis) density of drying material (kg/m3 )
drying air within 1 °C; and the humidity was determined by measuring the dry and wet bulb temperatures of the drying air. The sample was hung in the fluidized bed by means of a light string so that the sample could move freely with the inert particles. The rate of water loss from the sample was determined off-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 0.005 g. The weighting procedure took no more than 10 s after removing the sample out from the column. It has been demonstrated by previous researchers that this method is sufficiently accurate for generating reproducible drying curves (Ajibola, 1989; Suarez, Violaz, & Chirife, 1985; Zhou et al., 1998). Measurements of temperature, weight loss, and diameter were recorded simultaneously. The initial moisture content of the samples was determined by drying in an electrical oven at 105–110 °C for 24 h (AOAC, 1990). The operating variables were drying air temperature, moisture content, size of heat carrier, type of heat carrier, diameter of the drying solid, velocity of drying air, mass ratio of inert material to drying solids, and drying time.
Fig. 1. Schematic diagram of the experimental apparatus.
M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227
223
Table 1 The operating conditions for drying of green peas in a fluidized bed of inert particles Exp. #
Air flow rate (l/min)
Avg. diameter of sample (mm)
Inlet air temp. (°C)
Diameter of inerts (mm)
Type of inert
Amount of inert (kg)
GP1 GP2 GP3 GP4 GP5 GP6 GP7 GP8 GP9 GP10 GP11
600 600 750 600 600 600 600 600 600 600 700
10.5 10.4 10.5 8.5 8.6 7.4 8.3 7.6 8.1 8.6 8.3
60 60 60 70 60 40 70 60 60 60 26
2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 – 2.7
Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Without inert Steel balls
400 600 400 400 400 400 400 400 250 – 250
In order to show the effect of various parameters on drying of green peas and maize and obtaining the desired correlations, several sets of experiments were performed as follows. Each experiment was done at least twice and the maximum tolerance between duplicate runs was 2%. (1) Experiments with a specific inert material at constant temperature and sample diameter at various air velocities. (2) Experiments with a specific inert material at constant air velocity and various temperatures. (3) Experiments at constant temperature, velocity and sample diameter with various inert material diameters. (4) Experiments at constant temperature, air velocity, sample diameter and inert material diameter but with various inert materials. (5) Experiments at constant temperature, air velocity, inert material diameter, inert material, but with various sample diameters. The operating conditions are summarized in Tables 1 and 2. Considering the obtained experimental data, the variations of shrinkage, density and diffusivity with change of moisture content, could be obtained.
3. Results and discussion 3.1. Determination of shrinkage Figs. 2–5 show the effects of air velocity, amount of inert and air temperature on drying curve of green peas and maize. It can be found that air temperature is the main factor that has significant effect on drying curve. The variation of ðd=d0 Þ of green peas and maize with change of moisture content was plotted at various air temperatures. It was found that the overall trend of the
Fig. 2. Effect of air velocity on drying curve of green peas (Exp. GP1, GP3).
Table 2 The operating conditions for drying of maize in a fluidized bed of inert particles (for 400 g of glass beds with 2.7 mm diameter and 600 l/min air flow rate) Exp. #
Avg. diameter of sample (mm)
Inlet air temp. (°C)
M1 M2 M3 M4 M5 M6
9.3 8.3 8.0 9.0 8.7 9.2
70 70 40 60 60 40
Fig. 3. Effect of amount of inert on drying curve of green peas (Exp. GP1, GP2).
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Fig. 4. Effect of air temperature on drying curve of green peas. (Exp. GP4, GP5, GP6).
Fig. 6. Comparison of experimental and calculated shrinkage data for green peas.
Fig. 5. Effect of air temperature on drying curve of maize (M1, M3, M5).
Fig. 7. Comparison of experimental and calculated shrinkage data for maize.
function is linear. Therefore, at first glance it can be concluded that d ¼ AX þ B d0
ð1Þ
The values of parameters A and B were obtained for each temperature by non-linear regression, and are given in Table 3. No meaningful relations were found for values of A and B with temperature. Therefore it can be found that temperature has no significant effect on shrinkage and the average values of calculated values A and B were selected as the desired parameters. This finding is consistent with our previous finding on shrinkage of carrot (Hatamipour & Mowla, 2002). The comparison between the calculated and experimental values show that the maximum absolute deviation between the calculated and experimental values of d=d0 is about 2.5% and the average absolute deviation is about 1.2%. So the following correlations could be proposed d ¼ 0:094X þ 0:7491 d0
ð2Þ
for green peas
d ¼ 0:1355X þ 0:696 d0
ð3Þ
for maize
Figs. 6 and 7 show the comparison of the results obtained from Eqs. (2) and (3) and other sets of experimental data. The good agreement confirms the validity of the obtained correlations for shrinkages of green peas and maize during drying. 3.2. Determination of density The experimental values of densities of green peas and maize during drying were plotted against moisture content. Density of green peas––unlike many other foods––was decreased with decreasing moisture content. The experimental values were obtained by dividing the mass of a single sample to its measured volume. Measurement of the final volume of the sample in toluene was a good check for volume calculations. The trend lines determine the general form of density correlations as follows:
Table 3 The calculated values of A and B (Eq. (1)) for various temperatures T ¼ 40 °C Green peas Maize
T ¼ 60 °C
T ¼ 70 °C
A
B
R2
A
B
R2
A
B
R2
0.0941 0.1560
0.7596 0.6580
0.9778 0.9713
0.1036 0.1387
0.723 0.7036
0.9784 0.9884
0.0844 0.1421
0.7647 0.6711
0.9821 0.9725
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Table 4 The calculated values of a and b (Eq. (4)) for various temperatures T ¼ 40 °C Green peas Maize
qs ¼ a
X X0
T ¼ 60 °C 2
T ¼ 70 °C 2
a
b
R
A
b
R
a
b
R2
1.0297 1.057
0.1584 )0.0467
0.978 0.977
1.0272 1.0575
0.1711 )0.0535
0.985 0.987
1.0556 1.0536
0.168 )0.0456
0.988 0.977
b ð4Þ
The values of parameters a and b are obtained for each temperature by non-linear regression, and are given in Table 4. No meaningful relations were found for values of a and b with temperature. Therefore it can be found that temperature has no significant effect on density and the average values of calculated values a and b were selected as the desired parameters. The comparison between the calculated and experimental values show that the maximum absolute deviation between the calculated and experimental values of density is about 2.5% and the average absolute deviation is about 1.2%. Therefore the following correlations could be proposed 0:1585 X qs ¼ 1030 for green peas ð5Þ X0
X qs ¼ 1060 X0
0:048 ð6Þ
for maize
The experimental data can also be fitted to the model proposed by Lozano, Rotstein, and Urbicain (1983) as follows: q ¼ 1138:3 34:270X 573:1eX
for green peas
ð7Þ
q ¼ 1000:0 þ 14:556X þ 217:2eX
for maize
ð8Þ
The maximum absolute error occurred when using Eq. (7) was 5% with an average absolute error of 1.98%. These values for Eq. (8) are 1.25% and 0.41%. Figs. 8 and 9 show comparison of calculated values of density based on correlations (5)–(8) and other sets of experimental data.
Fig. 8. Comparison of calculated and experimental values of density for green peas.
Fig. 9. Comparison of calculated and experimental values of density for maize.
3.3. Determination of moisture diffusivity Moisture diffusivity of green peas and maize dried at 40, 60 and 70 °C was calculated by the well-known method of slopes (Karatanos, Villalobos, & Saravacos, 1990; Medeiros & Sereno, 1994; Perry & Green, 1984). In this method, first the theoretical moisture ratio (W ), is evaluated numerically for a range of Fourier numbers Fo ðFo ¼ Deff t=R2 Þ. Then the same ratio is evaluated using experimental data. Both curves of experimental and theoretical moisture ratio (W ), are plotted versus time and Fourier number, respectively, on a semi-logarithmic diagram as shown in Fig. 10. For spherical particles the solution of FickÕs equation for idealized initial and boundary conditions can be written as (Crank, 1975) W ¼
1 X Xe 6 X 1 ¼ 2 expðn2 p2 F0 Þ X0 Xe p n¼1 n2
ð9Þ
By comparing the slopes of the theoretical and experimental drying curves (Fig. 10), at a specified moisture
Fig. 10. Method of slopes, example for the evaluation of moisture diffusivity.
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M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227 Table 5 Comparison between the experimental and calculated values of moisture diffusivity of green peas
Fig. 11. Effective diffusivity of green peas as a function of temperature and moisture content.
T (°C)
X (kg/kg d.b.)
Dexp
Dcal
% Deviation
70.0000 70.0000 70.0000 70.0000 70.0000 70.0000 60.0000 60.0000 60.0000 60.0000 60.0000 40.0000 40.0000 40.0000 40.0000
1.6250 1.4242 1.0979 0.7249 0.3986 0.0720 1.4560 1.2200 0.9360 0.7470 0.0862 1.7727 1.6364 1.5000 1.1818
7.0850 6.8998 6.3001 5.9820 5.6719 5.5060 5.7679 5.0871 4.8773 4.5376 4.3614 3.5821 3.3217 3.1397 3.0032
7.1408 6.8759 6.4661 6.0276 5.6684 5.3303 5.4302 5.1941 4.9237 4.7515 4.1956 3.3910 3.3050 3.2213 3.0339
)0.788E þ 00 0.346E þ 00 )0.263E þ 01 )0.763E þ 00 0.617E ) 01 0.319E þ 01 0.586E þ 01 )0.210E þ 01 )0.950E þ 00 )0.472E þ 01 0.380Eþ01 0.533Eþ01 0.500Eþ00 )0.260Eþ01 )0.102Eþ01
Table 6 Comparison between the experimental and calculated values of moisture diffusivity of maize
Fig. 12. Effective diffusivity of maize as a function of temperature and moisture content.
content, diffusivity can be evaluated from (Perry & Green, 1984) dX D¼
dt dX dF0
exp R2
ð10Þ
theo
Plots of effective moisture diffusivity versus moisture content for green peas and maize at three different temperatures are presented in Figs. 11 and 12, respectively. Since the method of slopes is valid for the linear portion of the above mentioned semi-logarithmic plot (i.e. W < 0:6), and by knowing that moisture diffusivity decreases by decreasing moisture content, it can be assumed that moisture diffusivity for W > 0:6 could be estimated by extrapolating the linear portion of the curve. Therefore, the following correlation could be obtained for moisture diffusivity of green peas and maize by non-linear regression analysis of experimental data 2764:6 D 106 ¼ exp 9:7198 þ 0:18829X T for green peas 5033:2 6 D 10 ¼ exp 14:845 þ 0:3546X T for maize
ð11Þ
ð12Þ
Tables 5 and 6 show the percent deviation between experimental and calculated values of diffusivities at
T (°C)
X (kg/kg d.b.)
Dexp
Dcal
% Deviation
70.0000 70.0000 70.0000 70.0000 70.0000 70.0000 60.0000 60.0000 60.0000 60.0000 60.0000 40.0000 40.0000 40.0000 40.0000
1.6588 1.4403 1.1853 0.9668 0.7847 0.6754 1.8205 1.6068 1.2650 1.0513 0.9658 2.1000 2.0230 1.6357 1.4421
2.1498 2.0035 1.8471 1.7117 1.5532 1.4837 1.4371 1.3458 1.2253 1.1002 1.0206 0.6011 0.5821 0.5269 0.5091
2.1362 1.9769 1.8061 1.6714 1.5669 1.5073 1.4560 1.3498 1.1957 1.1084 1.0753 0.6120 0.5956 0.5191 0.4847
0.631Eþ00 0.133Eþ01 0.222Eþ01 0.235Eþ01 )0.880Eþ00 )0.159Eþ01 )0.132Eþ01 )0.297Eþ00 0.241Eþ01 )0.749Eþ00 )0.537Eþ01 )0.183Eþ01 )0.232Eþ01 0.147Eþ01 0.479Eþ01
various temperatures and moisture contents. As it can be seen, for green peas the maximum absolute deviation is 6.17% and average absolute deviation is 2.3%. These values for maize are 5.37% and 1.97%, respectively. The obtained diffusivities are consistent with the results of Medeiros and Sereno (1994).
4. Conclusion All of the above-mentioned figures show a good agreement between the experimental data and calculated values of different parameters obtained by the proposed correlations. This means that shrinkage and density of green peas and maize during drying in a fluidized bed with inert particles depend only on its moisture content, but diffusivity is dependent on temperature and moisture content. The diffusivities of moisture in maize at various temperatures were lower than those of green peas, and
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this can be related to the difference in case hardening behavior and the physical structures of these materials. References Abid, M., Gibert, R., & Laguerie, C. (1990). An experimental and theoretical analysis of the mechanisms of heat and mass transfer during the drying of corn grains in a fluidized bed. International Chemical Engineering, 30, 632–642. AOAC (1990). Official methods of analysis, Method No. 934.06. Washington DC: Association of Official Chemists. Ajibola, O. O. (1989). Thin-layer drying of melon seed. Journal of Food Engineering, 9, 305–320. Chancellor, W. J. (1968). Transactions of ASAE, 11, 857–867. Cobbinah, S., Laguerie, C., & Gibert, H. (1987). Simultaneous heat and mass transfer between a fluidized bed of fine particles and immersed coarse porous particles. International Journal of Heat Mass Transfer, 30(2), 395–400. Crank, J. (1975). The mathematics of diffusion (2nd ed). London: Oxford University Press. Grabowski, S., Mujumdar, A. S., Ramaswamy, H. S., & Strumillo, C. (1994). Osmo-convective drying of grapes. Drying Technology, 12(5), 1211–1219. Hatamipour, M. S., & Mowla, D. (2002). Shrinkage of carrots during drying in an inert medium fluidized bed. Journal of Food Engineering, 55(3), 247–252. Jariwara, S. L., & Hoelscher, H. E. (1970). Model for oxidative thermal decomposition of starch in a fluidized reactor. Industrial & Engineering Chemistry, 9, 278–284.
227
Karatanos, V. T., Villalobos, G., & Saravacos, G. D. (1990). Comparison of two methods of estimation of the effective moisture diffusivity from drying data. Journal of Food Science, 55(1), 218– 223,231. Kirkwood, M. K., & Olson, K. E. (1986). Enzyme drying process. U.S. patent 4,617,272. Lee, D. H., & Kim, S. D. (1993). Drying characteristics of starch in an inert medium fluidized bed. Chemical Engineering Technology, 16, 263–269. Lee, D. H., & Kim, S. D. (1999). Mathematical model for batch drying in an inert medium fluidized bed. Chemical Engineering Technology, 22, 443–450. Lozano, J. E., Rotstein, E., & Urbicain, M. J. (1983). Shrinkage, porosity and bulk density at changing moisture contents. Journal of Food Science, 48, 1497–1502. Medeiros, C. L., & Sereno, A. (1994). Physical and transport properties of peas during warm air drying. Journal of Food Engineering, 21, 355–363. Perry, R. H., & Green, D. W. (1984). PerryÕs chemical engineersÕ handbook (6th ed). New York: McGraw-Hill. Suarez, C., Violaz, P. E., & Chirife, J. (1985). Diffusion analysis of air drying of grain sorghum. Journal of Food Technology, 15, 523–531. Strumillo, C., & Kudra, T. (1996). Drying: Principles, applications, and design. USA: Gordon & Breach Science Publishers. Taracatac, C. A., Flores, L., & Chaudhry, V. (1985). Gel tableting agent. U.S. patent 4,495,177. Zhou, S. J., Mowla, D., Wang, F. Y., & Rudolph, V. (1998). Experimental investigation of food drying processes in dense phase fluidized bed with energy carrier. CHEMECA 98, Port Douglas, North Queenslands, Australia.
Correlations for shrinkage, density and diffusivity for drying of maize and green peas in a fluidized bed with energy carrier M.S. Hatamipour a
a,*
, D. Mowla
b
Department of Chemical Engineering, Isfahan University, Isfahan, Iran Department of Chemical Engineering, Shiraz University, Shiraz, Iran
b
Received 2 September 2002; accepted 19 November 2002
Abstract Drying behavior of maize and green peas investigated in a pilot scale fluidized bed dryer with inert energy carriers. The variations of drying material density, size and mass diffusivity with change of moisture content were investigated. It was found that, air temperature, inert material, and air velocity had no significant effect on physical properties and therefore, shrinkage and density are only functions of moisture content, but diffusivity is a function of temperature and moisture content. Based on the experimental data obtained, some correlations were developed for variation of shrinkage, density and diffusivity of green peas and maize during drying in a fluidized bed with inert particles. The shrinkage, density and moisture diffusivity of green peas and maize could be predicted by an average accuracy of 98% by use of proposed correlations. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Fluidized drying; Diffusivity; Shrinkage; Inert material; Density; Green peas; Maize
1. Introduction Simulation of drying behavior of agricultural products is an important task in food engineering. Production of corns such as maize has a great economic importance due to the large quantity of starch, corn syrup, ethanol, oil, chemicals and other products which could be produced from it. Maize and some other corns are characterized by a high initial moisture content at harvest. Hence drying becomes an essential operation before storage. Drying is a difficult task due to the variation in harvest moisture, deterioration of corn quality, the environmental, health and safety regulations and the need of energy savings. In addition hydrodynamics of the movement of particles in the dryer, different mechanisms of moisture transport within the solid material, and shrinkage are some of other problems associated with drying of foodstuffs. Considering the thermal efficiencies of the equipment, fluidized bed dryers are among the most efficient (Strumillo & Kudra, 1996). Use of these dryers for drying of maize is very
*
Corresponding author. E-mail addresses: [email protected] [email protected] (D. Mowla).
(M.S.
Hatamipour),
common today. Improving the rate of heat transfer can provide significant benefits to the drying process. Use of inert particles is one of the proposed methods for improving the drying process. This subject has been of special interest during recent decades, from which the works of Abid, Gibert, and Laguerie (1990); Chancellor (1968); Cobbinah, Laguerie, and Gibert (1987); Grabowski, Mujumdar, Ramaswamy, and Strumillo (1994); Jariwara and Hoelscher (1970); Kirkwood and Olson (1986); Lee and Kim (1993, 1999); Taracatac, Flores, and Chaudhry (1985); Zhou, Mowla, Wang, and Rudolph (1998), are of interest. The objectives of this work were to determine the changes of density, shrinkage and mass diffusivity of green peas and maize in a fluidized bed with and without inert particles, and proposing correlations for them.
2. Materials and procedure 2.1. Materials In this work, green peas and maize were chosen as the drying materials. These vegetables have natural moisture contents about 75% and during drying they
0260-8774/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0260-8774(02)00461-2
222
M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227
Nomenclature A B a b d d0 D R t Ta
parameter in Eq. (1) constant in Eq. (1) parameter in Eq. (4) constant in Eq. (4) drying solid diameter (m) initial solid diameter (m) diffusivity (m2 /h) outer radius of solid to be dried (m) time (s) air temperature (K)
maintain their shape; although the size change deriving from the great water loss during the process, cannot be ignored. In order to ensure reproducible results, all peas and maize were obtained from a single region and kept in a refrigerator at 4 °C until required. Several measurements of the spherical dimensions were made using a micrometer and only samples within a 5% tolerance of the average dimensions were used. In each run, the final volume of dried sample was determined by immersing it in toluene and measuring the volume change. 2.2. Drying apparatus A pilot-scale fluidized bed dryer with inert particles was set up for performing the drying experiments. The schematic diagram of the experimental apparatus is shown in Fig. 1. The dryer was a 77 mm cylindrical Pyrex column equipped with a porous plate as an air distributor. Drying air was supplied from a high-pressure air source and a pressure regulator adjusted its pressure. Air was passed through a rotameter and then heated by a controlled electrical heater. A temperature controller was used for regulating the temperature of
X X0 X Xe qs
moisture content of drying solid (kg/kg, dry basis) initial moisture content of drying solid (kg/ kg, dry basis) average moisture content of drying solid (kg/ kg, dry basis) equilibrium moisture content (kg/kg, dry basis) density of drying material (kg/m3 )
drying air within 1 °C; and the humidity was determined by measuring the dry and wet bulb temperatures of the drying air. The sample was hung in the fluidized bed by means of a light string so that the sample could move freely with the inert particles. The rate of water loss from the sample was determined off-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 0.005 g. The weighting procedure took no more than 10 s after removing the sample out from the column. It has been demonstrated by previous researchers that this method is sufficiently accurate for generating reproducible drying curves (Ajibola, 1989; Suarez, Violaz, & Chirife, 1985; Zhou et al., 1998). Measurements of temperature, weight loss, and diameter were recorded simultaneously. The initial moisture content of the samples was determined by drying in an electrical oven at 105–110 °C for 24 h (AOAC, 1990). The operating variables were drying air temperature, moisture content, size of heat carrier, type of heat carrier, diameter of the drying solid, velocity of drying air, mass ratio of inert material to drying solids, and drying time.
Fig. 1. Schematic diagram of the experimental apparatus.
M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227
223
Table 1 The operating conditions for drying of green peas in a fluidized bed of inert particles Exp. #
Air flow rate (l/min)
Avg. diameter of sample (mm)
Inlet air temp. (°C)
Diameter of inerts (mm)
Type of inert
Amount of inert (kg)
GP1 GP2 GP3 GP4 GP5 GP6 GP7 GP8 GP9 GP10 GP11
600 600 750 600 600 600 600 600 600 600 700
10.5 10.4 10.5 8.5 8.6 7.4 8.3 7.6 8.1 8.6 8.3
60 60 60 70 60 40 70 60 60 60 26
2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 – 2.7
Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Without inert Steel balls
400 600 400 400 400 400 400 400 250 – 250
In order to show the effect of various parameters on drying of green peas and maize and obtaining the desired correlations, several sets of experiments were performed as follows. Each experiment was done at least twice and the maximum tolerance between duplicate runs was 2%. (1) Experiments with a specific inert material at constant temperature and sample diameter at various air velocities. (2) Experiments with a specific inert material at constant air velocity and various temperatures. (3) Experiments at constant temperature, velocity and sample diameter with various inert material diameters. (4) Experiments at constant temperature, air velocity, sample diameter and inert material diameter but with various inert materials. (5) Experiments at constant temperature, air velocity, inert material diameter, inert material, but with various sample diameters. The operating conditions are summarized in Tables 1 and 2. Considering the obtained experimental data, the variations of shrinkage, density and diffusivity with change of moisture content, could be obtained.
3. Results and discussion 3.1. Determination of shrinkage Figs. 2–5 show the effects of air velocity, amount of inert and air temperature on drying curve of green peas and maize. It can be found that air temperature is the main factor that has significant effect on drying curve. The variation of ðd=d0 Þ of green peas and maize with change of moisture content was plotted at various air temperatures. It was found that the overall trend of the
Fig. 2. Effect of air velocity on drying curve of green peas (Exp. GP1, GP3).
Table 2 The operating conditions for drying of maize in a fluidized bed of inert particles (for 400 g of glass beds with 2.7 mm diameter and 600 l/min air flow rate) Exp. #
Avg. diameter of sample (mm)
Inlet air temp. (°C)
M1 M2 M3 M4 M5 M6
9.3 8.3 8.0 9.0 8.7 9.2
70 70 40 60 60 40
Fig. 3. Effect of amount of inert on drying curve of green peas (Exp. GP1, GP2).
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Fig. 4. Effect of air temperature on drying curve of green peas. (Exp. GP4, GP5, GP6).
Fig. 6. Comparison of experimental and calculated shrinkage data for green peas.
Fig. 5. Effect of air temperature on drying curve of maize (M1, M3, M5).
Fig. 7. Comparison of experimental and calculated shrinkage data for maize.
function is linear. Therefore, at first glance it can be concluded that d ¼ AX þ B d0
ð1Þ
The values of parameters A and B were obtained for each temperature by non-linear regression, and are given in Table 3. No meaningful relations were found for values of A and B with temperature. Therefore it can be found that temperature has no significant effect on shrinkage and the average values of calculated values A and B were selected as the desired parameters. This finding is consistent with our previous finding on shrinkage of carrot (Hatamipour & Mowla, 2002). The comparison between the calculated and experimental values show that the maximum absolute deviation between the calculated and experimental values of d=d0 is about 2.5% and the average absolute deviation is about 1.2%. So the following correlations could be proposed d ¼ 0:094X þ 0:7491 d0
ð2Þ
for green peas
d ¼ 0:1355X þ 0:696 d0
ð3Þ
for maize
Figs. 6 and 7 show the comparison of the results obtained from Eqs. (2) and (3) and other sets of experimental data. The good agreement confirms the validity of the obtained correlations for shrinkages of green peas and maize during drying. 3.2. Determination of density The experimental values of densities of green peas and maize during drying were plotted against moisture content. Density of green peas––unlike many other foods––was decreased with decreasing moisture content. The experimental values were obtained by dividing the mass of a single sample to its measured volume. Measurement of the final volume of the sample in toluene was a good check for volume calculations. The trend lines determine the general form of density correlations as follows:
Table 3 The calculated values of A and B (Eq. (1)) for various temperatures T ¼ 40 °C Green peas Maize
T ¼ 60 °C
T ¼ 70 °C
A
B
R2
A
B
R2
A
B
R2
0.0941 0.1560
0.7596 0.6580
0.9778 0.9713
0.1036 0.1387
0.723 0.7036
0.9784 0.9884
0.0844 0.1421
0.7647 0.6711
0.9821 0.9725
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Table 4 The calculated values of a and b (Eq. (4)) for various temperatures T ¼ 40 °C Green peas Maize
qs ¼ a
X X0
T ¼ 60 °C 2
T ¼ 70 °C 2
a
b
R
A
b
R
a
b
R2
1.0297 1.057
0.1584 )0.0467
0.978 0.977
1.0272 1.0575
0.1711 )0.0535
0.985 0.987
1.0556 1.0536
0.168 )0.0456
0.988 0.977
b ð4Þ
The values of parameters a and b are obtained for each temperature by non-linear regression, and are given in Table 4. No meaningful relations were found for values of a and b with temperature. Therefore it can be found that temperature has no significant effect on density and the average values of calculated values a and b were selected as the desired parameters. The comparison between the calculated and experimental values show that the maximum absolute deviation between the calculated and experimental values of density is about 2.5% and the average absolute deviation is about 1.2%. Therefore the following correlations could be proposed 0:1585 X qs ¼ 1030 for green peas ð5Þ X0
X qs ¼ 1060 X0
0:048 ð6Þ
for maize
The experimental data can also be fitted to the model proposed by Lozano, Rotstein, and Urbicain (1983) as follows: q ¼ 1138:3 34:270X 573:1eX
for green peas
ð7Þ
q ¼ 1000:0 þ 14:556X þ 217:2eX
for maize
ð8Þ
The maximum absolute error occurred when using Eq. (7) was 5% with an average absolute error of 1.98%. These values for Eq. (8) are 1.25% and 0.41%. Figs. 8 and 9 show comparison of calculated values of density based on correlations (5)–(8) and other sets of experimental data.
Fig. 8. Comparison of calculated and experimental values of density for green peas.
Fig. 9. Comparison of calculated and experimental values of density for maize.
3.3. Determination of moisture diffusivity Moisture diffusivity of green peas and maize dried at 40, 60 and 70 °C was calculated by the well-known method of slopes (Karatanos, Villalobos, & Saravacos, 1990; Medeiros & Sereno, 1994; Perry & Green, 1984). In this method, first the theoretical moisture ratio (W ), is evaluated numerically for a range of Fourier numbers Fo ðFo ¼ Deff t=R2 Þ. Then the same ratio is evaluated using experimental data. Both curves of experimental and theoretical moisture ratio (W ), are plotted versus time and Fourier number, respectively, on a semi-logarithmic diagram as shown in Fig. 10. For spherical particles the solution of FickÕs equation for idealized initial and boundary conditions can be written as (Crank, 1975) W ¼
1 X Xe 6 X 1 ¼ 2 expðn2 p2 F0 Þ X0 Xe p n¼1 n2
ð9Þ
By comparing the slopes of the theoretical and experimental drying curves (Fig. 10), at a specified moisture
Fig. 10. Method of slopes, example for the evaluation of moisture diffusivity.
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M.S. Hatamipour, D. Mowla / Journal of Food Engineering 59 (2003) 221–227 Table 5 Comparison between the experimental and calculated values of moisture diffusivity of green peas
Fig. 11. Effective diffusivity of green peas as a function of temperature and moisture content.
T (°C)
X (kg/kg d.b.)
Dexp
Dcal
% Deviation
70.0000 70.0000 70.0000 70.0000 70.0000 70.0000 60.0000 60.0000 60.0000 60.0000 60.0000 40.0000 40.0000 40.0000 40.0000
1.6250 1.4242 1.0979 0.7249 0.3986 0.0720 1.4560 1.2200 0.9360 0.7470 0.0862 1.7727 1.6364 1.5000 1.1818
7.0850 6.8998 6.3001 5.9820 5.6719 5.5060 5.7679 5.0871 4.8773 4.5376 4.3614 3.5821 3.3217 3.1397 3.0032
7.1408 6.8759 6.4661 6.0276 5.6684 5.3303 5.4302 5.1941 4.9237 4.7515 4.1956 3.3910 3.3050 3.2213 3.0339
)0.788E þ 00 0.346E þ 00 )0.263E þ 01 )0.763E þ 00 0.617E ) 01 0.319E þ 01 0.586E þ 01 )0.210E þ 01 )0.950E þ 00 )0.472E þ 01 0.380Eþ01 0.533Eþ01 0.500Eþ00 )0.260Eþ01 )0.102Eþ01
Table 6 Comparison between the experimental and calculated values of moisture diffusivity of maize
Fig. 12. Effective diffusivity of maize as a function of temperature and moisture content.
content, diffusivity can be evaluated from (Perry & Green, 1984) dX D¼
dt dX dF0
exp R2
ð10Þ
theo
Plots of effective moisture diffusivity versus moisture content for green peas and maize at three different temperatures are presented in Figs. 11 and 12, respectively. Since the method of slopes is valid for the linear portion of the above mentioned semi-logarithmic plot (i.e. W < 0:6), and by knowing that moisture diffusivity decreases by decreasing moisture content, it can be assumed that moisture diffusivity for W > 0:6 could be estimated by extrapolating the linear portion of the curve. Therefore, the following correlation could be obtained for moisture diffusivity of green peas and maize by non-linear regression analysis of experimental data 2764:6 D 106 ¼ exp 9:7198 þ 0:18829X T for green peas 5033:2 6 D 10 ¼ exp 14:845 þ 0:3546X T for maize
ð11Þ
ð12Þ
Tables 5 and 6 show the percent deviation between experimental and calculated values of diffusivities at
T (°C)
X (kg/kg d.b.)
Dexp
Dcal
% Deviation
70.0000 70.0000 70.0000 70.0000 70.0000 70.0000 60.0000 60.0000 60.0000 60.0000 60.0000 40.0000 40.0000 40.0000 40.0000
1.6588 1.4403 1.1853 0.9668 0.7847 0.6754 1.8205 1.6068 1.2650 1.0513 0.9658 2.1000 2.0230 1.6357 1.4421
2.1498 2.0035 1.8471 1.7117 1.5532 1.4837 1.4371 1.3458 1.2253 1.1002 1.0206 0.6011 0.5821 0.5269 0.5091
2.1362 1.9769 1.8061 1.6714 1.5669 1.5073 1.4560 1.3498 1.1957 1.1084 1.0753 0.6120 0.5956 0.5191 0.4847
0.631Eþ00 0.133Eþ01 0.222Eþ01 0.235Eþ01 )0.880Eþ00 )0.159Eþ01 )0.132Eþ01 )0.297Eþ00 0.241Eþ01 )0.749Eþ00 )0.537Eþ01 )0.183Eþ01 )0.232Eþ01 0.147Eþ01 0.479Eþ01
various temperatures and moisture contents. As it can be seen, for green peas the maximum absolute deviation is 6.17% and average absolute deviation is 2.3%. These values for maize are 5.37% and 1.97%, respectively. The obtained diffusivities are consistent with the results of Medeiros and Sereno (1994).
4. Conclusion All of the above-mentioned figures show a good agreement between the experimental data and calculated values of different parameters obtained by the proposed correlations. This means that shrinkage and density of green peas and maize during drying in a fluidized bed with inert particles depend only on its moisture content, but diffusivity is dependent on temperature and moisture content. The diffusivities of moisture in maize at various temperatures were lower than those of green peas, and
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