A review of computational fluid dynamics for forced-air

Applied Energy 168 (2016) 314–331

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A review of computational fluid dynamics for forced-air cooling process Chun-Jiang Zhao a,⇑, Jia-Wei Han a,b, Xin-Ting Yang a, Jian-Ping Qian a, Bei-Lei Fan a a b

National Engineering Research Center for Information Technology in Agriculture, Beijing 100097, China College of Computer Science and Technology, Beijing University of Technology, Beijing 100124, China

h i g h l i g h t s
We review the fundamentals of applying CFD to precooling of fresh produce.
We summarize the parameters used to analyze packaging performance.
We review recent studies that focus on optimizing the design of fresh produce packaging.
We discuss various challenging issues.

a r t i c l e

i n f o

Article history: Received 16 December 2015 Received in revised form 25 January 2016 Accepted 28 January 2016

Keywords: Computational Fluid Dynamics (CFD) Numerical analysis Porous medium Forced-air precooling Package

a b s t r a c t Optimizing the design of fresh produce packaging is vital for ensuring that future food cold chains are more energy efficient and for improving produce quality by avoiding chilling injuries due to nonuniform cooling. Computational fluid dynamics models are thus increasingly used to study the airflow patterns and heat transfer inside ventilated packaging during precooling. This review discusses detailed and comprehensive mathematical modeling procedures for simulating the airflow, heat transfer, and mass transfer that occurs during forced-air precooling of fresh produce. These models serve to optimize packaging design and cooling efficiency. We summarize the most commonly used parameters for performance, which allows us to directly compare the cooling performance of various packaging designs. Ó 2016 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals of computational fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Discretization schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of computational fluid dynamics to precooling of fresh produce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Porous-medium approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Airflow in porous media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Heat and mass transfer in porous media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Single-phase models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Two-phase models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Direct computational fluid dynamics simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. Airflow, heat- and mass-transfer models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parameters used to analyze package performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Cooling time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Cooling rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⇑ Corresponding author. Tel.: +86 10 51503092; fax: +86 10 51503750. E-mail addresses: [email protected], [email protected] (C.-J. Zhao). http://dx.doi.org/10.1016/j.apenergy.2016.01.101 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

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5.

6.

4.3. Cooling uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Energy consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Mechanical strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Physical-parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Energy conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Even after separation from the parent plant, fresh horticultural produce (e.g., fruits and vegetables) is composed of living dynamic systems [1]. The respiration and transpiration of living biological entities results in a loss of the organic material and moisture from these systems. In general, these alterations result in the degradation of the quality of agro-products and limit their shelf life [2,3], to the detriment of transregional and transnational long-distance sales of fresh produce and of the economic performance of the entire cold chain. The physiological changes due to respiration, transpiration, and biosynthesis are affected by intrinsic (i.e., the thermal properties of the produce or climacteric vs. nonclimacteric commodities) and extrinsic (i.e., temperature, concentration of ethylene, O2, and CO2) factors [1,4], of which temperature is the single most important environmental factor affecting the deterioration rate and postharvest lifetime of produce [5–8]. To ensure the quality and safety of horticultural products and extend their storage and shelf life across the entire cold chain, a critical step in the postharvest cold chain is rapid precooling after harvest to remove field heat [9–12]. In this way, horticultural produce is cooled from the harvest temperature to an optimal temperature, which slows the physiological activities within the produce, reduces disease development and weight loss by transpiration, and minimizes the destruction of the pigments, colors, texture, and nutrients [13–16]. Thus, precooling fruits and vegetables after harvest effectively extends the shelf life of the produce and extends the sales zone, making it the most essential of all value-adding services demanded by increasingly more sophisticated consumers [1,17,18]. The performance and rate of the precooling process for fresh produce depend on the packaging design (vent area, shape, number, position, etc.), the fruit-stacking pattern within the package, the thermophysical properties, physiological mechanisms, air-toproduce initial temperature difference, air-to-produce final desired temperature difference, produce geometry (size, shape, surface/ volume ratio, internal structure, etc.), and ambient relative humidity [19,20]. All of these factors are important because they affect heat and mass transfer during the precooling process [2,9] and directly affect the uniformity of airflow and cooling as well as energy consumption. Because packaging strongly impacts the quality and shelf life of produce, the relatively low cost of packaging and the ease of altering its design [21,22] is one of most costeffective ways to enhance rapid and uniform cooling of horticultural produce, increase precooling throughput, reduce precooling energy consumption, and prevent cold damage. For fresh, highly perishable produce, packaging serves several purposes. It not only promotes rapid and uniform precooling to quickly remove field heat but also protects the produce from mechanical damage during handling, processing, storage, and transport. Therefore, packaging technology plays a critical role in transportation, preservation, and marketing of fresh produce [23–27].

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326 327 327 328 328 328 328 329 329 329

In recent years, an increasing effort [12,17,28–32] has been devoted to in-depth studies and analyses of the characteristics of airflow and heat transfer inside ventilated packaging during precooling. These studies were based on laboratory experiments, numerical simulations (e.g., Computational Fluid Dynamics, CFD), or a combination of both. The aim of these studies was to improve packaging design, ensure rapid and uniform cooling of agricultural products, avoid hot spots, and prevent cold damage. Table 1 summarizes the recent studies on precooling of fresh produce and packaging design. During precooling, the complexity of the coldair movement inside a single fruit-packing crate or through the entire ensemble of goods renders difficult the task of measuring temperature variations solely via field tests. As a result, obtaining detailed information on the local airflow rate and heat- and mass-transfer processes within complex packaging structures is a serious challenge. In addition, extending the test cycle requires significant human and material resources. The last two decades, however, has seen enormous advances in computing power and commercial CFD codes to meet the sophisticated modelling requirements of the food-processing industry (e.g., drying, cooking, sterilization, chilling, cold storage, etc.). Thus, the above-mentioned difficulties can be reduced or avoided by using numerical CFD simulations to create three-dimensional spatio-temporal distributions of airflow and temperature during precooling [33–40]. Despite this vast amount of research on packaging design for fresh horticultural produce, most researchers have concentrated mainly on a single unit of produce during precooling or on only one or a few particular functions of the packaging (e.g., cooling performance or energy consumption). Thus, conflicting packaging design requirements often result when multiple cold-chain operations or different functions are simultaneously targeted [10]. For example, increasing the number of box vents and the air-inflow speed can improve cooling rate, throughput, and cooling uniformity but compromises the mechanical strength of the packaging and induces more chilling injuries and moisture loss. Furthermore, a preferential pathway is created when too many box vents are used because the airflow can easily bypass the produce, thereby reducing the airflow rate through the produce and consequently increasing the energy required for precooling [11]. Thus, to comprehensively evaluate the performance of ventilated packaging, all functions of the packaging across the entire cold chain should be simultaneously assessed in future studies. In addition, future studies should also compare the cooling performance of packaging designs as a function of how the produce is stacked on a pallet. The goal of this paper is to review the current state of CFD as applied to the design of ventilated packaging for fresh produce. Because new packaging can be evaluated from several viewpoints, we summarize herein the most commonly used performance parameters, which we use to quantitatively compare existing packaging with regard to each function separately or for multiple functions at the same time. In addition, to improve the accuracy of CFD

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Table 1 Summary of recent studies (2004–2015) that focus on evaluating packaging performance in cold chain for fresh horticultural produce. Reference

Material

TD

Method

PPs

2004 [61,65]

PVC & water/agar-agar filled spheres

–

Expt.

HCT, CR, CU

Remark: Study how container opening area and airflow rate affect cooling efficiency. More open areas enhance the cooling efficiency; however, the cooling efficiency does not significantly differ from the fully open condition by considering CR, CU, EC, and MS when container opening area exceeds a specific value (a total opening area of 6% and 14% was recommended by Refs. [61,65], respectively). Airflow rate strongly affects HCT: increasing the airflow rate can compensate for the negative effect of smaller opening area, but it raises the APD and EC 2004 [72]

Apple & chicory

Steady

Porous medium & Expt.

APD (i.e. EC)

Remark: Study how airflow velocity, shape, surface roughness and confinement ratio affect APD. For a confined batch of product, Eq. (9) is more accurate than Eq. (4) [i.e., the error in the pressure drop predicted by Eqs. (4) and (9) are 65% and 20%, respectively]. The accuracy is further improved by accounting for the shape and roughness of the product 2005 [9]

PS

–

Expt.

HCT

Remark: Study how area of container opening and airflow rate affect CT and APD. For the same total open area, the position does not influence the air-approach velocity or APD, except when the number of holes varies. However, vent position has a significant effect on CU (similar results were found by Dehghannya et al. [12,17,35]) 2005 [66]

PS

–

Expt.

HCT, APD

Remark: Study how opening configuration, total area and position, and airflow rate affect overall cooling system efficiency and how produce respiration rate affects energy consumption. The energy-added ratio (EAR) of the cooling process decreases as the opening area increases, but only a slight decrease is observed when the opening area exceeds 8%. The lower EC is obtained with the holes distributed uniformly on the package surface at specific airflow rates and respiration activity, compared with the holes distributed on the corners of the package surface 2005 [20]

PS

–

Expt.

CR

Remark: Study how airflow velocity affects cooling rate and determine the relationship between the two. Cooling rate of the produce simulator correlates significantly with air-approach velocity when the individual cooling-rate-index effect is considered 2006 [120]

Empty corrugated boxes

–

Expt.

MS

Remark: Study how shape, position, and size of carrying slots affect the compressive strength of corrugated boxes. Of the various possible shapes, circles reduce compressive strength the least. Furthermore, compressive strength of the board decreases as the slot position moves away from the center of the board. Also, the smaller the slot size, the higher the compressive strength 2006 [141]

PS

–

Expt.

HCT, CU, APD

Remark: Study how package-opening configurations and airflow rate affect cooling efficiency and energy requirements of precooling system. For packing low-respiration-rate produce, increasing airflow rate may compromise the process-energy efficiency because of air-circulation obstruction for less-vented containers. For high-respiration-rate produce, to enhance the energy efficiency of cooling, enlarging the opening area above 2.4% is recommended rather than increasing the airflow rate 2006 [91,98]

Apple

Steady & transient

Porous medium & Expt.

CU

Remark: Development and verification of CFD modeling, predict airflow patterns and temperature profiles in ventilated packaging systems during cooling. In general, good agreement between the model predictions and the experimental data are obtained, and the lack of fits in certain positions of the packaging system may be attributed to inaccurate temperature measurements and uncertainties in the data input into the model 2007 [69]

Empty corrugated boxes

–

FEM & Expt.

MS

Remark: Study how various vent- or hand-hole designs affect compression strength of box. To achieve a minimum decrease in box-compression strength, the following factors should be considered: (1) Depth of the holes should be less than 1/4 of the depth of the box. (2) Ratio of width to depth of holes should be 1/3.5–1/2.5. (3) Even-numbered holes should be positioned symmetrically 2007 [32]

Apple

Transient

D-CFD-S & Expt.

CU

Remark: Study how airflow velocity, opening area, and trays affect cooling efficiency. Sensitivity tests show that inaccurate input values (within 10% of correct value) for the inlet-air velocity contribute to an inaccuracy of about 0.5 K in the model predictions, which is within the measurement error of most temperature-measuring devices used in the postharvest industry 2008 [142]

FS spheres

Steady

D-CFD-S & Expt.

CU

Remark: Predict airflow field within complex packed structure where ratio of container to product diameter is less than 10. One of the major results of this study was the demonstration of using a 2D PIV system to trace the flow field within a packed structure without disturbing the flow. PIV provides a physical insight into the flow-field behavior within a complex structure. Experimental and predicted velocities are consistent 2008 [35]

PS

Transient

Porous medium (two-phase) & Expt.

CU

Remark: Study how different geometric location of ventilation holes affects cooling uniformity. Model prediction and measured data are consistent. The higher the vent area, the better is the air uniformity during the process 2008 [100]

Spheres

Steady

D-CFD-S & Expt.

APD

Remark: Study of stacking of products, product size, TOA, porosity, airflow rate on APD, and airflow pattern through stacks of boxes with horticultural products. Uses discrete-element method to generate random stacking of products. The flow resistance is affected by the confinement ratio, product size, porosity, box-vent-hole ratio, and much less by random filling. The study provides more accurate pressure-drop correlations to predict large-scale cooling of boxes containing horticultural products 2009 [28–30]

Strawberries & FS spheres

Steady & transient

D-CFD-S & Expt.

CU

Remark: Study how structure and design of packaging system affects cooling uniformity. Experimental validation of flow and energy models. Airflow bypass is not necessarily negative because this can imply that colder air reaches the clamshells farther downstream, which can improve the uniformity cooling between individual clamshells

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C.-J. Zhao et al. / Applied Energy 168 (2016) 314–331 Table 1 (continued) Reference

Material

TD

Method

PPs

2009 [143]

Strawberries

Steady & transient

D-CFD-S & Expt.

CT, CU

Remark: Study how package-design parameters affect the CT and CU. The results indicate that the vent area significant affects the cooling rate, but not on the uniformity of cooling. A novel packaging design that leads to a higher percentage of airflow through the clamshells will not necessarily increase the cooling rate. Although this approach decreases the resistance for convective heat transfer within clamshells, its effect on the variation of air temperature along the system is not as straightforward 2009 [103,144]

Strawberries

Steady & transient

Porous medium & Expt.

CU

Remark: Describe space-and-time-dependent mathematical formulation for perforation-mediated MAPs that consider all relevant biological and transport phenomena (respiration, transpiration, condensation, heat transfer evaporative, convection, and conduction), and convective and diffusive transport of O2, CO2, H2O, and N2. The mathematical model is based essentially on fundamental laws, which are supplemented by the minimum possible amount of empirical information 2009 [55]

Spheres

Steady & transient

D-CFD-S

CT, CU

Remark: Study how turbulence intensity, mesh sensitivity, opening size and ratios, and air inflow rate affect airflow patterns and temperature distribution in simulated ventilated container. The results show that the choice of flow modeling (laminar versus turbulent) for the selected geometry (opening area and 3D geometry) and boundary conditions (air-inflow velocity and inflow turbulence) could be crucial at the very beginning of the simulation procedure. This study should provide a better method for analyzing the cooling performance of ventilated packages 2010 [67]

Not specified

–

Expt.

EC

Remark: Collects information on electricity consumption of commercial forced-air cooling facilities and describes conservation options for reducing heat input and improving facility management. The average EC for all facilities is 0.4, which is the same as reported 20 years ago by Thompson and Chen [113] 2011 [12]

PS

Transient

D-CFD-S & Expt.

CT, CR, CU

Remark: Study how different package vent configurations affect produce temperature distribution during forced convection cooling of produce. The methodology developed in this study can be used as a design tool to provide the homogeneous temperature distribution in ventilated packages during forced convection cooling of produce 2011 [145]

Strawberries

Steady & transient

D-CFD-S & Expt.

CR, CU, EC

Remark: Study how design of individual clamshells and trays on CR, CU, and EC of forced-air cooling system. Optimization of forced-air cooling system designs. For the same airflow conditions, the new design significantly improves the uniformity and energy efficiency of the process, while still replicating of the cooling rate of commercial designs 2012 [17]

PS

Transient

D-CFD-S & Expt.

CT, CR, CU

Study how number of vents positions affects CR and CU. The results show that increasing vent area does not necessarily shorten the cooling time, and it can even increase the cooling time if the vents are not properly distributed on the package walls. Additionally, increasing vent area beyond a specific level cannot have a positive effect on cooling uniformity and time 2012 [124]

Corrugated paperboard panel

–

FEM & Expt.

MS

Remark: The work presented studies one possible reason for the discrepancy between the analytical and experimental results for the buckling problem of a simply supported uniaxially compressed corrugated paperboard panel. Some in-sight analysis of the gaps and future trends are given, which would reduce the discrepancy (e.g., considering the difference with a multi-term analytical solution, improving the material modeling of corrugated paperboard and changing the out-of-plane boundary conditions to more closely resemble the experimental conditions) 2012 [44]

Grapes

–

Expt.

APD, CR

Remark: Study how different components (i.e., liner films, the carrying bag, the grapes, and the container) of multi-scale packaging affect airflow resistance and cooling rate. The results show that liner films contribute by far the greatest resistance to airflow compared with the rest of the package components of the grape multi-packaging 2013 [11]

Oranges

Steady & transient

D-CFD-S & Expt.

HCT, SECT, CR, CU

Remark: Comparison of cooling performance of different package designs based on a single container or stacked on a pallet. The cooling performance of different package designs was evaluated by the CT, and CU and the magnitude of CHTC in a specific container and between different containers on the pallet 2013 [6,7]

Water-filled plastic spheres

Steady & transient

D-CFD-S & Expt.

HCT, SECT, APD, CU

Remark: Study how vent parameters (vent area, shape, number, position) affect cooling efficiency (airflow characteristics, APD, CU, EC). Develop and verify model. Vent size and position more strongly influence the cooling efficiency of horticultural produce than does vent shape. This modelling approach can be used to study any horticultural-produce-packaging system. However, the study used plastic spheres instead of real produce, so the simulation results from the study may be of questionable accuracy 2013 [40]

Grape

Transient

Porous medium & Expt.

CU (temperature and RH)

Remark: Study how different package components (box, liner, and pads), product stacking, and cooling procedures affect airflow, heat transfer, and mass transfer processes. The results show that non-perforated liners produce the highest RH inside the package that gives the lowest moisture loss but the highest condensation. The results demonstrate clearly that CFD models may be used to determine the optimum table grape packaging and cooling procedures 2014 [21]

Orange

Steady & transient

D-CFD-S & Expt.

HCT, SECT, APD, CR, CU, EC

Remark: Study how cooling conditions (airflow rate and cooling temperature) affect fruit cooling rate and the system energy consumption. This study mainly provides basic information for preliminary design decisions or for altering existing cooling protocols or cooling systems 2015 [139]

Oranges

Steady & transient

Porous medium & Expt.

SECT, CR, CU

Remark: Identify differences in cooling rate and uniformity between individual boxes at different heights on a pallet and between individual fruit within a given box. This study proposes strategies for future improvements of the ambient loading protocol, which includes optimizing box design and stacking on the pallet specifically for vertical airflow and reducing the airflow short circuits between the pallets (continued on next page)

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Table 1 (continued) Reference

Material

TD

Method

PPs

2015 [5]

Apple

Transient

D-CFD-S & Expt.

HCT, CU

Remark: Study how number of vents affects CT and CU. Optimize designs for fresh-fruit packaging. The results indicate that the region with the highest produce temperature corresponds to the region with lowest cooling-air velocity. Cooling performance is significantly improved by increasing the number of vent numbers on the windward and leeward sides of the existing container Note: TD: time dependency, PPs: performance parameters; PVC: polychlorinated vinyl, PS: polymer spheres, PIV: particle image velocimetry, Expt.: experimental methods, HCT: half-cooling time, SECT: seven-eighths cooling time, CT: cooling time, CR: cooling rate, CU: cooling uniformity, CHTC: convective heat transfer coefficients, APD: air pressure drop, EC: energy consumption, MS: mechanical strength, FEM: finite element modeling, D-CFD-S: direct CFD simulations, FS: fused silica, TOA: total opening area, RH: relative humidity of the air.

Fig. 1. Number of peer-reviewed publications concerning CFD applications to cold chain. ‘‘PT” denotes the ratio of postharvest treatment to total; ‘‘ST” denotes the ratio of supply chain to total.

solutions and to allow the current forced-air precooling systems to maintain the produce quality for a longer period of time, some challenging issues are discussed in the hopes of indicating some future directions of research in this area.

play cases); however, Fig. 1 is based on the statistical analysis of incomplete data. As shown in Fig. 1, the number of peerreviewed publications on CFD applications has increased steadily over the years.

2. Fundamentals of computational fluid dynamics

2.1. Governing equations

Computational Fluid Dynamics (CFD) is a simulation tool for modelling fluid-flow problems and is based on solving the governing flow equations. It is also a sophisticated design and analysis tool that uses the modern computation power of computers to simulate fluid flow, heating (drying, cooking, sterilization, chilling), mass transfer (transpiration or dissolution), phase change (freezing, melting, or boiling), chemical reactions (combustion or rusting), mechanical movement (impellers, pistons, fans or rudders), stress or deformation of related structures, and interactions between solids and fluids [41]. With the rapid development of computing power and commercial CFD packages, the accuracy of such simulations and their reliability are being constantly improved. This technology has been widely used in agricultural cold-chain logistics for the past few years, particularly in the precooling process of fresh horticultural produce. If used correctly, CFD can provide a detailed understanding the complex flow through the intricate and chaotic structure within agricultural produce packages. However, verifying the accuracy of such simulations requires making traditional measurements, which is impossible without disturbing the packaging arrangement [42,43]. Fig. 1 summarizes the peer-reviewed publications concerning CFD applications to postharvest treatment (e.g., drying, cooking, sterilization, chilling, precooling, etc.) and to the supply chain (i.e., refrigerated transportation, cold storage, and refrigerated dis-

All CFD simulations are based on the fundamental governing equations of fluid dynamics (i.e., continuity, momentum, and energy equations). These equations are the mathematical statements of the conservation laws (conservation of mass, momentum, and energy) that govern all fluid flow, heat transfer, and associated phenomena. These conservation laws describe the rate of change of a given property of a fluid as a function of external forces [13,41,44]. Conservation of mass. The mass flow entering a fluid element must balance the departing mass flow:

@q @ ðqui Þ ¼ 0 þ @t @xi

ð1Þ

Conservation of momentum (Newton’s second law). The net force on a fluid element equals the rate of change of its momentum:

@ @ @P @ ðqui Þ þ ðqui uj Þ ¼  þ @t @xj @xi @xj




l

 @ui  qu0i u0j þ Si @xj

ð2Þ

Conservation of energy (the first law of thermodynamics). The rate of change of energy inside a fluid element equals the sum of the net heat flux into the element and the rate of work done on the element by body and surface forces:

C.-J. Zhao et al. / Applied Energy 168 (2016) 314–331




@ðqTÞ @ @ k ðqui TÞ ¼ gradT þ @t @xi @xi C a

 þ ST

ð3Þ

2.2. Discretization schemes The first step in any CFD simulation is to discretize the computational domain; that is, the spatially continuous computational domain is partitioned into several nonoverlapping subdomains in which the computational grid is created. Next, the governing equations are discretized over the mesh; that is, the governing partial differential equations are transformed into the corresponding algebraical equations at each node, and the physical quantities are obtained by iteratively solving the algebraical equations at each node within computational domain. Time must also be discretized to deal with transient problems. Because the dynamics differ depending on the distributional hypothesis governing the dependent variables between nodes and the derivation of the discrete equation, CFD software developers can choose between many different numerical techniques to discretize the computational domain. The most important of these techniques include finite differences, finite elements, and finite volumes. Because of the stringent requirements regarding mesh quality (i.e., difficulty in processing a complex geometrical model) and because the integral conservation law of discrete equations is satisfied only for extremely fine meshes, finite-difference techniques are rarely used in engineering fields. The finite-element method is especially adapted to solving problems with complex geometrical structure, for numerical analysis of solid mechanical structures, and for electromagnetic problems involving an inhomogeneous medium. Although the finite-element method has been used to simulate airflow and heat and mass transfer within packaging [12,17,35,45], this approach has a lower resolving speed than the methods of finite differences and finite volumes, so it is not widely used in commercial CFD packages. The finite-volume methods, being easy to understand, to program, and with its high computation efficiency has become the most popular numerical technique in CFD codes [13,46,47]. Thus, the finite-volume method is the method of choice for simulating all phases of the cold chain (i.e., precooling, cold storage, refrigerated transport, refrigerated display cabinets, etc.). A CFD simulation can be divided into three phases: preprocessing, solving, and post-processing. The following three sections briefly introduce each of these three phases. 2.3. Pre-processing Pre-processing is crucial for obtaining reliable results from CFD simulations. It alone consumes almost 50% of the time required for the entire CFD simulation. Before determining the appropriate computational domain, the physics of the problem and factors that could influence airflow should be understood in detail. For example, the simulation designer must determine whether, during forced-air precooling, the produce zone should be regarded as a porous medium inside the packaging, or whether the domain can be reduced by exploiting symmetries or periodicity, thereby reducing the computational time and simulation costs. Next, the designer must determine the shape of the computational domain that is to be subdivided into numerous cells, also known as volumes and elements. Most commercial CFD packages contain programs to simultaneously define the domain and construct the mesh. This stage of the process is very important because the reliability of the solution depends on the size of these elements (i.e., the solution is ‘‘grid dependent”) [48]. As the elements decrease in size, the accuracy of the solution, the computation time, and the memory requirements all increase. However, to achieve a good

319

level of accuracy, the element size should be smaller in areas where the gradient of the physical quantities being simulated is large or in areas of particular interest (e.g., areas of strong turbulence, or close to solid boundaries). The key to optimizing computational grids is to find the proper balance between calculation accuracy and computation cost. Once meshing is completed, the properties of the fluids and of the solids involved in the simulation must also be specified, as well as the boundary conditions at each interface and the initial conditions for all the variables [48,49]. In some case, the boundary conditions will change with time or space. For the model to be as realistic as possible, these boundary conditions should be defined in a user-defined function coded in C. 2.4. Solving The governing partial differential equations mentioned above cannot be directly solved in the entire computation domain, so they must be discretized and solved numerically to estimate the value of each variable at specific points in the domain [13,41,48,49]. This step is known as equation discretization and is applied to each individual cell of the mesh. Different discretization schemes are described in Section 2.2. The main difference between them lies in the approximate form of flow variables and the corresponding process of discretization. Methods to solve discretized equations can be categorized into two types: the couple method and the segregate method. The segregate method includes the semi-implicit method for pressure-linked equations (SIMPLE), which is used by most commercial CFD packages and determines the pressure field indirectly by closing the discretized momentum equations with the continuity equations in a sequential manner [50]. However, to enhance convergence rates, some improved methods have been proposed, such as SIMPLEC, SIMPLER, and PISO. A comprehensive description of these methods is available elsewhere [51–53]. Within all commercial CFD packages, the solver environment organizes the mathematical input from the pre-processor into numerical arrays and solves them by using iterative methods [48,49]. This approach is very computationally intensive and usually requires solving a huge number of equations at each step. This process is iterated until the convergence is acceptable. Before launching the solver, a choice must be made between using a steady-state or non-steady-state simulation—a choice that depends on the phenomena to be investigated. A non-steady-state simulation is appropriate when the evolution of a phenomenon over time is being investigated. The cooling of fresh horticultural produce requires a non-steady-state simulation to accurately reproduce the dynamics of the heat and mass transfer within the packaging. 2.5. Post-processing The results of the simulation are generated when the solving process is completed. To facilitate scrutinizing, analyzing, and evaluating the resulting field solution, the results are typically displayed in the form of temperature and velocity maps, plots of the velocity field, plots of other scalar variables, and animations. Post-processing can also give information on the instantaneous value of all variables at certain positions in the domain [48]. In addition, most CFD packages also allow the field data to be exported to third-party software, where they can be further processed. Above all, the post-processing task is essential for a comprehensive evaluation of the simulation from the point of view of accuracy, authenticity, and satisfaction. Fig. 2 shows an example of the visualization techniques. The figure shows clearly the airflow characteristics inside the package after 300 min of cooling.

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Fig. 2. Airflow characteristics inside packaging after 300 min of cooling:(a) velocity streamlines, (b) turbulent kinetic-energy contour 13 cm above bottom of box, (c) instantaneous-velocity field 13 cm above bottom of box, (d) distribution of cooling-air velocity 13 cm above bottom of box [5].

3. Applications of computational fluid dynamics to precooling of fresh produce To slow the rate of metabolism and reduce deterioration of horticultural products before they are put in long-term refrigerated storage or transportation, a critical step in the postharvest cold chain is rapid precooling after harvest to remove field heat. This vital postharvest treatment technique also ensures the quality and safety of horticultural products and extends their storage and shelf life across the entire cold chain. A variety of precooling techniques are available for use in the agricultural industry. Room cooling, forced-air cooling, hydro-cooling, vacuum cooling, and liquid icing are common methods of precooling systems, among others [54–60]. The choice of precooling method is greatly influenced by produce type, because different commodities have different cooling requirements (e.g., refrigeration temperature, sensitivity to water) [16,32]. Although no complete cooling method satisfies the cooling requirements of all crops, forced-air precooling can be adapted to a wider range of fresh produce than any other cooling method. Forced-air precooling consists of forcing cold air through stacked packages and around each individual unit of produce. This process uses a powerful fan to generate the necessary driving force to create a pressure differential across the container, which draws air in from the surroundings, through the container openings, and around the produce [54]. Its efficiency may be evaluated by the speed of the process (e.g., cooling rate, half-cooling time, seven-eighths-cooling time) and the uniformity of the produce temperature [9,19,61]. In the forced-convection-cooling process, transient convective heat transfer occurs between the fluid medium and the units of solid food, which is the main reason field heat is removed from fresh produce. Information about the product’s surface heattransfer coefficient is also essential for obtaining rapid and uniform

cooling within packaged horticultural produce. An experimental investigation that used different air-inflow velocities was done to determine the precooling characteristics of perishable food during forced-air precooling [62]. The results demonstrate that the product’s surface heat-transfer coefficient and cooling rate increase upon increasing the speed of the cooling fluid over the product. Delele et al. [6] and Tutar et al. [55] arrived at a similar conclusion; namely, that a reasonable increase in cooling rate occurs upon increasing the airflow speed to a certain constant value above which further increasing the airflow speed is essentially a waste of energy because it leads only to a relatively modest increase in heat transfer across the product’s surface. As shown by Alvarez and Flick [63,64], cooling is very heterogeneous during forced-air precooling due to poor temperature management. Commodities located behind blind walls may not be sufficiently cooled, whereas others exposed to higher airflow speeds are overcooled, leading to freezing, chilling, or drying damages. In addition, the packaging material itself also increases the resistance to airflow and thereby to cooling, because it prevents direct contact between the cooling air and the produce [6]. Therefore, the cooling efficiency is also directly affected by the design of the ventilated packages that reused during the precooling process. A proper design of the package vents may not only provide uniform airflow through the entire mass of produce and consequently uniform cooling of the produce, but also decrease the amount of the energy required to operate any precooling system by reducing the cooling time and the air-pressure drop through the produce [65–67]. The package must have sufficient openings to provide uniform airflow around the produce without sacrificing mechanical resistance [20,54,61]. Dehghannya et al. [12,17] demonstrated that increasing the vent area does not necessarily lead to homogeneous cooling and can even increase cooling heterogeneity if the vents are not properly distributed on the package walls. Thus, to ensure

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uniform airflow during the cooling process, the vents must be properly distributed on the package walls. A proper design of package vents, including both vent area [1,65,68] and positions is necessary to enhance the efficiency of forced-air precooling systems and still maintain adequate mechanical support for the produce [19]. Unfortunately, the current design of packaging is largely based on the criterion of mechanical strength and ease of manufacturing, with minimal consideration for how the vent pattern affects cooling efficiency. As a result, much packaging remains inefficient in promoting rapid and uniform cooling of the package produce [19,69]. Thus, meeting the demand from the market for fresh produce for standardization and globalization, a remaining challenge is to design a vented package to maximize the cooling and ventilation uniformity and minimize deterioration of the packed produce without affecting the mechanical integrity of the package. In recent decades, an increasing number of in-depth experimental or numerical studies and analyses have been done on how package design affects the cooling efficiency. In addition, experimental studies have proven to be more expensive and time consuming, and thus difficult to undertake. With the rapid development of CFD modeling, numerical models have become very popular in various fields because they reduce the need for complex field experiments. In particular, the attractiveness of CFD modelling is also because it provides airflow patterns and temperatures with high spatiotemporal resolution [5,11,42,48]. Generally, two methods exist for modeling forced-air precooling of fresh produce: the porous-medium method and direct CFD simulation. The following two sections provide a detailed introduction to each of these two methods. 3.1. Porous-medium approach A porous medium (or a porous material) is a solid matrix containing pores (voids) that typically are filled with a fluid (liquid or gas).Transport phenomena (the transport of fluid, heat, and mass) in porous media play an important role in many areas of applied science and engineering (e.g., food industry, energy, metallurgy, chemical industry, materials science, space science, environmental science, life sciences, medicine, etc.), making it a point from which an intersecting science frontier may emerge. In the food industry, an enormous range of processes with different scales can involve the transport of fluid, heat, and mass through porous media (e.g., mixing, drying, cooking, sterilization, and cold storage as well as cooling of stacked bulk produce such as apples and tomatoes with or without packaging) [42,70]. For forced-convection cooling of fresh produce, the airflow and produce-cooling characteristics inside vented packaging must be understood for proper cooling and optimum design of fresh-fruit packaging. However, because of limitations in computational resources and complex packaging structures, the porous-medium approach to understanding airflow, heat, and mass transfer has until recently been the only means of modeling transport phenomena within ventilated packages, because it allows the mathematical model to be simplified and therefore reduces computing time and simulation costs. In this case, the space-average approach is required and the fluid flow is characterized by the superficial velocity (i.e., velocity based on volumetric flow rate). Below, based on the porous-medium method, a detailed discussion of the fundamental theory of airflow in porous media is presented together with the important aspects related to heat and mass transfer. 3.2. Airflow in porous media For small airflow in porous media (i.e., the particle Reynolds number Rep < 1), the airflow rate is proportional to the pressure drop, which constitutes the well-known Darcy law. Darcy was

the first to experimentally establish a linear relationship between pressure drop $p (Pa/m) and volume-averaged velocity caused by viscous drag in porous media:

l

$p ¼  u; Rep ¼

ð4Þ

K qjujdeff

;

l

ð5Þ

where l (kg m1 s1) is the dynamic viscosity of the fluid, and K (m2) is the Darcy permeability of the porous matrix and depends on many factors including pore geometry, produce diameter, pore size, and pore distribution. The vector u (m/s) is known as the superficial velocity. The physical air velocity (or the intrinsic air velocity), which is the true velocity through the pores of the medium, is calculated by v = u/e, where e is the porosity. Rep is the particle Reynolds number, and q (kg/m3) is the fluid density. deff (m) is the effective diameter of the product and, for nearly spherical items, is expressed as deff = 6V/A, where V and A are the volume (m3) and the surface area (m2) of the product, respectively. However, Gaskell [71] gave another way to calculate the effective product diameter: deff = (6V/p)1/3. For produce of nonuniform size, a mean diameter can be used, which is derived from the weighted distribution of produce diameters [72]. As highlighted by Miguel [73], the linear relationship between pressure drop and velocity is violated when Rep > 1, which corresponds to most practical situations for food-cooling applications, such as precooling and cold storage. For higher velocities, a quadratic term (i.e., the resistance due to inertial effects) should be added to Eq. (4), forming what is commonly known as the Darcy–Forchheimer equation:




l



C

F ffi juju; rp ¼  u  q pffiffiffi

K

K

ð6Þ

where CF is the dimensionless Forchheimer coefficient that mainly depends on the geometry of the pore space. The experimental study of Lage et al. [74] demonstrated that the Forchheimer coefficient CF is linear in fluid velocity when the particle Rep > 300; thus, in the turbulent regime the pressure drop correlates with a polynomial that is cubic in fluid velocity. However, the validity of the Darcy– Forchheimer equation is still questioned for fully developed turbulent flow (Rep > 300) [74–76]. The main difficulty in resolving this question is the near inaccessibility of porous media for detailed flow measurements [77]. For near-spherical produce, the coefficient in Eq. (6) can be computed by using the Ergun relations [78]:

1 K 1 ð1  eÞ2 ¼ ; 2 K deff e3 CF ¼

K2 3=2 K 1=2 1 e

:

ð7Þ ð8Þ

For randomly stacked spheres, the constants K1 and K2 vary from source to source; the original parameters were 150 and 1.75 [35], respectively, whereas others suggested using 180 and 1.80 [67,73]. However, for packed beds with objects having other shapes or rough surfaces, the parameters K1 and K2 can take on other values [44]. Shahbazi [79] experimented with the resistance of airflow through a bulk of chickpea seeds. The results showed that Ergun’s model fit well to the experiment data for airflow rates in the range of 0.02–0.50 m3 s1 m2. Moreover, the pressure drop increases with increasing airflow rate and bed depth, but the resistance increases more rapidly with airflow rate compared with bed depth. The accuracy (expressed as the summed relative deviation of the pressure drop) of the Ergun equation was demonstrated by van der Sman [77] to be at most 6.6% for both potatoes and oranges, although a refitted apparent-porosity value was used for

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the latter. In the study of Alvarez et al. [80] the values of K and CF were determined experimentally for stacked spheres. The results reveal that sphere stacking significantly affects the difference between experiment results and results calculated by using Ergun’s law. Therefore, the produce size, airflow rate, porosity, and stacking pattern considerably affect the values of K1 and K2. However, in the case of a porous medium of irregular structure, these coefficients must be determined experimentally. As highlighted by Verboven et al. [81] and Tasnim et al. [82], the Darcy–Forchheimer equation is strictly valid only for unbounded porous media without walls. However, in forced-convection cooling of fresh produce, packaging confines the foods within a finite volume. For flow through a confined packed bed, such as for vented packaging, current investigations focus on how the confining walls and the ratio of package-to-produce diameter affect the pressure drop within packed beds. Properly representing this confinement effect requires adding an additional viscous term (i.e., the Brinkman term) to Eq. (6) [72,81]:

l




ð9Þ

K

where leff is the effective dynamic viscosity in the boundary layer at the solid-porous interface in the medium, which depends mainly on porosity and tortuosity of the porous medium. In most cases, the tortuosity in neglected and leff = l/e is used [42,72,81]. As reported by Vafai and Tien [83], leff  l can be assumed for porous media with large porosity. The Darcy–Forchheimer–Brinkman (DFB) equation accounts for the boundary-layer development, macroscopic shear stress, microscopic shear stress, and inertial force. A porous medium and clear fluid interface is best dealt with by the DFB equation and by assuming continuity of velocities and stresses at the interface [84,85]. However, the Brinkman term does not significantly influence the pressure drop over the packed bed. The effect of the Brinkman term is to give rise to a small boundary layer where the velocity reduces to zero exactly at the solid wall [77,81]. If this term is omitted from Eq. (9), the numerical solution of the velocity profile near the wall will contain a nonphysical numerical artifact [83,84]. Therefore, this term is important near the walls in the porous media. Any reduction in velocity in the boundary layer due to the Brinkman term is counter balanced by an increased velocity resulting from higher porosity near wall, where produce items cannot be packed in the same way as in the interior of the porous medium. According to Nield [86], the walls cause two counteracting effects: The first effect is an extra resistance due to wall friction. The second effect is that, near the wall, produce is positioned so as to create a region of increased porosity, extending approximately half a particle diameter into the packed bed [72]. Some researchers claim that the counteracting effect depends on the Reynolds number [87–89], with a low Reynolds number leading to an increase in the pressure drop as a result of wall friction and to a decrease of the turbulent regime due to the increased void fraction near the wall, which reduces resistance [42,72,81]. Furthermore, Eisfeld and Schnitzlein [89] indicate that, for high Reynolds-number flow through a confined packed bed, the drop increases with increasing ratio of package-to-produce diameter,

Table 2 Coefficients K1, k1, and k2 [89]. Particle shape

Spheres Cylinders All particles

1 K 1 A2w ð1  eÞ2 ¼ ; 2 K deff e3 CF ¼

1 Bw K 11=2 e3=2

Aw ¼ 1 þ



C

F ffi juju þ leff r2 u; $p ¼  u  q pffiffiffi

K

whereas the trend is the opposite for low Reynolds numbers. Moreover, they proposed the correlation of Reichelt [88] for a confined bed, where the effect of the ratio of package-to-produce confinement is considered. The accuracy of this new correction is always slightly better than that of the Ergun equations (7) and (8), particularly for a ratio of package-to-product diameter that is less than ten, which is common for retail packaging of horticultural products (e.g., apples, strawberries, tomatoes, etc.). The following coefficients are used in Eq. (9):

Coefficients K1

k2

k3

154 190 155

1.15 2.00 1.42

0.87 0.77 0.83

Bw ¼

ð10Þ

;

ð11Þ

2 ; 3ðDh =deff Þð1  eÞ

ð12Þ

k1 þ k2 ; Dh =deff

ð13Þ

where Aw is an analytical expression to account for how the confining wall affects the hydraulic radius of the bed voids of the porous medium, Bw expresses the porosity effect of the walls at high Reynolds number, and Dh (m) is the hydraulic diameter of the package. The values of the coefficients K1, k1, and k2 are listed in Table 2. 3.3. Heat and mass transfer in porous media 3.3.1. Single-phase models To analyze the macroscopic heat flow through porous media, the porous medium is often considered to be saturated with a single-phase Newtonian fluid and is further assumed to be in local thermal equilibrium with the working fluid [82]. The local volumeaveraged properties are used under the local thermal equilibrium, i.e., hTis = hTif = hTi, where hTi is the intrinsic volume-averaged temperature, T (K) is the temperature, and s and f are the solid and fluid phase, respectively. The intrinsic volume-averaged temperature is given by

hTis ¼ hTif ¼ hTi ¼ ¼

1 Vf

Z

1 Vf

Z T f dV ¼ Vf

1 Vf

Z T f dV Vf

ð14Þ

T f dV; Vf

V ¼ V f þ V s;

ð15Þ

where V is the elementary volume, and Vs and Vf are the volume of the solid and fluid phases, respectively. Based on the assumption of local thermal equilibrium, the phase-averaged energy-conservation equation for porous media is

½eqf C f þ ð1  eÞqs C s 

@hTi þ qf C f urhTi @t

¼ ke r2 hTi þ qf C f rðeDd rhTiÞ þ ½eqf þ ð1  eÞqs ;

ð16Þ

where qf is the fluid density (kg/m3), Cf is the fluid specific-heat capacity(J kg1 K1), qp is the solid density (kg/m3), cp is the solid specific-heat capacity (J kg1 K1), ke = ekf + (1  e)kp is the effective thermal conductivity (W m1 K1), kf is the thermal conductivity of the fluid(W m1 K1), kp is the thermal conductivity of the solid (W m1 K1), Dd is the effective diffusion tensor and depends on fluid velocity and takes into account the axial and radial fluid dispersion due to solid obstacles [42,90], and q is the heat-source term (W/m3).

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3.3.2. Two-phase models If the porous medium has a nonzero thermal conductivity, significant heat is generated in all phases (fluid or solid). If the fluid velocity is high, the local thermal equilibrium assumption is not valid, so separate energy equations must be solved for the porous solid matrix and the fluid parts [82]. In two-phase models, each phase is assumed to be continuous and is represented by total effective thermal conductivity. In this case, the thermal coupling between phases is calculated by using the parameter hsf, which is the interfacial convective-heat-transfer coefficient [42,81,91]. The energy equation for each phase can then be written as

"

eqf C f

# @hTif þ u  $hTif ¼ ekf r2 hTif þ Afs hfs ðhTis  hTif Þ @t þ eqf ;

ð1  eÞqs C s

ð17Þ

@hTis ¼ ð1  eÞks r2 hTis þ Afs hfs ðhTis  hTif Þ þ ð1  eÞqs ; @t ð18Þ

where Afs is the specific interfacial surface area (m2), and hfs is the heat-transfer coefficient between fluid and solid surfaces (W m2 K1). Wakao and Kaguei [92] critically examined the experiment results that determined the interfacial convective heat-transfer coefficients. They found the following correlation for spherical particles:

Nu ¼

hfs deff ¼ 2 þ 1:1Re0:6 Pr 1=3 : kf

Fig. 4. A three-dimensional physical model of ventilated packaging during forcedconvection cooling of produce.

of individual packages of horticultural produce. Furthermore, for transient forced-air precooling, the two-temperature model is inadequate because of the significant difference between center and surface temperatures of the produce [81]. With the rapid development of computer hardware and software in recent years, accurately simulating the details of the airflow and heat- and mass-transfer processes inside a complex packaged structure is more often done by direct CFD simulation rather than by using the porous-medium approach.

ð19Þ 3.4. Direct computational fluid dynamics simulations

The two-phase model has been used to describe the forced-air precooling process, including heat generation (e.g., heat of respiration, transpiration, and condensation), mass transfer (dehydration), and the effects of packaging walls and trays [93–97]. Zou et al. [91,98] experimentally verified this model for the case of cooling apples. The results of the model were consistent with experiment results. In most positions, the predicted central temperatures of the produce fit well with the experiment measurements, with the temperature differences after 4 h of cooling being less than 2 K. Despite extensive efforts, the accuracy of using the porous-medium approach to model the airflow and heattransfer process within packaging has always been questioned, particularly for layered packaging [98]. The main drawback of this approach is that it neglects internal product gradients. Another significant limitation of this approach is the nonvalidity of the continuous-medium assumption when the ratio of package-toproduce diameter is less than ten, which often occurs in the case

In direct CFD simulations, the geometrical complexities are not simplified by the effective medium, in contrast with the porousmedium approach [90,99]. Instead, a direct model based on the explicit geometry of produce stacked in boxes was developed and used to study the local and average airflow through stacks of horticultural products (e.g., the packaging wall, trays, produce, etc.). Because this approach deals with local quantities, it is not constrained to any ratio of package-to-produce diameter and does not require any additional parameters [43]. The accuracy of the model is seriously limited by the accuracy of the model parameters, especially for the porous-medium approach. Many studies developed detailed simulations of the local-airflow field and heat-transfer process within the packaging of various fresh produce by using the explicit geometry of produce stacked in boxes [40,100]. However, most studies did not consider heat transfer by contact between the produce (resulting in so-called ‘‘near-miss”

Fig. 3. ‘‘Near-miss” model.

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models; see Fig. 3) [99,101]. Logtenberg et al. [102] used direct CFD simulations to predict the fluid flow and heat transfer in a packed bed of ten solid spheres, both under laminar and turbulent flow, but considering sphere contact and heat generation from the spheres. This can contribute not only to obtaining the real-flow situation, but also to significantly improving the accuracy of the results of the simulation. Geometric modeling and grid generation become complicated because of the explicit geometry of the produce included in direct CFD simulations, which increases the computational requirements and numerical difficulties. However, the method can lead to a more fundamental understanding of how local behavior of the fluid flow affects the heat- and mass-transfer processes within the packaging of various fresh produce during cooling. This method is more significant than the porous-medium approach for improving the design of packaging systems, so that, during the forced-convection cooling of produce, these systems now provide rapid and uniform cooling of produce with minimal energy consumption. 3.4.1. Airflow, heat- and mass-transfer models We require a three-dimensional mathematical model of airflow and heat transfer for analyzing simultaneously the aerodynamic and thermal forced-convection cooling of vented packaging (see Fig. 4). The following equations are applied for different zones (e.g., air, produce, packaging walls, or tray zone). The flow in the free-airflow zone is obtained by solving the Reynolds-average Navier–Stokes equations. Conservation of mass gives

@ qa þ divðqa UÞ ¼ 0: @t

ð20Þ

Conservation of momentum gives

@ðqa uÞ @p þ divðqa uUÞ ¼ divðla graduÞ  @t @x " # @ðqa u02 Þ @ðqa u0 v 0 Þ @ðqa u0 w0 Þ þ    @x @y @z

ity (J kg1 K1), and Su, Sv, and Sw represent source terms in the x, y, and z directions, respectively. This work only considers the effect of gravity in the free-airflow zone, so Su = Sw = 0, Sv = qag, where g is the acceleration due to gravity (m/s2), u0i u0j is the specific Reynolds

stress term, and i and j are Cartesian coordinates. In the produce zone, the heat of respiration (Qr, W) and transpiration (Qe, W), the convective heat transfer from the commodity surface (Qconv, W), and the release of heat due to condensation on the commodity surface are the main heat sources internal to each apple. Therefore, heat flow inside the produce zone is [17,30,103]

@T p ¼ kp r2 T p þ Se ; @t Q  Q e þ Q con  Q conv Se ¼ r ; Vp

qp cp;p

ð21aÞ @ðqa v Þ @p þ divðqa vUÞ ¼ divðla gradv Þ  @t @y " # 0 @ðqa u v 0 Þ @ðqa v 02 Þ @ðqa v 0 w0 Þ þ    @x @y @z þ Sv ; ð21bÞ @ðqa wÞ @p þ divðqa wUÞ ¼ divðla gradwÞ  @t @z " # @ðqa u0 w0 Þ @ðqa v 0 w0 Þ @ðqa w0 2 Þ   þ  @x @y @z þ Sw : ð21cÞ Conservation of energy gives

where qa is the air density (kg/m3), t is time (s), U is the velocity vector (m/s), u, v, and w are the air-velocity components (m/s) in

ð24Þ

ps ¼ VPL  pw ;

ð25Þ

pw ¼ 0:041081186T 3a  32:431887T 2a þ 8567:5269T a  757070:1; 1 : kt ¼ 1=ka þ 1=ks

ð26Þ ð27Þ

In these equations, Ta is the pre-cooling air temperature, RH is the relative humidity of the air, and VPL is the vapor-pressurelowering effect of the produce. The water VPL effect for various fruits and vegetables are provided by Becker et al. [104]. The quantity ka is the air-film mass-transfer coefficient (kg m2 s1 Pa1), and ks is the skin mass-transfer coefficient (kg m2 s1 Pa1), which describes the resistance to moisture migration through the produce skin and is related to the structure and properties of the produce skin. Becker et al. [104] tabulated skin mass-transfer coefficients for different commodities. The value of ka can be estimated by using the Sherwood–Reynolds–Schmidt correlations [35,45,103,104],

Sh ¼ D¼

ð22Þ

ð23Þ

where qp is the produce density (kg/m3), cp,p is the produce specific-heat capacity (J kg1 K1), Tp is the produce temperature (K), kp is the thermal conductivity of the produce (W m1 K1), and Se is the heat-source term (W/m3). The heat of respiration (W) is Qr = qpqrVp, and qr = 0.003f (1.8Tp + 32)g is the respiratory-heat generation per unit mass of commodity (W/kg), where the respiration coefficients (f and g) for different crops are given by Becker et al. [104]. Vp is the volume of the produce (m3), Qe = LpmtAp is the evaporative heat-transfer rate due to transpiration (W), Lp = C1T2p + C2Tp + C3 is the latent heat of evaporation (J/kg), with C1 = 0.0091  103, C2 = 7.5129  103, and C3 = 3875.1  103. The quantity Ap is the surface area of the produce (m2), and mt is the rate of moisture loss from the product (kg m2 s1). When pw > ph and ps > ph, mt = kt(ps  ph), otherwise mt = 0. kt is the transpiration coefficient (kg m2 s1 Pa1) [see Eq. (27)] [35,104]. The quantity pw is the saturation partial water vapor pressure (Pa), ps is the partial pressure of water vapor at the evaporating surface (Pa), and ph is the partial pressure of water in air (Pa) [103,104]:

ph ¼ RH  pw ;

þ Su;


 @ðqa TÞ k þ divðqa UTÞ ¼ div gradT @t cp;a " # 0 0 0 @ðqa u T Þ @ðqa v T 0 Þ @ðqa w0 T 0 Þ þ S;   þ  @x @y @z

the x, y, and z directions, respectively, p is the fluid pressure (N/m2),

la is the dynamic viscosity (Pa s), cp,a is the air specific-heat capac-

ka dRT a ¼ 2:0 þ 0:552Re0:53 Sc0:33 ; DMH2 O

9:1  109 T 2:5 a ; T a þ 245:18

ð28Þ ð29Þ

where Sh, Re, and Sc are the Sherwood number, Reynolds number, and Schmidt number, respectively. R = 8.314 J mol1 K1 is the universal gas constant, D is the diffusion coefficient of water vapor in air (m2/s), MH2 O is the molecular mass of water vapor, Re = (qaud)/la, and Sc = la/(qaD). Qcon = LpmconAp is the release of heat due to condensation on the commodity surface, and mcon is

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Fig. 5. Various packaging and stacking of different products [5,8,11,63,64,100,139,140].

the condensation coefficient (kg m2 s1). When ph > pw, mcon = ka(ph  ps), otherwise mcon = 0. The parameter Qconv is the convective heat transfer from the commodity surface:

Q conv ¼ hp ðT p  T a ÞAp ;

ð30Þ

hp d Nu ¼ ¼ 2 þ 1:1Re0:6 Pr 1=3 ; ka

ð31Þ

where hp is the heat-transfer coefficient at the surface of the produce (W m2 K1), and Pr is the Prandtl number. For the solid zone, the heat flow inside the corrugated boxes and tray zone was modeled by using Eq. (23) with zero heat source (Se = 0). The walls of the corrugated boxes are very thin for modified atmosphere packaging and the temporal variations in temperature through the wall are also quite small. Therefore, the total heat flux qw into the packaging is assumed to be the sum of a steady-state heat-conduction flux and a heat flux due to condensation on the packaging wall [103]. The total heat flux through the packaging wall can be expressed as

qw ¼

Ta  T þ qwcon ; 1=hi þ lw =kw þ 1=ho

ð32Þ

where T is the gas-mixture temperature inside the package (K), qwcon = Lwmwcon is heat flux due to condensation (W/m2), and lw is the package-wall thickness (m).The latent heat of vaporization Lw = (3151.37 + 1.805T  4.186T)103 J/kg is based on the gasmixture temperature [105]. The parameter mwcon is the condensation coefficient for the package wall (kg m2 s1). When ph > pw, mwcon = ka(ph  pw), otherwise mwcon = 0. kw is the thermal conductivity of the packaging wall (W m1 K1). The parameters hi and ho are the inner and outer heat-transfer coefficients of the packaging wall, respectively (W m2 K1). To simplify the calculations, we assume that the inner heat-transfer coefficient is the same as the heat-transfer coefficient at the surface of the apple; thus, hi is calculated based on Eq. (31). For cuboid packages, ho can be determined from the following expression:

ho ¼ 0:332

kw 1=2 1=3 Re Pr ; db

ð33Þ

where db is the width of the package, and Re is the Reynolds number and is based on the width of the package and the air-inflow velocity surrounding the package.

4. Parameters used to analyze package performance Optimization of fresh-fruit packaging design is required to reduce energy loss by minimizing the precooling time and to enhance fruit quality by providing more uniform cooling without inducing chilling injuries. From the studies done to date, no unique container concept appears suitable for all crops. The performance of packaging depends on the specific case in question and is determined by a multitude of variables and conditions [10]. A non-exhaustive summary of the different packaging and stacking of different products is given in Fig. 5. To obtain the optimal design of packaging structure for a specific product, some packaging performance parameters are widely used in the literature (i.e., cooling time, cooling rate, cooling uniformity, energy consumption, and mechanical strength). These parameters not only allow quantitatively comparison between the performance of existing packaging designs, but also, in a more integrated way, between the performances of new designs. 4.1. Cooling time Packaging materials increase cooling airflow resistance and block direct contact between cooling air and produce [6,7]. The negative effects significantly affect produce cooling time and rates. Therefore, quantifying the cooling time and rate is particularly relevant for evaluating the effectiveness of package design during precooling of fresh produce, because this determines how fast the field heat can be removed [1,10]. In addition, these quantities are also directly related to product quality, shelf life, precooling throughput, operational costs, and energy losses in the system. The cooling time depends primarily on many factors, including heat-transfer rate, the difference in temperature between the produce and the cooling medium, the thermal properties of the produce, the size and shape of the produce, the nature of the cooling medium, the type of packaging, and the stacking arrangement [1,106,107]. In general, product cooling is evaluated by the temperature ratio (Y), which is the ratio of the unaccomplished temperature change at anytime to the total temperature change possible for a particular cooling condition. It can be determined from the temperature profiles as follows:

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Y ¼ ðT P  T a Þ=ðT pin  T a Þ; n 1X V iTi; T vwa ¼ V t i¼1

ð34Þ ð35Þ

where Y is the dimensionless temperature, Ta (K) is the precoolingair temperature, and Tpin (K) is the initial product temperature. Ti (K) is the produce temperature at cell position i = 1 to i = n, Vi (m3) is the volume of mesh cell i, and Vt (m3) is the total volume of the fruit zone. Tp (K) is the product temperature. Three different temperatures Tp can be used to define Y: (1) the core temperature of the product (Tp,c), which is often measured in field or laboratory experiments since it is easily done there. However, this is true because most of the product mass is in the outer portion, and thus large errors may occur by using the center temperature [1]. (2) The volume-weighted average temperature of an entire product is Tvwa [see Eq. (35)] and can be obtained from CFD numerical modelling. (3) The surface temperature at the produce-air interface (Tp,s), which is rarely used in scientific research. Moreover, Smith and Bennett [108] recommend that the product mass-average temperature should be used for Eq. (34). The mass-average temperature is the single value obtained from the transient-temperature distribution, which becomes the uniform produce temperature when the produce is maintained under adiabatic conditions. For Newtonian heat transfer (a negligible temperature gradient within the product during cooling, Tp,c  Tvwa  Tp,s), the dimensionless temperature Y is expressed as an exponentially decaying function over time t [109]:

Y p;s ðtÞ ¼ Y vwa ðtÞ ¼ Y p;c ðtÞ ¼ eCt ;

ð36Þ

where C is the cooling coefficient, which gives the change in product temperature per unit time for each degree temperature difference between the product and the cooling medium [1,10,58]. As a result of rapid heat transfer, a temperature gradient (Tp,c > Tvwa > Tp,s) develops within the cooling product, with faster cooling causing larger gradients. Consequently, conditions for Newton’s law are rarely satisfied, and the temperature change in the interior of the produce lags considerably behind the change in surface temperature. In such cases, the limiting factor is the rate of heat conduction to the surface of the produce, and the dimensionless cooling curve Y(t) can be expressed as [1,10,110]

YðtÞ ¼ je

Ct

;

ð37Þ

where j is the lag factor (i.e., core temperature divided by surface temperature), which depends on the size, shape, and thermal properties of the product as well as on the Biot number [111]. The lag factor varies from 1 to 2 when based on Tp,c [1,111]. The cooling time is evaluated based on the dimensionless cooling curve Y(t) [Eq. (37)] by determining the half-cooling time (HCT, s) or the seven-eighths cooling time (SECT, s). These are the times required to reduce by half the temperature difference between the produce and the cooling air (Y = 1/2) or seven eighths (Y = 1/8). They can also be calculated by using

HCT ¼ ½lnð2JÞ=C;

ð38Þ

SECT ¼ ½lnð8JÞ=C:

ð39Þ

In general, J and C were determined by regression analyses based on Eq. (34). Therefore, the magnitudes of HCT, SECT, J, and C critically depend on the choice of Tp to define Y [Eq. (34)]. The SECT is particularly interesting in commercial-cooling operations because the fruit temperature is then acceptably close to the required storage temperature. At this point, the fruit can be transferred to storage facilities where the remaining heat load can be removed with less energy cost [1,11]. In principle, the HCT and SECT are independent of the initial product temperature and the temperature difference Tpin  Ta, and remain constant throughout

the cooling period, as is evident from the idealized cooling curve [Eq. (36)]. However, Defraeye et al. [21] demonstrated that slight variations in HCT and SECT with (Tpin  Ta) do appear. Castro et al. [65] investigated packages with thirteen different opening configurations and four airflow rates during a horticultural produce forced-air cooling process. The airflow rate (AFR, L s1 kg1), total opening area (TOA, %), and produce positioning all significantly affect the HCT. Although straight stacking of produce results in the same porosity as randomly stacked produce, straight stacking generates a better defined airflow path and, consequently, a higher cooling rate for the same airflow rate and total opening area. The research results show that the HCT does not significantly decrease when the total opening area is more than 8%. The opening area only affects the HCT for the lower AFRs; the HCT is almost the same for different opening areas when AFRs exceed 4 L s1 kg1. In addition, a nonlinear model to infer the HCT is defined as a function of AFR and TOA: HCT ¼ 26:1544AFR  58:5849 lnðAFRÞ þ 2:6618 lnðTOAÞ; R2 ¼ 0:892:

ð40Þ

4.2. Cooling rate When warm produce is cooled, the rate of cooling is not constant but diminishes exponentially as the temperature difference reduces, with rapid cooling initially followed by a slower and slower rate [1]. Because of this, the cooling coefficient C (h1) is usually adapted to quantify the cooling process. This coefficient (>0) equals the magnitude of the (negative) slope of the ln(Y) vs t curve. C is constant at any time for an idealized cooling curve [1]. However, the coefficient cannot give detailed variations in cooling rate with time for different packing-structure designs during cooling. Therefore, the cooling rate is sometimes quantified by the momentary (instantaneous) cooling rate (Rtx, K/h) at time tx [109], where Rtx is defined as

Rt;x ¼ CðT p;x  T a Þ ¼

lnð2JÞ ðT p;x  T a Þ HCT

ð41Þ

with Tp,x being the product temperature at tx. In addition, the cooling rate of the fruit is also quantified by means of convective heat-transfer coefficients [CHTCs = qc,s/(Tp,s  Tref) W m2 K1] at the surface of the produce [11,21], which relate the convective heat flux normal to the surface(qc,s, W/m2) with that resulting from CFD simulations. The reference temperature Tref is often taken as the cooling-air temperature because it is easily measured in experiments. Kondjyan [112] reported that the energy exchanged by convection is directly related to the CHTCs, so this is a more intuitive way to evaluate with high spatiotemporal resolution the cooling rate of different packaging designs. 4.3. Cooling uniformity The heterogeneity index for temperature or velocity is often used to quantify the cooling uniformity. This parameter demonstrates the deviation of the instantaneous value (temperature or velocity) at different positions from the average value inside the ventilated packaging. The heterogeneity indices for temperature or velocity are respectively defined as [12,17,35]

HIT ¼

HIV ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðT  TÞ T

 100;

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðV  VÞ V

 100;

ð42Þ

ð43Þ

C.-J. Zhao et al. / Applied Energy 168 (2016) 314–331

where T and V is the instantaneous value of temperature and velocity obtained at a specific position, respectively. T and V are the average temperature and velocity, respectively, obtained at different positions. For the heterogeneity index of temperature, the denominator (T) is close to zero when the product temperatures approach 0 °C during cooling. Therefore, to avoid this problem, the temperature should be expressed in Kelvin [10]. In addition, the inverse of the standard deviation of the HCT and SECT between individual products in a box, pallet, or container can also be used to reflect the uniformity of the cooling process. Alternatively, Defraeye et al. [11,21] reported that the CHTCs at the surface of the produce can used to analyze the heterogeneity of convective-heat loss from produce within a specific container and between individual containers by using steady-state CFD simulations. This method is even available for evaluating the cooling heterogeneity of an individual produce, which because the CHTCs at the surface of the produce can be determined based on each computational cell.

4.4. Energy consumption The efficiency of the forced-air cooling process is mainly indicated by the cooling rate and the cooling uniformity in produce temperature reduction in contrast to the energy input required by precooling and refrigeration systems [66,113]. However, reducing energy consumption will further improve the cooling efficiency and overall economics of cold-chain. The energy required for forced-air cooling of horticultural produce is directly proportional to the total heat load. The composition of the total heat load comes from the product, surroundings, air infiltration, containers and other heat-producing devices [67,114], among them the field heat and respiration heat of fresh produce account for the majority of the total heat load [66]. The energy required to operate any precooling system is affected by the airflow rate through the fans and the air-pressure drop through the produce [115,116] as well as the opening area and position of the packaging [9,54,65,66,115,116]. As shown by Defraeye et al. [21], the relation between the total pressure drop over the packaging (DP, Pa) and the airflow rate through it (Ga, m3/s) is expressed as

DP ¼ n1 G2a þ n2 Ga ;

ð44Þ

where n1 and n2 are pressure-loss coefficients. The first term of this second-order polynomial represents the pressure drop due to inertial effects (Forchheimer term), which dominates the pressure drop at high speeds, and the second term represents the pressure drop due to viscous effects (Darcy term) [74], which becomes important at low flow speeds. In addition, DP could also be calculated as DP = 37.487 TOA1.5 G2a [65], where TOA is the total opening area of the package. The relationship is consistent with the results of many studies [54,117] that found that DP through a vented package follows approximately a quadratic relationship with the average airflow velocity which is related to airflow rate. Van der Sman et al. [77] also stated that pressure drop scales as TOA1.5. The optimization of fresh-fruit packaging designs has recently been put forward as one of the key factors for minimizing energy consumption during forced-convection cooling of produce [10,21,66,67,114]. Unfortunately, very few studies exist that focus on this topic. The energy required for a ventilation system is associated with many factors (e.g., the refrigeration equipment, lights, fans, etc.) [67]; however, this energy only includes the contribution of the packaging, which enables a direct comparison of the energy efficiency of different packaging designs, that of boxes, or the stacking pattern [10].

327

4.5. Mechanical strengths Ventilated packaging not only maintains an airflow channel between the surroundings and the inside of the packages, but it also needs to be sufficiently strong to prevent the produce from mechanical damage due to one or more types of loading; compression, impact, or vibration during handling, cooling, transport, storage, and marketing [10,118,119]. However, no unified standards or regulations currently exist for packaging designs for various fresh produce, and the packaging was designed and fabricated mainly based on the experience of the workers. To improve the mechanical strength of packaging, manufacturers often use higher-grade raw materials but give little thought to how the ventilation holes (e.g., the location, size, and shape) affect mechanical strength, which will undoubtedly increase manufacturing costs. Especially for corrugated boxes, the box strength also depends on distribution hazards such as high relative humidity, excessive stacking load, long-term storage, or offset stacking [120]. Recent research has shown that, when the relative humidity of the storage air increases gradually from 30% to 90%, the edge compressive strength decreases by 19%. The strength of the corrugated box reduces by up to 52% when the moisture content of the corrugated package increases from 7.7% to 16.4% [121]. A negative exponential relationship between the compression strength (CS) of corrugated board boxes and their moisture content is [122]

CS ¼ CS0 10mx ;

ð45Þ

where CS0 is the compressive strength of the box at zero moisture, m is the average slope of the logarithm of compressive strength versus moisture, and x is the dry-based moisture content (ratio between the weight of water in the board and the oven dry weight of the board). Therefore, the influence of environmental factors on the box performance must be considered in designing the corrugated box for precooling, transportation, or long-term storage [119,123]. The box compression test (BCT) and the edge crush test (ECT) are usually used to evaluate the compression strength of the boxes in the laboratory. In recent years, the use of finite element modeling (FEM) and experiments (i.e., BCT and ECT) have emerged for analyzing the box material [124–126] or the impact of the geometric location, sizes, and shapes of the ventilation holes on boxcompression strength [69,127], by which the accuracy of the FEM could also be evaluated. The aim of such studies is to provide a more detailed understanding how various designs of ventilation holes affect box strength. Han and Park [69] used FEM to analyze the compression performance of boxes with ventilation holes of various shapes and sizes. The study tested 41  30  25 cm3 double-walled corrugated boxes with 15 different ventilation and hand-hole designs. The numerical model was verified by comparing the results of simulations to those of experiments, and the FEM simulation was consistent with laboratory results. The study reported that an increase in the radius of curvature at both ends of the hand hole provided better stress relaxation and lower stress. Some factors were recommended; for example, the length of the major axis of the ventilation hole should be less than 1/4 of the depth of the box, the ratio of the minor axis to the major axis should be 1/3.5–1/2.5, and even-numbered holes should be located symmetrically, which could achieve the minimum decrease in boxcompression strength. Biancolini and Brutti [127] also used a FEM model to evaluate the mechanical characteristics of paperboard, starting from the paper characteristics and microgeometry. The reliability of the proposed model was checked by comparing the numerical results with the experiment results, obtaining an excellent agreement first from the ECT test and then from the BCT test. However, these studies are

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based on single boxes, which are often not filled with fresh produce. Therefore, the method cannot be used to effectively evaluate the strength of boxes filled with produce. In addition, pallet stacking strength is usually not explicitly quantified because it involves lengthy and more complex experiments [128]. Thus, future research should be directed towards analyzing the stacking strength for entire pallets of boxes filled with produce with various vent openings and various stacking and storage arrangements. 5. Future developments 5.1. Physical-parameter estimation Parameter estimation plays an important role in physical modeling and is directly affect the accuracy of the simulation results. Excessively simplified models often ignore some parameters and therefore fail to capture the essential dynamics of a system, while excessive consideration of certain parameters may amplify the complexity of the entire simulation, which is a disadvantage for predicting the change of specific physical phenomenon and significantly increases computational cost due to some nonlinear models that are included in the iterative computations (e.g., respirationrate models, evaporation-rate model, condensing-rate model, etc.) [129]. Some research has shown that the very low heat rate generated by respiration (about 0.5% of the total heat load) is unlikely to significantly affect the cooling rate in a typical precooling process [96,130]. In addition, the uncertainty of the respiration rate is also significantly influenced by the uncertainty of the simulation results. The respiration-rate model used, as with most respirationrate models found in the literature, does not consider changes in respiration rate due to commodity senescence, the sudden change of storage conditions, or even different batches of the same commodity. Therefore, additional nonlinear models should be chosen to properly account for different produce or processing surroundings (i.e., humidity, temperature, and duration) rather than using ‘‘the more the better” approach [129]. For large spaces (e.g., cold room, refrigerated vehicle, refrigerated containers) the packageto-produce equivalent-diameter ratio is greater than ten, the purpose of model-based analysis is usually to understand the macro phenomenon of spatiotemporal heat and mass transfer. For this case, the porous-medium approach may be the best approach due to the simplified geometrical models of produce (i.e., the size, shape, surface heat, and mass-transfer coefficients of agricultural products are ignored) and may significantly reduce computational time and simulation costs. For a single package or for several packages stacked on a pallet (where the ratio of package-to-produce diameter is less than ten), a direct CFD simulation must be used to obtain the detailed characteristics of airflow and heat transfer within packages. In this case, some other models (e.g., biochemical reaction, microbial reaction, mechanical stress, etc.) and more complex multiphysical and multiscale models should also be incorporated into the direct CFD simulation when these models greatly influence the quality of fresh produce. All above, the selection of physical parameters should aim at the important physical phenomenon to be observed in modelling, so as to realize the improvement of pertinence and high efficiency of CFD numerical simulations. 5.2. Model validation Concurrent experimentation should be done to verify predictions, particularly where assumptions are incorporated into the model (e.g., simplified geometrical shape, constant surface heat and mass-transfer coefficients, no volume change during processing, etc.). However, the validity of a simulation is directly

determined by the accuracy of experiment results. Due to the complexity of internal structure within packages when they filled with trays and produce, some physical phenomena are difficult to be measured with high spatial and temporal resolution (e.g., the characteristics of airflow and heat transfer inside ventilated packages, the CHTCs, the temperature variation of the whole fruit, etc.) [131]. As mentioned previously (see Section 4.1), the point temperature is often used to represent the temperature of the whole product in field or laboratory experiments, which leads to a great deviation between experiment results and actual values. Therefore, the accuracy of CFD models will be erroneous is these experimental data are used to validate advanced numerical simulations. These shortages limit CFD models in cold-chain applications. In particular, they limit the use of the CFD models to study transport processes down to the microscale level. These limitations are the main motivations behind research toward more advanced experiment techniques. Future developments are expected to lead to better integration of advanced technologies with experimental equipment and to the establishment of laboratories specially equipped for forced-air precooling of fresh produce [132]. In this way, detailed experimental data can not only be obtained but also be more accurate, allowing CFD models to be validated. In addition, this will also greatly promote the application of CFD in other fields. 5.3. Energy conservation Energy coefficient (EC) is usually used to measure the effect of a particular cooling method on the cooling-system efficiency during precooling [66,67]. EC is defined as the ratio of total thermal energy removed from the product (i.e. field and respiration heat)during precooling and the total electrical energy used through the cooling process (i.e. the energy inputted to the refrigeration system and the forced-air precooling equipment).As such, EC can also be known as a kind of coefficient of performance (COP) of the entire cooling facility. As shown by Thompson [67], the average EC for forced-air cooling facilities did not improve significantly over the last of 20 years. Therefore, an international research priority should be to improve the EC of cooling processes, which is also an important challenge for further improving the overall economic benefits of the cold chain. The demand for fresh produce have been increasing through the world, and the worldwide exports of fruits and vegetables exceeded 150 billion USD in 2010 [133]. However, to maintain product quality, extend shelf life, and reduce food loss, the energy consumed in the food industry accounts for approximately 30% of the world’s energy consumption [134], and 8% of the electrical energy used in this industry is for refrigeration [135]. This is especially problematic because electricity mainly comes from coal-fired power plants in some countries, especially in the developing world [136–138]. Therefore, improving EC in the cooling process not only effectively reduces the amount of electrical energy used in the entire cold-chain system, but also reduces food, energy, and resource insecurity. In addition, this approach is also conducive to reducing the carbon emissions and thereby alleviating the associated environmental problems. Airflow rate, cooling time, and pressure drop are directly related to the amount of energy input to operate the cooling equipment (compressor and fans). The ventilating rate of packages and the fruit-stacking pattern in the package are major factors in increasing cooling airflow resistance and prevent direct contact between cooling air and produce. Thus, further research on packaging designer mains an important way to reduce the energy required for precooling different kinds of fresh produce in the future. CFD is an indispensable research tool in the continuous process of improvement. In addition, hardware innovations in cooling

C.-J. Zhao et al. / Applied Energy 168 (2016) 314–331

equipment is another important direction for future research to reduce the operating power in conformity with the demand of precooling, but this subject is beyond the scope of this paper. However, a comprehensive and effective way to reduce energy consumption of precooling is by combining packaging design and hardware innovations. 6. Conclusion This paper reviews the application of CFD to analyze forcedconvection cooling of horticultural products. CFD is an efficient tool for simulating different cooling processes in the freshproduce industry and also provides a better understanding of the airflow, heat, and mass transfer that occurs with different packaging vent designs. Understanding the cooling process is a prerequisite for optimizing the cooling system. The current trend towards direct CFD modeling of transport phenomena inside complex packaging structures will advance the detailed understanding and analysis the velocity and temperature distributions for various combinations of package size and shape; size, number, and location of vents; produce packing arrangements; size and shape of produce; airflow rate, and air temperature. For fresh horticultural produce, packaging or containers are usually provided with vent openings. The cooling performance, strength and ventilation capability of boxes depend heavily on vent design parameters (vent area, shape, number, position). This review outlines the relevant packaging functions that should be addressed in analyses of ventilated package performance, which can provide a direct and integrated comparison of the cooling efficiency of different packaging designs. Furthermore, simulation by the FEM is a useful tool for the mechanical design of ventilated packaging by taking into account the shape, location and size of the vents and hand holes. Therefore, to meet and balance the structural requirements of packaging and the cold-chain requirements of fresh produce, future efforts should be directed toward a more integrated analysis, in which all performance parameters of ventilated packaging are evaluated simultaneously by combining FEM and CFD. Finally, a main contribution of the review is a reliable theoretical and experimental basis for improving the design of packaging systems so that they provide rapid and uniform cooling of produce with minimal energy consumption during the forcedconvection cooling of produce. Acknowledgments This work was funded by the National Key Technology R&D Program of China (Grant No. 2013BAD19B04) and FP7 International Research Staff Exchange Scheme Project (PIRSES-GA-2013612659). References [1] Brosnan T, Sun DW. Precooling techniques and applications for horticultural products – a review. Int J Food Eng 2001;24:154–70. [2] Ambaw A, Delele MA, Defraeye T, Ho QT, Opara LU, Nicolaï BM, et al. The use of CFD to characterize and design post-harvest storage facilities: post, present and future. Comput Electron Agric 2013;93:184–94. [3] Dennis C. Effect of storage and distribution conditions on the quality of vegetables. Acta Hortic 1984;163:85–104. [4] Kader AA. Prevention of ripening in fruits by the use of controlled atmosphere. Food Technol 1980;34:50–4. [5] Han JW, Zhao CJ, Yang XT, Qian JP, Fan BL. Computational modeling of airflow and heat transfer in a vented box during cooling: optimal package design. Appl Therm Eng 2015;91:883–93. [6] Delele MA, Ngcobo MEK, Getahun ST, Chen L, Mellmann J, Opara UL. Studying airflow and heat transfer characteristics of a horticultural produce packaging system using a 3-D CFD model. Part I: Model development and validation. J Food Eng 2013;86:536–45.

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