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

Abstract Vacuum cooling is a rapid cooling method widely used in cooling some food products. Simulating the vacuum cooling process with mathematical models helps to acquire a more intuitive understanding and optimize the whole cooling process. However, there is no review summarizing the mathematical models of vacuum cooling. In this review, heat and mass transfer process during vacuum cooling, types of mathematical models for vacuum cooling, and numerical methods including finite difference method, finite element method and finite volume method used for process simulation are introduced in details. The food products used in numerical simulation study of vacuum cooling generally include liquid food, vegetables and cooked meat. The ranges of application of various numerical methods are also discussed. Moreover, heat and mass transfer coefficients have a great influence on the accuracy of the model, and are generally provided by the literature. The investigations presented in this review invariably demonstrate that mathematical modeling can provide good prediction of key information of vacuum cooling process, and has a great potential to improve vacuum cooling process in the food industry. However, more efforts are still needed to realize the industrial translation of laboratory results.

[1]  Riadh Ben Salah,et al.  Lwt-Food Science And Technology , 2011 .

[2]  E. Jorge,et al.  THERMAL PROPERTIES OF FOODS , 1997 .

[3]  Wenyuan Qi,et al.  Quantitative study on the influence of bubble explosion on evaporation characteristics of flash boiling spray using UV-LAS technique , 2018, Experimental Thermal and Fluid Science.

[4]  Rodolfo H. Mascheroni,et al.  Modeling and Simulation of Microwave Heating of Foods Under Different Process Schedules , 2012, Food and Bioprocess Technology.

[5]  Jitendra Paliwal,et al.  Computational Fluid Dynamics in Drying Process Modelling—a Technical Review , 2018, Food and Bioprocess Technology.

[6]  Rudolf Zitny,et al.  Vacuum cooling process modelling , 1994 .

[7]  Adélio Rodrigues Gaspar,et al.  A mathematical model describing the two stages of low-pressure-vaporization of free water , 2012 .

[8]  Da-Wen Sun,et al.  Rapid cooling of porous and moisture foods by using vacuum cooling technology , 2001 .

[9]  Da-Wen Sun,et al.  CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process , 2003 .

[10]  Jun-Hu Cheng,et al.  Classification of fresh and frozen-thawed pork muscles using visible and near infrared hyperspectral imaging and textural analysis. , 2015, Meat science.

[11]  Da-Wen Sun,et al.  Vacuum cooling technology for the agri-food industry: Past, present and future , 2006 .

[12]  Hongbin Pu,et al.  Application of Vis–NIR hyperspectral imaging in classification between fresh and frozen-thawed pork Longissimus Dorsi muscles , 2015 .

[13]  Liana Drummond,et al.  Evaluation of the immersion vacuum cooling of cooked beef joints—mathematical simulation of variations in beef size and porosity and pressure reduction rates , 2012 .

[14]  Da-Wen Sun,et al.  Heat transfer characteristics of cooked meats using different cooling methods , 2000 .

[15]  Murat O. Balaban,et al.  Modeling of heat conduction in elliptical cross section: II. Adaptation to thermal processing of shrimp , 1998 .

[16]  Pedro D. Sanz,et al.  Characterising the detachment of thermal and geometric centres in a parallelepipedic frozen food subjected to a fluctuation in storage temperature , 1996 .

[17]  A. C Cleland,et al.  Prediction of chilling times of foods in situations where evaporative cooling is significant—Part 3. Applications , 1998 .

[18]  Hongchao Yin,et al.  A new flash boiling model for single droplet , 2017 .

[19]  Noemí E. Zaritzky,et al.  Mathematical Modeling and Simulation of Microwave Thawing of Large Solid Foods Under Different Operating Conditions , 2010 .

[20]  Yasuyuki Sagara,et al.  Measurement of Evaporation Coefficient of Water During Vacuum Cooling of Lettuce , 1994 .

[21]  Yongjun Zhao,et al.  Effects of modified atmosphere vacuum cooling (MAVC) on the quality of three different leafy cabbages , 2018, LWT.

[22]  E. Celik,et al.  THE EFFECT OF VACUUM PRECOOLING ON THE HALF COOLING PERIOD AND QUALITY CHARACTERISTIC OF ICEBERG LETTUCE , 1993 .

[23]  Chunjiang Zhao,et al.  A review of computational fluid dynamics for forced-air cooling process , 2016 .

[24]  Mukund V. Karwe,et al.  Numerical Prediction of Temperature Distribution and Measurement of Temperature in a High Hydrostatic Pressure Food Processor , 2009 .

[25]  L. Xu,et al.  Numerical study on the performance of vacuum cooler and evaporation-boiling phenomena during vacuum cooling of cooked meat , 2006 .

[26]  Hosahalli S. Ramaswamy,et al.  Modeling and Optimization of Microwave Osmotic Dehydration of Apple Cylinders Under Continuous-Flow Spray Mode Processing Conditions , 2012, Food and Bioprocess Technology.

[27]  Hongbin Pu,et al.  Prediction of textural changes in grass carp fillets as affected by vacuum freeze drying using hyperspectral imaging based on integrated group wavelengths , 2017 .

[28]  James K. Carson,et al.  Modelling Thermal Conductivity in Heterogeneous Media with the Finite Element Method , 2008 .

[29]  Da-Wen Sun,et al.  Modelling three-dimensional transient heat transfer of roasted meat during air blast cooling by the finite element method , 2002 .

[30]  Chongwen Cao,et al.  MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING , 2000 .

[31]  Qiaofen Cheng,et al.  Feasibility assessment of vacuum cooling of cooked pork ham with water compared to that without water and with air blast cooling , 2006 .

[32]  Zhongli Pan,et al.  Dry-peeling of Tomato by Infrared Radiative Heating: Part I. Model Development , 2014, Food and Bioprocess Technology.

[33]  Jun-Hu Cheng,et al.  Combining the genetic algorithm and successive projection algorithm for the selection of feature wavelengths to evaluate exudative characteristics in frozen-thawed fish muscle. , 2016, Food chemistry.

[34]  Da-Wen Sun,et al.  Modelling vacuum cooling process of cooked meat: part 1: analysis of vacuum cooling system , 2002 .

[35]  Hongbin Pu,et al.  Characterization of myofibrils cold structural deformation degrees of frozen pork using hyperspectral imaging coupled with spectral angle mapping algorithm. , 2018, Food chemistry.

[36]  Yuan-Yuan Pu,et al.  Prediction of moisture content uniformity of microwave-vacuum dried mangoes as affected by different shapes using NIR hyperspectral imaging , 2016 .

[37]  F. Stasa.  Applied finite element analysis for engineers , 1985 .

[38]  Baolin Liu,et al.  Mathematical simulation on the surface temperature variation of fresh-cut leafy vegetable during vacuum cooling , 2016 .

[39]  Zhiwei Zhu,et al.  Emerging techniques for assisting and accelerating food freezing processes: A review of recent research progresses , 2017, Critical reviews in food science and nutrition.

[40]  Da-Wen Sun,et al.  Recent developments in numerical modelling of heating and cooling processes in the food industry—a review , 2003 .

[41]  Yuan-Yuan Pu,et al.  Combined hot-air and microwave-vacuum drying for improving drying uniformity of mango slices based on hyperspectral imaging visualisation of moisture content distribution , 2017 .

[42]  V. M. Puri,et al.  The finite-element method in food processing: A review , 1993 .

[43]  Kannan Aravamudan,et al.  Quantifying Enhancement in Heat Transfer Due to Natural Convection During Canned Food Thermal Sterilization in a Still Retort , 2011 .

[44]  Da-Wen Sun,et al.  NUMERICAL ANALYSIS OF THE THREE–DIMENSIONAL MASS AND HEAT TRANSFER WITH INNER MOISTURE EVAPORATION IN POROUS COOKED MEAT JOINTS DURING VACUUM COOLING , 2003 .

[45]  Denis Flick,et al.  CFD Modeling and Simulation of Maltodextrin Solutions Spray Drying to Control Stickiness , 2010 .

[46]  Karel Petera,et al.  Vacuum Cooling of Liquids , 2000 .

[47]  V. S. Vaidhyanathan,et al.  Transport phenomena , 2005, Experientia.

[48]  Caroline M. McFarlane,et al.  The growth of Escherichia coli in a food simulant during conduction cooling : combining engineering and microbiological modelling , 2000 .

[49]  Suhas V. Patankar,et al.  Computation of Conduction and Duct Flow Heat Transfer , 2019 .

[50]  Thijs Defraeye,et al.  Multiparameter Analysis of Cooling Efficiency of Ventilated Fruit Cartons using CFD: Impact of Vent Hole Design and Internal Packaging , 2016, Food and Bioprocess Technology.

[51]  Liana Drummond,et al.  Temperature evolution and mass losses during immersion vacuum cooling of cooked beef joints - A finite difference model. , 2008, Meat science.

[52]  Yu Song,et al.  Study on water droplet flash evaporation in vacuum spray cooling , 2017 .

[53]  A. C Cleland,et al.  Prediction of chilling times of foods in situations where evaporative cooling is significant : Part 2. Experimental testing , 1998 .

[54]  Da-Wen Sun,et al.  Heat and mass transfer models for predicting freezing processes – a review , 2001 .

[55]  C. Anandharamakrishnan,et al.  Computational Fluid Dynamics (CFD) Modeling for Bread Baking Process—A Review , 2012, Food and Bioprocess Technology.

[56]  Umezuruike Linus Opara,et al.  Investigating the Effects of Table Grape Package Components and Stacking on Airflow, Heat and Mass Transfer Using 3-D CFD Modelling , 2012, Food and Bioprocess Technology.

[57]  Chongwen Cao,et al.  Mathematical simulation of temperature fields in a stored grain bin due to internal heat generation , 2000 .

[58]  Zhihang Zhang,et al.  Investigation of the effect of power ultrasound on the nucleation of water during freezing of agar gel samples in tubing vials. , 2012, Ultrasonics sonochemistry.

[59]  Da-Wen Sun,et al.  CFD predicting the effects of various parameters on core temperature and weight loss profiles of cooked meat during vacuum cooling , 2002 .

[60]  Milan Houška,et al.  Mathematical model of the vacuum cooling of liquids , 1996 .

[61]  Weiwei Cheng,et al.  Development of simplified models for nondestructive hyperspectral imaging monitoring of TVB-N contents in cured meat during drying process , 2017 .

[62]  F. A. Ansari.  Finite difference solution of heat and mass transfer problems related to precooling of food , 1999 .

[63]  Martin Dostál,et al.  Vacuum cooling of liquids: mathematical model , 2004 .

[64]  Luxiang Zong,et al.  Comparison of bubble growth process within a superheated water droplet and in superheated water due to rapid depressurization , 2017 .

[65]  Wenyuan Qi,et al.  Quantitative observation on characteristics and breakup of single superheated droplet , 2017 .

[66]  Jia,et al.  Computer simulation of temperature changes in a wheat storage bin. , 2001, Journal of stored products research.

[67]  Baolin Liu,et al.  Evaluation of Bubbling Vacuum Cooling for the Small-Size Cooked Pork , 2018, Food and Bioprocess Technology.

[68]  Da-Wen Sun,et al.  CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process , 2000 .

[69]  Zhi Wang,et al.  Effect of flash boiling on microscopic and macroscopic spray characteristics in optical GDI engine , 2017 .

[70]  Julio A. Luna,et al.  A mathematical model to describe potato chemical (NaOH) peeling. Energy and mass transfer model resolution , 1997 .

[71]  Da-Wen Sun,et al.  Vacuum cooling for the food industry—a review of recent research advances , 2004 .

[72]  Da-Wen Sun,et al.  Evaluation of performance of slow air, air blast and water immersion cooling methods in the cooked meat industry by the finite element method , 2002 .

[73]  Anguo Xie,et al.  Rapid detection of frozen pork quality without thawing by Vis-NIR hyperspectral imaging technique. , 2015, Talanta.

[74]  M. V. Krishna Murthy,et al.  Forced-air precooling of spherical foods in bulk: A parametric study , 1997 .

[75]  Da-Wen Sun,et al.  Vacuum cooling technology for the food processing industry: a review , 2000 .

[76]  Benan Cai,et al.  Modeling of spray flash evaporation based on droplet analysis , 2018 .

[77]  A. C Cleland,et al.  Prediction of chilling times of foods in situations where evaporative cooling is significant—Part 1. Method development , 1998 .

[78]  Da-Wen Sun,et al.  Development of a mathematical model for vacuum cooling of cooked meats , 2006 .

[79]  Karl McDonald,et al.  The formation of pores and their effects in a cooked beef product on the efficiency of vacuum cooling , 2001 .

[80]  Jun-Hu Cheng,et al.  Mapping moisture contents in grass carp (Ctenopharyngodon idella) slices under different freeze drying periods by Vis-NIR hyperspectral imaging , 2017 .

[81]  Da-Wen Sun,et al.  Modelling vacuum cooling process of cooked meat—part 2: mass and heat transfer of cooked meat under vacuum pressure , 2002 .

[82]  Thijs Defraeye,et al.  CFD modeling of industrial cooling of large beef carcasses. , 2016 .

[83]  L. Xu,et al.  Development and validation of moisture movement model for vacuum cooling of cooked meat , 2006 .

[84]  Hongbin Pu,et al.  Nondestructive Measurements of Freezing Parameters of Frozen Porcine Meat by NIR Hyperspectral Imaging , 2016, Food and Bioprocess Technology.

[85]  Zhihang Zhang,et al.  Vacuum Cooling of Meat Products: Current State-of-the-Art Research Advances , 2012, Critical reviews in food science and nutrition.