Mathematical modelling of thermal storage systems for the food industryModélisation mathématique de systèmes d'accumulation thermique utilisés par l'industrie alimentaire

Dynamic mathematical models of two thermal storage systems used in the food industry to produce chilled water are presented; an ice-bank system and a holding tank system. The variability of the refrigeration demand with time was taken into account in the model. A zoned approach using mass and energy balances was applied. Heat transfer phenomena in the evaporator were modelled using empirical correlations. The experimental validation of the mathematical models on an ice-bank system at pilot plant scale, and a centralized refrigeration system with a holding tank in a winery, showed accurate prediction. Simple models are adequate to predict the dynamic behaviour of these refrigeration systems under variable heat loads.     

Quantitative prediction of microbial behaviour during food processing using an integrated modelling approach: a review

Microbiological safety of food relies on microbial examination of raw materials and final products, coupled with monitoring process parameters and hygiene standards. The concept of predictive microbiology was developed to evaluate the effect of processing, distribution and storage operations on food safety. The objective of this paper is to review the approaches proposed by researchers to quantify the effect of competitiveness or fluctuating conditions on bacterial behaviour. The main microbial models that quantify the effects of various hurdles on microbial kinetics are presented. To provide complementary information for microbial models, three areas have to be considered: process engineering that characterises and models mass and heat transfer; microbiology that characterises and models bacterial behaviour and metabolite production, and; applied thermodynamics that characterises and models the physico-chemical properties of a food product. Global modelling approaches, developed by integrating the previous models, are illustrated with recent results.     

Passive thermal energy storage in refrigerated warehouses

This paper investigates operational strategies that use stored products as thermal mass to shift refrigeration loads to more favorable operational periods (low energy cost periods, lower outdoor air conditions, etc.) allowing an opportunity to reduce system operating costs. An integrated model of the stored product, warehouse air, and warehouse structure is developed and thermal response characteristics are predicted for a selected warehousing facility. Simulated results are validated with experimental measurements. Food quality impacts associated with the temperature cycling caused by potential operating strategies are discussed. Results from this investigation indicated that a full load-shifting control strategy would save $82,000 (US) ($0.40/ft²/year or $4.28/m²/year) annually over the test facility's current operational strategy, representing 53% of the total cooling cost. Predicted maximum warehouse temperature variation is 5.6°C, which is not expected to cause significant product quality changes in the temperature range (below−18°C) studied.     

A review of numerical models of airflow in refrigerated food applications

Temperature homogeneity in most food refrigeration systems is directly governed by the airflow patterns in the system. Numerical modelling of airflow provides an opportunity to develop improved understanding of the underlying phenomena influencing system performance, which can lead to reduced temperature heterogeneity and increased effectiveness and efficiency of refrigeration systems. With the rapid advances in computational power of recent years, the use of Computational Fluid Dynamics (CFD) techniques in this application has become popular. This paper reviews the application of CFD and other numerical modelling techniques to the prediction of airflow in refrigerated food applications including cool stores, transport equipments and retail display cabinets.     

Effective thermal conductivity of a high porosity model food at above and sub-freezing temperatures

The modelling of heat transfer within materials with high porosity is complicated by evaporation-condensation phenomena. The aim of this work is to develop a model for apparent thermal conductivity in these products. The effective thermal conductivity of a porous food model (sponge) having 0–60% moisture contents and 0.59–0.94 porosity was measured by a line-source heat probe system in the range −35 to 25 °C. Two predictive models of the effective thermal conductivity of porous food were developed (Krischer and Maxwell models). The effective thermal conductivity predicted by Krischer model were in good agreement with the experimental data. Also, it was shown that the model including the effect of evaporation-condensation phenomena in addition to heat conduction was useful to predict the effective thermal conductivity of sponges.     

Mechanical properties of Tylose gel and chocolate in the freezing range

The mechanical properties of solid foods have not been extensively studied. This is due to the fact that most foods behave as viscous fluids or viscoelastic “solids”. In the case of freezing of foods or by considering solid foods (i.e. chocolate), food can be considered as a solid system. This paper presents results obtained with Tylose^® (a model food made of a methyl cellulose gel – 74% water content) and chocolate. The Young's modulus, the Poisson ratio, the bulk modulus and the coefficient of thermal expansions have been determined using specific procedures. These results can be of interest to model the thermomechanical behavior of foods undergoing freezing.     

Transport et distribution de produits alimentaires: situation actuelle et tendances futuresTransport and distribution of foods: today''s situation and future trends

International regulations formerly focused on consumer safety. Now, attention is shifted towards the preservation of the global quality of goods. New control methods (HACCP) can increase the quality of the whole chain. A correct approach to weight losses is a primary goal in the cold chain. Direct fuel consumption (with respect to each mass unit transported) is reduced when the transported weight per vehicle is increased; indirect consumption is optimised when the efficiency of the refrigerating unit is increased and when the overall heat transfer coefficient of the insulated body is minimised. Ageing of the vehicles must be minimised. A voluntary energy labelling program of vehicles provides an excellent opportunity to reduce energy consumption. New insulating products can theoretically worsen the energy budget. Every effort should be made to improve the basic thermal characteristics of new insulating materials and new vehicle design should be studied. Energy and environmental benefits can be obtained by the optimisation of the logistic chain. Multi-temperature vehicles and mini-containers can solve certain specific problems.     

A review on surface heat and mass transfer coefficients during air chilling and storage of food products

Heat and mass transfer coefficients are needed for the mathematical simulation of air chilling and storage of solid food products. Average transfer coefficient values and distributions around cylinders are now quite well known while it is not the case for solids of more complex shapes. CFD models are more and more often used to calculate transfer coefficient values on a single food product or packaging. Experimental knowledge is reviewed and the way it can be used by scientists and engineers to determine their own transfer coefficient values is illustrated. The potentials and limitations of present CFD models are illustrated and future improvements are also discussed.     

Thermal stresses during freezing of a two-layer food

Thermal stresses during freezing of a two-layer material, that can contribute to crack formation, are studied. A 3D numerical model of a two-layer food with food analog Tylose^® and chocolate is presented. An apparent specific heat formulation was used to model the heat transfer with phase change over a temperature range. The mechanics model considered viscoelasticity in Tylose^®; thermal strains were imposed due to the increase in volume from ice formation in Tylose^® and the decrease in volume from freezing of the chocolate. Results show that complex evolution of stresses, that include compressive and tensile values, occur during freezing. Sensitivity analysis showed that the Poisson's ratio was a very important parameter that affects the magnitude of stress. Variations in calculated stresses were found to be proportional to variations in Young's modulus. Knowing the stresses, the possibilities of undesired cracking of a chocolate coating applied onto another material such as ice cream could be evaluated.