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Rotary semi-continuous drier for vegetables: effect of air recycling
Journal of Food Engineering 41 (1999) 215±219
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Rotary semi-continuous drier for vegetables: eect of air recycling A.H. Pelegrina, M.P. Elustondo, M.J. Urbicain * PLAPIQUI (UNS-CONICET), Camino La carrindanga Km 7, 12 de Octubre 1842, 8000 Bahõa Blanca, Argentina Received 27 November 1998; accepted 24 May 1999
Abstract In this work, the model of the rate of water removal in a stage of a modular vegetables drier, proposed by the authors in a former work (Pelegrina, A., Elustondo, M. P., & Urbicain, M. J., 1998. Design of a semi-continuous rotary drier for vegetables. Journal of Food Engineering, 37, 293±304) is applied to simulate the eect of the air recirculation rate on the unit performance, in particular the time taken and the heat requirements to attain a given ®nal solid water content. Experimental data was obtained previously in the equipment described the cited work (Pelegrina et al., 1998) consisting of a rotary drying device made of two concentric wire mesh cylinders, located in a closed box where hot air is blown. The drier cage has specially designed vanes and baes to induce the solid circulation. In this work the air heat and mass balances equations, together with the drying velocity equation are solved so that the complete operation can be simulated for any working time, if the initial conditions are known. The simulation assumes that part of the exhaust air is made to recycle and mix with the fresh air supply in controlled proportions, such that the conditions of the gas mixture blown to the drier can be set and the in¯uence of the amount of air recycled on the drier performance is calculated. It is shown that there is, for given working conditions, an optimal mixing proportion which makes the energy delivered a minimum. It is also shown the in¯uence of the recycle on the ®nal water contents if the drying time is the independent variable. Ó 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Air recycling; Vegetables drier; Drying velocity; Mass ¯ow rate
Nomenclature A c DHvap HR k1 and k2 k3 and k4 m P psat Q Rcar t T U w X
*
Y
air-drying material exchange area (m2 ) heat capacity (J sÿ1 kgÿ1 °Cÿ1 ) water latent heat of vaporization (J kgÿ1 water ) air relative humidity ®tting constants in Eq. (A.9) (K) ®tting constants in Eq. (A9) mass ¯ow rate (kg sÿ1 ) working pressure (Pa) water saturation pressure (Pa) heat exchanged by unit mass (J/kgwater ) initial loading ratio (kg mÿ3 ) time (h) temperature (o C) overall heat transfer coecient (J hÿ1 °Cÿ1 ) dry matter mass (kg) sample water content on dry basis (kgwater / kgdry matter ) air absolute humidity (kgwater /kg dry air )
Greek variables U1 and U2
functions in Eq. (9)
Subindexes d e
exit from drying chamber equilibrium
Corresponding author.
f o q ref s u v 1
air fresh feed initial inlet to the drying chamber reference dry air exit from splitter water vapor ®nal
1. Introduction During classical hot air drying, air is blown through a heater to the drying unit, where it transfers heat to the drying material and takes the water released by it. Then it leaves the equipment not fully saturated, which means a clear ineciency. Flink (1977) states that between 70 and 90 kcal kgÿ1 removed water is the energy lost by this way. A way to reduce that loss is to recycle the air until it becomes saturated but it means an undue increase in the drying time, for the mass transfer driving force reduces asymptotically to zero in addition to the recirculation costs. In order to avoid that eect, the exit air can be mixed with fresh air, so its relative humidity is reduced, heating
0260-8774/99/$ - see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 9 3 - X
216
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
the mixture to the working temperature to reduce it further and feed it back. For a given fresh air ¯ow rate, the recycled/fresh air ratio de®nes the drying time and the operation thermal eciency. According to Noden (1974), attention must be paid to the air ¯ow rate, as condensation can be produced within the equipment damaging the product. Meiering, Daynard, Brown and Otten (1977) reported a saving of 24% in energy in dierent grain dryers with air recirculation. When applied to drying of citrus fruits, Thompson, Chhinnan, Miller and Knutson, (1981) reported an energy reduction of 15% when drying prunes. Similar results are obtained by Lee and Pyun (1993) in tunnel dryers for radishes with co-current and countercurrent ¯ow arrangements. In a previous work (Pelegrina, Elustondo & Urbicain, 1998) the authors have presented a new type of rotary semi-continuous drier, fully describing its features and developing a model to express the mass transfer rate as a function of the air conditions and the material water content. The equipment was built to work with no recycle of the exhaust air. In this work a simulation of the same unit modi®ed to allow a controlled fraction of the exhaust air to be recycled is carried out, using previous experimental data and the mentioned equation of mass transfer rate. The mass ¯ow rate of recycled air upon the mass ¯ow rate of fresh air, is named recycling fraction r, de®ned as 0 6 r 6 1. The sketch of the simulated equipment is shown in Fig. 1. The unit named drier is the core of the former unit, including the rotary cylindrical module designed to make the material to circulate between the two concentric wire mesh cylinders and the box with the fan attached to the bottom to ensure the air is mixed properly and forced to contact the samples kept in the basket. The equipment is completed with the pipes, mixer and splitter to provoke the air recycling and the heater to rise the temperature to the selected values. It is recalled that the experiments carried out during the previous work were performed for 4 values of relative humidity (20%, 40%, 60% and 80%) and 3 values of
Ta (40°C, 50°C and 60°C), and samples were taken from onions of Valenciana variety having a typical initial solids content of 7%. The ®rst step of the simulation was the modeling of the drying stage, to obtain the balance equations governing the process. Then they were numerically solved for dierent working conditions detailed below and varying recycle fractions.
2. Stage modelling Modeling is based on the mass and energy macroscopic balances on the air stream plus the mass transfer equation from the product. It requires a model of the changes undergone by the drying material and another to describe the equipment behavior. The ®rst one was presented in a former publication by the same authors (Pelegrina et al., 1998). To pose the equipment model the following hypothesis are assumed: 1. Air temperature and relative humidity are uniformly distributed through out the control volume and hence are the same of those of the exit air. This assumption is supported by the existence of a fan at the bottom of the camera, which ensures a vigorous air agitation and circulation. 2. There are no leaks in the chamber, hence the water removed from the product goes to drying air stream only. 3. All energy released by the air to the product is used to vaporize the water. This is an approximation used by other authors (Kiranoudis, Maroulis & Marinos-Kouris, 1992). In our case, for a typical temperature increase of 45°C (from 10°C to 55°C) sensible heat is less than 5% of the latent heat involved. The following equations correspond to the heat and mass balances posed around the air mixer (M), the air heater (Q) and the drying chamber together with air splitter (U): 2.1. Mass balances Water balance: (a) Mixer and air heater: Yf mfs Yr mrs Ym mms Yq mqs ;
1
where subindex s refers to the dry air ¯ow rate in the stream considered. (b) Drying chamber: mds Yd ÿ mqs Yq ÿw
oX : ot
2
(c) Splitter: mds Yd mrs Yd mus Yd :
3
Dry air balance: Fig. 1. Sketch of a drier out®t with variables involved.
mfs mms :
4
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
2.2. Energy balances: Mixer: mf Hf Tf ; Yf mr Hr Tr ; Yr mm Hm Tm ; Ym :
5
Air heater: ÿ _ mq Hq Tq ; Yq mm Hm Tm ; Ym Q:
6
Drying chamber: ÿ mq Hq Tq ; Yq ÿ md Hd Td ; Yd ÿ UA Td ÿ Tamb DHvap Td w
oX : ot
7
Splitter: md Hd Td ; Yd mu Hd Td ; Yd mr Hd Td ; Yd :
217
work the maximum ®nal water content adopted was 5% of initial, that is X1 6 0.05 Xo 6 0.664 kg water/kg dry matter. 5. Initial wet product load 1.5 kg, in the form of prismatic pieces (0.01 ´ 0.01 ´ 0.003 m3 ) which corresponds to and initial loading ratio of 120 kg of drying matter/m3 of drier. 6. Recycling air was controlled to obtain recycling fractions from r 0 (only fresh air is fed to the drier) to r 0.84 (the maximum value allowing to dry up to the speci®ed ®nal water contents in less than 8 h). 4. Results
8
2.3. Mass transfer rate equation Mass transfer from the product to the air is given by the rate of water removal and was proposed by the authors in a former work (Pelegrina et al., 1998): oX /1 Td ; HRd /2 Td ; X : 9 ot Expressions to calculate the values of functions U1 and U2 are given in Appendix A, where expressions for mass ¯ow rates, wet enthalpies, speci®c heats and other terms required to solve the set of Eqs. (1)±(9) together with Eqs. (A.1)±(A.9) are presented. It was solved numerically for the case of onion pieces dried in the rotary drier presented in Pelegrina et al. (1998). 3. Simulation conditions Simulation runs were performed for the following conditions: 1. Fresh air properties: mfs 42.20 kg hÿ1 , Yf 0.0079 kg kgÿ1 , Tf 25°C, HRf 40%. 2. Initial water content of product on dry basis, Xo 13.3 kg/kg (93% on wet basis). 3. Air inlet temperature, constant Tq 55°C. 4. Final water content of product: this a very important parameter, as it has a de®nite eect on dried product quality and biological stability (Chirife & Iglesias, 1977; Ross, 1975), as well as physical and sensorial properties like color, aroma, texture and taste of the processed food (Rocland & Nishi, 1980). For onions, the maximum values of ®nal water content recommended lie between 4% and 10%, on dry basis, of the original one (Bansal & Garg, 1987; Tucker, 1970; van Arsdel & Copley, 1964; Hall, 1979). For this
Simulation was carried out for the dierent recycle fractions selected, and during the required drying times to obtain the product with the prescribed ®nal water contents, calculating the energy consumed, Q, to evaporate a kilogram of water. MATLAB 4.0 1984±1993 was the program used together with tool SIMULINK. Values of UA in the heat losses term of Eq. (7) was calculated by measuring air enthalpies at the entrance and exit of the empty drying chamber, the dierence being the heat lost to the surroundings computed by the mentioned term. The average calculated value resulted to be UA 706.5 J/h °C, which was assumed constant for all experimental conditions, neglecting the minor dierences in air enthalpies due to humidity and temperatures dierences. It must be remarked that initial time corresponds to the instant at which the dry air mass ¯ow rate of all streams reach steady state, which in practice takes very short time since the equipment is small and recycle is rapidly set up. That means that at t 0, fresh air is mixed with the wettest possible recycled air after its ®rst pass through the drier. When the recycle fraction r increases, the absolute humidity Yq at the drying chamber inlet also increases, reducing the mass transfer driving force in the chamber and imposing longer times to achieve the prescribed ®nal water contents of the material. Hence, for Xf given, selecting r determines univocally the drying time required. Reciprocally, for a given recycle fraction the ®nal water content X1 is necessarily a function of the drying time, dependence which is shown for the two extreme values of r in Fig. 3. It is apparent that the ®nal value of X1 /Xo 0.05 is attained in quite dierent times (5.6 and 8 h, respectively), but also that the curves show quite dierent behaviors. Then, if the drying time is taken as the independent variable and the operation is planned for shorter times, the recycle fraction should be selected carefully to obtain a product within speci®cations. Another eect of increasing the recycle is that the heat delivered to the air decreases due to the higher temperature of the hot air recycled. That means a saving
218
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
per kilogram of air blown into the drier with the tradeo of the longer times. Consequently it can be expected that it should be a particular pair of values (r,t) which would make optimal the operation in terms of energy consumed. To ®nd it, the product Q.t was calculated since it represents the total heat delivered to evaporate one kilogram of water, during the time required to dry the fresh material containing it to the prescribed ®nal moisture contents. That product was plotted against the operation time and presented in Fig. 2 indicating the recycle fraction r corresponding to each time. It is interesting to note that the curve shows a minimum at r 0.8, which corresponds to a total drying time of 7.46 h. That physically means that in the conditions of the experiment, setting the recycle fraction to r 0.8, it takes 7.46 h to evaporate 1 kg of water, that is, to dry 0.079 kg of dry matter from its initial state to the ®nal prescribed water contents. In fact the initial water contained is 1.05 kg while the ®nal is 0.053 kg. 5. Conclusions It has been shown that exhaust air recycling and mixing with fresh feed represents a signi®cant reduction in energy saving, when all other operating parameters are kept constant This suggests an obvious economical advantage. However, energy is not the only factor involved in the drying economy, and consideration must be paid to the operation time, as it is directly associated with the production rate and with the ®nal product quality in terms of color and aroma. In those cases lower times are mandatory so lower recycle fractions must be used and higher energy demand must be accepted.
Fig. 3. Water content as a function of drying time for and maximum allowed recycle.
Finally, the ®nal water content plays an important role in the quality and stability of the dried product and it is the third variable to be considered carefully. It is felt that the methods and techniques presented in this work can help the engineer to balance all factors involved in a proper design and operation of a drying device as that presented here. Appendix A The following are the expressions of the variables involved in the mass and energy balance represented by Eqs. (1)±(9) above: Wet air mass ¯ow rate can be expressed in terms of the dry air mass ¯ow rate and the absolute humidity (Strumillo & Kudra, 1986): mi mis 1 Yi
A:1
and enthalpies as a function of temperature and absolute humidity (Treybal, 1970; Wilhelm, 1975; Kiranoudis et al., 1994): Hi Ti ; Yi cs Ti ÿ Tref Yi fDHref cv Ti ÿ Tref g;
A:2
where subindex i represents any stream. Constant pressure speci®c heat of wet air is the linear combination of both dry air and water speci®c heats (Treybal, 1970). C a cs Y cv Fig. 2. Total energy consumption to evaporate 1 kg of water as a function of drying time.
being cs 310.715 J °C kgÿ1 .
A:3 ÿ1
ÿ1
kg , and cv 585.598 J °Cÿ1
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
Absolute and relative humidities of air are related by (Strumillo & Kudra, 1986) Y 0:622
HRpsat ; P ÿ HRpsat
A:4
where psat is the water saturation pressure at prevailing P and T conditions of the system. It can be calculated by an Antoine form correlation (Himmelblau, 1970): log10 psat A1 ÿ
A2 ; A3 ÿ T d
A:5
where constants A1 , A2 and A3; are equal to 10.2325°C, 1750.286°C and 235.0°C, respectively for water. Latent heat of vaporization of water is usually expressed as a function of temperature (Thorpe, 1987; Imre & K ornyey, 1990; Pezzutti, 1995). For the working temperature span, the latter proposes: DHvap 2 503 673 ÿ 2405 Td :
A:6
Functions U1 and U2 in Eq. (9) are calculated by means of the following expressions: 2
U1 a b Td d HRd c HRd Td ;
A:7
U1 X ÿ Xe g u k Td X ÿ Xe :
A:8
Constants a, b, d, c, g and k can be found in the paper by Pelegrina et al. (1998). The equilibrium value of the solid water content Xe , de®ned by the onion±air system isotherm under the prevailing conditions, was calculated by means of the correlation proposed by Crapiste and Rotstein (1986): ÿk3 1 1 Xe ÿ ln HR ÿk1 T 273 k2 1 Xe k 4 Xe : A:9 exp ÿ 1 Xe Values of constants k1 , k2; k3 and k4 were determined by Pezzuti (1995) by ®tting experimental points. References Bansal, N. K., & Garg, H. P. (1987). Solar Crop Drying. In A. Mujumdar, Advances in Drying (Chapter 6, vol. 4, pp. 279±358).
219
Chirife, J. E., & Iglesias, H. A. (1977). El Agua en la Estabilidad de Alimentos Deshidratados. La Alimentaci on Americana, 105, 56±65. Crapiste, G. H., & Rotstein, E. (1986). Sorptional equilibrium at changing moisture contents. In A.S. Mujundar (Ed.), Drying of Solids. New York: Wiley. Flink, J. M. (1977). Energy analysis in dehydration process. Food Technology, 31(3), 76±83. Hall, C. W. (1979). Dictionary of drying, New York: Marcel Dekker. Himmelblau, D. (1970). Principios y C alculos Basicos de la Ingenierõa Quõmica, Compa~ nia Editorial Continental S.A.. Imre, L., & K ornyey, T. (1990). Computer simulation of salami drying. International Journal for Numerical methods in Engineering, 30, 767±777. Kiranoudis, C. T., Maroulis, Z. B., & Marinos-kouris, D. (1992). Drying kinetics of onion and green pepper. Drying Technology, 10(4), 995±1011. Kiranoudis, C. T., Maroulis, Z. B., & Marinos-Kouris, D. (1994). Modelling and design of conveyor belt dryers. Journal of Food Engineering, 23, 375±396. Lee, D. S., & Pyun, Y. R. (1993). Optimization of operating conditions in tunnel drying of food. Drying Technology, 11(5), 1025±1052. Meiering, A. G., Daynard, T. B., Brown, R., Otten, L. (1977). Drier perfomance and energy use in corn drying. Canadian Agricultural Engineering, 19 (1). Noden, D. (1974). Ecient Energy Utilization in Drying. Processing, December 1974. Pelegrina, A., Elustondo, M. P., & Urbicain, M. J. (1998). Design of a semi-contiuous rotary drier for vegetables. Journal of Food Engineering, 37, 293±304. Pezzutti, A. (1995). Tesis Doctoral, Universidad Nacional del Sur. Rockland, L. B., & Nishi, S. K. (1980). In¯uence of water activity on food product quality and stability. Food Technology, 42-51, y59. Ross, K. D. (1975). Estimation of water activity in intermediate moisture foods. Food Technology, 27-34. Strumillo, C. & Kudra, T. (1986). Drying: Principles, applications and design, vol. III, London: Gordon and Breach. Thompson, J. F., Chhinnan, M. S., Miller, M. W., & Knutson, G. D. (1981). Energy conservation in drying of fruits in tunnel dehydrators. Journal of Foods Process Engineering, 4, 155±169. Thorpe, G. R. (1987). The thermodynamic perfomance of a continuous-¯ow ¯uidized bed disinfestor and drier. Journal Agricultural Engineering Research, 37, 27±41. Treybal, R. E. (1970). Operaciones con Transferencia de Masa; H.A.S.A. Editorial. Mexico. Tucker, C. G. (1970). Dehydration. In A. Woollen (Ed.), Food Industries Manual (pp.159±184). Chemical Publishing. van Arsdel, A., & Copley, M. (1964). Products and Technology. The Avi Publishing Co., Inc., as number 14 and 30 respectively. Wilhelm, L.R. (1975). Numerical calculation of psychrometric properties. American Society of Agricultural Engineers, Paper No. 754019.
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Rotary semi-continuous drier for vegetables: eect of air recycling A.H. Pelegrina, M.P. Elustondo, M.J. Urbicain * PLAPIQUI (UNS-CONICET), Camino La carrindanga Km 7, 12 de Octubre 1842, 8000 Bahõa Blanca, Argentina Received 27 November 1998; accepted 24 May 1999
Abstract In this work, the model of the rate of water removal in a stage of a modular vegetables drier, proposed by the authors in a former work (Pelegrina, A., Elustondo, M. P., & Urbicain, M. J., 1998. Design of a semi-continuous rotary drier for vegetables. Journal of Food Engineering, 37, 293±304) is applied to simulate the eect of the air recirculation rate on the unit performance, in particular the time taken and the heat requirements to attain a given ®nal solid water content. Experimental data was obtained previously in the equipment described the cited work (Pelegrina et al., 1998) consisting of a rotary drying device made of two concentric wire mesh cylinders, located in a closed box where hot air is blown. The drier cage has specially designed vanes and baes to induce the solid circulation. In this work the air heat and mass balances equations, together with the drying velocity equation are solved so that the complete operation can be simulated for any working time, if the initial conditions are known. The simulation assumes that part of the exhaust air is made to recycle and mix with the fresh air supply in controlled proportions, such that the conditions of the gas mixture blown to the drier can be set and the in¯uence of the amount of air recycled on the drier performance is calculated. It is shown that there is, for given working conditions, an optimal mixing proportion which makes the energy delivered a minimum. It is also shown the in¯uence of the recycle on the ®nal water contents if the drying time is the independent variable. Ó 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Air recycling; Vegetables drier; Drying velocity; Mass ¯ow rate
Nomenclature A c DHvap HR k1 and k2 k3 and k4 m P psat Q Rcar t T U w X
*
Y
air-drying material exchange area (m2 ) heat capacity (J sÿ1 kgÿ1 °Cÿ1 ) water latent heat of vaporization (J kgÿ1 water ) air relative humidity ®tting constants in Eq. (A.9) (K) ®tting constants in Eq. (A9) mass ¯ow rate (kg sÿ1 ) working pressure (Pa) water saturation pressure (Pa) heat exchanged by unit mass (J/kgwater ) initial loading ratio (kg mÿ3 ) time (h) temperature (o C) overall heat transfer coecient (J hÿ1 °Cÿ1 ) dry matter mass (kg) sample water content on dry basis (kgwater / kgdry matter ) air absolute humidity (kgwater /kg dry air )
Greek variables U1 and U2
functions in Eq. (9)
Subindexes d e
exit from drying chamber equilibrium
Corresponding author.
f o q ref s u v 1
air fresh feed initial inlet to the drying chamber reference dry air exit from splitter water vapor ®nal
1. Introduction During classical hot air drying, air is blown through a heater to the drying unit, where it transfers heat to the drying material and takes the water released by it. Then it leaves the equipment not fully saturated, which means a clear ineciency. Flink (1977) states that between 70 and 90 kcal kgÿ1 removed water is the energy lost by this way. A way to reduce that loss is to recycle the air until it becomes saturated but it means an undue increase in the drying time, for the mass transfer driving force reduces asymptotically to zero in addition to the recirculation costs. In order to avoid that eect, the exit air can be mixed with fresh air, so its relative humidity is reduced, heating
0260-8774/99/$ - see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 9 3 - X
216
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
the mixture to the working temperature to reduce it further and feed it back. For a given fresh air ¯ow rate, the recycled/fresh air ratio de®nes the drying time and the operation thermal eciency. According to Noden (1974), attention must be paid to the air ¯ow rate, as condensation can be produced within the equipment damaging the product. Meiering, Daynard, Brown and Otten (1977) reported a saving of 24% in energy in dierent grain dryers with air recirculation. When applied to drying of citrus fruits, Thompson, Chhinnan, Miller and Knutson, (1981) reported an energy reduction of 15% when drying prunes. Similar results are obtained by Lee and Pyun (1993) in tunnel dryers for radishes with co-current and countercurrent ¯ow arrangements. In a previous work (Pelegrina, Elustondo & Urbicain, 1998) the authors have presented a new type of rotary semi-continuous drier, fully describing its features and developing a model to express the mass transfer rate as a function of the air conditions and the material water content. The equipment was built to work with no recycle of the exhaust air. In this work a simulation of the same unit modi®ed to allow a controlled fraction of the exhaust air to be recycled is carried out, using previous experimental data and the mentioned equation of mass transfer rate. The mass ¯ow rate of recycled air upon the mass ¯ow rate of fresh air, is named recycling fraction r, de®ned as 0 6 r 6 1. The sketch of the simulated equipment is shown in Fig. 1. The unit named drier is the core of the former unit, including the rotary cylindrical module designed to make the material to circulate between the two concentric wire mesh cylinders and the box with the fan attached to the bottom to ensure the air is mixed properly and forced to contact the samples kept in the basket. The equipment is completed with the pipes, mixer and splitter to provoke the air recycling and the heater to rise the temperature to the selected values. It is recalled that the experiments carried out during the previous work were performed for 4 values of relative humidity (20%, 40%, 60% and 80%) and 3 values of
Ta (40°C, 50°C and 60°C), and samples were taken from onions of Valenciana variety having a typical initial solids content of 7%. The ®rst step of the simulation was the modeling of the drying stage, to obtain the balance equations governing the process. Then they were numerically solved for dierent working conditions detailed below and varying recycle fractions.
2. Stage modelling Modeling is based on the mass and energy macroscopic balances on the air stream plus the mass transfer equation from the product. It requires a model of the changes undergone by the drying material and another to describe the equipment behavior. The ®rst one was presented in a former publication by the same authors (Pelegrina et al., 1998). To pose the equipment model the following hypothesis are assumed: 1. Air temperature and relative humidity are uniformly distributed through out the control volume and hence are the same of those of the exit air. This assumption is supported by the existence of a fan at the bottom of the camera, which ensures a vigorous air agitation and circulation. 2. There are no leaks in the chamber, hence the water removed from the product goes to drying air stream only. 3. All energy released by the air to the product is used to vaporize the water. This is an approximation used by other authors (Kiranoudis, Maroulis & Marinos-Kouris, 1992). In our case, for a typical temperature increase of 45°C (from 10°C to 55°C) sensible heat is less than 5% of the latent heat involved. The following equations correspond to the heat and mass balances posed around the air mixer (M), the air heater (Q) and the drying chamber together with air splitter (U): 2.1. Mass balances Water balance: (a) Mixer and air heater: Yf mfs Yr mrs Ym mms Yq mqs ;
1
where subindex s refers to the dry air ¯ow rate in the stream considered. (b) Drying chamber: mds Yd ÿ mqs Yq ÿw
oX : ot
2
(c) Splitter: mds Yd mrs Yd mus Yd :
3
Dry air balance: Fig. 1. Sketch of a drier out®t with variables involved.
mfs mms :
4
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
2.2. Energy balances: Mixer: mf Hf Tf ; Yf mr Hr Tr ; Yr mm Hm Tm ; Ym :
5
Air heater: ÿ _ mq Hq Tq ; Yq mm Hm Tm ; Ym Q:
6
Drying chamber: ÿ mq Hq Tq ; Yq ÿ md Hd Td ; Yd ÿ UA Td ÿ Tamb DHvap Td w
oX : ot
7
Splitter: md Hd Td ; Yd mu Hd Td ; Yd mr Hd Td ; Yd :
217
work the maximum ®nal water content adopted was 5% of initial, that is X1 6 0.05 Xo 6 0.664 kg water/kg dry matter. 5. Initial wet product load 1.5 kg, in the form of prismatic pieces (0.01 ´ 0.01 ´ 0.003 m3 ) which corresponds to and initial loading ratio of 120 kg of drying matter/m3 of drier. 6. Recycling air was controlled to obtain recycling fractions from r 0 (only fresh air is fed to the drier) to r 0.84 (the maximum value allowing to dry up to the speci®ed ®nal water contents in less than 8 h). 4. Results
8
2.3. Mass transfer rate equation Mass transfer from the product to the air is given by the rate of water removal and was proposed by the authors in a former work (Pelegrina et al., 1998): oX /1 Td ; HRd /2 Td ; X : 9 ot Expressions to calculate the values of functions U1 and U2 are given in Appendix A, where expressions for mass ¯ow rates, wet enthalpies, speci®c heats and other terms required to solve the set of Eqs. (1)±(9) together with Eqs. (A.1)±(A.9) are presented. It was solved numerically for the case of onion pieces dried in the rotary drier presented in Pelegrina et al. (1998). 3. Simulation conditions Simulation runs were performed for the following conditions: 1. Fresh air properties: mfs 42.20 kg hÿ1 , Yf 0.0079 kg kgÿ1 , Tf 25°C, HRf 40%. 2. Initial water content of product on dry basis, Xo 13.3 kg/kg (93% on wet basis). 3. Air inlet temperature, constant Tq 55°C. 4. Final water content of product: this a very important parameter, as it has a de®nite eect on dried product quality and biological stability (Chirife & Iglesias, 1977; Ross, 1975), as well as physical and sensorial properties like color, aroma, texture and taste of the processed food (Rocland & Nishi, 1980). For onions, the maximum values of ®nal water content recommended lie between 4% and 10%, on dry basis, of the original one (Bansal & Garg, 1987; Tucker, 1970; van Arsdel & Copley, 1964; Hall, 1979). For this
Simulation was carried out for the dierent recycle fractions selected, and during the required drying times to obtain the product with the prescribed ®nal water contents, calculating the energy consumed, Q, to evaporate a kilogram of water. MATLAB 4.0 1984±1993 was the program used together with tool SIMULINK. Values of UA in the heat losses term of Eq. (7) was calculated by measuring air enthalpies at the entrance and exit of the empty drying chamber, the dierence being the heat lost to the surroundings computed by the mentioned term. The average calculated value resulted to be UA 706.5 J/h °C, which was assumed constant for all experimental conditions, neglecting the minor dierences in air enthalpies due to humidity and temperatures dierences. It must be remarked that initial time corresponds to the instant at which the dry air mass ¯ow rate of all streams reach steady state, which in practice takes very short time since the equipment is small and recycle is rapidly set up. That means that at t 0, fresh air is mixed with the wettest possible recycled air after its ®rst pass through the drier. When the recycle fraction r increases, the absolute humidity Yq at the drying chamber inlet also increases, reducing the mass transfer driving force in the chamber and imposing longer times to achieve the prescribed ®nal water contents of the material. Hence, for Xf given, selecting r determines univocally the drying time required. Reciprocally, for a given recycle fraction the ®nal water content X1 is necessarily a function of the drying time, dependence which is shown for the two extreme values of r in Fig. 3. It is apparent that the ®nal value of X1 /Xo 0.05 is attained in quite dierent times (5.6 and 8 h, respectively), but also that the curves show quite dierent behaviors. Then, if the drying time is taken as the independent variable and the operation is planned for shorter times, the recycle fraction should be selected carefully to obtain a product within speci®cations. Another eect of increasing the recycle is that the heat delivered to the air decreases due to the higher temperature of the hot air recycled. That means a saving
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A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
per kilogram of air blown into the drier with the tradeo of the longer times. Consequently it can be expected that it should be a particular pair of values (r,t) which would make optimal the operation in terms of energy consumed. To ®nd it, the product Q.t was calculated since it represents the total heat delivered to evaporate one kilogram of water, during the time required to dry the fresh material containing it to the prescribed ®nal moisture contents. That product was plotted against the operation time and presented in Fig. 2 indicating the recycle fraction r corresponding to each time. It is interesting to note that the curve shows a minimum at r 0.8, which corresponds to a total drying time of 7.46 h. That physically means that in the conditions of the experiment, setting the recycle fraction to r 0.8, it takes 7.46 h to evaporate 1 kg of water, that is, to dry 0.079 kg of dry matter from its initial state to the ®nal prescribed water contents. In fact the initial water contained is 1.05 kg while the ®nal is 0.053 kg. 5. Conclusions It has been shown that exhaust air recycling and mixing with fresh feed represents a signi®cant reduction in energy saving, when all other operating parameters are kept constant This suggests an obvious economical advantage. However, energy is not the only factor involved in the drying economy, and consideration must be paid to the operation time, as it is directly associated with the production rate and with the ®nal product quality in terms of color and aroma. In those cases lower times are mandatory so lower recycle fractions must be used and higher energy demand must be accepted.
Fig. 3. Water content as a function of drying time for and maximum allowed recycle.
Finally, the ®nal water content plays an important role in the quality and stability of the dried product and it is the third variable to be considered carefully. It is felt that the methods and techniques presented in this work can help the engineer to balance all factors involved in a proper design and operation of a drying device as that presented here. Appendix A The following are the expressions of the variables involved in the mass and energy balance represented by Eqs. (1)±(9) above: Wet air mass ¯ow rate can be expressed in terms of the dry air mass ¯ow rate and the absolute humidity (Strumillo & Kudra, 1986): mi mis 1 Yi
A:1
and enthalpies as a function of temperature and absolute humidity (Treybal, 1970; Wilhelm, 1975; Kiranoudis et al., 1994): Hi Ti ; Yi cs Ti ÿ Tref Yi fDHref cv Ti ÿ Tref g;
A:2
where subindex i represents any stream. Constant pressure speci®c heat of wet air is the linear combination of both dry air and water speci®c heats (Treybal, 1970). C a cs Y cv Fig. 2. Total energy consumption to evaporate 1 kg of water as a function of drying time.
being cs 310.715 J °C kgÿ1 .
A:3 ÿ1
ÿ1
kg , and cv 585.598 J °Cÿ1
A.H. Pelegrina et al. / Journal of Food Engineering 41 (1999) 215±219
Absolute and relative humidities of air are related by (Strumillo & Kudra, 1986) Y 0:622
HRpsat ; P ÿ HRpsat
A:4
where psat is the water saturation pressure at prevailing P and T conditions of the system. It can be calculated by an Antoine form correlation (Himmelblau, 1970): log10 psat A1 ÿ
A2 ; A3 ÿ T d
A:5
where constants A1 , A2 and A3; are equal to 10.2325°C, 1750.286°C and 235.0°C, respectively for water. Latent heat of vaporization of water is usually expressed as a function of temperature (Thorpe, 1987; Imre & K ornyey, 1990; Pezzutti, 1995). For the working temperature span, the latter proposes: DHvap 2 503 673 ÿ 2405 Td :
A:6
Functions U1 and U2 in Eq. (9) are calculated by means of the following expressions: 2
U1 a b Td d HRd c HRd Td ;
A:7
U1 X ÿ Xe g u k Td X ÿ Xe :
A:8
Constants a, b, d, c, g and k can be found in the paper by Pelegrina et al. (1998). The equilibrium value of the solid water content Xe , de®ned by the onion±air system isotherm under the prevailing conditions, was calculated by means of the correlation proposed by Crapiste and Rotstein (1986): ÿk3 1 1 Xe ÿ ln HR ÿk1 T 273 k2 1 Xe k 4 Xe : A:9 exp ÿ 1 Xe Values of constants k1 , k2; k3 and k4 were determined by Pezzuti (1995) by ®tting experimental points. References Bansal, N. K., & Garg, H. P. (1987). Solar Crop Drying. In A. Mujumdar, Advances in Drying (Chapter 6, vol. 4, pp. 279±358).
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Chirife, J. E., & Iglesias, H. A. (1977). El Agua en la Estabilidad de Alimentos Deshidratados. La Alimentaci on Americana, 105, 56±65. Crapiste, G. H., & Rotstein, E. (1986). Sorptional equilibrium at changing moisture contents. In A.S. Mujundar (Ed.), Drying of Solids. New York: Wiley. Flink, J. M. (1977). Energy analysis in dehydration process. Food Technology, 31(3), 76±83. Hall, C. W. (1979). Dictionary of drying, New York: Marcel Dekker. Himmelblau, D. (1970). Principios y C alculos Basicos de la Ingenierõa Quõmica, Compa~ nia Editorial Continental S.A.. Imre, L., & K ornyey, T. (1990). Computer simulation of salami drying. International Journal for Numerical methods in Engineering, 30, 767±777. Kiranoudis, C. T., Maroulis, Z. B., & Marinos-kouris, D. (1992). Drying kinetics of onion and green pepper. Drying Technology, 10(4), 995±1011. Kiranoudis, C. T., Maroulis, Z. B., & Marinos-Kouris, D. (1994). Modelling and design of conveyor belt dryers. Journal of Food Engineering, 23, 375±396. Lee, D. S., & Pyun, Y. R. (1993). Optimization of operating conditions in tunnel drying of food. Drying Technology, 11(5), 1025±1052. Meiering, A. G., Daynard, T. B., Brown, R., Otten, L. (1977). Drier perfomance and energy use in corn drying. Canadian Agricultural Engineering, 19 (1). Noden, D. (1974). Ecient Energy Utilization in Drying. Processing, December 1974. Pelegrina, A., Elustondo, M. P., & Urbicain, M. J. (1998). Design of a semi-contiuous rotary drier for vegetables. Journal of Food Engineering, 37, 293±304. Pezzutti, A. (1995). Tesis Doctoral, Universidad Nacional del Sur. Rockland, L. B., & Nishi, S. K. (1980). In¯uence of water activity on food product quality and stability. Food Technology, 42-51, y59. Ross, K. D. (1975). Estimation of water activity in intermediate moisture foods. Food Technology, 27-34. Strumillo, C. & Kudra, T. (1986). Drying: Principles, applications and design, vol. III, London: Gordon and Breach. Thompson, J. F., Chhinnan, M. S., Miller, M. W., & Knutson, G. D. (1981). Energy conservation in drying of fruits in tunnel dehydrators. Journal of Foods Process Engineering, 4, 155±169. Thorpe, G. R. (1987). The thermodynamic perfomance of a continuous-¯ow ¯uidized bed disinfestor and drier. Journal Agricultural Engineering Research, 37, 27±41. Treybal, R. E. (1970). Operaciones con Transferencia de Masa; H.A.S.A. Editorial. Mexico. Tucker, C. G. (1970). Dehydration. In A. Woollen (Ed.), Food Industries Manual (pp.159±184). Chemical Publishing. van Arsdel, A., & Copley, M. (1964). Products and Technology. The Avi Publishing Co., Inc., as number 14 and 30 respectively. Wilhelm, L.R. (1975). Numerical calculation of psychrometric properties. American Society of Agricultural Engineers, Paper No. 754019.