Computational fluid dynamics (CFD)

Trends in Food Science & Technology 17 (2006) 600e620

Review

Computational fluid dynamics (CFD) e an effective and efficient design and analysis tool for the food industry: A review Toma´s Norton and Da-Wen Sun* Food Refrigeration and Computerised Food Technology Research (FRCFT) Group, Department of Biosystems Engineering, National University of Ireland, University College Dublin, Earlsfort Terrace, Dublin 2, Ireland (Tel.: D353 1 7165528; fax: D353 1 4752119; e-mail: [email protected]) Computational fluid dynamics (CFD) is a powerful numerical tool that is becoming widely used to simulate many processes in the food industry. Recent progression in computing efficacy coupled with reduced costs of CFD software packages has advanced CFD as a viable technique to provide effective and efficient design solutions. This paper discusses the fundamentals involved in developing a CFD solution. It also provides a state-of-the-art review on various CFD applications in the food industry such as ventilation, drying, sterilisation, refrigeration, cold display and storage, and mixing and elucidates the physical models most commonly used in these applications. The challenges faced by modellers using CFD in the food industry are also discussed.

Introduction Computational fluid dynamics (CFD) was originally developed from the pioneering accomplishments of enthusiasts such as Richardson (1910) and Courant, Friedrichs, * Corresponding author. 0924-2244/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tifs.2006.05.004

and Lewy (1928), who in their endeavours to procure insight into fluid motion instigated the development of powerful numerical techniques that have advanced the numerical description of all types of fluid flow (Shang, 2004). CFD is now maturing into a powerful and pervasive tool in many industries, with each solution representing a rich tapestry of mathematical physics, numerical methods, user interfaces, and state-of-the art visualisation techniques (Xia & Sun, 2002). So great has the impetus been to propel CFD that it is now used as much as the traditional didactic methods of experimentation and analytical modelling to solve fluid flow problems. This recent adoption of CFD has been both inevitable and progressive, as the high costs and time consumption associated with experimentation has often precluded the desire to produce efficient in-depth results. Moreover, the assumptions, generalisations and approximations associated with analytical models have swayed their reduction in the development of flow solutions. By considering these limitations coupled with recent achievements in the development of numerical solutions for the NaviereStokes equations and the amelioration of computing power and efficiency, it is easy to understand why confidence has both increased and advanced the application of CFD as a viable alternative in industry and science. The links between CFD and the processes associated with the food and beverage industry such as mixing, drying, cooking, sterilisation, chilling and cold storage are profound. Such processes are used regularly to enhance quality, safety and shelf life of foodstuffs (Wang & Sun, 2003). With direct benefits for both consumer and the natural environment, applications of CFD have become more widespread in the food industry. CFD research has meant that products can be processed and stored in more efficient systems. Furthermore, CFD can aid food companies to respond to an expanding marketplace by enhancing and developing processing strategies, whilst endeavouring to maintain high levels of product quality. The technical achievements observed in the last two decades include vast improvements in numerical algorithms and CFD modelling techniques (Xia & Sun, 2002). This means that features like unstructured and adaptive meshing, moving boundaries and multiple frames of reference now cooperate with physical models to confront complex phenomena involving Newtonian and non-Newtonian fluid flow, quasi-fluid substances, product taste, packaging and storage that have faced the food industry over the decades

T. Norton, D.-W. Sun / Trends in Food Science & Technology 17 (2006) 600e620

(Fluent News, 2000). Today CFD solutions are being used to optimise and develop equipment and processing strategies in the food industry and their rate of use has grown exponentially, as evidenced by the steady increase in peer-reviewed journal papers over the years (Fig. 1). The many areas within the food industry where CFD has been routinely used to quantify governing physical phenomena include food production facilities (Burfoot, Hall, Brown, & Xu, 1999; Harral & Burfoot, 2005), sterilisation (Siriwattanayotin, Yoovidhya, Meepadung, & Ruenglertpanyakul, 2006; Varma & Kannan, 2006), mixing (Song & Han, 2005) and drying processes (Huang, Kumar, & Mujumdar, 2003) to name but a few, with the range of applications being continuously extended. The objective of this paper was to provide a state-of-theart review of CFD and its current applications in the food industry. The advancements of physical models and numerical techniques are examined comprehensively with particular attention placed on enhancing the accuracy of CFD solutions. The Cost and unique features associated with the important players in the CFD market are also discussed.

601

2. The law of conservation of momentum (Newton’s second law of motion), which states that the sum of the external forces acting on a fluid particle is equal to its rate of change of linear momentum. 3. The law of conservation of energy (the first law of thermodynamics), which states that the rate of change of energy of a fluid particle is equal to the heat addition and the work done on the particle. By enforcing these conservation laws over discrete spatial volumes in a fluid domain, it is possible to achieve a systematic account of the changes in mass, momentum and energy as the flow crosses the volume boundaries. The resulting equations can be written as: Continuity equation: vr v þ ruj ¼ 0 vt vxi

ð1Þ

Momentum equation: v v v vui vuj ðrui Þ þ þ pdij þ m þ rgi rui uj ¼ vt vxj vxj vxj vxi ð2Þ

Fundamentals of CFD Governing equations The governing equations of fluid flow and heat transfer can be considered as mathematical formulations of the conservation laws of fluid mechanics and are referred to as the NaviereStokes equations. When applied to a fluid continuum, these conservation laws relate the rate of change of a desired fluid property to external forces and can be considered as: 1. The law of conservation of mass (continuity), which states that the mass flows entering a fluid element must balance exactly with those leaving. 100 90

Number of Papers

80 70 60

v v v vT ðrCa TÞ þ l ¼ sT ruj Ca T vt vxj vxj vxj

ð3Þ

There are two ways to model the density variations that occur due to buoyancy. The first is to assume that the density differentials in the flow are only required in the momentum equations and are represented by: r ¼ rref 1 b T Tref ð4Þ This method is known as the Buossinesq approximation and has been used successfully in many food engineering applications (Abdul Ghani, Farid, Chen, & Richards, 1999). However, at high temperature differentials, the approximation is no longer valid and another method must be applied (Ferziger & Peric, 2002). One way is to treat the fluid as an ideal gas and express the density difference by means of the following equation: pref Wa ð5Þ RT This method can be considered as a weakly compressible formulation, which means that the density of the fluid is dependent on temperature and composition but not pressure. This assumption has also been used successfully in food engineering applications. However, solutions were found to be more difficult to converge using this method (Foster, Barrett, James, & Swain, 2002). r¼

50 40 30 20 10 0 1993-1995

Energy equation:

1996-1998

1999-2001

2002-2004

2005-2006

Period Fig. 1. The number of published peer-reviewed papers with CFD applications in the food industry.

Numerical analysis A fundamental consideration for CFD code developers is the choice of suitable techniques to discretise the modelled

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fluid continuum. Of the many existing techniques, the most important include finite difference, finite elements and finite volumes. Although all these produce the same solution at high grid resolutions, the range of suitable problems is different for each. This means that the employed numerical technique is determined by the conceived range of code applications. Finite difference techniques are of limited use in many engineering flows due to difficulties in their handling of complex geometries. This has led to increased use of finite elements and finite volumes, which employ suitable meshing structures to deal appropriately with arbitrary geometry. Finite elements can be shown to have optimality properties for some types of equations (Ferziger & Peric, 2002). However, only a limited number of commercial finite element packages exist, which is undoubtedly a reflection of the difficulties involved in the programming and understanding of this technique. Fortunately, such difficulties are obviated through implementation of finite volumes methods. When the governing equations are expressed through finite volumes, they form a physically intuitive method of achieving a systematic account of the changes in mass, momentum and energy as fluid crosses the boundaries of discrete spatial volumes within the computational domain (Versteeg & Malalsekeera, 1995). The ease in the understanding, programming and versatility of finite volumes has meant that they are now the most commonly used techniques by CFD code developers. Solving the flow problem In order to solve for a flow field a CFD code must take the mathematical statements inputted by the user, structure them into a suitable arrangement and solve them for the specified boundary conditions. Iterative methods are commonly used by CFD codes to solve a whole set of discretised equations so that they may be applied to a single dependent variable. The segregated solver SIMPLE (Semi-Implicit Method for Pressure-Linked Equations), devised by Patankar and Spalding (1972), or its descendents are conventionally employed by many commercial packages. SIMPLE determines the pressure field indirectly by closing the discretised momentum equations with the continuity equations in a sequential manner. Consequently, as the number of cells increases, the elliptic nature of the pressure field becomes more profound and the convergence rate decreases substantially (Ferry, 2002). This has led to the development of multigrid techniques that compute velocity and pressure corrections in a simultaneous fashion, thereby enhancing convergence rates. Unfortunately, the improvement in solver efficiency afforded by multigrid is foiled by memory requirements that increase in tandem with the number of cells, thus making it difficult, in some cases, to achieve grid independency with current computing capabilities. Nevertheless, many CFD packages, even those based on unstructured grids now successfully employ

multigrid as the default solver option. Detailed techniques used by multigrid are described in the literature (Ferry, 2002). Interpreting the solution Visualisation is often necessary to represent the resulting field solution. Contour, vector and line plots enhance the accurate interpretation of results and have been used successfully in many studies to aid in system design (Foster, Madge, & Evans, 2005). In addition, field data are often easily exported to external modelling programs so that they can be processed further. Fig. 2 illustrates how visualisation techniques can provide sufficient information to move forward in the design process. Animated flow fields have also become increasingly popular and can now accompany peer-reviewed studies on scientific journal websites (D’Agaro, Cortella, & Croce, 2006). Commercial CFD packages Over the last two decades, there has been enormous development of commercial CFD codes to enhance their marriage with the sophisticated modelling requirements of many research fields, thereby accentuating their versatility and attractiveness. Spalding (1999) illuminated the many obstacles that face the CFD community when developing codes to cater for incessantly expanding fields of applications like the food industry. These challenges have led to unprecedented competition between commercial CFD developers and have expedited non-uniform development, causing the range of afforded functionalities to vary from code to code. Thus, among the many codes that exist today not all provide the features required by the food engineer. Such requirements include the provision of powerful preprocessor, solver and post-processor environments, the power to import grid geometry, boundary conditions and

Fig. 2. Contours of isotemperatures in the most sensitive plane of a refrigerated truck with (a) and without (b) air ducts (Moureh & Flick, 2004).


initial conditions from an external text file, and the capability to model non-Newtonian fluids, two-phase flows, flow dependent properties, phase change and flow through porous media (Kopyt & Gwarek, 2004). Therefore, intuitive functional considerations of a code should be taken into account before selection. The commercial software packages featured in this review incorporate at least a minimum number of all these functionalities, employ graphical user interfaces, and support Windows, UNIX and Linux platforms. State-of-the-art features of the most commonly used general-purpose codes available are elucidated with their associated cost in Table 1. Details on three of the most routinely used commercial codes are elaborated below. CFXÒ (ANSYS Inc.) CFXÒ was recently (in 2003) taken over by ANSYS Inc. and is now branded as ANSYS CFXÒ. Within the framework of ANSYS CFXÒ numerous different types of software packages exist that can be used to solve various types of flow problems. There are also a large number of up-to-date fully functional physical models, which include multiphase flow, porous media, heat transfer, combustion and radiation models. Advanced turbulence models are also a feature of ANSYS CFXÒ and it contains a predictive laminar to turbulent flow transition model (MentereLangtry

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gq model). ANSYS CFXÒ also affords an easy-to-use fully parametrical CAD tool with a bi-directional link compatible with most CAD software. FLUENTÒ (FLUENT Inc.) FLUENT Inc. offers three software packages within the CFD framework that are suitable for the food engineer’s modelling needs. The three packages are FLUENTÒ (general purpose with multiphysics capabilities), FIDAPÒ (modelling complex physics) and POLYFLOWÒ (polymer modelling). FLUENTÒ Inc. is presently one of the leading suppliers of CFD software in the world. The most interesting features of the FLUENTÒ software include models for heat exchangers, discrete phase models for multiphase flows, numerous high quality reaction models and the phase change model which tracks the melting and freezing in the bulk fluid. FIDAPÒ is a finite element based software that offers unique abilities for modelling non-Newtonian flows and free surface flows. It also contains sophisticated radiation, dispersion and heat transfer models. POLYFLOWÒ is a general-purpose finite element CFD tool for the analysis of polymer processing such as glass forming, thermoforming and fibre spinning. POLYFLOWÒ also has a range of applications that can be extended into the food industry (Fernandes et al., 2006).

Table 1. Common commercial CFD software used in the food industry Company

Location

ANSYS Inc., www.ansys.com

ANSYS CFX Southpointe, Canonsburg, PA, 10.1 (FV) USA

CHAM Ltd., www.cham.co.uk

Wimbledon PHOENICS 3.6 Village, London, (FV) UK

CD Adapco Group, London, UK www.cd-adapco.com

FLUENT Inc., www.fluent.com

Lebanon, NH, USA

Software package

STAR-CD 3.2 (FV)

Features

Price

Recently published applications in food industry

Menter-Langtry turb, Coupled Lagrangian and particle tracker. Coupled multiphase and interphase models LEVL and MFM turb, PARSOL, IMMERSOL CHEMKIN, MTSM

V2.4k1, V11.2k3,4,5

D’Agaro et al. (2006), Siriwattanayotin et al. (2006), Varma & Kannan (2006)

Large amount of meshing capabilities, chemical solvers STAR-CCMþ 1 State-of-the-art (FV) modelling interface FLUENT 6.1 (FV) Dynamic mesh, chemical mixing and reaction models, wall film models FIDAP 8.6 (FE) Complex rheology and electrohydrodynamic modelling POLYFLOW 3.1 Integral and (FE) differential viscoelastic flow modelling

V1.21; V4.8k2 (þV0.9k)5; Abdul Ghani et al. (2003), V3.75k3; V14.5k4 Dincov, Parrott, & Pericleous (2004), (þV2.2k)5 Moureh, Menia, & Flick (2002) V2.19k1; V18.33k3,4,5 Jensen & Friis (2004)

V2.19k1; V18.33k3,4,5

None

V3.88k1; V21.5k3,4,5

Chen & Yuan (2005), Kumaresan & Joshi (2006), Wong et al. (2006a)

V3.88k1; V21.5k3,4,5

Jung & Fryer (1999), Tattiyakul et al. (2001, 2002) Fernandes et al. (2006)

V3.88k1; V21.5k3,4,5

License types: 1annual educational, 2permanent educational, 3annual commercial, 4permanent commercial, 5technical support. Abbreviations: FV ¼ finite volume, FE ¼ finite element, turb ¼ turbulence model, LEVL ¼ wall distance turbulence model, MFM ¼ multi-fluid turbulence model, PARSOL ¼ partial solids modelling, IMMERSOL ¼ radiation model, CHEMKIN ¼ chemical kinetics, MTSM ¼ mechanical and thermal stress modelling.

604


PHOENICSÒ (CHAM Ltd.) PHOENICSÒ is a multipurpose CFD package that has numerous modelling capabilities to embrace many scenarios faced by the food engineer, including Newtonian and non-Newtonian fluid modelling, flow through porous media with direction-dependent resistances, and conjugate heat transfer. There is also an extensive suite of embedded turbulence models including the unique wall distance turbulence model (LVEL), which circumvents the inaccuracies associated with wall-function computations of most turbulence models by using the knowledge of wall distances, and local velocities to compute the near-wall flow. PHOENICSÒ is a structured grid code and it necessitates the use of body fitted coordinates to model complex geometry. This can substantially increase the pre-processing and solution times of a simulation. Additional models for food processes On their own the NaviereStokes equations have a limited amount of applications in many areas of food engineering. This means that the additional processes that may play a major role in influencing the dynamics of a system must be taken into account in simulations. In these cases the governing equations may need to be fortified with additional approximations or physical models to fully represent the flow regime. Important physical models commonly used in food engineering applications include turbulence models, porous media and multiphase models, and non-Newtonian models. Turbulence modelling Turbulence momentum and scalar transport play an essential role in many engineering applications and its simulation has undergone intensive research throughout the years. In order to develop safe and efficient plant processes in the food industry, it is often necessary to predict surface heat and mass transfer coefficients, thermal dependent properties of food, and flow characteristics of systems, under various scenarios (Delgado & Sun, 2001; Wang & Sun, 2003). These processes are usually associated with turbulent flows, primarily due to the complex geometry and/or high flow rates involved. Whilst the NaviereStokes equations can be solved directly for laminar flows, the current state of computational capability is unable to resolve the fluid motion in the Kolmogorov microscales associated with turbulent flow regimes (Friedrich, Huttl, Manhart, & Wagner, 2001). In most cases however, engineers are not interested in the detailed structures of turbulence but just need a few quantitative features to undertake suitable design strategies (Ferziger & Peric, 2002). These details are afforded by the Reynolds averaged NaviereStokes equations (RANS), and are determined by averaging the ergodic processes that typify turbulent flows. Reynolds averaging essentially disregards the stochastic properties of the flow and results in six additional unknowns (Reynolds stresses) that preclude the direct closure of the equations.

The eddy viscosity hypothesis The Reynolds stresses need to be modelled by a physically well-posed equation system to obtain closure that is consistent with the flow regime. The eddy viscosity hypothesis states that an increase in turbulence can be represented by a concomitant increase in effective fluid viscosity, and that the Reynolds stresses are proportional to the mean velocity gradients via this viscosity (Ferziger & Peric, 2002). The eddy viscosity hypothesis forms the foundation on which many of today’s most widely used turbulence models are based. These range from simple one equation models based on empirical relationships to variants of the sophisticated but inveterate two-equation ke3 model which describes the eddy viscosity through the production and destruction of turbulence. Recent applications of turbulence models There are many turbulence models embedded in commercial codes and it is left to the user to assert which one is appropriate for the application in hand. As illustrated by Bartosiewicz, Aidoun, and Mercadier (2006), large discrepancies can occur in predictions made by different models. This emphasises the need for concurrent validation with experimental measurements. Of all turbulence models available, the standard ke3 model still remains an industrial standard and its successful applications are found in recent literature (Foster et al., 2005; Margaris & Ghiaus, 2006). In some cases it has even been found to perform as well as more advanced turbulence models (D’Agaro et al., 2006). Unfortunately, due to the assumptions and empiricism upon which the model is based, there have been many situations where the ke3 model has failed to sufficiently represent the modelled turbulent regime and predictions have proved inadequate (Langrish & Fletcher, 2001; Wang & Sun, 2003). Consequently, engineers have turned to other advanced turbulence models like the renormalisation group (RNG) and Reynolds stress transport (RST) models which are not so reliant on empiricism and can account for anisotropy of highly strained flows. However, although there are cases in which the RNG and RST models have proven superior to the standard ke3 model (Moureh & Flick, 2005; Rouaud & Havet, 2002), there are also others where the limitations of computational power or convergence difficulties precluded the use of these models (Hoang, Verboven, De Baerdemaeker, & Nicola€ı, 2000; Mirade & Daudin, 2006; Nahor, Hoang, Verboven, Baelmans, & Nicolai, 2005). Moreover, the advantages of such models will be inhibited if used with first-order convection schemes (Hoang et al., 2000; Verboven, Scheerlinck, De Baerdemaeker, & Nicolai, 2001). More complex turbulence simulation Engineers have also addressed other simulation methodologies such as direct eddy simulation (DNS), detached eddy simulation (DES) and large eddy simulation (LES) to correctly predict turbulent flow structure and transport


phenomena. DNS is a solution to the three-dimensional, time dependent NaviereStokes set of equations. Because no turbulence models are involved in the governing equations, a DNS is conducted on a fine mesh to reproduce all length scales within turbulent flow regime. This obviously necessitates the invocation of intensive computer power, much of which is presently unavailable to the engineer, thereby rendering DNS a research tool for studying turbulence momentum and heat transfer dynamics. The advantages afforded to the food industry by DNS include detailed information regarding turbulent channel flows of dilute polymer solutions, the effect of buoyancy on turbulent transfer and information regarding the effective control of turbulence and heat transfer (Moin & Bewley, 1995). Large eddy simulation (LES) forms a solution in response to the fact that large turbulent eddies are highly anisotropic and dependent on both the mean velocity gradients and geometry of the flow domain. With the advent of more powerful computers, LES now offers a way of alleviating the errors caused by the use of RANS turbulence models. However, the lengthy time involved in arriving at a solution means that this is an expensive technique (Turnbull & Thompson, 2005). LES provides an accurate solution to the large-scale eddy motion in methods akin to those employed for DNS. It also acts as spatial filtering, thus only the turbulent fluctuation below the filter size is modelled. This is because smaller eddies possess length scales determined by the viscosity of the fluid and are consequently isotropic at high Reynolds numbers. Over recent years, LES has been applied in areas related to food processing (Xu, Sang Lee, Pletcher, Mohsen Shehata, & McEligot, 2004). More recently, a methodology has been proposed by which the user specifies a region where the LES should be performed with RANS modelling completing the rest of the solution; this technique is known as DES and has been found to increase the solution rate by up to four times (Turnbull & Thompson, 2005). Porous media and two-phase modelling Many large-scale processes in the food industry may have the potential to be grid point demanding in CFD models owing to the complex geometry of the modelled structures. For example, to predict the detailed transfer processes within a cold store containing stacked foods, one must mesh all associated geometry with a complex unstructured or body fitted system, which is a highly arduous and in many cases inaccessible task. In any case, both computational power and CFD algorithms have not yet reached such levels of maturity that these types of computations can be achieved. Therefore, other methods must be used to exploit the physical relationships that exist on a macroscopic level and sufficiently represent the dynamic flow effects that are representative of the modelled material. The porous media assumption, which relates the effects of particle size and shape, alignment with airflow and void fraction on pressure drop over the modelled products, has been

605

used in recent studies (Hoang et al., 2000; Mirade, Rougier, Daudin, Picque, & Corrieu, 2006; Verboven, Hoang, Baelmans, & Nicola€ı, 2004). This method basically applies Darcy’s law to porous media by relating the velocity drop through the pores to the pressure drop over the material. An extension of this law to account for most commonly encountered non-linear relationships between pressure drop and velocity is represented by the DarcyeForchheimer equation (Verboven et al., 2004): vp m ¼ vþrCF u2 ð6Þ vx K Equation (1) is the most common relationship used to represent pressure drop through packed beds. In the CFD model, this equation is added as an additional sink term to the momentum equations. The general relationships to determine both the permeability and the inertial loss coefficient can be obtained by inference from the Ergun equation. These have recently been adjusted to suit the geometry of the stacked food material and showed good agreement with experimental results (Verboven et al., 2004). However, considerable information regarding the detailed flow and transfer processes taking place within the stacked material is lost in this type of modelling strategy. Consequently, there have been studies where the CFD models employing porous media have not yielded predictions that agree well with measurements (Mirade et al., 2006). These poor predictions may have arisen from differences in the shape, surface roughness and void fractions throughout the physical media that cannot be accounted for in the CFD model. Therefore, before modelling porous media, one must ensure that the parameters in the momentum source terms fully represent the physical media. Verboven et al. (2004) illustrated this point by modifying the DarcyeForchheimer pressure drop relation using experimental results in order to accurately represent the resistance to airflow imposed by beds of apples and chicory roots. Other means of circumventing detailed meshing whilst improving upon accuracy of pressure drop relationships is to organise the model to comprise the main geometry, within which lies a sub-domain filled with a porous medium to represent the stacked foods. Fluid flow, and heat and mass transfer are described in the sub-domain by the laws of conservation of mass, momentum and energy. These particular forms of transport equations in porous media are derived in terms of macroscopic variables. The macroscopic velocity is provided by the volume-averaged NaviereStokes equations, which are a generalized version of Darcy’s law. This type of computational model can be regarded as a two-phase flow. Because the volume averaging process causes loss of details regarding the microscopic flow regime, empirical parameters such as the Forchheimer constant, thermal and mass dispersion, and interfacial heat and mass transfer coefficients are required to complete the equation system (Zou, Opara, & McKibbin, 2006a). Recent studies have

606


employed a two-phase modelling technique to predict the environmental conditions of product stores (Nahor et al., 2005). Zou et al. (2006a) and Zou, Opara, and McKibbin (2006b) used this method successfully to predict temperature distribution and airflow patterns in ventilated stacked goods. Non-Newtonian fluid modelling Any fluid that does not obey the Newtonian relationship between the shear stress and shear rate is called a nonNewtonian fluid. Many food-processing media have nonNewtonian characteristics and the shear thinning or shear thickening behaviour of these fluids greatly affects their thermalehydraulic performance (Fernandes et al., 2006). Over recent years, CFD has provided better understanding of the mixing, heating, cooling and transport processes of non-Newtonian substances. Indeed, a source of continuous research within this modelling discipline is the effect imposed by the rheological behaviour of materials like yoghurt, soup and milk on equipment design and performance (Grijspeerdt, Hazarika, & Vucinic, 2003; Sun et al., 2004). Processing equipment such as heat exchangers, stirred tanks, heaters and flow conveyors are all connected with the rheological properties of foods and CFD studies have elucidated numerous methods of equipment optimisation (Liu, Hrymak, & Wood, 2006). Of the several constitutive formulas that describe the rheological behaviour of substances, some are the Newtonian model, the powerlaw model, the Bingham model, and the Herschel Bulkley model. The power law is the most commonly used model in food engineering applications (Welti-Chanes, VergaraBalderas, & Bermu´dez-Aguirre, 2005). This governs the relationship between shear thinning fluids and the shear rate, and can be shown as: n1 m¼ m g_

ð7Þ

This model has been used to represent the shear thinning effect in many non-Newtonian CFD simulations with success. However, as shown by Abdul Ghani, Farid, Chen, and Richards (2001), the complex functions that relate fluid viscosity to the performed operation need not always be described and in some cases the fluid may be treated as Newtonian. Methods for improving modelling accuracy Oftentimes the details of NaviereStokes equations are smeared with general assumptions and poor modelling techniques that can impair the quality of CFD simulations. Past examples of this range from inadequate application of turbulence models to the inaccuracies afforded by poor quality geometry, meshes and first-order convection schemes (Gosman, 1998). Fortunately as the uptake of CFD has grown, emphasis on developing quantitatively accurate solutions for all types of flow applications has increased. Now CFD codes offer a large range of convection schemes,

turbulence models and meshing features such as unstructured mesh, sliding mesh and multiple frames of reference, which can be used to improve modelling accuracy and meet the demands of the food industry (Kumaresan & Joshi, 2006; Wong, Zhou, & Hua, 2006a). Meshing Unstructured mesh Most commercial CFD codes have emerged from typical Cartesian type academic programs. This has meant that for many years the actual geometry criteria of the modelled process could not be fully met and had to be altered to suit the code configuration (Gosman, 1998). One of the major advances to occur in meshing technology over recent years was the ability for hexahedral hybrid meshes to be incorporated into general codes. This allowed a mesh to be fit to any arbitrary geometry, thereby enhancing the attainment of CFD solutions for many industrial applications. A major advantage of unstructured and hybrid meshes is their relaxation of the block structure, a formal requirement of many general CFD codes (Gosman, 1998). This means that local mesh refinement can now be achieved both more effectively and efficiently, and a solution can be developed to capture all desired flow features without creating badly distorted cells that deteriorate convergence behaviour. The versatility of these meshes has led to an increased take-up by the CFD community and their uses are finding accurate and efficient solutions in many applications within the food industry (Foster et al., 2002; Mirade, 2003). This form of meshing requires different programming and solution techniques that are not quite as intuitive in implementation as their Cartesian based counterparts. Therefore, unstructured meshing has not yet fully infiltrated the CFD market, with codes such as PHOENICS remaining faithful to traditional structured methods (Abdul Ghani, Farid, & Zarrouk, 2003). Sliding mesh This type of meshing technique is commonly used to model the stirring or moving effect of adjacent geometry and can therefore simulate factory processes such as baking and mixing. This methodology has been used in some areas of food engineering. It allows certain portions of a mesh to slide relative to each other at a common interface, which in the case of a mixing tank is the interface between the tips of the blades and the baffles, and in baking is the continuous movement of the product in the oven (Aubin, Fletcher, & Xuereb, 2004; Wong, Zhou, & Hua, 2006b). Multiple frames of reference This type of meshing introduces an additional assumption that can account for any stationary parts of a flow existing in sliding mesh simulations. Instead of invoking the rotation of the grid directly, the rotation is simulated by inserting suitable body force terms in the momentum equations. This means that by making suitable transformations


in the CFD calculations at the interface between rotating and stationary flow regimes, a steady-state simulation can then be conducted on a static mesh (Gosman, 1998). For example, in applying this approach to stirred tanks, which is its most common application in the food industry, the equations in the flow domain attached to the impeller are solved in a simulated rotating frame of reference, whereas the equations in the remaining domain are solved in a frame of reference at rest (Li, White, Wilkinson, & Roberts, 2005).

Convection schemes As mentioned previously, the partial differential equations governing fluid flow are solved over discrete volumes within the computational domain. It is therefore necessary to represent these equations as accurately as possible at each location. By increasing the number of volumes on subsequent CFD computations, one would intuitively expect the difference between the solutions to be reduced. However, this leads to an unfavourable increase in computational time, especially when using segregated solvers. Consequently, over recent years there has been continual improvement in the representations of the convection terms in the finite volume equations to reduce the number of grid points involved in a solution. The ultimate accuracy, stability and boundedness of the solution depend on the numerical scheme used for these terms. A convection (or numerical) scheme can be perceived as a vehicle through which the boundary conditions are transmitted into the computational domain. The performance of a convection scheme is delimited by the ability of the scheme to reduce the error once the mesh is refined. The first-order HYBRID or UPWIND convection schemes are bounded and stable but predisposed to numerical diffusion and exhibit a sluggish response to grid refinement. Nevertheless, owing to their favourable convergence attributes these schemes are still prevalent in the food engineering literature. This obviously casts serious doubts on the validity of some solutions especially when grid refinement studies proved unattainable (Hoang et al., 2000; Mirade & Daudin, 2006). This point was also illustrated by Harral and Boon (1997) when they showed that experimental measurements agreed more favourably with coarse grid predictions than with a grid independent solution. A higher order scheme such as QUICK (upstream interpolation for convective kinematics) is more accurate and responsive to grid refinement but due to its unbounded nature exhibits unphysical under-shoots and over-shoots when strong convection is present. Convergence may also be difficult, especially when non-linear sources are present in the simulation. Nevertheless, favourable results have been attained when high order schemes have been used (Aubin et al., 2004; D’Agaro et al., 2006; Verboven, Datta, Anh, Scheerlinck, & Nicolai, 2003).

607

Convergence techniques When designing a CFD model, one must preconceive potential gradients that may occur so that the computational domain can be suitably meshed. This mesh must then be refined to obtain as nearest to a grid independent solution as possible. Unfortunately, with today’s computational power it is still not yet possible to obtain a grid independent solution in some cases (Mirade & Daudin, 2006; Sorensen & Nielsen, 2003). Therefore, the requirements must be relaxed whilst still maintaining confidence in the discrete solutions for the governing equations. A spatial convergence technique proposed by Roache (1998) based on Richardson extrapolation (1910) has been used in many CFD engineering applications (Sorensen & Nielsen, 2003). The basic priority of this method is to furnish the CFD user with a conservative estimate of the error (GCI) between the fine-grid solution and the unknown exact solution. The requirement is a solution set of the same governing equations from two different grid resolutions. Both CFD solutions must be on a grid that is within the asymptotic range of convergence. This means that the fine-grid CFD solution must be obtained at, or close to, the upper limit of the computer power available. The coarse grid solution can be achieved by removing grid lines in each coordinate direction. To ensure that the coarse grid does not fall outside the asymptotic range of convergence, the grid refinement ratio (r) between the two grids should be a minimum of 1.1. This also allows the discretisation error to be differentiated from other error sources (Slater, 2006). The GCI can be then described as: GCI ¼

Fs j3j ðr p 1Þ

ð8Þ

where the relative error 3 between fine and coarse grid solutions is defined as: 3¼

f2 f1 f1

ð9Þ

Fs is the factor of safety which is usually 3 for two grid comparisons (Slater, 2006), fn is the solution function (i.e. velocity at a location) and p is the formal order of accuracy of the convection scheme (i.e. UPWIND is first order, therefore, p ¼ 1). This method has been successfully used in the food industry to show the convergence of surface averaged heat transfer coefficients of food in a microwave oven using the QUICK convection scheme by Verboven et al. (2003). Nevertheless, no other recent applications of this technique have been found in the literature pertaining to the food industry. However, it would seem conceivable that this type of method should take preference in CFD studies, especially where grid independency is unattainable due to computational power, or when first-order convection schemes are used (Nahor et al., 2005).

608


Applications of CFD in the food industry Applications in flow fields The simulation of flow fields is the simplest application of CFD in the food industry as no heat and mass transfer are involved in the calculations. Nevertheless, flow field modelling is necessary in many food-processing applications ranging from ventilation systems to mixing tanks, and can provide essential information regarding system design. Many scenarios including the positioning of fluid inlets and outlets, and the influence of flow obstructions can be simulated by CFD. Flow field studies can also be used to assert the level of confidence that a solution has before more transport models are added. A number of CFD studies, which have focused on the prediction of flow fields, are summarised in Table 2. Modelling ventilation and contaminant dispersion Food production facilities continuously face challenges in reducing contamination risk by airborne microorganisms. These facilities place heavy demands on ventilation systems to maintain indoor air quality at near optimal levels for processes to operate successfully. CFD coupled with experimental techniques has been used to study ventilation flow fields and provide information on system design as a function of various aspects including room geometry, outdoor climate, and contaminant sources and has become increasingly popular over recent years (Burfoot et al., 1999; Quarini, 1995). Ventilation studies generally quantify the efficiency of fresh air delivery and effectiveness of removing contaminants through the use of ventilation scales. These can be computed within the framework of CFD and are related to the flow quantities that play an individual part in the quality of the indoor environment. The most regularly used scales in the food industry are a function of the mean age of air. A traditional method of calculating this was to determine the mean turnover time or residence time in a system irrespective of the amount of air recirculation. This led to the development of scales that gave a crude description of the ventilation effectiveness (Quarini, 1995). Another more descriptive method of calculating the local mean age of air is to passively track the airflow in the system. This is done by adding another equation to the CFD model, which is derived from a passive scalar that statistically expresses the mean time taken for air to reach any arbitrary point after entering the system: vq v m m vq þ rui q lam þ turb ¼1 vt vxi slam slturb vxi

ð10Þ

This has been used alongside a passive contaminant transport equation in a recent clean room study and has found reasonable agreement with experimental measurements (Rouaud & Havet, 2005). The development of ventilation scales based on the solution of these equations have

provided better insight into system design (Rouaud & Havet, 2005). Flow regimes in stirred tanks Many numerical studies on the isothermal mixing of liquids within stirred tanks have been carried out over the last two decades (Aubin et al., 2004). The main problem facing modellers is in the development of a system that proffers the most efficient blending of fluids. This depends on a number of fundamental requirements including correct choice of tank and impeller geometry, rotation speed and location of fluid inlet and outlets. Essential requirements for tank development are knowledge of power consumption, flow velocity and mixing characteristics of different stirred tank configurations. Accurate CFD simulations can afford this knowledge. Early attempts to solve the flow system and select suitable impeller geometry using CFD were made by Ranade, Joshi, and Marathe (1989). However, the conclusions drawn from their results were questionable and conflicted with other studies (Nienow, 1997). Nevertheless, as computer power became increasingly cheaper and CFD techniques rapidly advanced, numerical predictions have found better agreement with experimental data. Some CFD studies have examined the effects of different modelling approaches such as sliding mesh, moving reference frames, and turbulence modelling. Aubin et al. (2004) found that turbulence model had little effect on mean flow compared to effects created by the choice of convection scheme or meshing approach. These types of studies provide people with beneficial information for finding a compromise between modelling accuracy and calculation times. A recent application has used CFD to solve the mixing regime in a Kenics static mixer (Song & Han, 2005). CFD has also been used to examine the effects of tank and impeller parameters on enzyme deactivation (Ghadge, Patwardhan, Sawant, & Joshi, 2005), and blending behaviour for highly viscous flow (Fourcade, Wadley, Hoefsloot, Green, & Iedema, 2001). Certainly, it is evident from these studies that CFD will continuously develop and optimise stirred tank processes for many types of flow regimes. Validating flow fields Validation is a necessary part of the modelling process and the yardstick of success is the level of agreement that can be attained between numerical predictions and experiments (Xia & Sun, 2002). CFD models do not generally contain all the microscopic details of the modelled process due to computer limitations, and need some form of simplification to reduce the number of calculations in forming a solution. These simplifications range from modelling the fluid continuum to the numerical representation of the physical process. Awareness of the inaccuracies associated with simplified CFD modelling has led to the publication of several flow field validation studies (Hoang et al., 2000; Verboven, Scheerlinck, Baerdemaeker, & Nicolai, 2000).

Application

Authors

Code

Dim

Aim

Time dep

Turb model

Extra models

Order of CS

GIS

Agreement with exp

Outcome

Ventilated rooms

Mirade & Daudin (2006) Moureh & Flick (2005) Mirade & Picgirard (2001) Hoang et al. (2000) Montante, Mosˇteˇk, Jahoda, & Magelli (2005) Kumaresan & Joshi (2006) Liu et al. (2006)

FLUENT 6

3D

Steady

1st

No

Reasonable

3D

Steady

Std ke3, RNG, keu RNG, RST

Porous media

FLUENT

d

3rd

Yes

FLUENT

2D

Steady

Std ke3

d

1st

No

RNG ¼ poor, RST ¼ good Reasonable

CFX 4.3

3D

Steady

Porous media

1st

No

Reasonable

3D

Transient

Std ke3, RNG Std ke3

Only ke3 model converged RST predicted separation accurately Optimised chiller layout Validated model

CFX 4

To predict the AP and gas distribution To validate the AP in refr truck To determine the AP To build a simplified model To assess homogenisation To analyse impeller design To observe shear thinning

Lagrangian SM

1st

No

Good

Validated model

Transient

Std ke3

SM

NS

No

Reasonable

Steady

None

Non-New PL

2nd

No

Good

Steady

Std ke3

NS

Yes

Good

Suitable designs proposed Correlation developed between Dp and Non-New PL Correlation developed in terms of three parameters

Airflow in cold stores

Stirred tank

Static mixer

Song & Han (2005)

3D FLUENT 5

3D

FLUENT 6

3D

To obtain correlation for Dp

Dim ¼ dimension, dep ¼ dependence, Turb ¼ turbulence, CS ¼ convection scheme, GIS ¼ grid independence study, exp ¼ experiment, AP ¼ airflow patterns, Std ¼ standard, RNG ¼ renormalisation group ke3 model, refr ¼ refrigeration, RST ¼ Reynolds stress transport model, SM ¼ sliding mesh, NS ¼ not specified, Non-New PL ¼ non-Newtonian power-law model, Dp ¼ pressure drop.


Table 2. Recent CFD applications in isothermal flows

609

610


These studies outline in detail the simplified modelling techniques employed and place emphasis on the level of agreement attained between predictions and measurements. When good agreement is achieved, more studies can be carried out with these models without the need for comprehensive flow field validation. Applications in combined flow and heat transfer Food processes involving coupled fluid flow and heat transfer are ubiquitous in the food industry. Baking, sterilisation and refrigeration represent applications where the accurate quantification of combined flow and heat transfer can lead to improving both food quality and safety alongside reducing energy consumption. The recent advances in modern computing power mean that CFD can now be used to accurately solve heat transfer problems in many food processes (Wang & Sun, 2003). This reduces the amount of experimentation and empiricism associated with a design process. Table 3 summarises some of the recent studies that use CFD to predict combined fluid flow and heat transfer. Calculation of heat transfer coefficients The rate of heat transfer between air and food products is proportional to the heat transfer coefficients and therefore affects the surface and core temperatures of food products. Numerous CFD models have been used to calculate the local surface convective heat transfer from the cooling media to food products. Many studies have found that ke3 turbulence models are generally poor at predicting solutions that closely correspond to experimental data (Hu & Sun, 2001b; Kondjoyan & Boisson, 1997; Olsson, Ahrne, & Tragardh, 2004). Kondjoyan and Boisson (1997) attributed this reason to the misrepresentation of the near-wall flow by the standard wall functions and suggested that this wall treatment be abandoned for heat transfer calculations. Olsson et al. (2004) and Olsson, Ahrne, and Tragardh (2005) assessed the heat transfer characteristics of a jet impinging on a cylindrical food product under various conditions with the SST turbulence model. Heat transfer predictions agreed with measurements in the upper part of the cylinder but not in the wake. This was similarly experienced by Kondjoyan and Boisson (1997). Verboven et al. (2001) noted that due to the complexities involved in resolving the governing equations in the boundary layer, obtaining appropriate heat transfer solutions was still an active area of research in thermal analysis. Creating a thermal air barrier in refrigerated display cases The use of refrigerated display cases allows good visibility and ensures free access to stored food for shop costumers. A virtual insulation barrier called the air curtain is developed by the recirculation of air from the top to the bottom of the case (Cortella, 2002). This is a nonphysical barrier between cold air in the case compartments

and the warm shop environment. As the air curtain falls from the inlet at the top of the case, it entrains cooled air from the back of each case compartment. This air passes over all the food products resulting in heat transfer from the food to the air, which allows the food to be maintained at a predefined temperature. Heat transfer also occurs between shop environment and the air curtain. This causes the temperature of the air curtain to increase and reduces the effectiveness of the air curtain in the lower compartments of the display case (Foster et al., 2005). Numerous CFD studies on the ability of the air curtain to maintain food at a predetermined temperature have been conducted over recent years (Cortella, Manzan, & Comini, 2001; D’Agaro et al., 2006; Foster et al., 2002, 2005; Navaz, Henderson, Faramarzi, Pourmovahed, & Taugwalder, 2005). The effectiveness of the air curtain can be impaired by irregularities in the ambient shop environment; thus, it is easily understood why display cases may be perceived as one of the weakest links in the chilled food chain (Sun, 2002). Because these environmental irregularities cannot be directly incorporated into CFD models, steadystate and two-dimensional assumptions are often made that may in some cases blemish solution quality (D’Agaro et al., 2006). Nevertheless, numerous successful design solutions have been developed on the basis of CFD studies (Cortella et al., 2001; Foster et al., 2005; Navaz et al., 2005). Foster et al. (2005) modelled different regions of a display case to evaluate problems and develop subsequent design solutions. The study highlighted the exacerbating effect of cabinet sidewalls on maintaining design temperature and energy consumption. D’Agaro et al. (2006) also found that sidewall effects were the main mechanism for increasing the rate of heat transfer with the ambient environment. Navaz et al. (2005) have shown through Digital Particle Image Velocimetry (DPIV) and CFD simulations that the entrainment of ambient environment exhibits a linear relationship with the turbulence intensity in the air curtain. The need to maintain turbulence within the air curtain was also studied by Chen and Yuan (2005), who proposed a minimum Reynolds number to enhance the sealing ability of the air curtain. Their analysis provided a quantitative understanding of heat transfer from the ambient environment to the air curtain as a function of different Grashof, Reynolds, and Richardson numbers. The considerable advances made through the CFD modelling of display cases in the last few years will undisputedly lead to improving their efficiency, and thus strengthen their link in the chilled food chain. Heat transfer in the sterilisation process Sterilisation is one of the many heat transfer applications in which CFD is enjoying more widespread use. In the thermal processing of foods, rapid and uniform heating is desirable to achieve a predetermined level of sterility with minimum destruction of the colour, texture and nutrients of food products (Jung & Fryer, 1999; Tattiyakul, Rao, &

Application

Authors

Code

Dim

Aim

Time dep

Turb model

Extra models

Order of CS

GIS

Agreement with exp

Outcome

Industrial ovens

Mirade, Daudin, Ducept, Trystram, & Clement (2004) Therdthai et al. (2004a,b) Verboven et al. (2003) Kocer & Karwe (2005) Mirade (2003)

FLUENT 6.0

3D

To predict the AP and Temp

Steady

Std ke3

d

1st

No

Reasonable

Temp sensors required for accurate validation

CFD-ACE

2D þ 3D

d

NS

No

Reasonable

3D

Steady þ transient Steady

NS

CFX 4.3

Laminar

Radiation

3rd

Yes

Good

FLUENT 6.0

3D

Steady

Std ke3

Radiation

NS

Yes

Good

FLUENT 5.4

2D

Steady

RST

d

2nd

Yes

Limited

PHOENICS 3.6

3D

Steady

Std ke3

d

NS

NS

Limited

FLUENT 6.1

3D

Steady

RNG

Yes

Good

3D

Steady

Std ke3

Lagrangian atomisation Lagrangian

NS

CFX 4.3

To predict the AP and Temp To predict the RT, AP and HTC To predict the AP and HTC To predict the AP in meat dryer To optimise tray dryer To validate the model To predict the flow characteristics

3rd

Yes

Limited

FLUENT

3D

Transient

RST

d

3rd

Yes

Reasonable

Optimised AP and Temp distribution Optimisation strategy for uniform heating HT mainly a function of impinging jet velocity AP homogeneity being mainly a function of ventilation cycle Optimised tray arrangement þ AP Better utilisation of chamber with spinning disc atomiser Wall interaction model leads to under-prediction of particle moisture Ventilation duct produced leads to more uniform airflow

Microwave ovens

Drying chambers

Spray dryers

Cold stores

Margaris & Ghiaus (2006) Huang et al. (2003) Harvie et al. (2002) Moureh & Flick (2004)

To validate the turb model

Dim ¼ dimension, dep ¼ dependence, Turb ¼ turbulence, CS ¼ convection scheme, GIS ¼ grid independence study, exp ¼ experiment, AP ¼ airflow patterns, Temp ¼ temperature, Std ¼ standard, NS ¼ not specified, RT ¼ radiative heat transfer, HTC ¼ heat transfer coefficient, HT ¼ heat transfer, RST ¼ Reynolds stress transport model, RNG ¼ renormalisation group ke3 model.


Table 3. Recent CFD applications in combined flow and heat transfer

611

612


Datta, 2001). Traditionally, mean temperature approximations have been used in analytical studies to calculate both the sterility and quality of food products. However, CFD studies have proved that both of these parameters are over-estimated using this approximation (Jung & Fryer, 1999). The ubiquity of canned food has resulted in many numerical studies investigating canned food quality and sterility. Two techniques of assessing these parameters with CFD are calculation of spore survival rate and temperature history at the slowest heating zone (SHZ) (Siriwattanayotin et al., 2006). CFD has shown the transient nature of the slowest heated zone (SHZ) in the sterilisation of a canned food in a stationary position (natural convection) (Abdul Ghani et al., 1999). Fig. 3 illustrates the deactivation of bacteria in the sterilisation process of a canned food. These studies illustrated the considerable time needed for heat to be transferred throughout food in a static process. CFD studies have found that uniform heating can be obtained throughout the food by rotating the can (forced convection) intermittently throughout the sterilisation process (Tattiyakul et al., 2001; Tattiyakul, Rao, & Datta, 2002). Abdul Ghani et al. (2003) studied the combined effect of natural and forced convection heat transfer during sterilisation of viscous soup and showed that the forced convection was about four times more efficient than natural convection. More recently, CFD has been used to study the effect of container shape on the efficiency of the sterilisation process (Varma & Kannan, 2005, 2006). Conical shaped vessels pointing upwards were found to reach the appropriate sterilisation temperature the quickest (Varma & Kannan, 2006). Full cylindrical geometries performed best when sterilised in a horizontal position (Varma & Kannan, 2005). The sterilisation of food pouches has also been studied using CFD (Abdul Ghani, Farid, & Chen, 2002).

Designing for thermal uniformity in drying chambers Drying of different types of food products has been a challenge faced by the food industry over the centuries. Over recent years not only have substantial improvements been made to traditional techniques such as tray and spray drying but new innovative drying methods like pulse combustion have been developed and optimised using CFD (Langrish & Fletcher, 2001). The non-uniformity of the air-drying process is a common problem associated with batch type drying and CFD modelling techniques are employed to provide design solutions to overcome deficiencies (Margaris & Ghiaus, 2006; Mathioulakis, Karathanos, & Belessiotis, 1998). Mathioulakis et al. (1998) were one of the first people to use CFD to model the airflow in a tray-drying chamber and highlighted the high level of non-uniformity that existed in such processes. Recently Margaris and Ghiaus (2006) used CFD to successfully optimise the tray arrangement and inlet configuration within a tray-drying chamber.

Applications in combined flow, heat and mass transfer In the cooling or heating of foods, mass (moisture) transfer between the food and environment is inevitable. This means that accurate predictions of heating and cooling systems require a comprehensive suite of models describing fluid flow, heat transfer and mass transfer. However, the coupling of these models is complicated; therefore, CFD is commonly used to predict the phenomena occurring in applications involving combined flow, heat transfer and mass transfer (Hu & Sun, 2001b). Such applications include cold stores, air blast chillers, ovens, and spray dryers. Some recent examples of the CFD applications in this area are summarised in Table 4. Simulating the transport phenomena in cold storage facilities Horticultural produce is commonly cooled by forced air-ventilation through ventilated packaging to achieve efficient and uniform cooling. The cooling rate depends on the rate of heat and mass transfer between the cooling medium and the produce, which is directly related to the air velocity within the packaging. Cost-effective design strategies proffered by CFD have led numerous studies to employ this technique in predicting the environmental variables within ventilated packaging and refrigerated store rooms (Tassou & Xiang, 1998; Zou et al., 2006a,b). The storage process can be simulated in a CFD model by representing the contained goods as a porous medium by employing a predetermined void fraction and average diameter of the produce, and specifying the medium as a source of heat and moisture. This method has in the past yielded reasonable agreement with measurements, although it has been recognised that results could be further improved by adding more model details (Tassou & Xiang, 1998). Other CFD studies have successfully used a two-phase modelling technique to simulate cooling conditions within bulk containers (Nahor et al., 2005; Zou et al., 2006a). Hu and Sun (2001a,b) have also successfully examined the heat and mass transfer phenomena associated with the air-blast chilling process through CFD simulations. Modelling the spray drying process Spray drying is another traditional drying technique and is used to produce powders from products associated with the dairy, food and pharmaceutical industries. Its main objective is to create a product that is easy to store, handle and transport (Nijdam & Langrish, 2006). Many numerical studies have been conducted to optimise spray dryers so that the resultant product has the appropriate rheological properties, particle size distribution, and solubility to achieve its desired function (Huang et al., 2003; Straatsma, Van Houwelingen, Steenbergen, & De Jong, 1999). Fig. 4 illustrates the streamline trajectories of milk particles in a tall form spray dryer (Harvie, Langrish, & Fletcher, 2002). In early studies, Straatsma et al. (1999) developed


613

Fig. 3. Temperature, bacteria deactivation and flow pattern profiles in a can filled with sodium carboxy-methyl cellulose at 19 min (above) and 43 min (below) (Abdul Ghani et al., 1999).

a drying model based on CFD to calculate flow pattern, temperature, particle trajectories and particle drying behaviour and two case studies were presented to illustrate the ability of the model to optimise dryer design. Langrish and Fletcher (2001) presented a comprehensive review of the use of CFD in spray dryer modelling. Recent numerical studies have focused on investigating the dispersion and fouling rates of particles as well as their evaporation and coalescence within a spray dryer (Athanasia, Adamopoulos, & Konstantinos, 2004; Nijdam, Guo, Fletcher, & Langrish, 2004). Challenging issues confronting CFD modellers Physical properties of fluids The production of food ingredients has evolved over recent years and it now holds a considerable market share in

the food industry. Powder formulations of food products allow for longer shelf life and therefore presently act as a primary mechanism for sustaining product quality over long time periods. An issue of contention with food powders is maintaining the stability of ingredient functionality from production right through to final powder application (Fitzpatrick & Ahrne, 2005). Any change in the properties of the ingredients or process conditions in the manufacturing of a product can seriously impinge on the quality of the product and the integrity of the processing system. Predicting the variation of food properties through the production process presents many challenges to the CFD community. For example, a lot of work needs to be done in order to accurately predict the spatial variation of moisture content of powders in the spray drying process (Fletcher et al., in press). Adhesion and cohesion of

Reasonable Yes NS two-phase model, electromagnetic solver None Transient 3D PHOENICS

3D

3D FLUENT 5.3

CFX

3D CFX

Microwave oven

Cold stores

Hu & Sun (2001a) Athanasia et al. (2004) Nahor et al. (2005) Dincov et al. (2004) Air-blast chilling Spray drying

Dim ¼ dimension, dep ¼ dependence, Turb ¼ turbulence, CS ¼ convection scheme, GIS ¼ grid independence study, exp ¼ experiment, PHE ¼ plate heat exchanger, NS ¼ not specified, NonNew PL ¼ non-Newtonian power-law model, HTC ¼ heat transfer coefficient, Std ¼ standard, WL ¼ weight loss, RNG ¼ renormalisation group ke3 model, LRN ¼ low Reynolds number ke3 model.

Reasonable No 1st two-phase model Std ke3 Transient

NS Transient

NS

Mass transfer model Lagrangian model Std ke3, RNG, LRN Std ke3 Transient

NS None Jun & Puri (2006) Plate heat exchangers

Developed in-house

2D

To predict fouling process of milk in PHE To predict HTC and WL To predict fouling rate Validate CFD model Predict Temp and moisture

Transient

Non-New PL, fouling model

NS

RNG ¼ good, others ¼ limited Reasonable NS

Shapes of corrugations being able to inhibit fouling RNG performed best Good No

Outcome Agreement with exp GIS Order of CS Extra models Turb model Time dep Aim Dim Code Authors Application

Table 4. Recent CFD applications in combined flow and mass transfer

Successful prediction and optimisation Model validated but limited in accuracy Moisture movement due to pressure gradients in food


614

Fig. 4. Trajectories of milk particles in a spray dryer (Harvie et al., 2002).

particles and effects on fouling rates are also continuing areas of research in the food industry (Nijdam et al., 2004). It has been recognised that with accurate knowledge of these effects, process strategies can be designed to reduce wall deposits, produce greater dryer throughputs, and enhance the coupling of flavour and aroma loss factors (Langrish & Fletcher, 2003). However, it is also felt that CFD techniques are dubious as to whether they will ever be useful for modelling real cohesive powders (Fitzpatrick & Ahrne, 2005). Non-homogenous fluid domain Both Eulerian and Lagrangian techniques can be used to model flows with two or more phases, e.g. water vapour, airborne microbes and powder. The Eulerian representation treats the particulate phase as a continuum and describes the temporal and spatial concentration of the flow. However, the disadvantages which include loss of time history of particles, outweigh the potential benefits of this technique (Fletcher et al., in press). Moreover, the Eulerian concept is invalid when particles of size z1 mm are present in the flow regime (Reynolds, 1997). Lagrangian stochastic models, i.e. random flight models (using a Lagrangian autocorrelation function) allow particles that are thrown into the near boundary region of the flow stream to experience velocities lower than those sufficient to maintain streamline trajectory. Particles then disengage from the turbulent regime and become deposited on the boundaries. Lagrangian and Eulerian techniques have been used by the spray dryer community, with the former allowing far more opportunities for design as it can take into account turbulent structures and inertia crossing (Fletcher et al., in press). However, it has been noted that rigorous random flight models are necessary to ensure accurate predictions (Burfoot et al., 1999). Moreover, a lot of work still has to be


done to ensure comprehensive validation of such models (Harral & Burfoot, 2005). Because CFD models consider the movement of fluid as a continuum, flows involving equal amounts of both fluids and powders cannot be modelled solely by CFD. Other techniques must be employed to account for the complex interactions of the individual particles. A modelling technique called the discrete element method (DEM) has recently been used with good qualitative accuracy to model a large range of granular mixing applications (Bertrand, Leclaire, & Levecque, 2005). DEM has the ability to take into account powder cohesion and can also be coupled with CFD to simulate the transport of powder materials through pneumatic pipes (Li et al., 2003). However, DEM is very computationally expensive and often simulations require many days before arriving at a solution. This has meant that the extension of this model to other modes of dense gasesolids flow exhibited by fine powders (particle size less than 100 mm) is impractical. Therefore, it may take some time before such techniques can be incorporated into process design (Fitzpatrick & Ahrne, 2005). Simplification of turbulence One of the main issues faced by the food industry over the last two decades is the lack of understanding surrounding the efficient discrete quantification of turbulence in fluids and its effect on system performance. Over the years, simplifying assumptions have been made by turbulence modellers in order to make this problem more approachable. However, these assumptions can often be unreasonable in many applications. A typical example is the Reynolds number assumption, whereby either a high or low Reynolds number flow regime is assumed a priori to a simulation. The most outstanding misapplication of this is in studies where turbulent and laminar flow regimes coexist, e.g. clean rooms or food factories. Recent modelling advancements have addressed this issue by developing a predictive laminar to turbulent flow transition model, which has recently been incorporated in the ANSYS CFXÒ 10.0 (ANSYS CFX Release, 2006) software. Unfortunately, as of yet no research employing this model is available. Certainly, modern variants of the ke3 model have proved to be more successful than the standard ke3 model in similar studies, and in applications involving swirling flow regimes or jet impingement (Olsson et al., 2005; Rouaud & Havet, 2002). Nevertheless, from published studies it can be concluded that confidence in the ke3 model can be upheld in other flow applications provided good agreement is found with measurements under grid independent conditions (D’Agaro et al., 2006). Another feature of RANS turbulence models is the nearwall treatment of turbulent flow. Treatment of the near-wall flow in all CFD software packages is specialised according to the employed turbulence model. For example, low Reynolds number turbulence models solve the governing equations all the way to the wall. This requires a high degree of

615

mesh refinement in the boundary layer in order to satisfactorily represent the flow regime, i.e. yþ 1. Conversely, high Reynolds number turbulence models use empirical relationships arising from the log-law condition that describe the flow regime in the boundary layer of a wall. This means that the mesh does not have to extend into this region and that the number of cells involved in a solution is reduced. The use of this method requires 30 < yþ < 500 (Versteeg & Malalsekeera, 1995), although yþ z 10 is also acceptable (Sorensen & Nielsen, 2003). Generally, these wall treatment assumptions do not adversely affect solutions and many studies have employed them with relative impunity provided yþ constraints specific to the turbulence model were adhered to. Unfortunately, standard wall treatment functions have failed to satisfactorily predict the phenomenon in applications involving the heat transfer associated with impinging airflow (Kondjoyan & Boisson, 1997). Recent studies have successfully circumvented this problem by using a blended wall treatment assumption that uses either the low Reynolds number or high Reynolds number relationship depending on the local flow condition in the wall region (Jensen & Friis, 2004; Olsson et al., 2004). It should be noted that before embarking on CFD modelling, the limitations of the available turbulence models and their associated wall functions must be taken into consideration. Models appropriate for the study should be chosen based on the experiences of similar applications in the literature. Meshing should be then carried out using an iterative procedure that involves repeated CFD solution and mesh adjustment until the yþ criterion is satisfied (Sorensen & Nielsen, 2003). Dimensions of the fluid domain Large-scale simulations have the potential to be very grid point demanding and can therefore take a large amount of computing time and effort to obtain a detailed field solution. CFD modellers in the food industry have simplified computational models to cut down on both pre-processing and solving time. For example, three-dimensional systems have been modelled in two dimensions (Cortella, 2002), and large-scale models have been reduced in size by modelling only the region of interest (Foster et al., 2005). Even though these models have been reasonably successful, it should be recognised that these simplifications can blemish the quality of solutions. In the physical world, all objects occupy a three-dimensional space. Thus, to accurately predict the phenomena occurring in any system, each dimension must be represented in a model. This is where CFD has an advantage over many other analytical techniques. However, some applications in the food industry are on such a large scale that modern workstations are not yet capable of efficiently yielding feasible CFD predictions (Mirade, 2003). Moreover, in other applications such as refrigerated display cases the interesting features of flow phenomena are not

616


occurring in the three dimensions (Cortella, 2002). The two-dimensional modelling technique assumes that the length of a system is much greater than its other two dimensions, and that the flow is normal to the system’s length. This assumption essentially disregards the effects of the confining geometry and will therefore preclude accurate solution development, unless it can be explicitly shown through experiments that three-dimensional flows do not impose any effects on the modelled system (Cortella, 2002; Mirade, 2003). In any case, three-dimensional simulations have provided better predictions and consequently should be used if at all possible (D’Agaro et al., 2006; Mirade, Kondjoyan, & Daudin, 2002). Other assumptions used in the literature include those involved when modelling the region of interest of large systems, i.e. refrigeration display cabinets (Foster et al., 2005), and those used when integrating CFD computations with analytical models and experimental data in optimisation of system design, i.e. food chillers (Mirade et al., 2002). Although these novel techniques may yield predictions in reasonably short time periods, the errors associated with the assumptions may preclude development of accurate solutions (Mirade et al., 2002). Precise predictions of the phenomena in large-scale systems may not be achievable until the capacity and calculation power of workstations is developed further. Nevertheless, reasonable solutions can be presently attained provided good modelling practices are enforced including circumspective selections of turbulence model and nearwall treatment, convection scheme, and time-step. Heat and mass transfer must also be taken into account especially when it is conceived that these processes may influence the flow regime. Additionally, concurrent validation of predictions with experimental measurements is paramount for the future success of simplified CFD modelling. Mesh arrangement Another important issue that arises is concerned with the accurate discrete numerical representation of the fluid domain. In CFD, the computational mesh provides the spatial discretisation of the governing equations and, especially in steady-state simulations, is a primary vehicle for enforcing accurate predictions of the fluid continuum. To achieve a good level of accuracy, one must ensure that the mesh is appropriately refined in areas of interest and in regions where gradients occur in the flow field. Unstructured meshing features generally overcome difficulties associated with mesh refinement. Nevertheless, problems can still arise, and even in recent studies the mesh has precluded the use of high order convection schemes and good quality turbulence models (Mirade et al., 2006). In some cases these difficulties are unavoidable but in many others, diagnosing and repairing the problematic regions of the mesh can obviate such difficulties. This means that to obtain an accurate and efficient representation of convective and diffusive fluxes, cells with high aspect ratios or highly skewed cells

must be removed from the simulation. Some CFD packages offer means of locating these cells. However, in many cases the CFD modeller often resorts to using his/her experience with a CFD software package to assert the quality of the mesh.

Time-step selection Many of the flow regimes encountered in the food industry are unsteady. Transient processes arise as a result of either moving boundaries, e.g. impeller blades in stirred tanks, unsteady boundary conditions, e.g. variable flow fans, or inherent physical instabilities, e.g. vortex shedding behind obstacle in free-stream flow. In these cases, a steadystate flow regime does not exist and numerical difficulties are often encountered when trying to solve the steady governing equations (D’Agaro et al., 2006). Nonetheless, a steady solution can be ‘forced’, which means that some constraining condition can be implemented to suppress the unsteady features of the flow regime. These typically include one or more of the following: first-order convection schemes, dissipative turbulence models (standard ke3 model), and two-dimensional or symmetrical boundary conditions. Because this forcing action does not exist in nature, the credibility of solutions arising from such computations has been questioned (D’Agaro et al., 2006). Time stepping is an important mechanism that allows a CFD solution to march forward in time. An optimum time-step can be considered as a trade-off between computational efficiency, temporal accuracy, and stability of the employed numerical scheme. Explicit numerical schemes generally require time-steps that are less than or equal to the CFL (CouranteFriedrichseLewy) condition in order to retain stability (Courant et al., 1928). To uphold this criterion, time-steps usually must be very small. Consequently, the computational overhead associated with explicit schemes has impeded their use in industry. The maximum time-step selection of implicit schemes is bounded by the accuracy requirements of the simulation. Therefore, the time-step must be small enough to resolve the frequencies of importance/interest in the unsteady phenomenon being modelled. This requires some intuitive knowledge of the flow a priori to the modelling exercise. Generally, an appropriate characteristic length and velocity of the problem is necessary in order to determine the dominant frequency of the flow regime. Sometimes, this can be got from non-dimensional numbers such as the Stroudal number, from experimental data, or from previous computations. An assumption of this frequency does not have to be precise in the first instance, as it can be refined in subsequent computations depending on the desired level of accuracy and what is demanded of the simulation. Using this technique should result in a small number of outeriterations required to converge each time-step, which has been shown to be the most accurate way of simulating transient flows (Liu, Moser, Gubler, & Schaelin, 2003).


Opportunities for the food industry and benefits for consumer Processing system design Enhancing the design of systems for the production of food products has benefits for both the food industry and consumer alike, and requires research and development of new tools and processing methodologies. Alongside the expansion of the food industry, energy and workforce costs are growing rapidly. Oil prices have reached levels not seen since the crisis in the nineteen seventies. Consequently, the impetus in recent research has been directed towards the development of processing systems that can integrate multiple operations, which, depending on the requirements of the system, allow the coupling and uncoupling of elementary processes (Charpentier, 2002). For example, the development of food powders requires both the drying and transport of ingredients. The governing dynamics in such systems include coupled heat and mass transfer and require in-depth knowledge for optimisation and development. CFD modelling can be seen as the next progressive step from expensive laboratory studies, and can account for the complex geometries experienced in industry to predict the governing phenomena of the processing system in an unobtrusive manner. As a result of CFD modelling, processing systems have been reduced in size and optimised to become more energy efficient. CFD can then create a climate in which both industry and consumer can benefit, and food products can be developed with better equipment performance, less pollution impact, faster time to market and lower design and production costs.

Product quality Food quality is an outstanding issue in food industry. The importance of food quality has heightened over recent years in tandem with the lifestyle changes experienced by many people. Convenience foods are becoming more prevalent and demand for ready-to-eat products, such as fresh delicatessen and frozen meals is growing rapidly (Burfoot, Brown, Xu, Reavell, & Hall, 2000). Sterilisation and hygiene protocols have thus become paramount, and thrust has been towards maintaining high quality food products from factory to fork. In sterilisation applications, CFD modelling has helped to alleviate the difficulties in relating heat transfer in food products to sterility levels and loss of both sensory and nutritional quality. CFD has also changed the way of thinking in the operation of conventional sterilisation practices. For example, CFD has proven the high temperature short time approximation to be invalid under some operating conditions (Jung & Fryer, 1999). In addition, CFD has shown the efficacy of the sterilisation process to be a function of both food properties and container geometry. Thus, CFD can assist the understanding of the physical mechanisms that govern the thermal, physical and rheological properties of foods and benefit the food

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industry by enhancing confidence and efficiency in sterilisation processes (Welti-Chanes et al., 2005). The transport of airborne microbes is significant in high-care food factories and CFD simulations have been used effectively to devise strategies that minimise the movement of contaminated air towards food products (Burfoot et al., 2000). Further advances in physical modelling techniques will allow the dynamic mapping of the airborne particle trajectories to be predicted before implementing cleaning strategies (Harral & Burfoot, 2005). Conclusions The objective of this review is to shed light not only on the recent intricacies of fluid flow expounded by leading academics but on the remunerative advantages that CFD can offer in a commercial setting. CFD has played an active part in system design including refrigeration, sterilisation, ventilation, mixing and drying. This has been aided by the ability of commercial companies to conform to the needs of the food industry. The recent developments in CFD include greater refinement in areas of adaptive meshing, moving reference frames and solver efficiency. Physical modelling has also reached levels of higher sophistication with turbulence and multiphase models being developed and validated by numerous experts and subsequently employed in the chemical and food industry. Notwithstanding this, the CFD modeller must maintain high level of accuracy during the modelling process to uphold confidence in CFD predictions. This means that concurrent experimentation must be carried out to validate predictions, particularly where simplifying assumptions are incorporated into the model. Undoubtedly, with current computing power progressing unrelentingly, it is conceivable that CFD will continue to provide explanations for more fluid flow, heat and mass transfer phenomena, leading to better equipment design and process control for the food industry.

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Nomenclature u: velocity component (m s1). t: time (s). g: acceleration due to gravity (m s2). Ca: specific heat capacity (W kg1 K1). x: Cartesian coordinates (m). sT: thermal sink or source (W m3). p: pressure (Pa). T: temperature (K). R: gas constant (J kmol1 K1). Wa: molecular weight of air (kg kmol1). fi: momentum source (N m3). CF: Forchheimer drag coefficient (m1). K: Darcy permeability (m2). n: power-law index. m: consistency index. Greek letters r: m: d: b: l: s: 3: _ g: q:

density (kg m3). dynamic viscosity (kg m1 s1). Kroneckor delta. thermal expansion coefficient (K1). thermal conductivity (W m1 K1). Prandtl number for enthalpy. turbulent dissipation rate (m2 s3). shear rate (s1). local mean age of air (s).

Subscripts i, j: Cartesian coordinate index. ref: reference. a: air.