Modelling of food transportation systems – a review

In 2002, over a million refrigerated road vehicles, 400,000 refrigerated containers and many thousands of other forms of refrigerated transport systems are used to distribute chilled and frozen foods throughout the world. All these transportation systems are expected to maintain the temperature of the food within close limits to ensure its optimum safety and high quality shelf life.Increasingly, modelling is being used to aid the design and optimisation of food refrigeration systems. Much of this effort has concentrated on the modelling of refrigeration processes that change the temperature of the food such as chilling, freezing and thawing. The purpose of a refrigerated transport system is to maintain the temperature of the food and appears to have attracted less attention from modellers. This paper reviews the work that has been carried out specifically on the modelling of food temperature, microbial growth and other parameters in the transportation of food.     

Extension of soil thermal conductivity models to frozen meats with low and high fat content

Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 to −40 °C. The model by deVries, with water+ice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from −1 to −20 °C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models.     

Cold chain database development and application as a tool for the cold chain management and food quality evaluation

Cold chain management can optimize freshness and safety to the consumer end. Within FRISBEE European project (http://frisbee-project.eu) a web-based platform was developed for temperature conditions data collection throughout the chilled and frozen food supply chain. Data including all cold chain stages (industry, distributors, retailers and consumers), were collected. This extensive database comprising more than 14,000 time-Temperature (t–T) profiles can serve as a valuable Cold Chain Management tool. The user can define a sequence of cold chain stages for selected food products. The Cold Chain Predictor (CCP) software based on the Cold Chain Database (CCD) allows calculation of product shelf-life status at different cold chain stages based on existing or user defined kinetic data. Conducted field tests expanded the Cold Chain Database and validated the software. The developed tools offer the potential to run simulation scenarios based on real cold chain data and contribute to effective cold chain improvement and management.     

CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process

A numerical simulation by using a computational fluid dynamics (CFD) code is carried out to predict heat and mass transfer during vacuum cooling of porous foods on the basis of mathematical models of unsteady heat and mass transfer. The simulations allow the simultaneous prediction of temperature distribution, weight loss and moisture content of the meats at low saturation pressure throughout the chilling process. The simulations are also capable of accounting for the effects of the dependent variables such as pressure, temperature, density and water content, thermal shrinkage, and anisotropy of the food. The model is verified by vacuum cooling of cooked meats with cylindrical shape within an experimental vacuum cooler. A data file for pressure history was created from the experimental pressure values, which were applied in the simulations as the boundary condition of the surface temperature.     

Process design data for prok chilling

In 1993 legislation is being enacted throughout the European Community (EC) that will require the maximum temperature of pork carcasses to be below 7°C before cutting or transportation. Results from a survey of UK abattoirs are summarized to highlight the problems and inadequacies of current commercial chilling systems. Design data are presented for conventional pork-chilling systems, which detail the effects of air temperature, air velocity and carcass weight on chilling times. Four novel or modified chilling systems are discussed: ultra-rapid chilling with air at −30°C; immersion chilling in brine at 0°C; ice-bank chilling in humid air at 2°C; and spray chilling in two stages, at 10°C for 2 h followed by 4°C for 21 h. The potential of such systems for the acceleration of chilling rates and for substantial weight savings is identified.     

Generalized model for the simulation of food refrigeration. Development and validation of the predictive numerical method

A generalized mathematical model was developed to simulate food refrigeration in air. The model takes into account surface water evaporation. It allows food physical properties to be considered as functions of temperature and/or composition, while providing means for including internal heat generation, composite materials (for instance, flesh and skin) and time-varying external temperature and humidity. Wetted surfaces and packaging can also be accounted for by the model, which can be used for spheres, infinite or finite cylinders, slabs. The numerical method was developed using the Crank-Nicolson scheme, and compared with exact analytical solutions as well as with experimental data on the refrigeration of various foods.     

A generalised mathematical modelling methodology for the design of horticultural food packages exposed to refrigerated conditions Part 2. Heat transfer modelling and testing

Sub-models required to implement the generalised simulation system, described in Part 1 for predicting in-package cooling rates of horticultural produce, are presented. These are based on heat transfer principles, but their derivation also involved application of heuristics derived by engineering judgement. Testing used two different products, eight package designs and data from four independent sources. Lack of fit between experiment and prediction was no larger than could be explained by likely data uncertainties so there is confidence that the simulation system will be accurate for a wide range of products and package designs. The object-oriented design of the simulation package allows individual sub-models to be updated without affecting any other sub-model, thereby ensuring the simulation package can remain up-to-date. In Part 3 the mass transfer sub-models are presented and test results reported.     

Modelling colour and chlorophyll losses of frozen green beans (Phaseolus vulgaris, L.)

Colour changes and chlorophyll degradation of frozen green beans (Phaseolus vulgaris, L., variety bencanta) were studied during 250 days of storage at −7, −15 and −30 °C. Chlorophyll a and b losses and colour Hunter a and b co-ordinates and total colour difference (TCD_H) changes were successfully described by first order and reversible first order models, respectively. The temperature effect was described by the Arrhenius law. Disagreement between the colour co-ordinates and chlorophyll content was obtained. Therefore, chlorophyll content is not a good colour index of frozen green beans. The results emphasise that colour is a more important parameter to assess frozen green beans visual quality.     

Measuring procedure and heat transfer modelling of a four-compartment isothermal liquid foodstuff tank tested according to the international ATP Agreement

The preservation of the cold chain is one of the most important requirements in order to maintain quality in the transport of perishable foodstuffs. A significant part of the aggregate of the universally transported perishable foodstuffs and more specific liquid foodstuffs like milk, wine, juice, etc. is carried out by multi-compartment isothermal tanks. According to the international ATP Agreement these special equipment used for international transport of perishable foodstuffs have to be tested periodically in officially recognized national ATP Test Stations to ensure that they meet the specifications. Because of the number of the compartments that have to be measured the testing of a multi-compartment isothermal tank presents special difficulties in comparison to the testing of a refrigerated truck. The instrumentation needed for testing a specimen in these cases is complex and that is why only few ATP Test Stations conduct such tests.In this study a heat transfer numerical simulation is described by a four compartment isothermal tank for the transport of perishable liquid foodstuffs tested inside an ATP chamber. The simulated tests were conducted according to the regulations specified in the United Nations ATP Agreement. A transient finite difference model is developed for a typical four compartment isothermal tank tested inside an ATP Testing Chamber with dimensions and specifications like that of the ATP chamber of the Zografou Campus of the National Technical University in Athens. For the control of the cooling/heating system a proportional–integral controller is employed. The study describes a method for measuring the k-coefficient of a four compartment isothermal tank according to ATP specifications using ordinary laboratory equipments. With the suggested method, the testing of a four compartment tank is possible using only one P–I controller and one thyristor instead of the normally needed four independent P–I controllers and four thyristors in order to adjust the heat power needed inside each compartment of the four compartment isothermal tank.     

Two- and three-dimensional CFD applied to vertical display cabinets simulation

A commercial CFD code has been employed to simulate the air flow pattern and the temperature distribution in a frozen food vertical display cabinet. At first the choice of solver parameters has been investigated in a 2D modelisation. 3D simulations have been then performed, and the effects of the cabinet length, of the warm air curtain and of longitudinal ambient air movement have been investigated. The results show that, in short cabinets, 3D secondary vortices at the side walls provide the most important mechanism for hot air entrainment. Comparison with experimental results shows that a 2D simulation is totally inadequate for such configurations, while 3D computations predict refrigeration power within engineering accuracy. Furthermore, the computed refrigerating power shows that even low room air velocity, due to its interaction with the end-wall vortices, has a significant impact on cabinet performance.