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Computational Fluid Dynamics (CFD) uses large scale numerical computation to solve problems of fluid flow phenomena. It is a powerful tool and widely used to simulate many processes in the food industry. Recent development in computing efficacy and availability of various algorithms and software packages has advanced CFD as powerful technique to predict effective fluid flow and efficient design solutions. CFD is used as a powerful tool for predicting fluid flow behavior in various applications from aviation industry to human blood flow. The Application of CFD in food industry is widely accepted and lots of research was performed, but it is not spread in the food packaging area. In this area, two basic types of analogies are mostly popular; heat transfer methodology and flow behavior modeling. Although, mostly research is based on heat transfer model and fluid flow model has less attention. Therefore, the present paper demonstrates the fundamentals involved in developing a CFD solution for food packaging application for fluid flow model. It also provides a brief review on various CFD applications in packaging including design, mass transfer and diffusion patterns inside the packaging container. A fluid flow model basically covers the injection of various gases apart from airflow inside or outside the food container. It leads to the development of laminar to turbulent flow model. It can also used for predicting the shelf life of a fresh food produce. Proper application of CFD technique enhances the designing feature of the food packaging equipments and packages.
Keywords: review, flow model, simulation, fresh produce, CFD
Maintaining a controlled environment all around the horticultural product is mainly done by forced air/water cooling to the required storage temperature. The cooling process of agricultural product is mainly depending on heat transfer between the cooling medium and produce items in the packaging container. The heat transfer processes are closely related to gas flow transport within the packages. Some types of food require closed packaging whereas some food items required ventilated packaging, which is obtained from fast and uniform cooling. The materials used in the food packaging system have also major impacts on the heat transfer and flow patterns during storage. A packaging system needs to be carefully designed and evaluated before implementing to the fresh food storage to ensure safety and quality. It is a global concern to protect the microbial safety of food items for longer period. Also some of the leafy vegetables affected by outbreaks of Escherichia coli O157:H7 and Salmonella (MMWR, 2005). Apart from these infected deceases in fresh produce, an outbreak of licteriosis produce by Listeria monocytogenes in coleslaw was reported by Cummings et.al., 1999.
Conducting extensive experiments for studying heat transfer and fluid flow patterns are considered as expensive, time consuming and occupy a variable floor space. It also depends upon human consistency and capability to conduct experiments for indefinite amount of time. Hence, mathematical modeling is overall a cost effective solution for predicting the fluid flow patterns and controlled environmental variables. Proper validation of simulation results is required with experimental data while applying a numerical approach to the food packaging application. One needs to have initial input data for packaging material, product condition, environmental condition and reaction kinematics for application of fluid flow equations. The simulation results obtained based on the input data may be used to apply and predict for design solution and effect on the various parameters on food items. Computational Fluid Dynamics (CFD) employs various numerical techniques to solve the fundamental fluid transport equations of conservation of mass, momentum, energy and species transport. Now-a-days, the application of CFD modeling is more knowledgeable and accepted with the increasing capability and decreasing cost of modern computer systems.
Typically CFD governs the equation of fluid flow, which are quite complex and can be difficult to simultaneously solve, especially if the geometry of a problem is intricate. These equations are nonlinear in the convection term and pressure difference terms, have singularities for variable buoyancy and Reynolds number, and they are difficult to solve in combination with the fluid flow. These fluid flow equations may be solved together with various algebraic solvers on high-speed computers as a computational tool for any arbitrary situation in fluid flow.
In this particular attempt, detailed fluid flow methodologies have been analyzed to give the reader an appropriate idea about fluid flow behavior in packaging application. Although this paper does not consider any electronics packaging application as lots of work have been conducted on electronic packaging and it is different from food packaging applications due to the character of the product like respiration, humidity, and microbiological load. Application of CFD in fresh food packaging has very limited attention in terms of design of a packaging system and effect of fluid flow inside any package. After conducting a detailed review on the possible application on packaging, this paper enhances the various aspects of CFD techniques applied for fresh produce safety.
2. Literature on CFD application
A better package is basically a combination of a good design that influences consumers, provide long life of a packaged food items, and use a sustainable packaging material. The most common materials used for food packaging appliances are glass, metal (aluminum and tinplate), corrugated board, wood, and plastic. Now a day, glass is mainly used for premium products and long shelf life applications. Aluminum packaging works well for carbonated beverages and as a barrier material. Tinplate is mainly used for canned perishables. Corrugated board packaging works for transporting frozen and fresh perishables. Currently, plastic is the most versatile material for a number of applications from frozen perishables, fresh perishables, snack food, bakery items and many more. Moreover in the CFD literature, it has been shown wide variety of applications for all these packaging material applications. A wide application of CFD in food processing area has been reported in the literature. They are mainly related to the ventilation in packaging, cold storage and refrigerated cabinets. Although a few peer review papers have been found on the application of CFD inside fresh food packaging application. Table 1 describes the application and suggested areas of the CFD for each concerned subjects. Basic knowledge of the subject and CFD is required to move further in the application area.
<Table 1: Insert here>
A review article published by Xia & Sun, 2002 for the application of CFD in the food industry provides a good summary of this required basic knowledge. The areas cited as application of CFD in food processing including drying, sterilization, refrigeration and mixing. They concluded that a CFD simulation should be appropriately validated through experimental results for making decision as simulation results are highly dependent upon the assumptions. They expected that future increase in computer capacity would provide better simulations. Also, the authors stated that thorough knowledge of processing involving the physical, chemical and micro-biological phenomena should be properly understood before applying CFD techniques to any food processing application. CFD techniques have been reviewed as a powerful, efficiently and effectively design tool at a reduced cost by Norton & Sun, 2006. Various fluid flow approximations were established for predicting turbulent modeling and porous media approach and non-Newtonian fluid modeling by these authors. The methods for improving the meshing were discussed like unstructured and sliding meshing scheme to improve the modeling accuracy. Furthermore, the applications of CFD were described for ventilation and contaminant dispersion, stirred tanks, cold store and as a static mixture, refrigerated display and spray drying process.
2.1 Ventilated package
A numerical method can be applied for solving conservative equations of fluid flow combining a distribution model, heat transfer model and porous medium model. The airflow patterns and heat transfer through computational fluid dynamics techniques in horticulture food products were demonstrated by Zou, Opara & McKibbin, 2006. They used a layers and bulk package modeling system for fresh food package. Porous media approach was used in layer package for proper ventilation. The volume-based formulation for conservative equation was developed for airflow model and energy based approach for heat transfer model.
The process of thermal sterilization of liquid food in the pouches has been analyzed by Ghani, Farid & Chen, 2001, 2002, 2004. They used CFD model to predict the transient temperature and developed heating profiles of concentrations of bacteria and vitamins in pouches and canned liquid food. A finite volume commercial code PHOENICS was used for the solution of the governing equations of continuity, momentum and energy together with bacteria and vitamins concentration. The dependency on thermal profiles on natural convection was verified and sterilizations profiles were obtained in the simulation results. A non-intrusive particle image velocimetry (PIV) was developed by Ferrua & Singh, 2008 for simulation of ventilated packaged container. They demonstrated various velocity profiles in the packaged container using laminar Navier-Stoked formulation using Gambit and FLUENT sotwares (Ansys Inc.). They concluded that modern CFD codes with nonintrusive flow measurement techniques offers a promising approach to develop the understanding of the airflow field within complex packed structures.
An innovative modeling system based CFD model has been generated for the thermal design and visualization of airflow patterns inside ventilated packages for fruits and vegetables by Opera & Zou, 2006. They concluded that proper airflow patterns and appropriate level of temperature and relative humidity are essential for storage stability, good shelf life and quality of fresh produce inside ventilated packages. Ho, 2004 developed a high Reynolds number (HRN) Îº-Îµ model for turbulent heat transfer model for the analysis of freezing beef patty and solid fluid interface between food items. The outcome of the study was that the turbulent flow, wall functions for velocity and thermal fields are used to provide smooth transitions when the energy equation is solved across the fluid-solid interface.
An airflow patterns and temperature distribution in ventilated containers including stacked layers of spheres using computational fluid dynamics and turbulence model was determined by Tutara, Erdogdub & Toka, 2009. Two different RANS equations based turbulence models (the standard Îº-Îµ and the RNG Îº-Îµ model) were tested in comparison with a laminar model to determine the effect of flow modeling technique on physical behavior of the flow. The effects of air inflow rate on the duration of cooling process were much more significant compared to the effects of size of opening area, turbulence effects and three dimensionality.
2.2 Modified atmosphere packaging
CFD techniques were discussed for assessing and improving the operation and indoor atmosphere of ripening rooms for fermented food products by Mirade, 2008. In order to model how a gas (CO2) added to air circulated in the volume of the pilot ripening chamber, the CFD model was adapted to determine the optimal injection mode for introducing an exogenous gas. Mahajan, Oliveira, Montanez & Frias, 2007 developed a software (PACKinMAPÂ®) as a tool to speedily analyze the adequacy of various packaging systems to generate a proper equilibrium modified atmosphere for each packaged fresh cut product. They simulated O2 and CO2 concentrations for different combinations of films, area, and weight, avoiding time-consuming experiments to determine the best film to be used in packaging each type of product. They expected a further research to demonstrate the effect of High Performance Carbon Dioxide (HPCD) preservation on the shelf life and safety of food products (Gonzalez et.al., 2007). They described that the HPCD treatment not only improves food quality, but also promote shelf life and safety by inactivating spoilage and pathogenic microorganisms.
A mathematical procedure to design a package for fresh-cut produce and variation in gas composition by Torrieri et.al., 2009. They also reported that the equilibrium gas composition was not exactly that predicted, but it lies within an acceptable range, and in addition the product was stored under a protective atmosphere throughout the storage. A CFD based mathematical model was developed for thermodynamic design of ventilated packaging systems by Opera & Zouy, 2007, and Opera, Zouy & Mckibbin, 2006. Their sensitivity tests showed that inaccurate input value of the inlet air velocity contribute to an inaccuracy of 10% in the model predictions. No further details about the improvement in CFD technique were reported.
2.3 Concentration analysis
A proper combination of gases (i.e., O2, CO2 & N2), may enhance color and shelf life of many food products (Jeremiah, 2001; Ray, 2001). Controlled CO2 application with critical temperature control may delay the growth of air borne bacteria. For example, a combination of 80% O2 and 20% CO2 is a common mixture used now-a-days for ready to eat products. The high oxygen concentration creates the more desirable effect on storage life of food product as well as improving microbial shelf life. Although a lot of work has been conducted to predict gas concentrations in packages (Jeremiah, 2001; Ray, 2001; Rennie and Taoularis, 2009; Torrieri et al, 2009), not much CFD modeling have been conducting to predict concentration profiles of gases inside packages.
2.4 Refrigerated food applications
Smale, Moureh & Cortella, 2006 reviewed various numerical methods used on refrigerated food application. They have also elaborated various turbulent flow models with recently developed numerical techniques. In order to understand these models, one has to understand the basic physical behavior of fluid flow and transport phenomena in food engineering application, which were summarized by Welti-Chanes, Vergara-Balderas & Bermudez-Aguirre, 2005. A mathematical model for the kinetics of the release of antimicrobial agents from cross linked poly-vinyl-alcohol into water is described by Buonocore, Nobile, Panizza, Corbo & Nicolais, 2003. The phenomena of water diffusion, macro molecular matrix relaxation and antimicrobial agent diffusion through the polymeric matrix was also considered.
Two types of packaging systems are generally considered for packaging fresh food items, rigid and flexible packages. These packages have variant sub sections for further packaging. Modeling of flexible packages or pouches is quite cumbersome as design of geometry is more complicated rather than a rigid package. Stern, Wilson, Coleman & Paterson, 2001 developed a methodology for verification and validation of a CFD code for a cargo container and derived equations for simulation errors and uncertainties. The approach was valid for a range of CFD codes, including RANS, Navier-Stokes, Euler, boundary-element methods, and others. They have suggested that for practical applications, analysis and interpretation of the results should be important in assessing variability for order of accuracy, levels of verification, and strategies for reducing numerical and modeling errors and uncertainties. The concept of local average for Navier-Stokes equation was applied in their CFD approach for solid-liquid flow simulations by Xu & Yu, 1997. Their proposed model shows the capacity of simulating the gas fluidization process realistically from a fixed to fully fluidized bed via an incipient fluidization stage. The motion of individual particles inside the bed was obtained by solving the combined Newton's second law of motion and gas flow by N-S equations. The effect of structure-fluid interaction was also studied by Pal, Bhattacharyya & Sinha, 2003. They obtained a non-linear motion of the liquid free surface in a partially filled laminated composite container, and developed a finite element based numerical scheme on the basis of a mixed Eulerian-Lagrangian approach.
2.5 Turbulent flow in food processing
A direct numerical simulation of the decay of 2D turbulent Navier-Stokes flows inside a square container with no-slip boundaries was presented by Clercx, Maassen & VanHeijst, 1998. They found a surprising observation of spontaneous spin-up of the flow during the initial stage due to normal and shear stresses exerted on the fluid by the rigid boundaries. Zhang, Zhang, Zhai & Chen, 2007 developed an enclosed space flow simulations with systematically eight turbulence models. The models include a zero-equation model, a low Reynolds number Îº-Îµ model, an RNG Îº-Îµ model, an SST Îº-Ï‰ model, v2f model, a Reynolds stress model (RSM), a detached-eddy-simulation model (DES), and a large-eddy-simulation model (LES). Their results showed that the LES and DES models provide rich flow details, v2f and the RNG models are slightly better in some cases. It was found that no model predicts as accurate because these models were not specifically developed for enclosed spaces. If any discrepancies were found between the calculated results and measured data, a benchmark cases should be used primarily and then factors contributing to complex flow features should be studied one by one. Most of the turbulence models tested were Reynolds Averaged Navier-Stokes (RANS) models.
A review on a CFD technique was presented for variable velocity with the RNG Îº-Îµ model of turbulence by Jensen, Stenby & Nielsen, 2007. They showed that increasing the flow rate increases velocity generally, but only very small increases were seen in areas already exposed to very low velocity. Changing the flow rate during cleaning does not have any effect on the location of the areas. The velocity distribution in enclosed space was predicted for turbulence models Îº-Îµ, Îº-Ï‰ and BSL models, and were well established within the main stream area and away from the solid wall by Rong & Nielsen, 2008. Also, the k-w and BSL models generated different streamline distribution near the floor and some corners. It has been shown that the velocity distribution was under predicted in some simulation of Îº-Îµ model; therefore, it was difficult to conclude which turbulence model is better for a particular application.
A wide literature is available for the application of the computational flow models in refrigerated food processing. A few papers have been found on application of computational flow models in specific fresh food packaging area. Moreover, extensive literature is available on the heat transfer phenomena on electronic packaging, which is not the subject of the current review. Most extensively used and validated model is the two-equation Îº-Îµ model developed by Launder and Spalding's for turbulent flow simulation. The unlimited use of this model is for validation for different application such as . All the turbulent flow models has been used to calculate fluid flow inside and outside enclosed spaces, and to report velocity profiles, turbulence components, pressure drops, shear, etc .
Predicting fluid flow profiles of various quantities like velocity, pressure and concentrations by turbulent numerical approach is the key concept of the current review work. Preliminary trials have been carried out to choose the appropriate mathematical model, which can reproduce physical conditions. These trials reveal the reliability of the RANS model, which is a solver resolving implicitly fluid flow equations. The turbulence modeling program based on two equation eddy-viscosity models such as Îº-Ï‰ and Îº-Îµ with corrected wall functions.
The aim of this review was to present various aspects of the CFD modeling for simulating flow process used in food packaging and therefore to predict flow patterns and profiles in food packaging systems. A CFD model may be utilized for evaluating various operations in packaging and assessing the alternative packaging designs for a range of fresh agricultural products. In the forthcoming part, a review of CFD methodology is presented to access the fluid flow process inside a package.
3. CFD models and methods
A packaging material acts as a barrier to gases, vapor, heat and microorganisms to extend the shelf-life of the food product. As a membrane continuously modify the gas environment by removing or adding gases and vapors to the headspace of the package. In the process, these gases and vapors react with the food. For a package to be model by CFD, it needs to be defined as a computational geometry and discredited into computational grid to obtain a numerical solution to a given flow depending on the relation between the flow and the mesh coordinates used to compute it. Therefore, selecting the proper mesh for a given problem is crucial for the accurate prediction of results. These meshes can be applied to a given geometry for the fluid as a continuous medium to a discrete approach. The computational method allows us to get results relatively quickly and visually results close to reality. These results can be used to guide experiments and even as a substitute for preliminary testing in situations where construction of prototypes might be prohibitively expensive and difficult to observe in detail in a laboratory environment. The difference between these techniques is in the forth-growing factor of accuracy and consistency. All these factors are interrelated to the proper testing and validation with benchmark solution. A detailed explanation of the CFD models and methods can be found in â€¦
3.1 Different CFD techniques
Three commonly used CFD techniques that can be applied to food packaging application are finite difference method, finite volume method and finite element methods. A very informative and extensive summary of the application of all these techniques was summarized by Peric, 1998. These techniques are criticality dependent on the fluid and solid model (Anderson, 2008). An analysis and detailed review can be found for all these techniques in Mattiussi (1997). To the best of the authors' knowledge, the application of finite difference method in food packaging is not found in the peer review literature, but finite volume supported by commercial software and finite element based flow solvers have been used in some of the application of food processing (Da-wen Sun, 2007). Also, reviews on numerical techniques were given by Smale et.al., (2006). Detailed investigations of pressure, velocity and wall shear stress distribution made by CFD model has been developed to investigate the complex flows used for packaging liquid products by Rahaman, Bari &Veale, 2008. They examined the effect of design, formation of reverse flow, low shear stresses and cavitation within the flow domain causing an objectionable sound level. Several methods were proposed to investigate these instabilities and reviewed results to verify with the practical simulations for the better prediction.
3.2 Simulation in CFD
CFD software packages always contain three processors; a) pre-processor, b) processor, and c) post-processor. A pre-processor involves the commonly input sequences to develop a model for the desired output. All the modeling parameters are defined in the pre-processor part of the CFD modeling software. In processing the desired equation of motions with other relevant equations are solved to obtain a subsequent output. For example, a numerical analysis of the forced-air cooling process of retail packages of strawberries was performed by solving the conservation equations of mass, momentum and energy within the system by Ferrua & Singh, 2008. The general formulations of the solved equations are given below as conservation of mass (eq. 1), conservation of momentum (eq. 2) and conservation of energy (eq. 3),
,ðœ•(ðœŒ,ð‘ˆ-ð‘-.)-ðœ•ð‘¡.+,ðœ•,(,(ð‘ˆ-ð‘-.ð‘ˆ-ð‘-.)-ðœ•,ð‘‹-ð‘-..=âˆ’,ðœ•ð‘ƒ-ðœ•,ð‘‹-ð‘-..+ðœ‡,,,ðœ•-2.,ð‘ˆ-ð‘-.-ðœ•,ð‘‹-ð‘--2..+ðœ‡,,ðœ•-2.,ð‘ˆ-ð‘-.-ðœ•,ð‘‹-ð‘--2...+ðœŒ,ð‘”-ð‘-.,1âˆ’ð›½âˆ†ð‘‡.+ ð‘ ð‘œð‘¢ð‘Ÿð‘ð‘’ ð‘¡ð‘’ð‘Ÿð‘š...(2)
,ðœ•(ðœŒ,ð¶-ð‘ƒ.ð‘‡)-ðœ•ð‘¡.+,ðœ•,(ðœŒ,ð¶-ð‘ƒ.ð‘‡ð‘ˆ-ð‘-.)-ðœ•,ð‘‹-ð‘-..=ðœ†,,ðœ•-2.ð‘‡-ðœ•,ð‘‹-ð½-2..+ ð‘ ð‘œð‘¢ð‘Ÿð‘ð‘’ ð‘¡ð‘’ð‘Ÿð‘šâ€¦â€¦â€¦â€¦â€¦..(3)
The results showed the potential use of this numerical approach as a design tool to optimize the forced-air cooling process of horticultural products. Three-dimensional finite volume heat transfer model was also developed using PHOENICS Computational Fluid Dynamics software by Moureh & Derens, 2000. The experiments were carried out with packaged frozen pallets placed on a closed or open dock separately.
A space and time dependent mathematical model describing perforation-mediated modified atmosphere packages was developed for respiring commodities by Rennie & Tavoularis, 2009. In the first part or this work, the computational domain was divided into various sub domains with rigid package walls of impermeable to gases and heat conducting. The commodity was treated as a homogenous porous medium with distributed sinks for oxygen consumption and distributed sources for carbon dioxide production due to respiration. The model permited the determination of the gas mixture velocity as the solution of Darcy's law and Navier-Stokes equations in the headspace, perforation, and surrounding ambient storage area. Transport of oxygen, carbon dioxide, water vapor and nitrogen was modeled based on Maxwell-Stefan equations coupled with the Navier-Stokes equations and Darcy's law. The gas mixture temperature was modelled as solutions of the energy equation in the appropriate sub domains, coupled through transpiration, condensation, and convective heat transfer at the commodity surface
A second article from the same authors described the numerical implementation of a space-and-time dependent mathematical model of perforation-mediated modified atmosphere packaging for respiring commodities in which the mathematical model was presviously described in Part-I (Rennie & Tavoularis, 2009). The model includes species transport of CO2, H2O, N2, and O2 through the Maxwell-Stefan equations, velocity and pressure through Darcy's law and the Navier-Stokes equations, and temperature of the gas mixture and the commodity through the energy equation. It was shown that neglecting the ambient space beyond the perforation over predicted the steady state concentration. Approximately 80% of the resistance to diffusion was found to occur within the perforation, with the remainder equally divided between the spaces.
<Table 2: Insert here>
4. Food packaging applications
In this section, an approach and an example of the CFD simulation in food packaging is demonstrated with some results for a fresh produce application. A general algorithm for the various stages involved in the CFD simulation has been shown in fig.1. It starts with defining the overall problem with the formation of geometry in the pre-processing section. The geometry should be divided into number of grid points, and it depends on the user requirement. Problem definition with boundary values and solver selection was performed before the iteration. The simulation results can be observed and stored in the post-processing section.
<Figure 1: Insert here>
Figure 2 (a) and (b) shows a meshing scheme applied to a standard cherry tomatoes box available in a general grocery store. Two types of grid have been used for poly(ethylene terephthalate), PET, packaging container. Very fine grid was used near the disinfecting gas injection port and near the boundaries. In fig. 3 (a) and (b), the streamlines plots depicts the unsteady flow behavior of disinfecting gas inside the package for empty and filled with very small cherry tomatoes.
<Figure 2: Insert here>
An inclusion of various equations depending upon the criteria could be included for the prediction of flow behaviors, shelf life and can be used in design of other types of necessary analysis. Further discussion of these applications is presented in future communications (___, __).
<Figure 3: Insert here>
5. General Conclusions
The review of the computational fluid dynamics techniques in food packaging showed that the CFD techniques play an important role in the prediction of fluid flow and design solutions in food packaging applications. While applying a CFD technique to the food packaging application, it is necessary to mention that the reactions within the package should separately determined and supplied properly with fluid flow equations. Meshing of near wall zones and fresh produce should be considered by applying various wall functions. This review indicated a wide gap between the use of CFD techniques for food packaging and other. Currently, CFD solutions describing fluid flow has advantages as well as drawbacks. These methods are relatively user friendly, less time consuming, cost effective and minimum space consuming, but their drawbacks have accuracy depends upon the information, complicated geometry formation, and not able to predict odor or smell.
Authors are grateful to the USDA (grant no. 2008-01573) under "National Integrated Food Safety Initiative" for funding this project. The high performance computing center (HPCC) at MSU for providing computational facility, and Drs. Andre Benard and Kirk Dolan for helping with general CFD discussions.