Abstract
The design strategy of a food process must be aimed to provide food safety while retaining optimal organoleptic and nutritional characteristics and, possibly, to optimize the energy consumption. As a matter of fact, it represents a challenge in food process engineering. In this framework, it is essential to determine the interactions among transport phenomena (mass, heat, and momentum) and any other relevant physics for further optimal design and for driving possible innovation. In other technological sectors (like automotive or aerospace industries), virtualization and mathematical modeling are standard methods used for optimal design, while in food process engineering the contribution of such tools has not been fully exploited. Since virtualization represents a new and sophisticated strategic tool to design and to innovate a process, the objective of this review was to introduce virtualization and mathematical modeling in the food processing industry. For this purpose, motivation and needs for virtualization in food processing were focused, mathematical modeling background and various approaches for modeling were introduced, and solution methods and required initial–boundary conditions with thermal-physical properties were outlined. Also complexity, computational cost, and model validation techniques were critically discussed. Virtualization and mathematical modeling dominate the major requirements to design, optimize, and innovate food processing with their vast opportunities and potentials and they will become a cornerstone of utmost importance to food engineering domain.
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References
IBM (2007) Virtualization in education. White Paper. http://www-07.ibm.com/solutions/in/education/download/Virtualization%20in%20Education.pdf
Verdouw CN, Wolfert J, Beulens AJ, Rialland A (2016) Virtualization of food supply chains with the internet of things. J Food Eng 176:128–136
Marra F (2016) Virtualization of processes in food engineering. J Food Eng 176:1
Singh RP, Erdogdu F (2004) Virtual experiments in food processing. RAR Press
Datta AK (2008) Status of physics-based models in the design of food products, processes and equipment. Compr Rev Food Sci Food Saf 7:121–129
Ho QT, Carmeliet J, Datta AK, Defraeye T, Delele MA, Herremans E, Opara L, Ramon H, Tijskens E, van der Sman R, Van Liedekerke P, Verboven P, Nicolaï BM (2013) Multiscale modeling in food engineering. J Food Eng 114:279–291
Kilic K, Boyaci IH, Koksel H, Kahramanoglu I (2007) A classification system for beans using computer vision system and artificial neural networks. J Food Eng 78:897–904
Omid M, Soltani M, Dehrouyeh MH, Mohtasebi SS, Ahmadi H (2013) An expert egg grading system based on machine vision and artificial intelligence techniques. J Food Eng 118:70–77
Benne M, Grondin-Perez B, Chabriat J-P, Herve P (2000) Artificial neural networks for modeling and predictive control of an industrial evaporation process. J Food Eng 46:227–234
Chen CR, Ramaswamy HS (2002) Modeling and optimization of variable retort temperature (VRT) thermal processing using coupled neural networks and genetic algorithms. J Food Eng 53: 209–2203.
Kashaninejad M, Dehghani AA, Kashiri M (2009) Modeling of wheat soaking using artificial neural networks (MLP and RBF). J Food Eng 91:602–607
Graf E, Saguy SI (1991) Food product development from concept to the market place. Chapman and Hall, London
MacFie H (1994) Computer assisted product development. World Ingredients 10:44–49
Rudder A, Ainsworth P, Holgate D (2001) New food product development: strategies for success? Br Food J 103(9):657–671
Nivière V, Grenier P, Roger JM, Sevila F, Oussalah M (1994) Intelligent simulation of plant operation in the wine industry. Food Control 5:91–95
López A, Esnoz A, Iguaz A, Vírseda P (2007) Integration of a malt drying model into a malt plant scheduling software. Dry Technol 25:1803–1808
López-Gómez A, Barbosa-Cánovas GV (2005) Food plant design. CRC Press, New York
European Commission (2010) http://epp.eurostat.ec.europa.eu/portal/page/portal/statistics/metadata
European Commission (2013) 2013 EU industrial research and development (R&D) investment scoreboard. Luxemburg, ISBN 978-92-79-33743-7
Chen Q, Wang M, Pan N, Guo Z-Y (2009) Optimization principles for convective heat transfer. Energy 34:1199–1206
López-Gómez A, Fernández PS, Palop A, Periago PM, Martinez-López A, Marin-Iniesta F, Barbosa-Cánovas GV (2009) Food safety engineering: an emergent perspective. Food Eng Rev 1:84–104
Sarghini F, Erdogdu F (2016) A computational study on heat transfer characteristics of particulate canned foods during end-over-end rotational agitation: effect of rotation rate and viscosity. Food Bioprod Process 100(Part B):496–511
Bimbenet JJ, Schubert H, Trystram G (2007) Advances in research in food process engineering. J Food Eng 78:390–404
Arroqui C, López A, Esnoz A, Virseda P (2003) Mathematical model of an integrated blancher/cooler. J Food Eng 59:297–307
Iguaz A, Esnoz A, Martinez G, López A, Virseda P (2003) Mathematical modelling and simulation for the drying process of vegetable wholesale by-products in a rotary dryer. J Food Eng 59:151–160
Balsa-Canto, E., Alonso, A.A., Arias-Méndez, A., García, M.R., López-Núñez, A., Mosquera-Fernández, M. and Vilas, C. 2016. Modeling and optimization techniques with applications in food processes, bio-processes and bio-systems. In: Numerical simulation in physics and engineering (pp. 187–216). Springer International Publishing, New York, NY.
Wedzicha B, Roberts C (2006) Modeling: a new solution to old problems in the food industry. Food Manuf Efficiency 1:1–7
Singh RP, Vijayan J (1998) Predictive modeling in food process design. Food Sci Technol Int 4:303–310
Datta AK, Halder A (2008) Status of food process modeling and where do we go from here (synthesis of the outcome from brainstorming). Compr Rev Food Sci Food Saf 7:117–120
Birkhoff, G. 1966. Dynamical systems. American Mathematical Society Colloquium Publication. 9. Providence. Rhode Island, AMS.
Sarghini F, Ruocco G (2004) Enhancement and reversal heat transfer by competing modes in jet impingement. Int J Heat Mass Transf 47(8–9):1711–1718
Olsson EEM, Ahrne LM, Tragardh AC (2004) Heat transfer from a slot air jet impinging. On a circular cylinder. J Food Eng 63:393–401
Sarghini F, Romano A, Masi P (2016) Experimental analysis and numerical simulation of pasta dough extrusion process. J Food Eng 176:56–70
Prosetya H, Datta A (1991) Batch microwave heating of liquids: an experimental study. J Microw Power Electromagn Energy 26:215–226
Marra F, Zhang L, Lyng JG (2009) Radio frequency treatment of foods: review of recent advances. J Food Eng 91(4):497–508
Teixeira AA, Dixon JR, Zahradnik JW, Zinsmeister GE (1969) Computer aided optimization of nutrient retention in the thermal processing of conduction-heated foods. Food Technol 23(6):137–142
Wang L, Sun D-W (2003) Recent developments in numerical modeling of heating and cooling processes in the food industry—a review. Trends Food Sci Technol 14:408–423
Nicolai BM, Verboven P, Scheerlinck N (2001) The modeling of heat and mass transfer. In: Tijskens LMM et al (eds) Food process modeling. Woodhead Publishing Ltd., Cambridge Chapter 4
Jasak H, Weller HG, Gosman AD (1999) High resolution differencing scheme for arbitrarily unstructured meshes. Int J Numer Methods Fluids 31:431–449
Clausing AM (1969) Numerical methods in heat transfer. In: Chao BT (ed) Advanced heat transfer. University of Illinois Press, Chicago
Palazoğlu TK, Erdogdu F (2009) Numerical solutions-finite difference methods. In: Erdogdu F (ed) Optimization in food engineering. CRC Press, Boca Raton Chapter 3
Finlayson A (1972) The method of weighted residuals and variational principles. Academic Press, New York
Gustafsson B, Kreiss H-O, Oliger J (2013) Time-dependent problems and difference methods, 2nd Ed, vol 123. John Wiley & Sons, New York
LeVeque RJ (2007) Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM, Basel
Moukalled F, Mangani L (2016) The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM and Matlab. Springer International Publishing AG, New York City
Thomas JW (2013) Numerical partial differential equations: finite difference methods, vol 22. Springer Science & Business Media, New York
Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics—the finite volume method, 2nd edn. Pearson Education Limited Edinburgh, England
Zienkiewicz OC, Taylor RL, Zhu JZ (2013) The finite element method: its basis and fundamentals, 7th edn. Butterworth-Heinemann, Oxford
Mauricio V-RJ, Francisco S-VW (2017) Modeling heat transfer during blanching of cubic particles of Loche (Cucurbita moschata Duch.) and potato (Solanum tuberosum L.) using finite difference method. J Food Process Eng. Article in press. doi:10.1111/jfpe.12451
Fabbri A, Cevoli C (2016) Rheological parameters estimation of non-Newtonian food fluids by finite elements model inversion. J Food Eng 169:172–178
Ahmad S, Khan MA, Kamil M (2015) Mathematical modeling of meat cylinder cooking. LWT Food Sci Technol 60:678–683
Feyissa AH, Christensen MG, Pedersen SJ, Hickman M, Adler-Nissen J (2015) Studying fluid-to-particle heat transfer coefficients in vessel cooking processes using potatoes as measuring devices. J Food Eng 163:71–78
Morawicki O, Schmalko ME (2011) Prediction of out-of-container pasteurization of pickled cucumbers using the finite difference method. J Food Eng 107:289–295
Datta AK (2002) Simulation-based design of food products and processes. In: Welti-Chanes J et al (eds) Engineering and food for the 21st century. CRC Press, Boca Raton Chapter 50
Boz Z, Erdogdu F, Tutar M (2014) Effects of mesh refinement, time step size and numerical scheme on the computational modeling of temperature evolution during natural-convection heating. J Food Eng 123:8–16
Roache PJ (1998) Verification and validation in computational science and engineering. Hermosa publishers, Albuquerque
Ferrua MJ, Singh RP (2009) Design guidelines for the forced-air cooling process of strawberries. Int J Refrig 32:1932–1943
Opara UL, Zou Q (2007) Sensitivity analysis of a CFD modelling system for airflow and heat transfer of fresh food packaging: inlet air flow velocity and inside-package configurations. Int J Food Eng 3:1556–3758
Delele MA, Ngcobo MEK, Getahun ST, Chen L, Mellman J, Opara UL (2013a) Studying airflow and heat transfer characteristics of a horticultural produce packaging system using a 3-D CFD model. Part I: Model development and validation. Postharvest Biol Technol 86:536–545
Ferrua MJ, Singh RP (2011) Improved airflow method and packaging system for forced-air cooling of strawberries. Int J Refrig 34:1162–1173
Delele MA, Ngcobo MEK, Getahun ST, Chen L, Mellman J, Opara UL (2013b) Studying airflow and heat transfer characteristics of a horticultural produce packaging system using a 3-D CFD model. Part II: Effect of package design. Postharvest Biol Technol 86:546–555
Alfaifi B, Tang J, Rasco B, Wang S, Sablani S (2016) Computer simulation analysis to improve radio frequency (RF) heating uniformity in dried fruits for insect control. Innovative Food Sci Emerg Technol 37:125–137
Chen L, Huang Z, Wang K, Li W, Wang S (2016) Simulation and validation of radio frequency heating with conveyor movement. J Electromagn Waves Appl 30:473–491
Li R, Kou X, Cheng T, Zheng A, Wang S (2017) Verification of radio frequency pasteurization process for in-shell almonds. J Food Eng 192:103–110
Uyar R, Bedane TF, Erdogdu F, Palazoglu TK, Marra F (2015) Radio-frequency thawing of food products—a computational study. J Food Eng 146:163–171
Cai R, Zhang N (2003) Explicit analytical solutions of 2-D laminar natural convection. Int J Heat Mass Transf 26:931–934
Carslaw HS, Jaeger JC (1959) Conduction heat transfer in solids, 2nd edn. Oxford University Press, London
Çengel YA (2007) Heat transfer: a practical approach. McGraw Hill Inc, New York
Özışık MN (1993) Heat conduction. Wiley, New York
Erdogdu F (2005) Mathematical approaches for use of analytical solutions in experimental determination of heat and mass transfer parameters. J Food Eng 68:233–238
Erdogdu F (2008) A review on simultaneous determination of thermal diffusivity and heat transfer coefficient. J Food Eng 86:453–459
Çengel YA, Cimbala JM (2006) Fluid mechanics fundamentals and applications. McGraw-Hill Inc., New York
Crank J (1984) Free and moving boundary problems. Clarendon Press, Oxford
ASHRAE (2006) Thermal properties of foods. In: Owen MS (ed) ASHRAE handbook 2006 refrigeration. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta Chapter 9
Heldman DR (2002) Prediction models for thermophysical properties of foods. In: Irudayaraj J (ed) Food processing operations modeling design and analysis. Marcel Dekker Inc., New York Chapter 1
Nesvadba P (2005) Thermal properties of unfrozen foods. In: Rao MA et al (eds) Engineering properties of foods. CRC Press, Boca Raton Chapter 4
Gulati T, Datta AK (2013) Enabling computer-aided food process engineering: property estimation equations for transport phenomena-based models. J Food Eng 116:483–504
Rao MA (2005) Rheological properties of fluid foods. In: Rao MA et al (eds) Engineering properties of foods. CRC Press, Boca Raton Chapter 2
Almeida M, Torrance KE, Datta AK (2006) Measurement of optical properties of foods in near- and mid-infrared radiation. Int J Food Prop 9:651–664
Sastry SK (2005) Electrical conductivity of foods. In: Rao MA et al (eds) Engineering properties of foods. CRC Press, Boca Raton Chapter 10
Venkatesh MS, Raghavan GSV (2004) An overview of microwave processing and dielectric properties of agri-food materials. Biosyst Eng 88:1–18
Datta AK, Sumnu G, Raghavan GSV (2005) Dielectric properties of foods. In: Rao MA et al (eds) Engineering properties of foods. CRC Press, Boca Raton Chapter 11
Rahman S (1995) Food properties handbook. CRC Press Inc, Boca Raton
Krokida MK, Zogzas NP, Maroulis ZB (2002) Heat transfer coefficient in food processing: compilation of literature data. Int J Food Prop 5:435–450
Zogzas NP, Krokida MK, Michailidis PA, Maroulis ZB (2002) Literature data of heat transfer coefficients in food processing. Int J Food Prop 5:391–417
Hulbert GJ, Litchfield JB, Schmidt SJ (1997) Determination of convective heat transfer coefficients using 2D MRI temperature mapping and finite element modeling. J Food Eng 34:193–201
Kondjoyan A, Boisson HC (1997) Comparison of calculated and experimental heat transfer coefficients at the surface of circular cylinders placed in a turbulent cross-flow of air. J Food Eng 34:123–143
Verboven P, Nicolai BM, De Baerdemaeker J (1997) The local surface heat transfer coefficient in thermal food process calculations: a CFD approach. J Food Eng 48:53–60
Curcio S, Aversa M, Chakraborty S, Calabrò V, Iorio G (2016) Formulation of a 3D conjugated multiphase transport model to predict drying process behavior of irregular-shaped vegetables. J Food Eng 176:36–55
Datta AK (2007a) Porous media approaches to studying simultaneous heat and mass transfer in food processes. I. Problem formulations. J Food Eng 80:80–95
Datta AK (2007b) Porous media approaches to studying simultaneous heat and mass transfer in food processes. I. Property data and representative results. J Food Eng 80:96–110
Marra F, De Bonis V, Ruocco G (2010) Combined microwaves and convection heating: a conjugate approach. J Food Eng 97:31–39
Marra F, Lyng J, Romano V, McKenna B (2007) Radio-frequency heating of foodstuff: solution and validation of mathematical model. J Food Eng 79:998–1006
Pace M, De Bonis MV, Marra F, Ruocco G (2011) Characterization of a combination oven prototype: effects of microwave exposure and enhanced convection to local temperature rise in a moist substrate. Int Commun Heat Mass Transfer 38:557–564
Kamonpatana P, Mohamed, H.M.H.m Shynkaryk, M., Heskitt, B., Yousef, A.E. and Sastry, S.K. (2013) Matmematical modeling and microbial verification of ohmic heating of a solid-liquid mixture in a continuous flow ohmic heated system with electric field perpendicular to flow. J Food Eng 118:312–325
Olivera DF, Salvadori VO, Marra F (2013) Ohmic treatment of fresh foods: effect on textural properties. Int Food Res J 20:1617–1621
Goni SM, Purlis E, Salvadori VO (2008) Geometry modelling of food materials from magnetic resonance imaging. J Food Eng 88:561–567
Cantre D, Herremans E, Verboven P, Ampofo-Asiama J, Nicolaï B (2014) Characterization of the 3-D microstructure of mango ( L. cv. Carabao) during ripening using X-ray computed microtomography. Innovative Food Sci Emerg Technol 24:28–39
Fanta SW, Abera MK, Aregawi WA, Ho QT, Verboven P, Carmeliet J, Nicolai BM (2014) Microscale modeling of coupled water transport and mechanical deformation of fruit tissue during dehydration. J Food Eng 124:86–96
Trystram G (2012) Modeling of food and food processes. J Food Eng 110:269–277
Lyng, J. G., Zhang, L., Marra, F. and Brunton, N.P. 2014. The effect of freezing rate and comminution on the dielectric properties of pork. Czech Journal of Food Science.
Feyissa AH, Gernaey KV, Adler-Nissen J (2012) Uncertainty and sensitivity analysis: mathematical model of coupled heat and mass transfer for a contact baking process. J Food Eng 109:281–290
Chen C, Abdelrahim K, Beckerich I (2010) Sensitivity analysis of continuous ohmic heating process for multiphase foods. J Food Eng 98:257–265
Nordhaus WD (2007) Two centuries of productivity growth in computing. J Econ Hist 67(1):128–159
Comsol (2014) Comsol Multiphysics 5.0, Stockolm
Buchhave P (1992) Particle image velocimetry—status and trends. Exp Thermal Fluid Sci 5:586–604
Beaumont F, Liger-Belair G, Polidori G (2016) Unveiling self-organized two-dimensional (2D) convective cells in champagne glasses. J Food Eng 188:58–65
Fayolle F, Belhamri R, Flick D (2013) Residence time distribution measurements and simulation of the flow pattern in a scraped surface heat exchanger during crystallization of ice cream. J Food Eng 116:390–397
Laguerre O, Ben Amara S, Charrier-Mojtabi M-C, Lartique B, Flick D (2008) Experimental study of air flow by natural convection in a closed cavity: application in a domestic refrigerator. J Food Eng 85:547–560
Cox PW, Bakalis S, Ismail H, Forster R, Fryer PJ (2003) Visualization of three-dimensional flows in rotating cans using positron emission particle tracking (PEPT). J Food Eng 60:229–240
Bakalis S, Coz PW, Wang-Nolan W, Parker DJ, Fryer PJ (2003) Use of positron emission particle tracking (PEPT) technique for velocity measurements in model food fluids. J Food Sci 68:2684–2692
Rafiee M, Bekalis S, Fryer PJ, Ingram A (2011) Study of laminar mixing in kenics static mixer by using positron emission particle tracking (PEPT). Procedia Food Sci 1:678–694
Yan Z, Fan H, Parker DJ, Fryer PJ, Bakalis S, Fan X (2014) Study on solids translational and rotational motions in cans. Food Sci Technol 2014:383–392
Hills B (1995) Food processing: an MRI perspective. Trends Food Sci Technol 6:111–117
Knoerzer K, Regier M, Hardy EH, Schuchmann HP, Schubert H (2009) Simultaneous microwave heating and three-dimensional MRI temperature mapping. Innovative Food Sci Emerg Technol 10:537–544
Jin X, van der Sman RGM, gerkema, E., Vergeldt, F.J., van As, H., van Boxtel, A.J.B. (2011) Moisture distribution in broccoli: measurements by MRI hot air drying experiments. Procedia Food Sci I:640–646
Caballero D, Caro A, Rodriguez PG, Duran ML, del Mar Avila M, Palacios R, Antequera T, Perez-Palacios T (2016) Modeling salt diffusion in Iberian ham by applying MRI and data mining. J Food Eng 189:115–122
Balasubramaniam VM, Sastry SK (1995) Use of liquid crystals as temperature sensors in food processing research. J Food Eng 26:219–230
Cuibus L, Castro-Giraldez M, Fito PJ, Fabbri A (2014) Application of infrared thermography and dielectric spectroscopy for controlling freezing process of raw potato. Innovative Food Sci Emerg Technol 24:80–87
Gowen AA, Tiwari BK, Cullen PJ, McDonnell K, O’Donnell CP (2010) Applications of thermal imaging in food quality and safety assessment. Trends Food Sci Technol 21:190–200
Fryer PJ, Robbins PT (2005) Heat transfer in food processing: ensuring product quality and safety. Appl Therm Eng 25:2499–2510
Arias-Mendez A, Vilas C, Alonso AA, Balsa-Canto E (2014) Time-temperature integrators as predictive temperature sensors. Food Control 44:258–266
Datta AK, Teixeira AA (1988) Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. J Food Sci 53:191–195
De Bonis MV, Ruocco G (2007) Modeling local heat and mass transfer in food slabs due to air jet impingement. 78:230–237
De Bonis MV, Ruocco G (2014) Conjugate heat and mass transfer by jet impingement over a moist protrusion. Int J Heat Mass Transf 70:192–201
Saguy S (2016) Challenges and opportunities in food engineering: modeling complexity, virtualization, open innovation and social responsibility. J Food Eng 176:2–8
Acknowledgements
The authors are participating the Special Interest Group “Virtualization in Food Engineering,” ISEKI Food Association (Vienna, Austria), and the Cost Action FoodMC – CA15118 “Mathematical and Computer Science Methods for Food Science and Industry”. They acknowledge these scientific communities for providing platforms to share the importance of virtualization and modeling in the food industry domain.
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Erdogdu, F., Sarghini, F. & Marra, F. Mathematical Modeling for Virtualization in Food Processing. Food Eng Rev 9, 295–313 (2017). https://doi.org/10.1007/s12393-017-9161-y
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DOI: https://doi.org/10.1007/s12393-017-9161-y