Review of effective thermal conductivity models for foods

The literature associated with modelling and predicting the thermal conductivities of food products has been reviewed. The uncertainty involved in thermal conductivity prediction increases as the differences between the food components' thermal conductivities increase, which means that there is greater uncertainty involved with predicting the thermal conductivity of foods which are porous and/or frozen, than with unfrozen, non-porous foods. For unfrozen, non-porous foods, a number of simple effective thermal conductivity models that are functions only of the components' thermal conductivities and volume fractions may be used to provide predictions to within ±10%. For frozen and/or porous foods, the prediction procedure is more complicated, and usually requires the prediction of porosity and/or ice fraction, which introduces another source of error. The effective thermal conductivity model for these foods may require an extra parameter (in addition to the components' thermal conductivities and volume fractions) whose value must often be determined empirically. Recommendations for selecting models for different classes of foods are provided. There is scope for more research to be done in this area.     

Modelling heat and mass transfer in frozen foods: a review

This paper reviews mathematical methods for modelling heat and mass transfer during the freezing, thawing and frozen storage of foods. It starts by considering the problems in modelling heat transfer controlled freezing (the Stefan problem): release of latent heat, sudden changes in thermal conductivity. The author gives a unified overview of the common numerical methods: finite difference, finite element and finite volume. Mass transfer is then considered, involving different phenomena and approaches for dense and porous foods. Supercooling, nucleation and trans-membrane diffusion effects during freezing, and recrystallization during frozen storage are considered next. High pressure thawing and thawing are considered in view of their recent popularity. Finally, the paper offers a brief look at mechanical stresses during freezing, a much neglected area. It is concluded that while modelling heat transferred controlled freezing is a settled problem, much work remains to be done in modelling associated phenomena in order to gain the ability to predict changes in food quality at the micro-level.     

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.     

Modeling the thawing of frozen foods using air impingement technology

With the continual growth in the use of frozen foods both in retail and in food service, there is a need to develop improved thawing methods. Current methods are often undesirably slow (still air) or are very expensive and cause uneven thawing (microwave). Air impingement technology is one possible method to improve the thawing of frozen foods. The objectives of this research were to develop a two-dimensional model for air impingement thawing frozen foods and to verify the model experimentally. Frozen products were thawed using a laboratory impingement system with a single impingement jet. A simulated meat product (Tylose gel) was used as the test material. Thawing of a Tylose disk (12.7 cm diameter, 1.98 cm thickness) with air at 6 °C without impingement required more than 12 h, while thawing under a single impingement jet took less than 3 h, over four times faster. Results from the finite difference model gave good agreement with experimental data. Moisture loss during thawing was typically over-predicted because moisture gain due to condensation was not modeled.     

Comparison of CFD analysis to empirical data in a commercial vortex tube

This paper presents a comparison between the performance predicted by a computational fluid dynamic (CFD) model and experimental measurements taken using a commercially available vortex tube. Specifically, the measured exit temperatures into and out of the vortex tube are compared with the CFD model. The data and the model are both verified using global mass and energy balances. The CFD model is a two-dimensional (2D) steady axisymmetric model (with swirl) that utilizes both the standard and renormalization group (RNG) k-epsilon turbulence models. While CFD has been used previously to understand the fluid behavior internal to the vortex tube, it has not been applied as a predictive model of the vortex tube in order to develop a design tool that can be used with confidence over a range of operating conditions and geometries. The objective of this paper is the demonstration of the successful use of CFD in this regard, thereby providing a powerful tool that can be used to optimize vortex tube design as well as assess its utility in the context of new applications.     

Application of thermal battery in the ice storage air-conditioning system as a subcooler

This article experimentally investigates the thermal performance of a thermal battery used in the ice storage air-conditioning system as a subcooler. The thermal battery utilizes the superior heat transfer characteristics of two-phase closed thermosyphon and eliminates the drawbacks found in convectional energy storage systems. Experimental investigations are first conducted to study the thermal behavior of thermal battery under different charge temperatures (−5 °C to −9 °C) in which water is used as the energy storage material. This study also examines the thermal performance of the subcooled ice storage air conditioner under different cooling loads. Experimental data of temperature variation of water, ice fraction, refrigerant mass flow rate and coefficient of performance (COP) are obtained. The results show that supercooling phenomenon appears in the water and it can be ended when the charge temperature is lower than −6 °C. The system gives 28% more cooling capacity and 8% higher COP by the contribution of the thermal battery used as a subcooler.     

Study on high performance ice slurry formed by cooling emulsion in ice storage (discussion on adaptability of emulsion to thermal storage material)

This study focuses on an emulsion as a new thermal storage material for ice storage. Two types of emulsions were formed using an oil–water mixture with a small amount of additive. A silicone, light and lump oils were used. The water contents of the emulsions were 70, 80 and 90%. The additive was an amino group modified silicone oil. No depression of freezing point was observed for the emulsions because of their hydrophobic properties. In order to determine the structure of the emulsions, their electrical resistances were measured. Moreover, components of the liquids separating from the emulsions were analyzed. The results indicated that one emulsion was a W/O type emulsion, while the other was an O/W type. Finally, adaptability of the two emulsions to ice storage was discussed, it was concluded that a high performance ice slurry could be formed by the W/O type emulsion.     

Use of compound desiccant to develop high performance desiccant cooling system

The paper is aimed to develop a high performance rotary solid desiccant cooling system using a novel compound desiccant wheel (DW). The unique feature of the desiccant wheel is that it can work well under a lower regeneration temperature and have a higher dehumidification capacity due to the contribution of the new compound desiccant materials. Experimental results indicate that the novel desiccant wheel under practical operation can remove more moisture from the process air by about 20–40% over the desiccant wheel employing regular silica gel. A mathematical model that is used to predict the system performance has been validated with the test results. By integrating the desiccant wheel with evaporative cooling, heat recovery and heating for regeneration sections, a solid desiccant cooling system can be formed. Simulation results show that because of the use of the new compound desiccant, the desiccant cooling system can work under much lower regeneration temperature and have a relative high COP, thus low grade thermal energy resources, such as solar energy, waste heat, etc., can be efficiently utilized to drive such a cooling cycle.     

Numerical modelling of the temperature increase in frozen food packaged in pallets in the distribution chainModélisation numérique de l'augmentation de température des produits alimentaires congelés palettisés dans la chaîne de distribution

Frozen food can undergo temperature rise essentially during handling processes which are the weakest links of the cold chain: delivery, loading or unloading operations and temporary storage where pallets are generally handled in an ambience above 0°C. In this study, the temperature rise in a pallet is investigated numerically and experimentally. A three-dimensional finite-volume heat transfer model is developed using Phoenics Computational Fluid Dynamics (CFD) software. Food temperature within the pallet is predicted as a function of time of exposure, ambient conditions, product initial temperature, palletization and thermal characteristics of products and packaging. The experiments are carried out with packaged frozen fish pallets placed on a closed or open dock. The temperatures are recorded, at different levels in pallets over 25- to 85-min periods. The model shows good agreement with experimental results.     

Viscosity and thermal conductivity of halogenated methane and ethane refrigerantsViscosité et conductivité thermique des frigorigènes à base de méthane ou d'éthane halogénés

Viscosity and thermal conductivity of liquid halogenated methane and ethane refrigerants from about 200 K to near the critical temperature, at saturation and also at pressures up to 50 MPa, are shown to be satisfactorily correlated on the basis of a scheme developed by Dymond and Assael from consideration of hard-sphere theory. For the 31 refrigerants considered here, from the 1445 viscosity and 1226 thermal conductivity measurements examined only 5.2% were found to deviate by more than 5% from the proposed scheme.     

Modeling of a domestic frost-free refrigerator

In the present study, a comprehensive thermo-fluidic model is developed for a domestic frost-free refrigerator. The governing equations, coupled with pertinent boundary conditions, are solved by employing a conservative control volume formulation, in the environment of a three-dimensional unstructured mesh. Experiments are also conducted to validate the results predicted by the present computational model. It is found that the computational and experimental results qualitatively agree with each other, although certain discrepancies can be observed in terms of the exact numerical values obtained. For the freezer compartment, the computationally predicted temperatures are somewhat higher than the experimental ones, whereas for the refrigerating compartment, the computed temperatures are lower than the corresponding experimental observations. The difference between experimental and computational results may be attributed to the lack of precise data on the airflow rates and the unaccounted heat transfer rates through the door gaskets and the compressor. From the heat transfer and fluid flow analysis, certain modifications in the design are also suggested, so as to improve the performance of the refrigerator.     

A mathematical model of variable displacement swash plate compressor for automotive air conditioning system

A mathematical model of control mechanism used in the variable displacement swash plate compressor (VDSC) is developed firstly based on the force balance equation, mass and energy conservation equation. The model of moving components dynamics is developed then by analyzing the forces and force moments acting on the pistons and the swash plate. The compression process model is obtained by fitting the data from our experiments. And finally, the steady-state mathematical model of VDSC is developed by combining the three sub-models above. In order to verify the mathematical model, a test bench for control mechanism and the test system for VDSC have been established, and the simulated results agree well with the experimental data. The simulation results show that, like the variable displacement wobble plate compressor, there are four operation modes for the VDSC, i.e. constant rotary speed and constant piston stroke length (PSL), variable rotary speed and constant PSL, constant rotary speed and variable PSL, variable rotary speed and variable PSL, which have included almost all operation modes of the refrigeration compressor in common use. And there is a hysteresis zone and multiple-valued relationship between the compressor parameters when PSL changes.     

Determining thermal parameters in the cooling of a small-scale high-pressure freezing vessel

High-pressure supported freezing processes need a more efficient refrigeration technique to be applied at industrial level. A cooling method consisting in the circulation of a refrigerant in ebullition around the product in the vessel has been tested on a lab-scale prototype built for that purpose. The cooling kinetic of a mixture of ethanol, ethylene glycol and water (a usual pressurizing medium) was followed, recording temperatures in the whole sample. A mathematical model has been developed to describe heat transfer during cooling of the sample in the vessel. The heat transfer coefficient between the refrigerant and the vessel was determined by a fitting procedure between the numerical simulation results and the experimental measurements. This model should be used to predict the cooling kinetics in other conditions (other products, larger vessels) and to optimise the process.     

Measurement of thermal conductivity of ice slurry made from solution by transient line heat-source technique (analytical discussion on influence of latent heat of fusion)

We have been studying on ice slurry in a dynamic type ice storage system. The ice slurry has many good characteristics. The ice slurry can be made from a solution. When designing the ice storage system using this ice slurry, thermal conductivity of the ice slurry is essential.When thermal conductivity of the ice slurry made from a solution is measured by a transient line heat-source technique, a measurement value of thermal conductivity is affected by a latent heat of fusion of ice. Therefore, the thermal conductivity measured is apparent thermal conductivity. In this study, influences of Stefan number, initial concentration of the solution, initial solid fraction (initial IPF) and Fourier number on the thermal conductivity was analytically discussed to improve measurement accuracy of the thermal conductivity of ice slurry in the transient line heat-source technique.     

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.     

Development and validation of “grey-box” models for refrigeration applications: A review of key concepts

“Grey-box” modelling combines the use of first-principle based “white-box” models and empirical “black-box” models, offering particular benefits when: (a) there is a lack of fundamental theory to describe the system or process modelled; (b) there is a scarcity of suitable experimental data for validation or (c) there is a need to decrease the complexity of the model. The grey-box approach has been used, for example, to create mathematical models to predict the shelf life of chilled products or the thermal behaviour of imperfectly mixed fluids, or to create models that combine artificial neural networks and dynamic differential equations for control-related applications. This paper discusses the main characteristics of white-box, black-box and their integration into grey-box models, the requirements and sourcing of accurate data for model development and important validation concepts and measures.     

Modelling a ground-coupled heat pump system using adaptive neuro-fuzzy inference systems

The aim of this study is to demonstrate the usefulness of an adaptive neuro-fuzzy inference system (ANFIS) for the modelling of ground-coupled heat pump (GCHP) system. The GCHP system connected to a test room with 16.24 m² floor area in Fırat University, Elazığ (38.41°N, 39.14°E), Turkey, was designed and constructed. The heating and cooling loads of the test room were 2.5 and 3.1 kW at design conditions, respectively. The system was commissioned in November 2002 and the performance tests have been carried out since then. The average performance coefficients of the system (COPS) for horizontal ground heat exchanger (GHE) in the different trenches, at 1 and 2 m depths, were obtained to be 2.92 and 3.2, respectively. Experimental performances were performed to verify the results from the ANFIS approach. In order to achieve the optimal result, several computer simulations have been carried out with different membership functions and various number of membership functions. The most suitable membership function and number of membership functions are found as Gauss and 2, respectively. For this number level, after the training, it is found that root-mean squared (RMS) value is 0.0047, and absolute fraction of variance (R²) value is 0.9999 and coefficient of variation in percent (cov) value is 0.1363. This paper shows that the values predicted with the ANFIS, especially with the hybrid learning algorithm, can be used to predict the performance of the GCHP system quite accurately.     

Experimental investigation and numerical simulation on the hysteresis zone of a variable displacement wobble plate compressor

A test system with the variable displacement compressor (VDC) for automotive air conditioning system is built to study the changing rule of piston stroke length (PSL). It is found from our experiments that the critical suction pressure where the PSL starts to decrease is less than that where the PSL starts to increase for the same PSL; between the two critical lines, a hysteresis zone is formed, within which all the steady-state points fall and there is a multiple-valued relationship between VDC parameters; and the PSL is kept invariable when the VDC parameters change within the hysteresis zone. In order to find out the reason causing the hysteresis zone and to analyze the influence of the compressor parameters on the hysteresis zone, a steady-state mathematical model of VDC is developed and verified by our experimental data. The theoretical analysis indicates that the hysteresis zone is caused by the frictional forces among the moving components of VDC, and the greater the frictional forces, the broader the hysteresis zone and the larger the changing range of suction pressure. The influence of the discharge pressure and rotary speed on the hysteresis zone is that the hysteresis zone moves in the direction of the suction pressure decreasing along with the increase of the discharge pressure or rotary speed.     

Modeling and experimental investigation of accumulators for automotive air conditioning systems

A stream analysis model was developed to simulate the behavior of accumulators and their influence on the automotive air conditioning (A/C) systems. It allows a comprehensive steady state simulation with a set of input conditions such as refrigerant vapor mass flow rate and pressure at the inlet of an accumulator. In this study, the refrigerant/oil mixture is R134a/PAG oil which are totally miscible, but could be any air conditioning refrigerant/oil, including carbon dioxide (CO₂)/oil. The model accounts for all major effects inside the accumulator, such as friction, bends, sudden expansion, sudden contraction and heat exchange. The outputs are vapor quality, pressure and temperature at various positions of accumulator. In order to verify the mathematical model, experiments are performed in an experimental setup made up of real size automotive air conditioning components. The simulated results agree well with the experimental data. The simulation and experimental results show an important function of accumulators that is to determine the vapor quality into compressor, and thus has influence on the performance of whole automotive A/C systems.     

An experimental investigation and modelling of the viscosity refrigerant/oil solutions

This paper presents experimental data for the viscosity of solutions of refrigerant R600a (isobutane) with mineral compressor oils Azmol, Reniso WF 15A, and R245fa (1,1,1,3,3-pentafluoropropane) with polyolester compressor oil Planetelf ACD 100 FY on the saturation line. The experimental data were obtained for solution of R600a with mineral compressor oil Azmol in the temperature range from 294.7 to 338.1 K and the concentration range 0.04399 ≤ w_R ≤ 0.3651, the solution of R600a with mineral compressor oil Reniso WF 15A at the temperatures from 285.8 to 348.4 K and the concentration range 0.03364 ≤ w_R ≤ 0.2911, the solution of R245fa with polyolester compressor oil Planetelf ACD 100 FY at the temperatures from 309 to 348.2 and the concentration range 0.06390 ≤ w_R ≤ 0.3845. The viscosity was measured using a rolling ball method. The method for prediction of the dynamic viscosity for refrigerant/oil solutions is reported.