1 s2.0 S0924224406001981 Main PDF

Trends in Food Science & Technology 17 (2006) 600e620
Review
Computational fluid
dynamics (CFD) e an and Lewy (1928), who in their endeavours to procure
insight into fluid motion instigated the development of
powerful numerical techniques that have advanced the nu-
effective and efficient merical description of all types of fluid flow (Shang, 2004).
CFD is now maturing into a powerful and pervasive tool in
design and analysis many industries, with each solution representing a rich tap-
estry of mathematical physics, numerical methods, user in-
terfaces, and state-of-the art visualisation techniques (Xia
tool for the food & 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
industry: A review 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
Tomás Norton and often precluded the desire to produce efficient in-depth
results. Moreover, the assumptions, generalisations and
Da-Wen Sun* approximations associated with analytical models have
Food Refrigeration and Computerised Food swayed their reduction in the development of flow solu-
Technology Research (FRCFT) Group, Department of tions. By considering these limitations coupled with recent
Biosystems Engineering, National University of achievements in the development of numerical solutions for
Ireland, University College Dublin, Earlsfort Terrace, the NaviereStokes equations and the amelioration of com-
Dublin 2, Ireland (Tel.: D353 1 7165528; fax: D353 1 puting power and efficiency, it is easy to understand why
4752119; e-mail: dawen.sun@ucd.ie) 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
Computational fluid dynamics (CFD) is a powerful numerical with the food and beverage industry such as mixing, drying,
tool that is becoming widely used to simulate many processes cooking, sterilisation, chilling and cold storage are pro-
in the food industry. Recent progression in computing efficacy found. Such processes are used regularly to enhance qual-
coupled with reduced costs of CFD software packages has ity, safety and shelf life of foodstuffs (Wang & Sun,
advanced CFD as a viable technique to provide effective and 2003). With direct benefits for both consumer and the nat-
efficient design solutions. This paper discusses the fundamen- ural environment, applications of CFD have become more
tals involved in developing a CFD solution. It also provides widespread in the food industry. CFD research has meant
a state-of-the-art review on various CFD applications in the that products can be processed and stored in more
food industry such as ventilation, drying, sterilisation, refriger- efficient systems. Furthermore, CFD can aid food compa-
ation, cold display and storage, and mixing and elucidates the nies to respond to an expanding marketplace by enhancing
physical models most commonly used in these applications. and developing processing strategies, whilst endeavouring
The challenges faced by modellers using CFD in the food to maintain high levels of product quality.
industry are also discussed. The technical achievements observed in the last two de-
cades include vast improvements in numerical algorithms
and CFD modelling techniques (Xia & Sun, 2002). This
Introduction means that features like unstructured and adaptive meshing,
Computational fluid dynamics (CFD) was originally de- moving boundaries and multiple frames of reference now
veloped from the pioneering accomplishments of enthusi- cooperate with physical models to confront complex phe-
asts such as Richardson (1910) and Courant, Friedrichs, nomena involving Newtonian and non-Newtonian fluid
flow, quasi-fluid substances, product taste, packaging and
* Corresponding author. storage that have faced the food industry over the decades
0924-2244/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tifs.2006.05.004
T. Norton, D.-W. Sun / Trends in Food Science & Technology 17 (2006) 600e620 601
(Fluent News, 2000). Today CFD solutions are being used 2. The law of conservation of momentum (Newton’s sec-
to optimise and develop equipment and processing strate- ond law of motion), which states that the sum of the ex-
gies in the food industry and their rate of use has grown ternal forces acting on a fluid particle is equal to its rate
exponentially, as evidenced by the steady increase in of change of linear momentum.
peer-reviewed journal papers over the years (Fig. 1). The 3. The law of conservation of energy (the first law of ther-
many areas within the food industry where CFD has been modynamics), which states that the rate of change of en-
routinely used to quantify governing physical phenomena ergy of a fluid particle is equal to the heat addition and
include food production facilities (Burfoot, Hall, Brown, the work done on the particle.
& Xu, 1999; Harral & Burfoot, 2005), sterilisation (Siriwat-
tanayotin, Yoovidhya, Meepadung, & Ruenglertpanyakul, By enforcing these conservation laws over discrete spa-
2006; Varma & Kannan, 2006), mixing (Song & Han, tial volumes in a fluid domain, it is possible to achieve a sys-
2005) and drying processes (Huang, Kumar, & Mujumdar, tematic account of the changes in mass, momentum and
2003) to name but a few, with the range of applications energy as the flow crosses the volume boundaries. The
being continuously extended. resulting equations can be written as:
The objective of this paper was to provide a state-of-the- Continuity equation:
art review of CFD and its current applications in the food in-
vr v
dustry. The advancements of physical models and numerical þ ruj ¼ 0 ð1Þ
techniques are examined comprehensively with particular vt vxi
attention placed on enhancing the accuracy of CFD solu- Momentum equation:
tions. The Cost and unique features associated with the
v v v vui vuj
important players in the CFD market are also discussed. ðrui Þ þ rui uj ¼ pdij þ m þ þ rgi
vt vxj vxj vxj vxi
ð2Þ
Fundamentals of CFD
Energy equation:
Governing equations

The governing equations of fluid flow and heat transfer v v v vT
can be considered as mathematical formulations of the con- ðrCa TÞ þ ruj Ca T l ¼ sT ð3Þ
vt vxj vxj vxj
servation laws of fluid mechanics and are referred to as the
NaviereStokes equations. When applied to a fluid contin- There are two ways to model the density variations that
uum, these conservation laws relate the rate of change of occur due to buoyancy. The first is to assume that the
a desired fluid property to external forces and can be con- density differentials in the flow are only required in the
sidered as: momentum equations and are represented by:

1. The law of conservation of mass (continuity), which r ¼ rref 1 b T Tref ð4Þ
states that the mass flows entering a fluid element This method is known as the Buossinesq approximation
must balance exactly with those leaving. and has been used successfully in many food engineering
applications (Abdul Ghani, Farid, Chen, & Richards,
100
1999). However, at high temperature differentials, the ap-
90 proximation is no longer valid and another method must
be applied (Ferziger & Peric, 2002). One way is to treat
80
the fluid as an ideal gas and express the density difference
70 by means of the following equation:
Number of Papers
60 pref Wa
r¼ ð5Þ
50 RT
40
This method can be considered as a weakly compress-
ible formulation, which means that the density of the fluid
30 is dependent on temperature and composition but not pres-
20
sure. This assumption has also been used successfully in
food engineering applications. However, solutions were
10 found to be more difficult to converge using this method
0 (Foster, Barrett, James, & Swain, 2002).
1993-1995 1996-1998 1999-2001 2002-2004 2005-2006
Period Numerical analysis
Fig. 1. The number of published peer-reviewed papers with CFD appli- A fundamental consideration for CFD code developers is
cations in the food industry. the choice of suitable techniques to discretise the modelled
602 T. Norton, D.-W. Sun / Trends in Food Science & Technology 17 (2006) 600e620
fluid continuum. Of the many existing techniques, the most multigrid as the default solver option. Detailed techniques
important include finite difference, finite elements and used by multigrid are described in the literature (Ferry, 2002).
finite volumes. Although all these produce the same solu-
tion at high grid resolutions, the range of suitable problems
Interpreting the solution
is different for each. This means that the employed numer-
Visualisation is often necessary to represent the resulting
ical technique is determined by the conceived range of code
field solution. Contour, vector and line plots enhance the
applications.
accurate interpretation of results and have been used suc-
Finite difference techniques are of limited use in many
cessfully in many studies to aid in system design (Foster,
engineering flows due to difficulties in their handling of
Madge, & Evans, 2005). In addition, field data are often
complex geometries. This has led to increased use of finite
easily exported to external modelling programs so that
elements and finite volumes, which employ suitable mesh-
they can be processed further. Fig. 2 illustrates how visual-
ing structures to deal appropriately with arbitrary geometry.
isation techniques can provide sufficient information to
Finite elements can be shown to have optimality properties
move forward in the design process. Animated flow fields
for some types of equations (Ferziger & Peric, 2002). How-
have also become increasingly popular and can now accom-
ever, only a limited number of commercial finite element
pany peer-reviewed studies on scientific journal websites
packages exist, which is undoubtedly a reflection of the dif-
(D’Agaro, Cortella, & Croce, 2006).
ficulties involved in the programming and understanding of
this technique.
Fortunately, such difficulties are obviated through imple- Commercial CFD packages
mentation of finite volumes methods. When the governing Over the last two decades, there has been enormous de-
equations are expressed through finite volumes, they form velopment of commercial CFD codes to enhance their mar-
a physically intuitive method of achieving a systematic ac- riage with the sophisticated modelling requirements of
count of the changes in mass, momentum and energy as many research fields, thereby accentuating their versatility
fluid crosses the boundaries of discrete spatial volumes and attractiveness. Spalding (1999) illuminated the many
within the computational domain (Versteeg & Malalse- obstacles that face the CFD community when developing
keera, 1995). The ease in the understanding, programming codes to cater for incessantly expanding fields of applica-
and versatility of finite volumes has meant that they are tions like the food industry. These challenges have led to
now the most commonly used techniques by CFD code unprecedented competition between commercial CFD
developers. developers and have expedited non-uniform development,
causing the range of afforded functionalities to vary from
Solving the flow problem code to code. Thus, among the many codes that exist today
In order to solve for a flow field a CFD code must take not all provide the features required by the food engineer.
the mathematical statements inputted by the user, structure Such requirements include the provision of powerful pre-
them into a suitable arrangement and solve them for the processor, solver and post-processor environments, the
specified boundary conditions. Iterative methods are com- power to import grid geometry, boundary conditions and
monly used by CFD codes to solve a whole set of discre-
tised equations so that they may be applied to a single
dependent variable. The segregated solver SIMPLE
(Semi-Implicit Method for Pressure-Linked Equations), de-
vised by Patankar and Spalding (1972), or its descendents
are conventionally employed by many commercial pack-
ages. SIMPLE determines the pressure field indirectly by
closing the discretised momentum equations with the con-
tinuity equations in a sequential manner. Consequently, as
the number of cells increases, the elliptic nature of the pres-
sure field becomes more profound and the convergence rate
decreases substantially (Ferry, 2002). This has led to the de-
velopment of multigrid techniques that compute velocity
and pressure corrections in a simultaneous fashion, thereby
enhancing convergence rates. Unfortunately, the improve-
ment 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 capa-
bilities. Nevertheless, many CFD packages, even those Fig. 2. Contours of isotemperatures in the most sensitive plane of a refrig-
based on unstructured grids now successfully employ erated truck with (a) and without (b) air ducts (Moureh & Flick, 2004).
initial conditions from an external text file, and the capabil- gq model). ANSYS CFXÒ also affords an easy-to-use
ity to model non-Newtonian fluids, two-phase flows, flow fully parametrical CAD tool with a bi-directional link
dependent properties, phase change and flow through po- compatible with most CAD software.
rous media (Kopyt & Gwarek, 2004). Therefore, intuitive
functional considerations of a code should be taken into ac-
FLUENTÒ (FLUENT Inc.)
count before selection. The commercial software packages
FLUENT Inc. offers three software packages within the
featured in this review incorporate at least a minimum num-
CFD framework that are suitable for the food engineer’s
ber of all these functionalities, employ graphical user inter-
modelling needs. The three packages are FLUENTÒ (gen-
faces, and support Windows, UNIX and Linux platforms.
eral purpose with multiphysics capabilities), FIDAPÒ
State-of-the-art features of the most commonly used
(modelling complex physics) and POLYFLOWÒ (polymer
general-purpose codes available are elucidated with their
modelling). FLUENTÒ Inc. is presently one of the leading
associated cost in Table 1. Details on three of the most
suppliers of CFD software in the world. The most interest-
routinely used commercial codes are elaborated below.
ing features of the FLUENTÒ software include models for
heat exchangers, discrete phase models for multiphase
CFXÒ (ANSYS Inc.) flows, numerous high quality reaction models and the phase
CFXÒ was recently (in 2003) taken over by ANSYS Inc. change model which tracks the melting and freezing in the
and is now branded as ANSYS CFXÒ. Within the frame- bulk fluid. FIDAPÒ is a finite element based software that
work of ANSYS CFXÒ numerous different types of soft- offers unique abilities for modelling non-Newtonian flows
ware packages exist that can be used to solve various and free surface flows. It also contains sophisticated radia-
types of flow problems. There are also a large number of tion, dispersion and heat transfer models. POLYFLOWÒ is
up-to-date fully functional physical models, which include a general-purpose finite element CFD tool for the analysis
multiphase flow, porous media, heat transfer, combustion of polymer processing such as glass forming, thermoform-
and radiation models. Advanced turbulence models are ing and fibre spinning. POLYFLOWÒ also has a range of
also a feature of ANSYS CFXÒ and it contains a predictive applications that can be extended into the food industry
laminar to turbulent flow transition model (MentereLangtry (Fernandes et al., 2006).
Table 1. Common commercial CFD software used in the food industry
Company Location Software Features Price Recently published

package applications in
food industry
ANSYS Inc., Southpointe, ANSYS CFX Menter-Langtry turb, V2.4k1, V11.2k3,4,5 D’Agaro et al. (2006),
www.ansys.com Canonsburg, PA, 10.1 (FV) Coupled Lagrangian Siriwattanayotin et al.
USA and particle tracker. (2006), Varma &
Coupled multiphase Kannan (2006)
and interphase models
CHAM Ltd., Wimbledon PHOENICS 3.6 LEVL and MFM turb, V1.21; V4.8k2 (þV0.9k)5; Abdul Ghani et al. (2003),
www.cham.co.uk Village, London, (FV) PARSOL, IMMERSOL V3.75k3; V14.5k4 Dincov, Parrott, &
UK CHEMKIN, MTSM (þV2.2k)5 Pericleous (2004),
Moureh, Menia, & Flick (2002)
CD Adapco Group, London, UK STAR-CD 3.2 Large amount of V2.19k1; V18.33k3,4,5 Jensen & Friis (2004)
www.cd-adapco.com (FV) meshing capabilities,
chemical solvers
STAR-CCMþ 1 State-of-the-art V2.19k1; V18.33k3,4,5 None
(FV) modelling interface
FLUENT Inc., Lebanon, NH, FLUENT 6.1 (FV) Dynamic mesh, V3.88k1; V21.5k3,4,5 Chen & Yuan (2005),
www.fluent.com USA chemical mixing and Kumaresan & Joshi (2006),
reaction models, wall Wong et al. (2006a)
film models
FIDAP 8.6 (FE) Complex rheology V3.88k1; V21.5k3,4,5 Jung & Fryer (1999),
and electrohydrodynamic Tattiyakul et al. (2001,
modelling 2002)
POLYFLOW 3.1 Integral and V3.88k1; V21.5k3,4,5 Fernandes et al. (2006)
(FE) differential viscoelastic
flow modelling
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.
PHOENICSÒ (CHAM Ltd.) The eddy viscosity hypothesis

PHOENICSÒ is a multipurpose CFD package that has The Reynolds stresses need to be modelled by a physi-
numerous modelling capabilities to embrace many scenar- cally well-posed equation system to obtain closure that is
ios faced by the food engineer, including Newtonian and consistent with the flow regime. The eddy viscosity hypoth-
non-Newtonian fluid modelling, flow through porous media esis states that an increase in turbulence can be represented
with direction-dependent resistances, and conjugate heat by a concomitant increase in effective fluid viscosity, and
transfer. There is also an extensive suite of embedded tur- that the Reynolds stresses are proportional to the mean ve-
bulence models including the unique wall distance turbu- locity gradients via this viscosity (Ferziger & Peric, 2002).
lence model (LVEL), which circumvents the inaccuracies The eddy viscosity hypothesis forms the foundation on
associated with wall-function computations of most turbu- which many of today’s most widely used turbulence models
lence models by using the knowledge of wall distances, are based. These range from simple one equation models
and local velocities to compute the near-wall flow. based on empirical relationships to variants of the sophisti-
PHOENICSÒ is a structured grid code and it necessitates cated but inveterate two-equation ke3 model which
the use of body fitted coordinates to model complex geom- describes the eddy viscosity through the production and
etry. This can substantially increase the pre-processing and destruction of turbulence.
solution times of a simulation.
Recent applications of turbulence models
Additional models for food processes There are many turbulence models embedded in com-
On their own the NaviereStokes equations have a lim- mercial codes and it is left to the user to assert which one
ited amount of applications in many areas of food engineer- is appropriate for the application in hand. As illustrated
ing. This means that the additional processes that may play by Bartosiewicz, Aidoun, and Mercadier (2006), large dis-
a major role in influencing the dynamics of a system must crepancies can occur in predictions made by different
be taken into account in simulations. In these cases the gov- models. This emphasises the need for concurrent validation
erning equations may need to be fortified with additional with experimental measurements. Of all turbulence models
approximations or physical models to fully represent the available, the standard ke3 model still remains an industrial
flow regime. Important physical models commonly used standard and its successful applications are found in recent
in food engineering applications include turbulence models, literature (Foster et al., 2005; Margaris & Ghiaus, 2006). In
porous media and multiphase models, and non-Newtonian some cases it has even been found to perform as well as
models. more advanced turbulence models (D’Agaro et al., 2006).
Unfortunately, due to the assumptions and empiricism
Turbulence modelling upon which the model is based, there have been many sit-
Turbulence momentum and scalar transport play an es- uations where the ke3 model has failed to sufficiently rep-
sential role in many engineering applications and its simu- resent the modelled turbulent regime and predictions have
lation has undergone intensive research throughout the proved inadequate (Langrish & Fletcher, 2001; Wang &
years. In order to develop safe and efficient plant processes Sun, 2003). Consequently, engineers have turned to other
in the food industry, it is often necessary to predict surface advanced turbulence models like the renormalisation group
heat and mass transfer coefficients, thermal dependent (RNG) and Reynolds stress transport (RST) models which
properties of food, and flow characteristics of systems, un- are not so reliant on empiricism and can account for anisot-
der various scenarios (Delgado & Sun, 2001; Wang & Sun, ropy of highly strained flows. However, although there are
2003). These processes are usually associated with turbu- cases in which the RNG and RST models have proven su-
lent flows, primarily due to the complex geometry and/or perior to the standard ke3 model (Moureh & Flick, 2005;
high flow rates involved. Whilst the NaviereStokes equa- Rouaud & Havet, 2002), there are also others where the
tions can be solved directly for laminar flows, the current limitations of computational power or convergence difficul-
state of computational capability is unable to resolve the ties precluded the use of these models (Hoang, Verboven,
fluid motion in the Kolmogorov microscales associated De Baerdemaeker, & Nicola€ı, 2000; Mirade & Daudin,
with turbulent flow regimes (Friedrich, Huttl, Manhart, & 2006; Nahor, Hoang, Verboven, Baelmans, & Nicolai,
Wagner, 2001). In most cases however, engineers are not 2005). Moreover, the advantages of such models will be in-
interested in the detailed structures of turbulence but just hibited if used with first-order convection schemes (Hoang
need a few quantitative features to undertake suitable de- et al., 2000; Verboven, Scheerlinck, De Baerdemaeker, &
sign strategies (Ferziger & Peric, 2002). These details are Nicolai, 2001).
afforded by the Reynolds averaged NaviereStokes equa-
tions (RANS), and are determined by averaging the ergodic More complex turbulence simulation
processes that typify turbulent flows. Reynolds averaging Engineers have also addressed other simulation method-
essentially disregards the stochastic properties of the flow ologies such as direct eddy simulation (DNS), detached
and results in six additional unknowns (Reynolds stresses) eddy simulation (DES) and large eddy simulation (LES)
that preclude the direct closure of the equations. to correctly predict turbulent flow structure and transport
phenomena. DNS is a solution to the three-dimensional, used in recent studies (Hoang et al., 2000; Mirade, Rougier,
time dependent NaviereStokes set of equations. Because Daudin, Picque, & Corrieu, 2006; Verboven, Hoang, Bael-
no turbulence models are involved in the governing equa- mans, & Nicola€ı, 2004). This method basically applies Dar-
tions, a DNS is conducted on a fine mesh to reproduce all cy’s law to porous media by relating the velocity drop
length scales within turbulent flow regime. This obviously through the pores to the pressure drop over the material.
necessitates the invocation of intensive computer power, An extension of this law to account for most commonly en-
much of which is presently unavailable to the engineer, countered non-linear relationships between pressure drop
thereby rendering DNS a research tool for studying turbu- and velocity is represented by the DarcyeForchheimer
lence momentum and heat transfer dynamics. The advan- equation (Verboven et al., 2004):
tages afforded to the food industry by DNS include
detailed information regarding turbulent channel flows of vp m
¼ vþrCF u2 ð6Þ
dilute polymer solutions, the effect of buoyancy on turbu- vx K
lent transfer and information regarding the effective control Equation (1) is the most common relationship used to
of turbulence and heat transfer (Moin & Bewley, 1995). represent pressure drop through packed beds. In the CFD
Large eddy simulation (LES) forms a solution in model, this equation is added as an additional sink term
response to the fact that large turbulent eddies are highly to the momentum equations. The general relationships to
anisotropic and dependent on both the mean velocity gradi- determine both the permeability and the inertial loss coef-
ents and geometry of the flow domain. With the advent of ficient can be obtained by inference from the Ergun equa-
more powerful computers, LES now offers a way of allevi- tion. These have recently been adjusted to suit the
ating the errors caused by the use of RANS turbulence geometry of the stacked food material and showed good
models. However, the lengthy time involved in arriving at agreement with experimental results (Verboven et al.,
a solution means that this is an expensive technique (Turn- 2004). However, considerable information regarding the
bull & Thompson, 2005). LES provides an accurate solu- detailed flow and transfer processes taking place within
tion to the large-scale eddy motion in methods akin to the stacked material is lost in this type of modelling strat-
those employed for DNS. It also acts as spatial filtering, egy. Consequently, there have been studies where the
thus only the turbulent fluctuation below the filter size is CFD models employing porous media have not yielded pre-
modelled. This is because smaller eddies possess length dictions that agree well with measurements (Mirade et al.,
scales determined by the viscosity of the fluid and are con- 2006). These poor predictions may have arisen from differ-
sequently isotropic at high Reynolds numbers. Over recent ences in the shape, surface roughness and void fractions
years, LES has been applied in areas related to food throughout the physical media that cannot be accounted
processing (Xu, Sang Lee, Pletcher, Mohsen Shehata, & for in the CFD model. Therefore, before modelling porous
McEligot, 2004). More recently, a methodology has been media, one must ensure that the parameters in the momen-
proposed by which the user specifies a region where the tum source terms fully represent the physical media. Ver-
LES should be performed with RANS modelling complet- boven et al. (2004) illustrated this point by modifying the
ing the rest of the solution; this technique is known as DES DarcyeForchheimer pressure drop relation using experi-
and has been found to increase the solution rate by up to mental results in order to accurately represent the resistance
four times (Turnbull & Thompson, 2005). to airflow imposed by beds of apples and chicory roots.
Other means of circumventing detailed meshing whilst
Porous media and two-phase modelling improving upon accuracy of pressure drop relationships is
Many large-scale processes in the food industry may to organise the model to comprise the main geometry,
have the potential to be grid point demanding in CFD within which lies a sub-domain filled with a porous me-
models owing to the complex geometry of the modelled dium to represent the stacked foods. Fluid flow, and heat
structures. For example, to predict the detailed transfer pro- and mass transfer are described in the sub-domain by the
cesses within a cold store containing stacked foods, one laws of conservation of mass, momentum and energy.
must mesh all associated geometry with a complex unstruc- These particular forms of transport equations in porous
tured or body fitted system, which is a highly arduous and media are derived in terms of macroscopic variables. The
in many cases inaccessible task. In any case, both compu- macroscopic velocity is provided by the volume-averaged
tational power and CFD algorithms have not yet reached NaviereStokes equations, which are a generalized version
such levels of maturity that these types of computations of Darcy’s law. This type of computational model can be
can be achieved. Therefore, other methods must be used regarded as a two-phase flow.
to exploit the physical relationships that exist on a macro- Because the volume averaging process causes loss of de-
scopic level and sufficiently represent the dynamic flow ef- tails regarding the microscopic flow regime, empirical pa-
fects that are representative of the modelled material. The rameters such as the Forchheimer constant, thermal and
porous media assumption, which relates the effects of par- mass dispersion, and interfacial heat and mass transfer
ticle size and shape, alignment with airflow and void frac- coefficients are required to complete the equation system
tion on pressure drop over the modelled products, has been (Zou, Opara, & McKibbin, 2006a). Recent studies have
employed a two-phase modelling technique to predict the turbulence models and meshing features such as unstruc-
environmental conditions of product stores (Nahor et al., tured mesh, sliding mesh and multiple frames of reference,
2005). Zou et al. (2006a) and Zou, Opara, and McKibbin which can be used to improve modelling accuracy and meet
(2006b) used this method successfully to predict tempera- the demands of the food industry (Kumaresan & Joshi,
ture distribution and airflow patterns in ventilated stacked 2006; Wong, Zhou, & Hua, 2006a).
goods.
Meshing
Non-Newtonian fluid modelling Unstructured mesh
Any fluid that does not obey the Newtonian relationship Most commercial CFD codes have emerged from typical
between the shear stress and shear rate is called a non- Cartesian type academic programs. This has meant that for
Newtonian fluid. Many food-processing media have non- many years the actual geometry criteria of the modelled
Newtonian characteristics and the shear thinning or shear process could not be fully met and had to be altered to
thickening behaviour of these fluids greatly affects their suit the code configuration (Gosman, 1998). One of the ma-
thermalehydraulic performance (Fernandes et al., 2006). jor advances to occur in meshing technology over recent
Over recent years, CFD has provided better understanding years was the ability for hexahedral hybrid meshes to be in-
of the mixing, heating, cooling and transport processes of corporated into general codes. This allowed a mesh to be fit
non-Newtonian substances. Indeed, a source of continuous to any arbitrary geometry, thereby enhancing the attainment
research within this modelling discipline is the effect of CFD solutions for many industrial applications. A major
imposed by the rheological behaviour of materials like advantage of unstructured and hybrid meshes is their relax-
yoghurt, soup and milk on equipment design and performance ation of the block structure, a formal requirement of many
(Grijspeerdt, Hazarika, & Vucinic, 2003; Sun et al., 2004). general CFD codes (Gosman, 1998). This means that local
Processing equipment such as heat exchangers, stirred mesh refinement can now be achieved both more effectively
tanks, heaters and flow conveyors are all connected with and efficiently, and a solution can be developed to capture
the rheological properties of foods and CFD studies have all desired flow features without creating badly distorted
elucidated numerous methods of equipment optimisation cells that deteriorate convergence behaviour. The versatility
(Liu, Hrymak, & Wood, 2006). Of the several constitutive of these meshes has led to an increased take-up by the CFD
formulas that describe the rheological behaviour of community and their uses are finding accurate and efficient
substances, some are the Newtonian model, the power- solutions in many applications within the food industry
law model, the Bingham model, and the Herschel Bulkley (Foster et al., 2002; Mirade, 2003). This form of meshing
model. The power law is the most commonly used model requires different programming and solution techniques
in food engineering applications (Welti-Chanes, Vergara- that are not quite as intuitive in implementation as their
Balderas, & Bermúdez-Aguirre, 2005). This governs the Cartesian based counterparts. Therefore, unstructured
relationship between shear thinning fluids and the shear meshing has not yet fully infiltrated the CFD market, with
rate, and can be shown as: codes such as PHOENICS remaining faithful to traditional
n1 structured methods (Abdul Ghani, Farid, & Zarrouk, 2003).
m¼ m g_ ð7Þ
This model has been used to represent the shear thinning Sliding mesh
effect in many non-Newtonian CFD simulations with suc- This type of meshing technique is commonly used to
cess. However, as shown by Abdul Ghani, Farid, Chen, model the stirring or moving effect of adjacent geometry
and Richards (2001), the complex functions that relate fluid and can therefore simulate factory processes such as baking
viscosity to the performed operation need not always be and mixing. This methodology has been used in some areas
described and in some cases the fluid may be treated as of food engineering. It allows certain portions of a mesh to
Newtonian. slide relative to each other at a common interface, which in
the case of a mixing tank is the interface between the tips of
Methods for improving modelling accuracy the blades and the baffles, and in baking is the continuous
Oftentimes the details of NaviereStokes equations are movement of the product in the oven (Aubin, Fletcher, &
smeared with general assumptions and poor modelling Xuereb, 2004; Wong, Zhou, & Hua, 2006b).
techniques that can impair the quality of CFD simulations.
Past examples of this range from inadequate application of Multiple frames of reference
turbulence models to the inaccuracies afforded by poor This type of meshing introduces an additional assump-
quality geometry, meshes and first-order convection schemes tion that can account for any stationary parts of a flow ex-
(Gosman, 1998). Fortunately as the uptake of CFD has isting in sliding mesh simulations. Instead of invoking the
grown, emphasis on developing quantitatively accurate so- rotation of the grid directly, the rotation is simulated by in-
lutions for all types of flow applications has increased. Now serting suitable body force terms in the momentum equa-
CFD codes offer a large range of convection schemes, tions. This means that by making suitable transformations
in the CFD calculations at the interface between rotating Convergence techniques

and stationary flow regimes, a steady-state simulation can When designing a CFD model, one must preconceive
then be conducted on a static mesh (Gosman, 1998). For potential gradients that may occur so that the computational
example, in applying this approach to stirred tanks, which domain can be suitably meshed. This mesh must then be re-
is its most common application in the food industry, the fined to obtain as nearest to a grid independent solution as
equations in the flow domain attached to the impeller are possible. Unfortunately, with today’s computational power
solved in a simulated rotating frame of reference, whereas it is still not yet possible to obtain a grid independent solu-
the equations in the remaining domain are solved in a frame tion in some cases (Mirade & Daudin, 2006; Sorensen &
of reference at rest (Li, White, Wilkinson, & Roberts, Nielsen, 2003). Therefore, the requirements must be re-
2005). laxed whilst still maintaining confidence in the discrete so-
lutions for the governing equations. A spatial convergence
technique proposed by Roache (1998) based on Richardson
extrapolation (1910) has been used in many CFD engineer-
Convection schemes ing applications (Sorensen & Nielsen, 2003). The basic pri-
As mentioned previously, the partial differential equa- ority of this method is to furnish the CFD user with
tions governing fluid flow are solved over discrete volumes a conservative estimate of the error (GCI) between the
within the computational domain. It is therefore necessary fine-grid solution and the unknown exact solution. The re-
to represent these equations as accurately as possible at quirement is a solution set of the same governing equations
each location. By increasing the number of volumes on sub- from two different grid resolutions. Both CFD solutions
sequent CFD computations, one would intuitively expect must be on a grid that is within the asymptotic range of
the difference between the solutions to be reduced. How- convergence. This means that the fine-grid CFD solution
ever, this leads to an unfavourable increase in computa- must be obtained at, or close to, the upper limit of the com-
tional time, especially when using segregated solvers. puter power available. The coarse grid solution can be
Consequently, over recent years there has been continual achieved by removing grid lines in each coordinate direc-
improvement in the representations of the convection terms tion. To ensure that the coarse grid does not fall outside
in the finite volume equations to reduce the number of grid the asymptotic range of convergence, the grid refinement
points involved in a solution. The ultimate accuracy, stabil- ratio (r) between the two grids should be a minimum of
ity and boundedness of the solution depend on the numer- 1.1. This also allows the discretisation error to be differen-
ical scheme used for these terms. tiated from other error sources (Slater, 2006). The GCI can
A convection (or numerical) scheme can be perceived as be then described as:
a vehicle through which the boundary conditions are trans-
mitted into the computational domain. The performance of Fs j3j
a convection scheme is delimited by the ability of the GCI ¼ ð8Þ
ðr p 1Þ
scheme to reduce the error once the mesh is refined. The
first-order HYBRID or UPWIND convection schemes are
where the relative error 3 between fine and coarse grid
bounded and stable but predisposed to numerical diffusion
solutions is defined as:
and exhibit a sluggish response to grid refinement. Never-
theless, owing to their favourable convergence attributes
these schemes are still prevalent in the food engineering lit- f2 f1
3¼ ð9Þ
erature. This obviously casts serious doubts on the validity f1
of some solutions especially when grid refinement studies
proved unattainable (Hoang et al., 2000; Mirade & Daudin, Fs is the factor of safety which is usually 3 for two grid
2006). This point was also illustrated by Harral and Boon comparisons (Slater, 2006), fn is the solution function (i.e.
(1997) when they showed that experimental measurements velocity at a location) and p is the formal order of accuracy
agreed more favourably with coarse grid predictions than of the convection scheme (i.e. UPWIND is first order,
with a grid independent solution. A higher order scheme therefore, p ¼ 1). This method has been successfully used
such as QUICK (upstream interpolation for convective in the food industry to show the convergence of surface av-
kinematics) is more accurate and responsive to grid refine- eraged heat transfer coefficients of food in a microwave
ment but due to its unbounded nature exhibits unphysical oven using the QUICK convection scheme by Verboven
under-shoots and over-shoots when strong convection is et al. (2003). Nevertheless, no other recent applications of
present. Convergence may also be difficult, especially this technique have been found in the literature pertaining
when non-linear sources are present in the simulation. Nev- to the food industry. However, it would seem conceivable
ertheless, favourable results have been attained when high that this type of method should take preference in CFD
order schemes have been used (Aubin et al., 2004; D’Agaro studies, especially where grid independency is unattainable
et al., 2006; Verboven, Datta, Anh, Scheerlinck, & Nicolai, due to computational power, or when first-order convection
2003). schemes are used (Nahor et al., 2005).
Applications of CFD in the food industry provided better insight into system design (Rouaud &
Applications in flow fields Havet, 2005).
The simulation of flow fields is the simplest application
of CFD in the food industry as no heat and mass transfer are Flow regimes in stirred tanks
involved in the calculations. Nevertheless, flow field mod- Many numerical studies on the isothermal mixing of liq-
elling is necessary in many food-processing applications uids within stirred tanks have been carried out over the last
ranging from ventilation systems to mixing tanks, and two decades (Aubin et al., 2004). The main problem facing
can provide essential information regarding system design. modellers is in the development of a system that proffers
Many scenarios including the positioning of fluid inlets and the most efficient blending of fluids. This depends on
outlets, and the influence of flow obstructions can be simu- a number of fundamental requirements including correct
lated by CFD. Flow field studies can also be used to assert choice of tank and impeller geometry, rotation speed and
the level of confidence that a solution has before more location of fluid inlet and outlets. Essential requirements
transport models are added. A number of CFD studies, for tank development are knowledge of power consump-
which have focused on the prediction of flow fields, are tion, flow velocity and mixing characteristics of different
summarised in Table 2. stirred tank configurations. Accurate CFD simulations can
afford this knowledge.
Modelling ventilation and contaminant dispersion Early attempts to solve the flow system and select suit-
Food production facilities continuously face challenges able impeller geometry using CFD were made by Ranade,
in reducing contamination risk by airborne microorgan- Joshi, and Marathe (1989). However, the conclusions drawn
isms. These facilities place heavy demands on ventilation from their results were questionable and conflicted with
systems to maintain indoor air quality at near optimal levels other studies (Nienow, 1997). Nevertheless, as computer
for processes to operate successfully. CFD coupled with ex- power became increasingly cheaper and CFD techniques
perimental techniques has been used to study ventilation rapidly advanced, numerical predictions have found better
flow fields and provide information on system design as agreement with experimental data.
a function of various aspects including room geometry, out- Some CFD studies have examined the effects of different
door climate, and contaminant sources and has become in- modelling approaches such as sliding mesh, moving refer-
creasingly popular over recent years (Burfoot et al., 1999; ence frames, and turbulence modelling. Aubin et al.
Quarini, 1995). Ventilation studies generally quantify the (2004) found that turbulence model had little effect on
efficiency of fresh air delivery and effectiveness of remov- mean flow compared to effects created by the choice of con-
ing contaminants through the use of ventilation scales. vection scheme or meshing approach. These types of studies
These can be computed within the framework of CFD provide people with beneficial information for finding a com-
and are related to the flow quantities that play an individual promise between modelling accuracy and calculation times.
part in the quality of the indoor environment. The most reg- A recent application has used CFD to solve the mixing re-
ularly used scales in the food industry are a function of the gime in a Kenics static mixer (Song & Han, 2005). CFD
mean age of air. A traditional method of calculating this has also been used to examine the effects of tank and impel-
was to determine the mean turnover time or residence ler parameters on enzyme deactivation (Ghadge, Patward-
time in a system irrespective of the amount of air recircula- han, Sawant, & Joshi, 2005), and blending behaviour for
tion. This led to the development of scales that gave a crude highly viscous flow (Fourcade, Wadley, Hoefsloot, Green,
description of the ventilation effectiveness (Quarini, 1995). & Iedema, 2001). Certainly, it is evident from these studies
Another more descriptive method of calculating the that CFD will continuously develop and optimise stirred
local mean age of air is to passively track the airflow in tank processes for many types of flow regimes.
the system. This is done by adding another equation to
the CFD model, which is derived from a passive scalar Validating flow fields
that statistically expresses the mean time taken for air to Validation is a necessary part of the modelling process
reach any arbitrary point after entering the system: and the yardstick of success is the level of agreement that
can be attained between numerical predictions and experi-
ments (Xia & Sun, 2002). CFD models do not generally

vq v m m vq contain all the microscopic details of the modelled process
þ rui q lam þ turb ¼1 ð10Þ due to computer limitations, and need some form of simpli-
vt vxi slam slturb vxi
fication to reduce the number of calculations in forming
a solution. These simplifications range from modelling
This has been used alongside a passive contaminant the fluid continuum to the numerical representation of the
transport equation in a recent clean room study and has physical process. Awareness of the inaccuracies associated
found reasonable agreement with experimental measure- with simplified CFD modelling has led to the publication of
ments (Rouaud & Havet, 2005). The development of venti- several flow field validation studies (Hoang et al., 2000;
lation scales based on the solution of these equations have Verboven, Scheerlinck, Baerdemaeker, & Nicolai, 2000).
T. Norton, D.-W. Sun / Trends in Food Science & Technology 17 (2006) 600e620
Table 2. Recent CFD applications in isothermal flows
Application Authors Code Dim Aim Time dep Turb model Extra models Order of CS GIS Agreement Outcome
with exp
Ventilated Mirade & FLUENT 6 3D To predict the AP Steady Std ke3, Porous media 1st No Reasonable Only ke3 model
rooms Daudin (2006) and gas distribution RNG, keu converged
Moureh & FLUENT 3D To validate the Steady RNG, RST d 3rd Yes RNG ¼ poor, RST predicted
Flick (2005) AP in refr truck RST ¼ good separation accurately
Airflow in Mirade & FLUENT 2D To determine Steady Std ke3 d 1st No Reasonable Optimised chiller
cold stores Picgirard (2001) the AP layout
Hoang et al. CFX 4.3 3D To build a Steady Std ke3, Porous media 1st No Reasonable Validated model
(2000) simplified model RNG
Stirred tank Montante, Moštěk, CFX 4 3D To assess Transient Std ke3 Lagrangian SM 1st No Good Validated model
Jahoda, & Magelli (2005) homogenisation
Kumaresan & 3D To analyse Transient Std ke3 SM NS No Reasonable Suitable designs
Joshi (2006) impeller design proposed
Static mixer Liu et al. (2006) FLUENT 5 3D To observe shear Steady None Non-New PL 2nd No Good Correlation developed
thinning between Dp and
Non-New PL
Song & Han FLUENT 6 3D To obtain Steady Std ke3 NS Yes Good Correlation developed
(2005) correlation for Dp in terms of three
parameters
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 renormal-
isation 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.
609
These studies outline in detail the simplified modelling and the warm shop environment. As the air curtain falls
techniques employed and place emphasis on the level of from the inlet at the top of the case, it entrains cooled air
agreement attained between predictions and measurements. from the back of each case compartment. This air passes
When good agreement is achieved, more studies can be car- over all the food products resulting in heat transfer from
ried out with these models without the need for comprehen- the food to the air, which allows the food to be maintained
sive flow field validation. at a predefined temperature. Heat transfer also occurs be-
tween shop environment and the air curtain. This causes
Applications in combined flow and heat transfer the temperature of the air curtain to increase and reduces
Food processes involving coupled fluid flow and heat the effectiveness of the air curtain in the lower compart-
transfer are ubiquitous in the food industry. Baking, sterili- ments of the display case (Foster et al., 2005).
sation and refrigeration represent applications where the ac- Numerous CFD studies on the ability of the air curtain to
curate quantification of combined flow and heat transfer maintain food at a predetermined temperature have been
can lead to improving both food quality and safety along- conducted over recent years (Cortella, Manzan, & Comini,
side reducing energy consumption. The recent advances 2001; D’Agaro et al., 2006; Foster et al., 2002, 2005;
in modern computing power mean that CFD can now be Navaz, Henderson, Faramarzi, Pourmovahed, & Taug-
used to accurately solve heat transfer problems in many walder, 2005). The effectiveness of the air curtain can be
food processes (Wang & Sun, 2003). This reduces the impaired by irregularities in the ambient shop environment;
amount of experimentation and empiricism associated thus, it is easily understood why display cases may be per-
with a design process. Table 3 summarises some of the re- ceived as one of the weakest links in the chilled food chain
cent studies that use CFD to predict combined fluid flow (Sun, 2002). Because these environmental irregularities
and heat transfer. cannot be directly incorporated into CFD models, steady-
state and two-dimensional assumptions are often made
Calculation of heat transfer coefficients that may in some cases blemish solution quality (D’Agaro
The rate of heat transfer between air and food products et al., 2006). Nevertheless, numerous successful design solu-
is proportional to the heat transfer coefficients and therefore tions have been developed on the basis of CFD studies
affects the surface and core temperatures of food products. (Cortella et al., 2001; Foster et al., 2005; Navaz et al., 2005).
Numerous CFD models have been used to calculate the lo- Foster et al. (2005) modelled different regions of a dis-
cal surface convective heat transfer from the cooling media play case to evaluate problems and develop subsequent
to food products. Many studies have found that ke3 turbu- design solutions. The study highlighted the exacerbating
lence models are generally poor at predicting solutions that effect of cabinet sidewalls on maintaining design tempera-
closely correspond to experimental data (Hu & Sun, 2001b; ture and energy consumption. D’Agaro et al. (2006) also
Kondjoyan & Boisson, 1997; Olsson, Ahrne, & Tragardh, found that sidewall effects were the main mechanism for
2004). Kondjoyan and Boisson (1997) attributed this reason increasing the rate of heat transfer with the ambient envi-
to the misrepresentation of the near-wall flow by the stan- ronment. Navaz et al. (2005) have shown through Digital
dard wall functions and suggested that this wall treatment Particle Image Velocimetry (DPIV) and CFD simulations
be abandoned for heat transfer calculations. that the entrainment of ambient environment exhibits a lin-
Olsson et al. (2004) and Olsson, Ahrne, and Tragardh ear relationship with the turbulence intensity in the air cur-
(2005) assessed the heat transfer characteristics of a jet im- tain. The need to maintain turbulence within the air curtain
pinging on a cylindrical food product under various condi- was also studied by Chen and Yuan (2005), who proposed
tions with the SST turbulence model. Heat transfer a minimum Reynolds number to enhance the sealing abil-
predictions agreed with measurements in the upper part ity of the air curtain. Their analysis provided a quantitative
of the cylinder but not in the wake. This was similarly ex- understanding of heat transfer from the ambient environ-
perienced by Kondjoyan and Boisson (1997). Verboven ment to the air curtain as a function of different Grashof,
et al. (2001) noted that due to the complexities involved Reynolds, and Richardson numbers. The considerable ad-
in resolving the governing equations in the boundary layer, vances made through the CFD modelling of display cases
obtaining appropriate heat transfer solutions was still an in the last few years will undisputedly lead to improving
active area of research in thermal analysis. their efficiency, and thus strengthen their link in the chilled
food chain.
Creating a thermal air barrier in refrigerated
display cases Heat transfer in the sterilisation process
The use of refrigerated display cases allows good visibil- Sterilisation is one of the many heat transfer applications
ity and ensures free access to stored food for shop cos- in which CFD is enjoying more widespread use. In the ther-
tumers. A virtual insulation barrier called the air curtain mal processing of foods, rapid and uniform heating is desir-
is developed by the recirculation of air from the top to able to achieve a predetermined level of sterility with
the bottom of the case (Cortella, 2002). This is a non- minimum destruction of the colour, texture and nutrients
physical barrier between cold air in the case compartments of food products (Jung & Fryer, 1999; Tattiyakul, Rao, &
T. Norton, D.-W. Sun / Trends in Food Science & Technology 17 (2006) 600e620
Table 3. Recent CFD applications in combined flow and heat transfer
Application Authors Code Dim Aim Time dep Turb Extra models Order of CS GIS Agreement Outcome
model with exp
Industrial Mirade, Daudin, FLUENT 6.0 3D To predict the Steady Std ke3 d 1st No Reasonable Temp sensors required
ovens Ducept, Trystram, AP and Temp for accurate validation
& Clement (2004)
Therdthai et al. CFD-ACE 2D þ 3D To predict the Steady þ NS d NS No Reasonable Optimised AP and
(2004a,b) AP and Temp transient Temp distribution
Microwave Verboven et al. CFX 4.3 3D To predict the Steady Laminar Radiation 3rd Yes Good Optimisation strategy
ovens (2003) RT, AP and HTC for uniform heating
Kocer & Karwe FLUENT 6.0 3D To predict the Steady Std ke3 Radiation NS Yes Good HT mainly a function of
(2005) AP and HTC impinging jet velocity
Drying Mirade (2003) FLUENT 5.4 2D To predict the Steady RST d 2nd Yes Limited AP homogeneity being
chambers AP in meat mainly a function of
dryer ventilation cycle
Margaris & PHOENICS 3.6 3D To optimise tray Steady Std ke3 d NS NS Limited Optimised tray
Ghiaus (2006) dryer arrangement þ AP
Spray dryers Huang et al. FLUENT 6.1 3D To validate Steady RNG Lagrangian NS Yes Good Better utilisation of chamber
(2003) the model atomisation with spinning disc atomiser
Harvie et al. CFX 4.3 3D To predict the Steady Std ke3 Lagrangian 3rd Yes Limited Wall interaction model leads
(2002) flow characteristics to under-prediction of particle
moisture
Cold stores Moureh & FLUENT 3D To validate Transient RST d 3rd Yes Reasonable Ventilation duct produced
Flick (2004) the turb model leads to more uniform airflow
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 stan-
dard, 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.
611
Datta, 2001). Traditionally, mean temperature approxima- Applications in combined flow, heat and mass transfer
tions have been used in analytical studies to calculate In the cooling or heating of foods, mass (moisture) trans-
both the sterility and quality of food products. However, fer between the food and environment is inevitable. This
CFD studies have proved that both of these parameters means that accurate predictions of heating and cooling sys-
are over-estimated using this approximation (Jung & Fryer, tems require a comprehensive suite of models describing
1999). fluid flow, heat transfer and mass transfer. However, the
The ubiquity of canned food has resulted in many nu- coupling of these models is complicated; therefore, CFD
merical studies investigating canned food quality and steril- is commonly used to predict the phenomena occurring in
ity. Two techniques of assessing these parameters with CFD applications involving combined flow, heat transfer and
are calculation of spore survival rate and temperature his- mass transfer (Hu & Sun, 2001b). Such applications in-
tory at the slowest heating zone (SHZ) (Siriwattanayotin clude cold stores, air blast chillers, ovens, and spray dryers.
et al., 2006). CFD has shown the transient nature of the Some recent examples of the CFD applications in this area
slowest heated zone (SHZ) in the sterilisation of a canned are summarised in Table 4.
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 Simulating the transport phenomena in cold
studies illustrated the considerable time needed for heat to storage facilities
be transferred throughout food in a static process. CFD Horticultural produce is commonly cooled by forced
studies have found that uniform heating can be obtained air-ventilation through ventilated packaging to achieve ef-
throughout the food by rotating the can (forced convection) ficient and uniform cooling. The cooling rate depends on
intermittently throughout the sterilisation process (Tattiya- the rate of heat and mass transfer between the cooling me-
kul et al., 2001; Tattiyakul, Rao, & Datta, 2002). Abdul dium and the produce, which is directly related to the air
Ghani et al. (2003) studied the combined effect of natural velocity within the packaging. Cost-effective design strat-
and forced convection heat transfer during sterilisation of egies proffered by CFD have led numerous studies to
viscous soup and showed that the forced convection was employ this technique in predicting the environmental var-
about four times more efficient than natural convection. iables within ventilated packaging and refrigerated store
More recently, CFD has been used to study the effect of rooms (Tassou & Xiang, 1998; Zou et al., 2006a,b). The
container shape on the efficiency of the sterilisation process storage process can be simulated in a CFD model by rep-
(Varma & Kannan, 2005, 2006). Conical shaped vessels resenting the contained goods as a porous medium by
pointing upwards were found to reach the appropriate ster- employing a predetermined void fraction and average
ilisation temperature the quickest (Varma & Kannan, 2006). diameter of the produce, and specifying the medium as a
Full cylindrical geometries performed best when sterilised source of heat and moisture. This method has in the past
in a horizontal position (Varma & Kannan, 2005). The ster- yielded reasonable agreement with measurements, although
ilisation of food pouches has also been studied using CFD it has been recognised that results could be further improved
(Abdul Ghani, Farid, & Chen, 2002). by adding more model details (Tassou & Xiang, 1998).
Other CFD studies have successfully used a two-phase
modelling technique to simulate cooling conditions within
Designing for thermal uniformity in drying chambers bulk containers (Nahor et al., 2005; Zou et al., 2006a). Hu
Drying of different types of food products has been and Sun (2001a,b) have also successfully examined the
a challenge faced by the food industry over the centuries. heat and mass transfer phenomena associated with the
Over recent years not only have substantial improvements air-blast chilling process through CFD simulations.
been made to traditional techniques such as tray and spray
drying but new innovative drying methods like pulse com- Modelling the spray drying process
bustion have been developed and optimised using CFD Spray drying is another traditional drying technique and
(Langrish & Fletcher, 2001). The non-uniformity of the is used to produce powders from products associated with
air-drying process is a common problem associated with the dairy, food and pharmaceutical industries. Its main ob-
batch type drying and CFD modelling techniques are em- jective is to create a product that is easy to store, handle and
ployed to provide design solutions to overcome deficiencies transport (Nijdam & Langrish, 2006). Many numerical
(Margaris & Ghiaus, 2006; Mathioulakis, Karathanos, & studies have been conducted to optimise spray dryers so
Belessiotis, 1998). Mathioulakis et al. (1998) were one of that the resultant product has the appropriate rheological
the first people to use CFD to model the airflow in properties, particle size distribution, and solubility to
a tray-drying chamber and highlighted the high level of achieve its desired function (Huang et al., 2003; Straatsma,
non-uniformity that existed in such processes. Recently Van Houwelingen, Steenbergen, & De Jong, 1999). Fig. 4
Margaris and Ghiaus (2006) used CFD to successfully op- illustrates the streamline trajectories of milk particles in
timise the tray arrangement and inlet configuration within a tall form spray dryer (Harvie, Langrish, & Fletcher,
a tray-drying chamber. 2002). In early studies, Straatsma et al. (1999) developed
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, the food industry. Powder formulations of food products
temperature, particle trajectories and particle drying behav- allow for longer shelf life and therefore presently act as
iour and two case studies were presented to illustrate the a primary mechanism for sustaining product quality over
ability of the model to optimise dryer design. Langrish long time periods. An issue of contention with food pow-
and Fletcher (2001) presented a comprehensive review of ders is maintaining the stability of ingredient functionality
the use of CFD in spray dryer modelling. Recent numerical from production right through to final powder application
studies have focused on investigating the dispersion and (Fitzpatrick & Ahrne, 2005). Any change in the properties
fouling rates of particles as well as their evaporation and of the ingredients or process conditions in the manufactur-
coalescence within a spray dryer (Athanasia, Adamopoulos, ing of a product can seriously impinge on the quality of
& Konstantinos, 2004; Nijdam, Guo, Fletcher, & Langrish, the product and the integrity of the processing system.
2004). Predicting the variation of food properties through the pro-
duction process presents many challenges to the CFD
Challenging issues confronting CFD modellers community. For example, a lot of work needs to be
Physical properties of fluids done in order to accurately predict the spatial variation
The production of food ingredients has evolved over re- of moisture content of powders in the spray drying pro-
cent years and it now holds a considerable market share in cess (Fletcher et al., in press). Adhesion and cohesion of
Shapes of corrugations
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, Non-
New 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
Successful prediction
RNG performed best
being able to inhibit
Model validated but
Moisture movement
limited in accuracy
gradients in food
and optimisation
due to pressure
Outcome
fouling
others ¼ limited
RNG ¼ good,
Reasonable
Reasonable
Reasonable
Agreement
with exp
Good
GIS
Yes
No
No
NS
NS
Order of CS
Fig. 4. Trajectories of milk particles in a spray dryer (Harvie et al.,

2002).
NS
NS
NS
NS
1st
Lagrangian model
two-phase model,
two-phase model
electromagnetic
particles and effects on fouling rates are also continuing

fouling model
Non-New PL,
Extra models
Mass transfer
areas of research in the food industry (Nijdam et al.,

2004). It has been recognised that with accurate knowl-
model
solver
edge 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 fac-
Turb model
RNG, LRN
tors (Langrish & Fletcher, 2003). However, it is also felt

Std ke3,
Std ke3
Std ke3
that CFD techniques are dubious as to whether they will

None
None
ever be useful for modelling real cohesive powders (Fitz-

patrick & Ahrne, 2005).
Time dep
Transient
Transient
Transient
Transient
Transient
Non-homogenous fluid domain

Both Eulerian and Lagrangian techniques can be used to
model flows with two or more phases, e.g. water vapour,
To predict fouling
To predict fouling
Table 4. Recent CFD applications in combined flow and mass transfer
To predict HTC
process of milk
airborne microbes and powder. The Eulerian representation

Validate CFD
Predict Temp
and moisture
treats the particulate phase as a continuum and describes

and WL
the temporal and spatial concentration of the flow. How-

in PHE
model
Aim
ever, the disadvantages which include loss of time history

rate
of particles, outweigh the potential benefits of this tech-

nique (Fletcher et al., in press). Moreover, the Eulerian con-
Dim
2D
3D
3D
3D
3D
cept is invalid when particles of size z1 mm are present in

the flow regime (Reynolds, 1997). Lagrangian stochastic
FLUENT 5.3
PHOENICS
Developed
models, i.e. random flight models (using a Lagrangian au-

in-house
tocorrelation function) allow particles that are thrown into

Code
CFX
CFX
the near boundary region of the flow stream to experience

velocities lower than those sufficient to maintain streamline
Dincov et al.
trajectory. Particles then disengage from the turbulent re-

et al. (2004)
Nahor et al.
Jun & Puri
Hu & Sun
Athanasia
gime and become deposited on the boundaries. Lagrangian

Authors
(2001a)
(2006)
(2005)
(2004)
and Eulerian techniques have been used by the spray

dryer community, with the former allowing far more oppor-
tunities for design as it can take into account turbulent
Spray drying
Application
Cold stores
exchangers
Microwave
structures and inertia crossing (Fletcher et al., in press).

Plate heat
Air-blast
chilling
However, it has been noted that rigorous random flight

model.
oven
models are necessary to ensure accurate predictions (Bur-

foot et al., 1999). Moreover, a lot of work still has to be
done to ensure comprehensive validation of such models mesh refinement in the boundary layer in order to satisfac-
(Harral & Burfoot, 2005). torily represent the flow regime, i.e. yþ 1. Conversely,
Because CFD models consider the movement of fluid as high Reynolds number turbulence models use empirical re-
a continuum, flows involving equal amounts of both fluids lationships arising from the log-law condition that describe
and powders cannot be modelled solely by CFD. Other the flow regime in the boundary layer of a wall. This means
techniques must be employed to account for the complex that the mesh does not have to extend into this region and
interactions of the individual particles. A modelling tech- that the number of cells involved in a solution is reduced.
nique called the discrete element method (DEM) has re- The use of this method requires 30 < yþ < 500 (Versteeg
cently been used with good qualitative accuracy to model & Malalsekeera, 1995), although yþ z 10 is also accept-
a large range of granular mixing applications (Bertrand, able (Sorensen & Nielsen, 2003). Generally, these wall
Leclaire, & Levecque, 2005). DEM has the ability to take treatment assumptions do not adversely affect solutions
into account powder cohesion and can also be coupled and many studies have employed them with relative impu-
with CFD to simulate the transport of powder materials nity provided yþ constraints specific to the turbulence
through pneumatic pipes (Li et al., 2003). However, DEM model were adhered to. Unfortunately, standard wall treat-
is very computationally expensive and often simulations re- ment functions have failed to satisfactorily predict the
quire many days before arriving at a solution. This has phenomenon in applications involving the heat transfer
meant that the extension of this model to other modes of associated with impinging airflow (Kondjoyan & Boisson,
dense gasesolids flow exhibited by fine powders (particle 1997). Recent studies have successfully circumvented this
size less than 100 mm) is impractical. Therefore, it may problem by using a blended wall treatment assumption
take some time before such techniques can be incorporated that uses either the low Reynolds number or high Reynolds
into process design (Fitzpatrick & Ahrne, 2005). number relationship depending on the local flow condition
in the wall region (Jensen & Friis, 2004; Olsson et al.,
Simplification of turbulence 2004).
One of the main issues faced by the food industry over It should be noted that before embarking on CFD mod-
the last two decades is the lack of understanding surround- elling, the limitations of the available turbulence models
ing the efficient discrete quantification of turbulence in and their associated wall functions must be taken into con-
fluids and its effect on system performance. Over the years, sideration. Models appropriate for the study should be cho-
simplifying assumptions have been made by turbulence sen based on the experiences of similar applications in the
modellers in order to make this problem more approach- literature. Meshing should be then carried out using an iter-
able. However, these assumptions can often be unreason- ative procedure that involves repeated CFD solution and
able in many applications. A typical example is the mesh adjustment until the yþ criterion is satisfied (Sorensen
Reynolds number assumption, whereby either a high or & Nielsen, 2003).
low Reynolds number flow regime is assumed a priori to
a simulation. The most outstanding misapplication of this Dimensions of the fluid domain
is in studies where turbulent and laminar flow regimes co- Large-scale simulations have the potential to be very
exist, e.g. clean rooms or food factories. Recent modelling grid point demanding and can therefore take a large amount
advancements have addressed this issue by developing of computing time and effort to obtain a detailed field solu-
a predictive laminar to turbulent flow transition model, tion. CFD modellers in the food industry have simplified
which has recently been incorporated in the ANSYS computational models to cut down on both pre-processing
CFXÒ 10.0 (ANSYS CFX Release, 2006) software. Unfor- and solving time. For example, three-dimensional systems
tunately, as of yet no research employing this model is have been modelled in two dimensions (Cortella, 2002),
available. Certainly, modern variants of the ke3 model and large-scale models have been reduced in size by mod-
have proved to be more successful than the standard ke3 elling only the region of interest (Foster et al., 2005). Even
model in similar studies, and in applications involving though these models have been reasonably successful, it
swirling flow regimes or jet impingement (Olsson et al., should be recognised that these simplifications can blemish
2005; Rouaud & Havet, 2002). Nevertheless, from pub- the quality of solutions.
lished studies it can be concluded that confidence in the In the physical world, all objects occupy a three-dimen-
ke3 model can be upheld in other flow applications pro- sional space. Thus, to accurately predict the phenomena
vided good agreement is found with measurements under occurring in any system, each dimension must be repre-
grid independent conditions (D’Agaro et al., 2006). sented in a model. This is where CFD has an advantage
Another feature of RANS turbulence models is the near- over many other analytical techniques. However, some
wall treatment of turbulent flow. Treatment of the near-wall applications in the food industry are on such a large scale
flow in all CFD software packages is specialised according that modern workstations are not yet capable of efficiently
to the employed turbulence model. For example, low Rey- yielding feasible CFD predictions (Mirade, 2003).
nolds number turbulence models solve the governing equa- Moreover, in other applications such as refrigerated display
tions all the way to the wall. This requires a high degree of cases the interesting features of flow phenomena are not
occurring in the three dimensions (Cortella, 2002). The must be removed from the simulation. Some CFD packages
two-dimensional modelling technique assumes that the offer means of locating these cells. However, in many cases
length of a system is much greater than its other two dimen- the CFD modeller often resorts to using his/her experience
sions, and that the flow is normal to the system’s length. with a CFD software package to assert the quality of the
This assumption essentially disregards the effects of the mesh.
confining geometry and will therefore preclude accurate
solution development, unless it can be explicitly shown
through experiments that three-dimensional flows do not Time-step selection
impose any effects on the modelled system (Cortella, Many of the flow regimes encountered in the food indus-
2002; Mirade, 2003). In any case, three-dimensional simu- try are unsteady. Transient processes arise as a result of
lations have provided better predictions and consequently either moving boundaries, e.g. impeller blades in stirred
should be used if at all possible (D’Agaro et al., 2006; tanks, unsteady boundary conditions, e.g. variable flow
Mirade, Kondjoyan, & Daudin, 2002). fans, or inherent physical instabilities, e.g. vortex shedding
Other assumptions used in the literature include those behind obstacle in free-stream flow. In these cases, a steady-
involved when modelling the region of interest of large sys- state flow regime does not exist and numerical difficulties
tems, i.e. refrigeration display cabinets (Foster et al., 2005), are often encountered when trying to solve the steady gov-
and those used when integrating CFD computations with erning equations (D’Agaro et al., 2006). Nonetheless,
analytical models and experimental data in optimisation a steady solution can be ‘forced’, which means that some
of system design, i.e. food chillers (Mirade et al., 2002). constraining condition can be implemented to suppress
Although these novel techniques may yield predictions in the unsteady features of the flow regime. These typically in-
reasonably short time periods, the errors associated with clude one or more of the following: first-order convection
the assumptions may preclude development of accurate schemes, dissipative turbulence models (standard ke3
solutions (Mirade et al., 2002). model), and two-dimensional or symmetrical boundary
Precise predictions of the phenomena in large-scale conditions. Because this forcing action does not exist in na-
systems may not be achievable until the capacity and ture, the credibility of solutions arising from such computa-
calculation power of workstations is developed further. tions has been questioned (D’Agaro et al., 2006).
Nevertheless, reasonable solutions can be presently attained Time stepping is an important mechanism that allows
provided good modelling practices are enforced including a CFD solution to march forward in time. An optimum
circumspective selections of turbulence model and near- time-step can be considered as a trade-off between compu-
wall treatment, convection scheme, and time-step. Heat tational efficiency, temporal accuracy, and stability of the
and mass transfer must also be taken into account espe- employed numerical scheme. Explicit numerical schemes
cially when it is conceived that these processes may influ- generally require time-steps that are less than or equal to
ence the flow regime. Additionally, concurrent validation of the CFL (CouranteFriedrichseLewy) condition in order
predictions with experimental measurements is paramount to retain stability (Courant et al., 1928). To uphold this cri-
for the future success of simplified CFD modelling. terion, time-steps usually must be very small. Conse-
quently, the computational overhead associated with
Mesh arrangement explicit schemes has impeded their use in industry. The
Another important issue that arises is concerned with the maximum time-step selection of implicit schemes is
accurate discrete numerical representation of the fluid do- bounded by the accuracy requirements of the simulation.
main. In CFD, the computational mesh provides the spatial Therefore, the time-step must be small enough to resolve
discretisation of the governing equations and, especially in the frequencies of importance/interest in the unsteady phe-
steady-state simulations, is a primary vehicle for enforcing nomenon being modelled. This requires some intuitive
accurate predictions of the fluid continuum. To achieve knowledge of the flow a priori to the modelling exercise.
a good level of accuracy, one must ensure that the mesh Generally, an appropriate characteristic length and velocity
is appropriately refined in areas of interest and in regions of the problem is necessary in order to determine the dom-
where gradients occur in the flow field. Unstructured mesh- inant frequency of the flow regime. Sometimes, this can be
ing features generally overcome difficulties associated with got from non-dimensional numbers such as the Stroudal
mesh refinement. Nevertheless, problems can still arise, and number, from experimental data, or from previous compu-
even in recent studies the mesh has precluded the use of tations. An assumption of this frequency does not have to
high order convection schemes and good quality turbulence be precise in the first instance, as it can be refined in sub-
models (Mirade et al., 2006). In some cases these difficul- sequent computations depending on the desired level of ac-
ties are unavoidable but in many others, diagnosing and re- curacy and what is demanded of the simulation. Using this
pairing the problematic regions of the mesh can obviate technique should result in a small number of outer-
such difficulties. This means that to obtain an accurate iterations required to converge each time-step, which has
and efficient representation of convective and diffusive been shown to be the most accurate way of simulating
fluxes, cells with high aspect ratios or highly skewed cells transient flows (Liu, Moser, Gubler, & Schaelin, 2003).
Opportunities for the food industry and benefits industry by enhancing confidence and efficiency in sterili-
for consumer sation processes (Welti-Chanes et al., 2005).
Processing system design The transport of airborne microbes is significant in
Enhancing the design of systems for the production of high-care food factories and CFD simulations have
food products has benefits for both the food industry and been used effectively to devise strategies that minimise
consumer alike, and requires research and development the movement of contaminated air towards food products
of new tools and processing methodologies. Alongside (Burfoot et al., 2000). Further advances in physical mod-
the expansion of the food industry, energy and workforce elling techniques will allow the dynamic mapping of the
costs are growing rapidly. Oil prices have reached levels airborne particle trajectories to be predicted before
not seen since the crisis in the nineteen seventies. Conse- implementing cleaning strategies (Harral & Burfoot,
quently, the impetus in recent research has been directed 2005).
towards the development of processing systems that can
integrate multiple operations, which, depending on the
requirements of the system, allow the coupling and un- Conclusions
coupling of elementary processes (Charpentier, 2002). The objective of this review is to shed light not only
For example, the development of food powders requires on the recent intricacies of fluid flow expounded by lead-
both the drying and transport of ingredients. The governing academics but on the remunerative advantages that
ing dynamics in such systems include coupled heat and CFD can offer in a commercial setting. CFD has played
mass transfer and require in-depth knowledge for optimi- an active part in system design including refrigeration,
sation and development. CFD modelling can be seen as sterilisation, ventilation, mixing and drying. This has
the next progressive step from expensive laboratory stud- been aided by the ability of commercial companies to
ies, and can account for the complex geometries experi- conform to the needs of the food industry. The recent de-
enced in industry to predict the governing phenomena of velopments in CFD include greater refinement in areas of
the processing system in an unobtrusive manner. As a adaptive meshing, moving reference frames and solver
result of CFD modelling, processing systems have been efficiency. Physical modelling has also reached levels
reduced in size and optimised to become more energy of higher sophistication with turbulence and multiphase
efficient. CFD can then create a climate in which both models being developed and validated by numerous ex-
industry and consumer can benefit, and food products perts and subsequently employed in the chemical and
can be developed with better equipment performance, food industry. Notwithstanding this, the CFD modeller
less pollution impact, faster time to market and lower must maintain high level of accuracy during the model-
design and production costs. ling process to uphold confidence in CFD predictions.
This means that concurrent experimentation must be car-
ried out to validate predictions, particularly where simpli-
Product quality fying assumptions are incorporated into the model.
Food quality is an outstanding issue in food industry. Undoubtedly, with current computing power progressing
The importance of food quality has heightened over recent unrelentingly, it is conceivable that CFD will continue
years in tandem with the lifestyle changes experienced by to provide explanations for more fluid flow, heat and
many people. Convenience foods are becoming more prev- mass transfer phenomena, leading to better equipment de-
alent and demand for ready-to-eat products, such as fresh sign and process control for the food industry.
delicatessen and frozen meals is growing rapidly (Burfoot,
Brown, Xu, Reavell, & Hall, 2000). Sterilisation and hy-
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Trends in Food Science & Technology 17 (2006) 600e620

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

Company Location Software Features Price Recently published

PHOENICSÒ (CHAM Ltd.) The eddy viscosity hypothesis

in the CFD calculations at the interface between rotating Convergence techniques

Model validated but

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

particles and effects on fouling rates are also continuing

areas of research in the food industry (Nijdam et al.,

edge of these effects, process strategies can be designed

tors (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 (Fitz-

Non-homogenous fluid domain

airborne microbes and powder. The Eulerian representation

treats the particulate phase as a continuum and describes

the temporal and spatial concentration of the flow. How-

ever, the disadvantages which include loss of time history

of particles, outweigh the potential benefits of this tech-

cept is invalid when particles of size z1 mm are present in

models, i.e. random flight models (using a Lagrangian au-

tocorrelation function) allow particles that are thrown into

the near boundary region of the flow stream to experience

trajectory. Particles then disengage from the turbulent re-

gime and become deposited on the boundaries. Lagrangian

and Eulerian techniques have been used by the spray

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 (Bur-

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