Developments of mathematical models for simulating vacuum cooling processes for food products – a review

References

• Analía-Campañone, L., N. E. Zaritzky, M. Zude, O. Schlüter, and A. Rosenthal. 2010. Mathematical modeling and simulation of microwave thawing of large solid foods under different operating conditions. Food & Bioprocess Technology 3:813–25.
   Web of Science ®Google Scholar
• Ansari, F. A. 1999. Finite difference solution of heat and mass transfer problems related to precooling of food. Energy Conversion & Management 40:795–802.
   Web of Science ®Google Scholar
• Augusto, C. M., J. B. Ribeiro, A. R. Gaspar, V. R. Ferreira, and J. J. Costa. 2012. A mathematical model describing the two stages of low-pressure-vaporization of free water. Journal of Food Engineering 112:274–81.
   Web of Science ®Google Scholar
• Azarpazhooh, E., and H. S. Ramaswamy. 2012. Modeling and optimization of microwave osmotic dehydration of apple cylinders under continuous-flow spray mode processing conditions. Food & Bioprocess Technology 5:1486–501.
   Web of Science ®Google Scholar
• Bellara, S. R., C. M. Mcfarlane, C. R. Thomas, and P. J. Fryer. 2000. The growth of escherichiacoli ja:math in a food simulant during conduction cooling: combining engineering and microbiological modelling. Chemical Engineering Science 55:6085–95.
   Web of Science ®Google Scholar
• Berry, T. M., T. Defraeye, B. M. Nicolaī, and U. L. Opara. 2016. Multiparameter analysis of cooling efficiency of ventilated fruit cartons using CFD: Impact of vent hole design and internal packaging. Food and Bioprocess Technology 9:1481–93.
   Web of Science ®Google Scholar
• Bird, R. B. 2002. Transport phenomena. Applied Mechanics Reviews 55:R1–4.
   Google Scholar
• Burfoot, D., R. Hayden, and R. Badran. 1989. Simulation of a pressure cook/water and vacuum cooled processing system. In Process engineering in the food industry: Developments and opportunities, eds. R.W. Field and J. Howell, 27–41. London, UK: Elsevier Applied Science.
   Google Scholar
• Cai, B., X. Tuo, Z. Song, Y. Zheng, H. Gu, and H. Wang. 2018. Modeling of spray flash evaporation based on droplet analysis. Applied Thermal Engineering 130:1044–51.
   Web of Science ®Google Scholar
• Campañone, L. A., C. A. Paola, and R. H. Mascheroni. 2012. Modeling and simulation of microwave heating of foods under different process schedules. Food & Bioprocess Technology 5:738–49.
   Web of Science ®Google Scholar
• Chavez, M. S., J. A. Luna, and R. L. Garrote. 1997. A mathematical model to describe potato chemical (NaOH) peeling. Energy and mass transfer model resolution. Journal of Food Engineering 32:209–223.
   Web of Science ®Google Scholar
• Cheng, Q., and D. W. Sun. 2006. Feasibility assessment of vacuum cooling of cooked pork ham with water compared to that without water and with air blast cooling. International Journal of Food Science & Technology 41:938–45.
   Web of Science ®Google Scholar
• Cheng, J.-H., D.-W. Sun, and H. Pu. 2016. Combining the genetic algorithm and successive projection algorithm for the selection of feature wavelengths to evaluate exudative characteristics in frozen-thawed fish muscle. Food Chemistry 197:855–863.
   PubMed Web of Science ®Google Scholar
• Cheng, L., D.-W. Sun, Z. Zhu, and Z. Zhang. 2017. Emerging techniques for assisting and accelerating food freezing processes: A review of recent research progresses. Critical Reviews in Food Science and Nutrition 57:769–781.
   PubMed Web of Science ®Google Scholar
• Cheng, W., D. –W. Sun, H. Pu, and Q. Wei. 2018. Characterization of myofibrils cold structural deformation degrees of frozen pork using hyperspectral imaging coupled with spectral angle mapping algorithm. Food Chemistry 239:1001–1008.
   PubMed Web of Science ®Google Scholar
• Chhanwal, N., A. Tank, K. S. M. S. Raghavarao, and C. Anandharamakrishnan. 2012. Computational fluid dynamics (CFD) modeling for bread baking process—A review. Food and Bioprocess Technology 5:1157–1172.
   Web of Science ®Google Scholar
• Chuntranuluck, S., C. M. Wells, and A. C. Cleland. 1998a. Prediction of chilling times of foods in situations where evaporative cooling is significant—part 1. Method development. Journal of Food Engineering 37:111–25.
   Web of Science ®Google Scholar
• Chuntranuluck, S., C. M. Wells, and A. C. Cleland. 1998b. Prediction of chilling times of foods in situations where evaporative cooling is significant—part 2. Experimental testing. Journal of Food Engineering 37:127–41.
   Web of Science ®Google Scholar
• Chuntranuluck, S., C. M. Wells, and A. C. Cleland. 1998c. Prediction of chilling times of foods in situations where evaporative cooling is significant—part 3. Applications. Journal of Food Engineering 37:143–157.
   Web of Science ®Google Scholar
• Delele, M. A., M. E. K. Ngcobo, U. L. Opara, and C. J. Meyer. 2013. Investigating the effects of table grape package components and stacking on airflow, heat and mass transfer using 3-D CFD modelling. Food and Bioprocess Technology 6:2571–2585.
   Web of Science ®Google Scholar
• Delgado, A. E., and D.-W. Sun. 2001. Heat and mass transfer models for predicting freezing process-a review. Journal of Food Engineering 47 (3):157–74.
   Web of Science ®Google Scholar
• Dostal, M., and K. Petera. 2004. Vacuum cooling of liquids: mathematical model. Journal of Food Engineering 61:533–9.
   Web of Science ®Google Scholar
• Drummond, L., and D.-W. Sun. 2008. Temperature evolution and mass losses during immersion vacuum cooling of cooked beef joints – a finite difference model. Meat Science 80:885–91.
   PubMed Web of Science ®Google Scholar
• Drummond, L., and D.-W. Sun. 2012. Evaluation of the immersion vacuum cooling of cooked beef joints—mathematical simulation of variations in beef size and porosity and pressure reduction rates. Innovative Food Science & Emerging Technologies 16:205–10.
   Web of Science ®Google Scholar
• Elvira, C. D., P. D. Sanz, and J. A. Carrasco. 1996. Characterising the detachment of thermal and geometric centres in a parallelepipedic frozen food subjected to a fluctuation in storage temperature. Journal of Food Engineering 29:257–68.
   Web of Science ®Google Scholar
• Erdogdu, F., M. O. Balaban, and K. V. Chau. 1998. Modeling of heat conduction in elliptical cross section. I. Development and testing of the model. Journal of Food Engineering 38:223–39.
   Web of Science ®Google Scholar
• Feng, C., L. Drummond, Z. Zhang, D. W. Sun, and Q. Wang. 2012. Vacuum cooling of meat products: current state-of-the-art research advances. Critical Reviews in Food Science & Nutrition 52 (11):1024–38.
   PubMed Web of Science ®Google Scholar
• Floury, J., J. Carson, and Q. T. Pham. 2008. Modelling thermal conductivity in heterogeneous media with the finite element method. Food & Bioprocess Technology 1:161–70.
   Web of Science ®Google Scholar
• Gianfrancesco, A., C. Turchiuli, D. Flick, and E. Dumoulin. 2010. CFD modeling and simulation of maltodextrin solutions spray drying to control stickiness. Food and Bioprocess Technology 3:946–55.
   Web of Science ®Google Scholar
• Gowda, B. S., G. S. V. L. Narasimham, and M. V. K. Murthy. 1997. Forced-air precooling of spherical foods in bulk: a parametric study. International Journal of Heat & Fluid Flow 18:613–24.
   Web of Science ®Google Scholar
• Guo, H., X. Ma, Y. Li, S. Liang, Z. Wang, H. Xu, and J. Wang. 2017. Effect of flash boiling on microscopic and macroscopic spray characteristics in optical GDI engine. Fuel 190:79–89.
   Web of Science ®Google Scholar
• Hous˘ka, M., S. Podloucký, R. Zitný, R. Grée, J. Sesták, M. Dostál, and D. Burfoot, 1996. Mathematical model of the vacuum cooling of liquids. Journal of Food Engineering 29:339–48.
   Web of Science ®Google Scholar
• Hous˘ka, M., R. Zitny, J. Sestak, J. Jeschke, &, and D. Burfoot. 1994. Vacuum cooling process modelling. Potravinářské Vědy 12:1–15.
   Google Scholar
• Hu, ZH., and D.-W. Sun. 2000. CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process. Journal of Food Engineering 45:189–197.
   Google Scholar
• Jia, C.-C., D.-W. Sun, and C.-W. Cao. 2000a. Mathematical simulation of temperature and moisture fields within a grain kernel during drying. Drying Technology 18:1305–25.
   Web of Science ®Google Scholar
• Jia, C.-C., D.-W. Sun, and C.-W. Cao. 2000b. Mathematical simulation of temperature fields in a stored grain bin due to internal heat generation. Journal of Food Engineering 43:227–33.
   Web of Science ®Google Scholar
• Jia, C., D.-W. Sun, and C. Cao. 2001. Computer simulation of temperature changes in a wheat storage bin. Journal of Stored Products Research 37 (2):165–77.
   PubMed Web of Science ®Google Scholar
• Jin, T. X., and L. Xu. 2006a. Development and validation of moisture movement model for vacuum cooling of cooked meat. Journal of Food Engineering 75:333–9.
   Web of Science ®Google Scholar
• Jin, T. X., and L. Xu. 2006b. Numerical study on the performance of vacuum cooler and evaporation-boiling phenomena during vacuum cooling of cooked meat. Energy Conversion and Management 47:1830–42.
   Web of Science ®Google Scholar
• Kiani, H., D.-W. Sun, A. Delgado, and Z. Zhang. 2012. Investigation of the effect of power ultrasound on the nucleation of water during freezing of agar gel samples in tubing vials. Ultrasonics Sonochemistry 19:576–581.
   PubMed Web of Science ®Google Scholar
• Koribilli, N., K. Aravamudan, and M. U. S. V. Aditya Varadhan. 2011. Quantifying enhancement in heat transfer due to natural convection during canned food thermal sterilization in a still retort. Food and Bioprocess Technology 4:429–50.
   Web of Science ®Google Scholar
• Khurana, M., M. V. Karwe, and M. Zude. 2009. Numerical prediction of temperature distribution and measurement of temperature in a high hydrostatic pressure food processor. Food & Bioprocess Technology 2:279–90.
   Web of Science ®Google Scholar
• Kuffi, K. D., T. Defraeye, B. M. Nicolai, S. D. Smet, A. Geeraerd, and P. Verboven. 2016. CFD modeling of industrial cooling of large beef carcasses. International Journal of Refrigeration 69:324–39.
   Web of Science ®Google Scholar
• Li, S., Y. Zhang, and W. Qi. 2018. Quantitative study on the influence of bubble explosion on evaporation characteristics of flash boiling spray using UV-LAS technique. Experimental Thermal & Fluid Science. https://doi.org/10.1016/j.expthermflusci.2018.03.025.
   Web of Science ®Google Scholar
• Li, S., Y. Zhang, W. Qi, and B. Xu. 2017. Quantitative observation on characteristics and breakup of single superheated droplet. Experimental Thermal & Fluid Science 80:305–12.
   Web of Science ®Google Scholar
• Li, X., and Z. Pan. (2014). Dry-peeling of tomato by infrared radiative heating: Part I. model development. Food and Bioprocess Technology 7:1996–2004.
   Web of Science ®Google Scholar
• Liu, L., W. Ma, M. Wang, and L. Zong. 2017. Comparison of bubble growth process within a superheated water droplet and in superheated water due to rapid depressurization. International Journal of Heat & Mass Transfer 109:659–67.
   Web of Science ®Google Scholar
• Ma, J., H. Pu, D.-W. Sun, W. Gao, J.-H. Qu, and K.-Y. Ma. 2015. Application of Vis-NIR hyperspectral imaging in classification between fresh and frozen-thawed pork Longissimus Dorsi muscles. International Journal of Refrigerator-Revue Internationale Du Froid 50:10–18.
   Web of Science ®Google Scholar
• Ma, J., D.–W. Sun, J.-H. Qu, and H. Pu. 2017. Prediction of textural changes in grass carp fillets as affected by vacuum freeze drying using hyperspectral imaging based on integrated group wavelengths. LWT-Food Science and Technology 82:377–385.
   Web of Science ®Google Scholar
• McDonald, K., and D.-W. Sun. 1999a. Effect of cooling rate on the quality of cooked beef. Paper No. P06/10. In 10th World Congress of Food Science and Technology, Sydney, Australia.
   Google Scholar
• McDonald, K., and D.-W. Sun. 1999b. Effects of different cooling methods on microbiological quality of large cooked beef joints. International Journal of Refrigeration 20 (2):173–90.
   Google Scholar
• McDonald, K., and D.-W. Sun. 2000. Vacuum cooling technology for the food processing industry: a review. Journal of Food Engineering 45 (2):55–65.
   Web of Science ®Google Scholar
• McDonald, K., and D.-W. Sun. 2001. The formation of pores and their effects in a cooked beef product on the efficiency of vacuum cooling. Journal of Food Engineering 47 (3):175–83.
   Web of Science ®Google Scholar
• Patankar, 1991. Computation of Conduction and Duct Flow Heat Transfer. Innovative Research Inc., 7846 Ithaca Lane North, Maple Grove, MN 55369-8549, USA.
   Google Scholar
• Pu, H., D.-W. Sun, J. Ma, and J.-H. Cheng. 2015. Classification of fresh and frozen-thawed pork muscles using visible and near infrared hyperspectral imaging and textural analysis. Meat Science 99:81–88.
   PubMed Web of Science ®Google Scholar
• Pu, Y.-Y., and D.-W. Sun. 2016. Prediction of moisture content uniformity of microwave-vacuum dried mangoes as affected by different shapes using NIR hyperspectral imaging. Innovative Food Science & Emerging Technologies 33:348–356.
   Web of Science ®Google Scholar
• Pu, Y.–Y., and D.-W. Sun. 2017. Combined hot-air and microwave-vacuum drying for improving drying uniformity of mango slices based on hyperspectral imaging visualisation of moisture content distribution. Biosystems Engineering 156:108–119.
   Web of Science ®Google Scholar
• Puri, V. M., and R. C. Anantheswaran. 1993. The finite-element method in food processing: a review. Journal of Food Engineering 19:247–74.
   Web of Science ®Google Scholar
• Qu, J. -H; D. –W. Sun, J. -H. Cheng, and H. Pu. 2017. Mapping moisture contents in grass carp (Ctenopharyngodon idella) slices under different freeze drying periods by Vis-NIR hyperspectral imaging. LWT-Food Science and Technology 75:529–536.
   Web of Science ®Google Scholar
• Ramachandran, R. P., M. Akbarzadeh, J. Paliwal, and S. Cenkowski. 2018. Computational fluid dynamics in drying process modelling—a technical review. Food & Bioprocess Technology 11:271–92.
   Web of Science ®Google Scholar
• Shewfelt, R. L., and R. D. Phillips. 1996. Seven principles for better quality of refrigerated fruits and vegetables. In New developments in refrigeration for food safety and quality, Refrigeration Science and Technology Proceedings of the Meeting of Commission C2, with Commissions B2, D1, and D2-3, October 2–4, 1996, Lexington, Kentucky.
   Google Scholar
• Song, X. Y., Z. Y. Guo, B. L. Liu, and G. K. Jaganathan. 2018. Evaluation of bubbling vacuum cooling for the small-size cooked pork. Food & Bioprocess Technology 11:18.
   Web of Science ®Google Scholar
• Song, X-y., B-L Liu, and G. K. Jaganathan. 2016. Mathematical simulation on the surface temperature variation of fresh-cut leafy vegetable during vacuum cooling. International Journal of Refrigeration 65:228–237.
   Web of Science ®Google Scholar
• Stas, A., L. Frank. 1985 Applied finite element analysis for engineers. 1st ed., New York: CBS Publishing.
   Google Scholar
• Sullivan, G. H., L. R. Davenport, and J. W. Julian. 1996. Precooling: key factor for assuring quality in new fresh market vegetable crops. Progress in new crops. Arlington: Virginia ASHS Press.
   Google Scholar
• Sun, D.-W., and Z. Hu. 2002. CFD predicting the effects of various parameters on core temperature and weight loss profiles of cooked meat during vacuum cooling. Computers & Electronics in Agriculture 34:111–27.
   Web of Science ®Google Scholar
• Sun, D.-W., and Z. Hu. 2003. CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process. International Journal of Refrigeration 26 (1):19–27.
   Web of Science ®Google Scholar
• Sun, D.-W., and L. Wang. 2000. Heat transfer characteristics of cooked meats using different cooling methods. International Journal of Refrigeration 23 (7):508–16.
   Web of Science ®Google Scholar
• Sun, D.-W., and L. Wang. 2006. Development of a mathematical model for vacuum cooling of cooked meats. Journal of Food Engineering 77 (3):379–85.
   Web of Science ®Google Scholar
• Sun, D.-W., and L. Zheng. 2006. Vacuum cooling technology for the Agri-food industry: past, present and future. Journal of Food Engineering 77 (2):203–14.
   Web of Science ®Google Scholar
• Sweat, V. E. 1986. Thermal properties of foods. In Engineering properties of foods, eds. M. A. Rao and S. S. H. Rizil, pp.49–87. New York, America: Marcel Dekker, Inc.
   Google Scholar
• Tambunan, A. H., Y. Seo, Y. Sagara, H. Morishima, and Y. Kawagoe. 1994. Measurement of evaporation coefficient of water during vacuum cooling of lettuce. In Developments in food engineering, pp. 328–30. Boston, MA: Springer.
   Google Scholar
• Turk, R., and E. Celik. 1993. The effect of vacuum precooling on the half cooling period and quality characteristic of iceberg lettuce. Acta Horticulture Postharvest 343:321–4.
   Google Scholar
• Wang, C., R. Xu, Y. Song, and P. Jiang. 2017. Study on water droplet flash evaporation in vacuum spray cooling. International Journal of Heat and Mass Transfer 112:279–88.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2001. Rapid cooling of porous and moisture foods by using vacuum cooling technology. Trends in Food Science & Technology 12:174–84.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2002a. Evaluation of performance of slow air, air blast and water immersion cooling methods in the cooked meat industry by the finite element method. Journal of Food Engineering 51 (4):329–40.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2002b. Modelling three-dimensional transient heat transfer of roasted meat during air blast cooling by the finite element method. Journal of Food Engineering 51 (4):319–28.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2002c. Modelling vacuum cooling process of cooked meat—part 1: analysis of vacuum cooling system. International Journal of Refrigeration 25 (7):854–61.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2002d. Modelling vacuum cooling process of cooked meat—part 2: mass and heat transfer of cooked meat under vacuum pressure. International Journal of Refrigeration 25 (7):862–71.
   Web of Science ®Google Scholar
• Wang, L., and D.-W. Sun. 2003a. Recent developments in numerical modelling of heating and cooling processes in the food industry--a review. Trends in Food Science & Technology 14 (10):408–23.
   Web of Science ®Google Scholar
• Wang, L. J., and D.-W. Sun. 2003b. Numerical analysis of the three-dimensional mass and heat transfer with inner moisture evaporation in porous cooked meat joints during vacuum cooling. Transactions of the ASAE 46 (1):107–15.
   Google Scholar
• Xi, X.,. H. Liu, M. Jia, M. Xie, and H. Yin. 2017. A new flash boiling model for single droplet. International Journal of Heat and Mass Transfer 107:1129–37.
   Web of Science ®Google Scholar
• Xie, A., D.-W. Sun, Z. Xu, and Z. Zhu. 2015. Rapid detection of frozen pork quality without thawing by Vis-NIR hyperspectral imaging technique. Talanta 139:208–215.
   PubMed Web of Science ®Google Scholar
• Xie, A., D.-W. Sun, Z. Zhu, and H. Pu. 2016. Nondestructive Measurements of Freezing Parameters of Frozen Porcine Meat by NIR Hyperspectral Imaging. Food and Bioprocess Technology 9:1444–1454.
   Web of Science ®Google Scholar
• Yang, Q., D.-W. Sun, and W. Cheng. 2017. Development of simplified models for nondestructive hyperspectral imaging monitoring of TVB-N contents in cured meat during drying process. Journal of Food Engineering 192:53–60.
   Web of Science ®Google Scholar
• Zhao, C. J., J. W. Han, X. T. Yang, J. P. Qian, and B. L. Fan. 2016. A review of computational fluid dynamics for forced-air cooling process. Applied Energy 168:314–31.
   Web of Science ®Google Scholar
• Zheng, L., and D.-W. Sun. 2004. Vacuum cooling for the food industry—a review of recent research advances. Trends in Food Science & Technology 15 (12):555–68.
   Web of Science ®Google Scholar
• Zhu, Z., X. Wu, Y. Geng, and D.-W. Sun. 2018. Effects of modified atmosphere vacuum cooling (MAVC) on the quality of three different leafy cabbages. LWT https://doi.org/10.1016/j.lwt.2018.04.002
   Web of Science ®Google Scholar