مدل سازی المان محدود خشک شدن همرفتی موز با اثر چروکیدگی شعاعی به روش اویلر-لاگرانژ دلخواه

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، مکانیک بیوسیستم، دانشگاه فردوسی مشهد

2 دانشیار، مکانیک بیوسیستم، دانشگاه فردوسی مشهد

3 استاد، مکانیک بیوسیستم، دانشگاه فردوسی مشهد

چکیده

روش المان محدود برای مدل سازی انتقال هم زمان جرم و حرارت در نمونه های استوانه ای موز مورد استفاده قرار گرفت. در مدل ارائه شده خواص ترموفیزیکی محصول به صورت تابعی از رطوبت و دمای محصول در طول فرایند در نظر گرفته شد. مدل سازی به کمک نرم افزار تجاری COMSOL نسخه 5.1 و به صورت تقارن محوری انجام شد. از روش اویلر لاگرانژ دلخواه (ALE) برای تعریف مرز متحرک جهت احتساب چروکیدگی در مدل استفاده شد. برای راستی آزمایی مدل، نمونه های موز در شرایط مختلف خشک شدند و تغییرات دما در مرکز نمونه و میانگین محتوی رطوبت نمونه ها با مقادیر پیش بینی شده توسط مدل مقایسه شدند. نتایج نشان داد درصد میانگین خطای نسبی برای تخمین رطوبت و دما به ترتیب در محدوده %83/8-23/4 و % 82/1-12/1 بود. بنابراین مدل ارائه شده قادر است محتوی رطوبت و دمای مرکز نمونه را در طول فرایند خشک شدن به طور موفقیت آمیزی پیش بینی کند. با توجه به اهمیت پیش بینی تغییرات دما و رطوبت، مدل ارائه شده می تواند به عنوان ابزار مفیدی در جهت بهینه کردن فرایند خشک کردن موز از نظر بازده آن وکیفیت محصول مورد استفاده قرار گیرد. انتظار می رود که مدل مذکور به راحتی قابل تعمیم برای خشک کردن محصول های مشابه با شکل استوانه ای باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Finite element modeling of convective drying of banana with radial shrinkage effect using Arbitrary Lagrangian-Eulerian method

نویسندگان [English]

  • Esmaeel Seyedabadi 1
  • Mehdi Khojastehpour 2
  • Mohammad Hossein Abbaspour-Fard 3
1 1- Ph.D Student of Department of Biosystems Engineering, College of Agriculture, Ferdowsi University of Mashhad
2 2- Associate Professor of Department of Biosystems Engineering, College of Agriculture, Ferdowsi University of Mashhad
3 3- Professor of Department of Biosystems Engineering, College of Agriculture, Ferdowsi University of Mashhad
چکیده [English]

Finite element method was used in order to model the simultaneous heat and mass transfer in cylindrical banana samples. The thermophysical properties of banana were considered as the function of moisture content and temperature. The simulation was carried out in the form of axisymmetric model. The Arbitrary Lagrangian-Eulerian (ALE) approach was used in order to incorporate the radial shrinkage effect in the model. The validation of the model was checked by comparing the predicted results with experimental data in various drying conditions. Results showed the mean relative error percent (E%) for estimating the moisture content and core temperature of banana samples in different drying conditions were in the range of 4.23-8.83% and 1.12-1.82% respectively. Therefore, the presented model was able to predict the average moisture content and core temperature satisfactorily. With considering the importance of estimating the moisture content and temperature, the model can be used as a confident tool in order to optimize drying process of banana from the quality and efficiency view. It is expected the presented model can be easily extended for drying of similar products with cylindrical shape.

کلیدواژه‌ها [English]

  • Finite Element
  • Shrinkage
  • Convective dryer
  • Arbitrary Lagrangian-Eulerian Method
  • Banana
 [1] Akbudak, N., Akbudak, B. (2013). Effect of vacuum, microwave, and convective drying on selected parsley quality. Int. J. Food Prop. 16, 205-215.

[2] Izli, N., Isik, E. (2015). Color and microstructure properties of tomatoes dried by microwave, convective, and microwave-convective methods. Int. J. Food Prop. 18, 241-249.

[3] Nguyen, M.-H., Price, W.E. (2007). Air-drying of banana: influence of experimental parameters, slab thickness, banana maturity and harvesting season. J. Food Eng. 79, 200-207.

[4] Aguilera, J.M. (2003). Drying and dried products under the microscope. Food Sci. Technol. Int. 9, 137-143.

[5] May, B., Perré, P. (2002). The importance of considering exchange surface area reduction to exhibit a constant drying flux period in foodstuffs. J. Food Eng. 54, 271-282.

[6] Zielinska, M., Markowski, M. (2010). Air drying characteristics and moisture diffusivity of carrots. Chem. Eng. Process. Process Intensif. 49, 212-218.

[7] Thuwapanichayanan, R., Prachayawarakorn, S., Kunwisawa, J., Soponronnarit, S. (2011). Determination of effective moisture diffusivity and assessment of quality attributes of banana slices during drying. LWT Food Sci. Technol. 44, 1502-1510.

[8] Milczarek, R.R., Dai, A.A., Otoni, C.G., McHugh, T.H. (2011). Effect of shrinkage on isothermal drying behavior of 2-phase olive mill waste. J. Food Eng. 103, 434-441.

[9] Mayor, L., Sereno, A. (2004). Modelling shrinkage during convective drying of food materials: a review. J. Food Eng. 61, 373-386.

[10] Katekawa, M., Silva, M. (2006). A review of drying models including shrinkage effects. Drying technol. 24, 5-20.

[11] De Lima, A., Queiroz, M., Nebra, S. (2002). Simultaneous moisture transport and shrinkage during drying of solids with ellipsoidal configuration. Chem. Eng. J. 86, 85-93.

[12] Jannot, Y., Talla, A., Nganhou, J., Puiggali, J.-R. (2004). Modeling of banana convective drying by the drying characteristic curve (DCC) method. Drying Technol. 22, 1949-1968.

[13] Dandamrongrak, R., Young, G., Mason, R. (2002). Evaluation of various pre-treatments for the dehydration of banana and selection of suitable drying models. J. Food Eng. 55, 139-146.

[14] Queiroz, M., Nebra, S. (2001). Theoretical and experimental analysis of the drying kinetics of bananas. J. Food Eng. 47, 127-132.

[15] Demirel, D.,Turhan, M. (2003). Air-drying behavior of Dwarf Cavendish and Gros Michel banana slices. J. Food Eng. 59, 1-11.

[16] Chua, K., Mujumdar, A., Chou, S., Hawlader, M., Ho, J. (2000). Convective drying of banana, guava and potato pieces: Effect of cyclical variations of air temperature on drying kinetics and color change. Drying Technol. 18, 907-936.

[17] Boudhrioua, N., Giampaoli, P., Bonazzi, C. (2003). Changes in aromatic components of banana during ripening and air-drying. LWT-Food Sci. Technol. 36, 633-642.

[18] Ah-Hen, K., Zambra, C.E., Aguëro, J.E., Vega-Gálvez, A.,Lemus-Mondaca, R. (2013). Moisture diffusivity coefficient and convective drying modelling of murta (Ugni molinae Turcz): Influence of temperature and vacuum on drying kinetics. Food Bioprocess Technol. 6, 919-930.

[19] Swasdisevi, T., Devahastin, S., Sa-Adchom, P., Soponronnarit, S. (2009). Mathematical modeling of combined far-infrared and vacuum drying banana slice. J. Food Eng. 92, 100-106.

[20] Ruiz-López, I., García-Alvarado, M. (2007). Analytical solution for food-drying kinetics considering shrinkage and variable diffusivity. J. Food Eng. 79, 208-216.

[21] Prachayawarakorn, S., Tia, W., Plyto, N., Soponronnarit, S. (2008). Drying kinetics and quality attributes of low-fat banana slices dried at high temperature. J. Food Eng. 85, 509-517.

[22] Talla, A., Puiggali, J.-R., Jomaa, W., Jannot, Y. (2004). Shrinkage and density evolution during drying of tropical fruits: application to banana. J. Food Eng. 64, 103-109.

[23] Hernandez, J., Pavon, G.,Garcıa, M. (2000). Analytical solution of mass transfer equation considering shrinkage for modeling food-drying kinetics. J. Food Eng. 45, 1-10.

[24] Brasiello, A., Adiletta, G., Russo, P., Crescitelli, S., Albanese, D., Di Matteo, M. (2013). Mathematical modeling of eggplant drying: shrinkage effect. J. Food Eng. 114, 99-105.

[25] Seyedabadi, E., Khojastehpour, M., Sadrnia, H. (2015). Predicting Cantaloupe Bruising Using Non-Linear Finite Element Method. Int. J. Food Prop. Int. J. Food Prop. 18, 2015-2025.

[26] Donea, J., Huerta, A., Ponthot, J., Rodríguez-Ferran, A. Arbitrary Lagrangian–Eulerian methods, Encyclopedia of computational mechanics, vol. 1. 2014, Wiley, Chichester.

[27] Anahid, M., Khoei, A. (2010). Modeling of moving boundaries in large plasticity deformations via an enriched arbitrary Lagrangian–Eulerian FE method. Scientia Iranica, Transaction A. Journal of Civil Engineering. 17, 141-160.

[28] Taciroglu, E., Acharya, A., Namazifard, A., Parsons, I. (2009). Arbitrary Lagrangian–Eulerian methods for analysis of regressing solid domains and interface tracking. Computers & Structures. 87, 355-367.

[29] Aprajeeta, J., Gopirajah, R., Anandharamakrishnan, C. (2015). Shrinkage and porosity effects on heat and mass transfer during potato drying. J. Food Eng. 144, 119-128.

[30] Curcio, S., Aversa, M. (2014). Influence of shrinkage on convective drying of fresh vegetables: A theoretical model. J. Food Eng. 123, 36-49.

[31] Sabarez, H.T. (2012). Computational modelling of the transport phenomena occurring during convective drying of prunes. J. Food Eng. 111, 279-288.

[32] AOAC. (1990). Official methods of analysis, 15th ed., Association of Official Analytical Chemists, Arlington, VA.

[33] Seyedabadi, E. (2015). Drying kinetics modelling of basil in microwave dryer. Agricultural Communications. 3, 37-44.

[34] Nadian, M.H., Abbaspour‐Fard, M.H., Sadrnia, H., Golzarian, M.R.,Tabasizadeh, M. (2016). Optimal pretreatment determination of kiwifruit drying via online monitoring. J. Sci. Food Agric. (in press),

[35] ASHRAE. (2010). chap. 19. Handbook-Refrigeration. 19.1-19.31.

[36] da Silva, W.P., e Silva, C.M., Gomes, J.P. (2013). Drying description of cylindrical pieces of bananas in different temperatures using diffusion models. J. Food Eng. 117, 417-424.

[37] Rodríguez, Ó., Eim, V.S., Simal, S., Femenia, A., Rosselló, C. (2013). Validation of a difussion model using moisture profiles measured by means of TD-NMR in apples (Malus domestica). Food Bioprocess Technol. 6, 542-552.

[38] Lemus-Mondaca, R.A., Zambra, C.E., Vega-Gálvez, A.,Moraga, N.O. (2013). Coupled 3D heat and mass transfer model for numerical analysis of drying process in papaya slices. J. Food Eng. 116, 109-117.

[39] Montanuci, F.D., Perussello, C.A., de Matos Jorge, L.M., Jorge, R.M.M. (2014). Experimental analysis and finite element simulation of the hydration process of barley grains. J. Food Eng. 131, 44-49.

[40] Singh, R.P., Heldman, D.R. (2009). Introduction to food engineering. fourth ed ed., United Kingdom: Elsevier.

[41] Earle, R.L. (2013). Unit operations in food processing. Elsevier.

[42] Holman, J. Heat transfer. (1986), McGraw-Hill Inc: New York. p. 621-676.

[43] Garau, M., Simal, S., Femenia, A., Rosselló, C. (2006). Drying of orange skin: drying kinetics modelling and functional properties. J. Food Eng. 75, 288-295.

[44] Cárcel, J., Garcia-Perez, J., Riera, E., Mulet, A. (2011). Improvement of convective drying of carrot by applying power ultrasound—Influence of mass load density. Drying Technol. 29, 174-182.

[45] Aral, S., Beşe, A.V. (2016). Convective drying of hawthorn fruit (Crataegus spp.): Effect of experimental parameters on drying kinetics, color, shrinkage, and rehydration capacity. Food chemistry. 210, 577-584.

[46] Horuz, E., Maskan, M. (2015). Hot air and microwave drying of pomegranate (Punica granatum L.) arils. J. Food Sci. Technol. 52, 285-293.

[47] Hatamipour, M., Mowla, D. (2002). Shrinkage of carrots during drying in an inert medium fluidized bed. J. Food Eng. 55, 247-252.

[48] Sturm, B., Vega, A.-M.N., Hofacker, W.C. (2014). Influence of process control strategies on drying kinetics, colour and shrinkage of air dried apples. Appl. Therm. Eng. 62, 455-460.

[49] Tzempelikos, D.A., Mitrakos, D., Vouros, A.P., Bardakas, A.V., Filios, A.E., Margaris, D.P. (2015). Numerical modeling of heat and mass transfer during convective drying of cylindrical quince slices. J. Food Eng. 156, 10-21.

[50] Kaymak-Ertekin, F., Gedik, A. (2005). Kinetic modelling of quality deterioration in onions during drying and storage. J. Food Eng. 68, 443-453.

[51] Ateeque, M., Mishra, R.K., Chandramohan, V., Talukdar, P. (2014). Numerical modeling of convective drying of food with spatially dependent transfer coefficient in a turbulent flow field. Int. J. Therm. Sci. 78, 145-157.

[52] Mohan, V.C., Talukdar, P. (2010). Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying. Int. J. Heat Mass Transfer. 53, 4638-4650.