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Critical Reviews in Food Science and Nutrition

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Computational Fluid Dynamics in the Design andAnalysis of Thermal Processes: A Review of RecentAdvances

Tomás Norton , Brijesh Tiwari & Da-Wen Sun

To cite this article: Tomás Norton , Brijesh Tiwari & Da-Wen Sun (2013) Computational FluidDynamics in the Design and Analysis of Thermal Processes: A Review of Recent Advances, CriticalReviews in Food Science and Nutrition, 53:3, 251-275, DOI: 10.1080/10408398.2010.518256

To link to this article: https://doi.org/10.1080/10408398.2010.518256

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Critical Reviews in Food Science and Nutrition, 53:251–275 (2013)Copyright C©© Taylor and Francis Group, LLCISSN: 1040-8398 / 1549-7852 onlineDOI: 10.1080/10408398.2010.518256

Computational Fluid Dynamics in theDesign and Analysis of ThermalProcesses: A Review of RecentAdvances

TOMAS NORTON,1 BRIJESH TIWARI,2 and DA-WEN SUN3

1Engineering Department, Harper Adams University College, Newport, Shropshire, UK2Manchester Metropolition University, UK3FRCFT Group, School of Biosystems Engineering, Agriculture and Food Science Center, University College Dublin,National University of Ireland, Belfield, Dublin, Ireland

The design of thermal processes in the food industry has undergone great developments in the last two decades due to theavailability of cheap computer power alongside advanced modelling techniques such as computational fluid dynamics (CFD).CFD uses numerical algorithms to solve the non-linear partial differential equations of fluid mechanics and heat transfer sothat the complex mechanisms that govern many food-processing systems can be resolved. In thermal processing applications,CFD can be used to build three-dimensional models that are both spatially and temporally representative of a physical systemto produce solutions with high levels of physical realism without the heavy costs associated with experimental analyses.Therefore, CFD is playing an ever growing role in the development of optimization of conventional as well as the developmentof new thermal processes in the food industry. This paper discusses the fundamental aspects involved in developing CFDsolutions and forms a state-of-the-art review on various CFD applications in conventional as well as novel thermal processes.The challenges facing CFD modellers of thermal processes are also discussed. From this review it is evident that present-dayCFD software, with its rich tapestries of mathematical physics, numerical methods and visualization techniques, is currentlyrecognized as a formidable and pervasive technology which can permit comprehensive analyses of thermal processing.

Keywords Computational fluid dynamics, CFD, drying, sterilization, cooking, modelling, heating

INTRODUCTION

The application of the principles of fluid motion and heattransfer to design problems in the food industry has undergoneremarkable development in the last couple of decades. Prob-lems involving heat and mass transfer, phase change, chemicalreactions, and complex geometry, which once required eitherhighly-expensive experimental rigs or over-simplified compu-tations, can now be modelled with a high level of spatial andtemporal accuracy on personal computers. This remarkable pro-gression is due to the development of advanced computer designand analysis tools, like computational fluid dynamics (CFD), asthese tackle complex problems in fluid mechanics and heat trans-fer, and many other physical processes with important industrial

Address correspondence to Tomas Norton, Engineering Department,Harper-Adams University College, Newport, Shropshire TF10 8NB, UK.E-mail: tnorton@harper-adams.ac.uk

applications. CFD is based on numerical methods that predictthe governing transport mechanisms over a multi-dimensionaldomain of interest and its physical basis is rooted in classi-cal fluid mechanics. Since the first computer implementationof CFD in the 1950s, it has continued to be developed con-temporaneously with the digital computer (Norton and Sun,2007). In its present-day form, CFD can be used to quantifymany complex thermal-hydraulic phenomena, and as a resulthas developed into a multi-faceted industry, generating billionsof Euros worldwide within a vast range of specializations (Xiaand Sun, 2002; Abbott and Basco, 1989).

In the food industry, thermal processes are widely recognizedas major preservation techniques, which can be applied by a pro-cessor to render a food product commercially sterile, as well asto modify sensory characteristics (Richardson, 2001). Duringthe thermal processing of foods, thermo-fluid dynamics governmany processes, and are involved in almost every process. Due tothe complexity of the physical mechanisms involved in thermal

251

252 T. NORTON ET AL.

processing, quantifying the phenomena must involve sophisti-cated design and analysis tools. Physical experimentation mayallow for direct measurement; however, a comprehensive analy-sis would not only necessitate expensive equipment and requireconsiderable time and expertise, but could also be intrusive andtherefore affect the quality of the results (Verboven et al., 2004).Fortunately, ubiquitous processes such as blanching, cooking,drying, sterilization, and pasteurization which rely on thermalexchange to raise a product thermal-center to a pre-specifiedtemperature, are highly amenable to CFD modelling, and haveunarguably contributed to its exponential take-up witnessed overrecent years. Coupled with other technological advancements,CFD has led to an improvement in both food quality and safetyalongside reducing energy consumption used in industrial pro-cesses, and has reduced the amount of empiricism associatedwith a design process (Norton and Sun, 2007).

General applications of CFD in the food industry have alsobeen reviewed by some authors (Scott and Richardson, 1997;Xia and Sun, 2002; Anandharamakrishnan, 2003; Norton andSun, 2007). All of these reviews have concluded that CFD is apowerful and pervasive tool for process and product improve-ment in food processing industry. Some of the many fascinat-ing subjects in which CFD has been applied include baking(Chhanwal et al., 2010), thermal sterilization (Abdul Ghaniet al., 2001), pasteurization (Kızıltas et al., 2010), mixing (Met-calfe and Lester, 2009), refrigeration (Moureh et al., 2009),spray-freeze drying (Anandharamakrishnan et al., 2010), coldstorage (Delele et al., 2009), and fluidized drying (Markowskiet al., 2010). Some of the current CFD software providers alongwith the various features of different CFD packages are listedin Table 1.

In the most recent review aimed specifically at CFD applica-tions in thermal processing, Verboven et al. (2004) highlightedthe existing limitations and challenges that face the current usersof this technology. In light of the rapid developments in boththermal processing and CFD technology that has taken placeover recent years, it is necessary to provide a critical and com-prehensive account of the latest advances, made through suc-cessful applications in research. First, the need for CFD to modelthermal processes will be presented. The main equations govern-ing the physical mechanisms encountered in thermal processingwill then be discussed, followed by an extensive overview of theconventional processes, which have been modelled with CFD.A focus of the CFD modelling studies of emerging thermalprocessing technologies will then be highlighted. Finally, anoverview of the challenges that are still encountered in the CFDmodelling of thermal processes will be given.

THE NEED FOR CFD MODELLING IN THERMALPROCESSING

Owing to the complex thermo-physical properties of food,heat transfer to and from foods can stimulate complex chemicaland physical alterations in them. Nowadays, with both foodpreservation and safety being equally important objectives of

Table 1 Commercial CFD software codes with associated companies andfeatures

Company CFD Code Features

CHAM Ltd.www.cham.co.uk

PHOENICS 2009 LEVL, SG, FV

ANSYS, Inc.www.ansys.com

ANSYS Fluent V12ANSYS CFXV12

USG, LAG + PT, MPH +IPHUSG, FV, FE CREM

CD Adapco Groupwww.cd-adapco.com

STAR-CD V4.12STAR-CCM+V5.02

STAR-CD: USG, LAG +PT, MPH + IPHSTAR-CCM+:Intuitive user interface,USG, LAG + PT, MPH+ IPH

Flow Science, Inc.www.flow3d.com

FLOW-3D 8.2 Advanced movingobstacle capabilities;SG, LAG + PT, MPH+ IPH

ADINA, Inc.www.adina.com

ANDINA-F FE + FV, SG, ALE

Metacomp Technologies, Inc.www.metacomptech.com

CFD++ UFG, LAG + PT, MPH +IPH

Abbreviations: FV, finite volume; SG, structured grid; LVEL, wall distanceturbulence model; USG, unstructured grid; LAG + PT, coupled Lagrangianand particle tracker; MPH + IPH, coupled multiphase and interphase models;CREM, complex rheology and electrohydrodynamic modeling; FE, finite ele-ment; ALE, arbitrary Lagrangian and Eulerian formulation; UFG, unified gridfor ease of treatment of complex geometries.

processing, it is necessary to promote quality characteristicsof food while eradicating the threat of spoilage. For this tohappen efficiently the appropriate temperature and duration ofheating need to be known. Mathematical models permit therepresentation of a physical process, from the analysis of mea-sured data or physical properties, over a range of experimentalconditions. During thermal processing heat transfer occurs dueto one or more of three mechanisms; conduction, convection,and radiation, and depending on the thermal process onemechanism is usually dominant (Wang and Sun, 2003). As thethermal exchange phenomena are either distributed in spaceor, space and time, their fundamental representation is bymeans of partial differential equations (PDE’s). These transportequations can be solved analytically for a small number ofboundary, and initial conditions (Nicolaı et al., 2001). With thisin mind, CFD codes have been developed around numericalalgorithms that can efficiently solve the PDEs governing allfluid flow, heat transfer, and many other physical phenomena.CFD techniques can be used to build distributed parametermodels that are spatially and temporally representative ofthe physical system, thereby permitting the achievement ofa solution with a high level of physical realism. With recentversatility, adaptability, and efficiency gained from progress ingeometrical, physical, and numerical modelling CFD can easilybe applied to conventional and novel thermal food processesranging from experimental models to the scaled-up systems(Kuriakose and Anandharamakrishnan, 2010).

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 253

NUMERICAL REPRESENTATION OF THE THERMALPROCESSES

Numerical Techniques

CFD code developers have a choice of many different numer-ical techniques to discretize the transport equations. The mostimportant of these include finite difference, finite elements, andfinite volume. The finite difference technique is the oldest oneused, and many examples of its application in the food industryexist. However, due to difficulties in coping with irregular ge-ometry, finite difference is not commercially implemented. Fur-thermore, the current trend of commercial CFD coding is aimedtowards developing unstructured meshing technology capableof handling the complex three-dimensional geometries encoun-tered in industry. Therefore, the prospects of finite differencebeing used in industrial CFD applications seem limited.

Finite element methods have historically been used in struc-tural analysis where the equilibrium of the solution must be sat-isfied at the node of each element. Nicolaı et al. (2001) provideda short introduction to the use of the finite elements method inconduction heat transfer modelling, and it will not be discussedhere. Suffice to say that as a result of the weighting functionsused by this method, obtaining a three-dimensional CFD so-lution with a large number of cells is impractical at present.Therefore, finite elements are not generally used by commer-cial CFD developers, especially as many of these CFD codesare marketed towards solving aerodynamic problems. Nonethe-less, finite elements methods have enjoyed use in the mod-elling of electromagnetic heating in microwave ovens (Verbovenet al., 2007; Geedipalli et al., 2007); vacuum microwave drying(Ressing et al., 2007); radio frequency heating of food (Marraet al., 2007), conduction, and mass transport during drying(Aversa et al., 2007).

With finite volume techniques the integral transport equationsgoverning the physical process are expressed in conservationform (divergence of fluxes) and the volume integrals are thenconverted to surface integrals using Gauss’s divergence theo-rem. This is a direct extension of the control volume analysis thatmany engineers use in thermodynamics and heat transfer appli-cations, etc., so it can be easily interpreted. Thus, expressing theequation system through finite volumes forms a physically in-tuitive method of achieving a systematic account of the changesin mass, momentum, and energy, as fluid crosses the boundariesof discrete spatial volumes within the computational domain.Also, finite volume techniques yield algebraic equations thatpromote solver robustness.

The Generic Equation and its CFD Approximation

The basic requirement of CFD is to obtain a solution to a set ofgoverning PDE’s of the transported variable. As discussed abovethe transport phenomena are generally described by commercialCFD developers using the finite volume method. The generic

conservation convection-diffusion equation, after application ofGauss’s theorem to obtain the surface integrals can be describedas follows:

∫V

∂ρφ

∂t+

∫A

n.(ρUφ)dA =∫

A

n.(�φgrad φ)dA +∫

V

Sφ (1)

The conservation principle is explicit in Eq. (1), that is, therate of increase of φ in the control volume plus the net rateof decrease of φ due to convection is equal to the increasein φ due to diffusion and an increase in φ due to the sources(Versteeg and Malaskeera, 1995). For a numerical solution, boththe surface and volume integrals need to be solved on a dis-crete level, which means numerical interpolation schemes arerequired. As the convection term, the only non-linear term inthe equation, needs to be approximated at each mesh elementface, it presents the greatest challenge in allowing the numericalscheme to preserve properties such as the stability, transportive-ness, boundedness, and accuracy of a solution. For the samereason, numerical schemes are often called convection schemesas the accurate and stable representation of the convection termis a major requirement (Patankar, 1980). The reader can refer tostandard CFD textbooks, for example, those of Patankar (1980),Versteeg and Malaskeera (1995) for a complete discussion onthe various properties of convection schemes.

The Numerical Mesh

The volume mesh in a simulation is a mathematical descrip-tion of the space or the geometry to be solved. One of the majoradvances to occur in meshing technology over recent years wasthe ability for tetrahedral, hexahedral hybrid and even polyhe-dral meshes to be incorporated into commercial codes. Thishas allowed mesh to be fit to any arbitrary geometry, therebyenhancing the attainment of solutions for many industrial ap-plications. In addition, some modern commercial CFD codespromote very little interaction between the user and individ-ual mesh elements, with regard to specifying the physics of theproblem. Through this decoupling of the physics from the mesh,the user is allowed to concentrate more on the details of the ge-ometry, and the transfer of simulation properties and solutionsfrom one mesh to another is easier when the mesh independenceof a simulation needs to be studied or when extra resolution isrequired.

As a result of unstructured meshing, local mesh refinementwithout creating badly distorted cells is achievable. However,as with structured meshes, mesh quality is still an importantconsideration, as poor quality can affect the accuracy of thecalculated convective and diffusive fluxes. A common measureof quality is the skewness angle, which determines whetherthe mesh elements permit the computation of bounded diffusionquantities. Code developers may use the actual angle or an indexbetween 0 and 1 as the metric for skewness. When a skewnessangle of 0o is obtained, the vector connecting the center of

254 T. NORTON ET AL.

two adjacent elements is orthogonal to the face separating theelements; this is the optimum value. With skewness angles of90o or greater problems in terms of accuracy are caused, thesolver may even divide by zero. Other than this, the versatilityof these meshes has led to an increased take-up by the CFDcommunity and their uses are finding accurate solutions in manyapplications within the food industry.

THE EQUATIONS GOVERNING THERMALPROCESSING

The Navier-Stokes Equations

The mathematical formulation of fluid motion has been com-plete for almost two hundred years, since the emergence of threevery important scientists in the field of fluid mechanics. The firstone being the Swiss mathematician and physicist Leonhard Eu-ler (1707–1783) who formulated the Euler equations, whichdescribe the motion of an invisid fluid based on the conserva-tion laws of physics, now defined as classical physics; namelythe conservation of mass, momentum, and energy. The Frenchengineer and physicist, Claude-Louis Navier (1785–1836), andthe Irish mathematician and physicist, George Gabriel Stokes(1819–1903) later introduced viscous transport into the Eulerequations by relating the stress tensor to fluid motion. The re-sulting set of equations now termed the Navier-Stokes equationsfor Newtonian fluids have formed the basis of modern day CFD(Anon., 2007).

∇ · −→v = 0 (2)

ρ∂vi

∂t+ ρ

−→v · ∇−→v i = −∇p + μ∇2−→v i + ρg (3)

Equation (2) is a mathematical formulation of the law of con-servation of mass (which is also called the continuity equation)for a fluid element where −→v consists of the components of −→v i ,the solution for each requires a separate equation. The conserva-tion of mass states that the mass flows entering a fluid elementmust balance exactly with those leaving for an incompressiblefluid. Equation (3) is the conservation of momentum for a fluidelement, that is, Newton’s second law of motion, which statesthat the sum of the external forces acting on the fluid particle isequal to its rate of change of linear momentum.

Any fluid that does not obey the Newtonian relationship be-tween the shear stress and shear rate is called a non-Newtonianfluid. The shear stress in a Newtonian fluid is represented by thesecond term on the right hand side of Eq. (2). Many food pro-cessing media have non-Newtonian characteristics and the shearthinning or shear thickening behavior of these fluids greatlyaffects their thermal-hydraulic performance (Fernandes et al.,2006). Over recent years, CFD has provided better understand-ing of the mixing, heating, cooling, and transport processes ofnon-Newtonian substances. Of the several constitutive formulas

that describe the rheological behavior of substances, which in-clude the Newtonian model, power law model, Bingham modeland the Herschel Bulkley model, the power law is the mostcommonly used in food engineering applications (Welti-Chaneset al., 2005). However, there are some circumstances wheremodelling the viscosity can be avoided as low velocities per-mit the non-Newtonian fluid to be considered Newtonian, forexample, as shown by Abdul Ghani et al. (2001).

The Heat Transfer Equation

The modelling of thermal processes requires that the energyequation governing the heat transfer within a fluid system to besolved. This equation can be written as follows:

ρ∂

(cp

−→v i

)∂t

+ ∇ (−→v · T) = λ∇2T + sT (4)

The transport of heat in a solid structure can also be con-sidered in CFD simulations, and becomes especially importantwhen conjugate heat transfer is under investigation, in whichcase it is important to maintain continuity of thermal exchangeacross the fluid-solid interface (Verboven et al., 2004). TheFourier equation which governs heat transfer in an isotropicsolid can be written as:

∂(ρcp

−→v i

)∂t

= λ∇2T + sT (5)

The main difference between the two equations is that theFourier equation lacks a convective mixing term for temperature,which is incorporated into Eq. (4). For a conjugate heat transfersituation where evaporation at the food surface is considered,and where the heat transfer coefficient is known, the boundarycondition for Eq. (5) may be written as

h(Tbf − Ts) + εσ (T 4bf − T 4

s ) = −λ∂T

∂n− α · Ns (6)

where ε is the emission factor coefficient and σ is the Stefan-Boltzmann constant. Heat transported by radiation and convec-tion from air to food raises the sample temperature and also goestowards evaporating the free water at the surface (Aversa et al.,2007). The solution of Eq. (6) can be used on the food surfaceto calculate the local heat transfer coefficients (Verboven et al.,2003),

h =−λ∂T

∂n

∣∣surface

(Tbf − Ts)(7)

Equation (7) can be used provided the surface temperature isassumed independent of the coefficient during calculations.

The equation of state relates the density of the fluid to itsthermodynamic state, that is, its temperature and pressure. The

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 255

profiles of thermal processing variables, that is, temperature,water concentration, and fluid velocity, are functions of densityvariations caused by the heating and cooling of fluids. Sincefluids flows encountered in thermal processing can be regardedas incompressible there are two means of modelling the densityvariations that occur due to buoyancy. The first is the well knownBoussinesq approximation (Ferziger and Peric, 2002). This hasbeen used successfully in many CFD applications (Abdul Ghaniet al., 2001):

ρ = ρref

⌊1 − β(T − Tref )

⌋(8)

The approximation assumes that the density differentials ofthe flow are only required in the buoyancy term of the momen-tum equations. In addition, a linear relationship between tem-perature and density, with all other extensive fluid propertiesbeing constant is also assumed. This relationship only considersa single-component fluid medium; however, by using Taylor’sexpansion theorem the density variation for a multi-componentfluid medium can also be derived.

Unfortunately, the Boussinesq approximation is not suffi-ciently accurate at large temperature differentials (Ferziger andPeric, 2002). Therefore, in such cases another method of achiev-ing the coupling of the temperature and velocity fields is neces-sary. This can be done by expressing the density difference bymeans of the ideal gas equation:

ρ = pref M

RT(9)

This method can model density variations in weakly com-pressible flows, meaning that the density of the fluid is dependenton temperature and composition but small pressure fluctuationshave no influence.

The Equation for Mass Transfer

In general, mass transfer in food products depends on localwater concentration and is governed by Fick’s law of diffusionof the form,

∂C

∂t= ϑ∇2C + sc (10)

where C is the water concentration in food (ppm or mol/m3 etc.),ϑ is the effective diffusion coefficient of water in food (m2/s).If the food is highly porous and dehydrated then water vapordiffusion may be significant. However, for products with a voidfraction lower than 0.3 (May and Perre, 2002) vapor diffusioncan be neglected. For mass transfer in the fluid medium, a pas-sive scalar can represent the diffusion of mass and be written

as,

∂C

∂t+ ∇ · (−→v C

) = ϑ∇2C + sc (11)

In flows involving gases mixing with air and chemicals inwater, diffusion coefficients can be found in the literature but forliquid foods a reasonable approach is to make an educated guessand conduct a sensitivity analysis (Verboven et al., 2004). Usinga passive scalar is only valid in low concentrations, and becomesinvalid when particulate sizes of about 1 μm are present, whichcan influence the flow properties.

Simulations of spray dryers, solid-gas flows, or non-homogenous liquid foods exemplify applications where solidand fluid phases coexist and interact with each other. For thismodelling, two approaches are used, the Eulerian-Lagrangianor the Eulerian-Eulerian. Using the Eulerian-Lagrangian frame-work, the bulk fluid is modelled as a continuum carrying discretesolid particles (Nijdam et al., 2006; Anandharamakrishnan et al.,2010). The Lagrangian equations of mass and momentum arethen solved to determine trajectory of each particle within thecontinuum, which has resulted in this technique often beingreferred to as “particle tracking” (Kuriakose and Anandhara-makrishnan, 2010). As discussed by Verboven et al. (2004), inturbulent flow simulations, the turbulent velocity fluctuationshave been averaged out by the RANS models and the turbulentdispersion of the particles require modelling by mimicking thesefluctuations. This is done by extracting random numbers froma Gaussian distribution with a computed mean and variance(Harral and Burfoot, 2005). When the particle passes throughany arbitrary mesh element, the energy, mass, and momentumtransferred to the fluid continuum are calculated and added to thesource terms of that element. In this way all trajectories are cal-culated one by one. In the next iteration the fluid flow is solvedusing these source terms, and the calculation loop is repeateduntil sufficient convergence is achieved. For a complete descrip-tion of how the Eurlerian-Lagrangian framework can be usedto determine particle distribution, and as subsequently predictparticle history, particle residence time, and particle collisionsin fluid-food systems, the reviewer is referred to the work ofKuriakose and Anandharamakrishnan (2010).

While the Eulerian-Lagrangian approach provides a directphysical interpretation of the particle-fluid, particle-particle,and particle-wall interactions, computational times can becomeexcessive, depending on the number of particles to be solvedin the system (Szafran and Kmiec, 2004). This means thatapplications of the Eulerian-Lagrangian approach are stilllimited to small scale computations. In the Eulerian approach,the fluid and particle phases are treated as interacting andinterpenetrating continua (Nijdam et al., 2006). The governingequations for each phase are convection-diffusion equations,which contain extra source terms to account for the turbulentdispersion of the particles. Coupling of the phases is achievedthrough pressure and interphase exchange coefficients. The

256 T. NORTON ET AL.

equations appropriate to the Eulerian-Eulerian approach arepresented by Verboven et al. (2004) and Nijdam et al. (2006).

Turbulence Models

Thermal processes are usually associated with turbulent mo-tion, primarily due to the involvement of high flow rates and heattransfer interactions. Presently, the Navier-Stokes equations canbe solved directly for laminar flows. For turbulent flow regimes,there are many turbulence models available, each being suc-cessful in different applications. It should be noted, however,that none of the existing turbulence models are complete, thatis, their prediction performance is highly reliant on turbulentflow conditions and geometry. In the following, some of thebest performing turbulence models are discussed.

Eddy Viscosity Models

In turbulent flow regimes, engineers are generally contentwith a statistical probability that processing variables (such asvelocity, temperature, and concentration) will exhibit a particu-lar value, in order to undertake suitable design strategies. Suchinformation is afforded by the Reynolds averaged Navier-Stokesequations (RANS), which determine the effect of turbulence onthe mean flow field through time averaging. By averaging inthis way, the stochastic properties of turbulent flow are essen-tially disregarded and six additional stresses (Reynolds stresses)result, which need to be modelled by a physically well-posedequation system to obtain closure that is consistent with therequirements of the study.

The eddy viscosity hypothesis (Boussinesq relationship)states that an increase in turbulence can be represented by an in-crease in effective fluid viscosity, and that the Reynolds stressesare proportional to the mean velocity gradients via this viscosity(Ferziger and Peric, 2002). For a k-ε type turbulence model thefollowing representation of eddy viscosity can be written as:

μt = ρCμ

k2

ε(12)

For the k-ω type turbulence without the low-Reynolds num-ber modifications, the eddy viscosity can be represented by(Wilcox, 1993),

μt = ρk

ω(13)

This hypothesis forms the foundation for many of to-day’s most widely used turbulence models, ranging from sim-ple models based on empirical relationships to variants ofthe two-equation k-ε model, which describes eddy viscositythrough turbulence production and destruction (Versteeg andMalaskeera, 1995). All eddy viscosity models have relative mer-its with respect to simulating thermal processes.

The standard k–ε model (Launder and Spalding, 1974),which is based on the transport equations for the turbulent ki-netic energy k and its dissipation rate ε, is semi-empirical andassumes isotropic turbulence. Although it has been successfulin numerous applications and is still considered an industrialstandard, the standard k–ε model is limited in some respects.A major weakness of this model is that it assumes an equi-librium condition for turbulence, that is, the turbulent energygenerated by the large eddies is distributed equally throughoutthe energy spectrum. However, in real life, energy transfer inturbulent regimes is not automatic and a considerable length oftime may exist between the production and the dissipation ofturbulence.

The renormalization group (RNG) k–ε model (Choudhury,1993) is similar in form to the standard k–ε model but owing tothe RNG methods from which it has been analytically derived,it includes additional terms for dissipation rate developmentand different constants from those in the standard k–ε model.As a result the solution accuracy for highly strained flows hasbeen significantly improved. The calculation of the turbulentviscosity also takes into account the low-Reynolds number ifsuch a condition is encountered in a simulation. The effect ofswirl on turbulence is included in the k–ε RNG model, therebyenhancing accuracy for recirculating flows. In the realizablek–ε model (Shih et al., 1995), Cμ, is expressed as a function ofmean flow and turbulence properties, instead of being assumedconstant, as in the case of the standard k–ε model. As a result itsatisfies certain mathematical constraints on the Reynolds stresstensor that are consistent with the physics of turbulent flows(for example the normal Reynolds stress terms must always bepositive). Also, a new model for the dissipation rate is used.

The k-ω model is based on modelled transport equations,which are solved for the turbulent kinetic energy k and thespecific dissipation rate ω, that is, the dissipation rate per unitturbulent kinetic. An advantage that the k-ω model has overthe k–ε model is that its performance is improved for boundarylayers under adverse pressure gradients as the model can beapplied to the wall boundary, without using empirical log-lawwall functions. A modification was then made to the linearconstitutive equation of k-ω model to account for the principalturbulence shear stress. This model is called the SST (shear-stress transport) k-ω model and provides enhanced resolutionof boundary layer of viscous flows (Menter, 1994).

Reynolds Stress Model

The Reynolds stress closure model (RSM) generally consistsof six transport equations for the Reynolds stresses—three trans-port equations for the turbulent fluxes of each scalar property andone transport equation for the dissipation rate of turbulence en-ergy. RSMs have exhibited far superior predictions for flows inconfined spaces where adverse pressure gradients occur. Termsaccounting for anisotropic turbulence, which are included inthe transport equations for the Reynolds stresses, means thatthese models provide a rigorous approach to solving complex

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 257

engineering flows. However, storage and execution time can beexpensive for three-dimensional flows.

Large Eddy Simulation and Direct Eddy Simulation

Large eddy simulation (LES) forms a solution given the factthat large turbulent eddies are highly anisotropic and dependanton both the mean velocity gradients and geometry of the flowdomain. With the advent of more powerful computers, LES of-fers a way of alleviating the errors caused by the use of RANSturbulence models. However, the lengthy time involved in ar-riving at a solution means that it is an expensive technique ofsolving the flow (Turnbull and Thompson, 2005). LES providesa solution to large scale eddy motion in methods akin to thoseemployed for direct numerical simulation. It also acts as spatialfiltering, thus only the turbulent fluctuations below the filter sizeare modelled. More recently a methodology has been proposedby which the user specifies a region where the LES should beperformed, with RANS modelling completing the rest of the so-lution; this technique is known as DES and has found to increasethe solution rate by up to four times (Turnbull and Thompson,2005).

Near-Wall Treatment

An important feature of many two-equation turbulence mod-els is the near wall treatment of turbulent flow. Low Reynoldsnumber turbulence models solve the governing equations all theway to the wall. Consequently, a high degree of mesh refinementin the boundary layer is required to satisfactorily represent theflow regime, that is, y+ ≤ 1. Conversely, high Reynolds numberk–ε models use empirical relationships arising from the log-lawcondition that describe the flow regime in the boundary layerof a wall. This means that the mesh does not have to extendinto this region; thus the number of cells involved in a solutionis reduced. The use of this method requires 30 < y+ < 500(Versteeg and Malalsakeera, 1995).

Radiation Models

In recent years the number of radiation models incorpo-rated into commercial CFD codes has increased, and some havebeen designed by the code developers themselves. The mostcommon radiation models used in thermal processing simula-tions include discrete ordinate (DO) or surface-to-surface (S2S)models. The DO model takes into account media participation(Modest, 1992). The S2S model considers the radiation heat ex-change between two surfaces only (Siegel and Howell, 1992),and the amount of radiation received and emitted by each sur-face is defined by the surface’s view factors and the thermalboundary conditions. In contrast to a S2S solution, the solutionfor the DO model is coupled to the flow solution and energyis exchanged between the fluid and the radiation field. There-fore, solution times for S2S model can be almost half those of

the DO model (Mistry et al., 2006). More recently, Chhanwalet al. (2010) compared three radiation models, namely discretetransfer radiation model (DTRM), surface to surface (S2S), anddiscrete ordinates (DO) for an electric heating oven and foundthat they all predicted similar temperature evolution in the bakedproduct.

OPTIMIZING CONVENTIONAL THERMAL PROCESSESWITH CFD

Over the years many of the conventional processes such assterilization, drying, and cooking have been optimized withCFD. Some of the studies conducted thus far are reviewed inthis section.

Sterilization and Pasteurization

Canned Foods

During the sterilization process, rapid and uniform heatingis desirable to achieve a suitable level of sterility with minimumdestruction of the color, texture, and nutrients of food products(Tattiyakul et al., 2001). CFD has been used to investigate theheat and mass transfer phenomena occurring in canned prod-ucts such as soup, carboxyl-methyl cellulose (CMC) or cornstarch undergoing sterilization (Fig. 1). In these investigations,CFD has highlighted the transient nature of the slowest heatedzone (SHZ), quantified the amount of time needed for heat tobe transferred fully throughout food, as well as illustrating thesharp heterogeneity in temperature profile of the product whenno agitation is applied to the can (Abdul Ghani et al., 1999).Abdul Ghani et al. (2002) conducted CFD studies of both nat-ural and forced convection (via can rotation) sterilization pro-cesses of viscous soup, and showed that forced convection wasabout four times more efficient. Further simulation studies of astarch solution undergoing transient gelatinization showed thatuniform heating could be obtained by rotating the can intermit-tently during the sterilization process (Tattiyakul et al., 2001).CFD simulations have also been used to generate the data re-quired for the development of a correlation to predict steriliza-tion time (Farid and Abdul Ghani, 2004). A more recent studysimulated the sterilization process of a solid-fluid mixture in acan, and showed that the position of the food in the can hasa large influence on the sterilization times experienced (AbdulGhani and Farid, 2006).

CFD has recently been used to study the effect of con-tainer shape on the efficiency of the sterilization process (Varmaand Kannan, 2005a;b). Conical shaped vessels pointing up-wards were found to reach appropriate sterilization temperaturethe quickest (Varma and Kannan, 2005a). Varma and Kannan(2005b) investigated the effects of modifying the geometry ofthe conventional cylindrical food can as well as the cans orien-tation on the rate of thermal sterilization of pseudoplastic foodfrom CFD simulations. A cone pointing upwards was found to

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Figure 1 Temperature profiles in a can filled with CMC and heated by condensing steam (top insulated) after periods of (a) 54 s; (b) 180 s; (c) 1157 s; (d) 2574 s.The right-hand side of each figure is centerline (Abdul Ghani et al., 2007). (Color figure available online.)

heat faster than the cylinder of equal volume while the conepointing downward heated the slowest. In a more recent study,Abdul Ghani (2006b) has also analyzed the cooling cycle of thefood sterilization process using CFD. The most recent recentCFD study on food sterilization of canned products has beenconducted by Kannan and Gourisankar Sandaka, P. Ch. (2008),in which the authors provide insight on the thermal sterilizationprocess in relatively long food cans of different aspect ratios.CFD studies were used to determine regimes during the heatingcycle, which led to the development of more realistic heat trans-fer correlations, which can be used to estimate the heat transferfluxes as a function of time, and subsequently upon integrationcan lead to estimation of energy consumption.

Foods in Pouches

In recent years, CFD has provided a rigorous analysis ofthe sterilization of three-dimensional pouches containing liquidfoods (Abdul Ghani et al., 2007). Coupling first-order bacteriaand vitamin inactivation models with the fluid flow has allowedtransient temperature, velocity, and concentration profiles ofboth bacteria and ascorbic acid to be predicted during naturalconvection. The concentrations of bacteria and ascorbic acidafter heat treatment of pouches filled with the liquid food weremeasured, and found close agreement with the numerical pre-dictions. The SHZ was found to migrate during sterilization untileventually resting in a position about 30% from the top of thepouch. As expected, the bacterial and ascorbic acid destructionwas seen to depend on both temperature distribution and flowpattern.

Intact Eggs

Denys et al. (2003; 2004; 2005) have used CFD to predict thetransient temperature and velocity profiles in intact eggs duringthe pasteurization process with the aim of making the process

more effective. Owing to its ability to account for complex ge-ometries, heterogeneous initial temperature distributions, tran-sient boundary conditions, and non-linear thermophysical prop-erties, CFD has permitted a comprehensive understanding ofthis thermal process (Denys et al., 2003). Such an analysis hasallowed the gap in the knowledge of this area to be filled, as upto recently little information on the correct processing tempera-tures and times for safe pasteurization, without loss of functionalproperties, was available (Denys et al., 2004). In the series of pa-pers published on this topic by Denys et al. (2003; 2004; 2005),a procedure to determine the surface heat transfer coefficientusing CFD simulations of eggs filled with a conductive mate-rial of known thermal properties was first developed. After this,conductive and convective heating processes in the egg weremodelled, as shown in Fig. 2 (Denys et al., 2004). From thisit was revealed that, similar to the phenomena noted by AbdulGhani et al. (1999) in canned food, the cold spot was found tomove during the process towards the bottom of the egg. More-over, again similar to the findings of Abdul Ghani et al. (1999), acold-zone as opposed to a cold-spot was predicted. The locationof the cold zone in the yolk was predicted to lay below its geo-metrical center, even for the case where the yolk was positionedat the top of the egg. It was concluded that no convective heatingtakes place in the egg yolk during processing.

In the final paper of the series Denys et al. (2005) coupleda first order kinetic approach to predict the rate of thermal mi-crobial inactivation for Salmonella Enteritidis (SE) during theheating process. First, SE was observed to be less heat sensi-tive in the yolk when compared to egg-white. Then they foundthat processing at a temperature of 57◦C enabled 5 log reduc-tions of SE within 40 minutes which was considered a rea-sonable process time after balancing the desire for efficientprocessing with the desire to retain raw egg properties. Theresults of the CFD analysis were then presented graphicallywith an aim to help egg processors to optimize the pasteurizingprocess.

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Figure 2 CFD-calculated velocity vector plots and velocity contours in a plane of symmetry of an egg filled with CMC and heated in a water bath after 30 sprocessing: (a) no yolk present, (b) conductive heating yolk present in the egg centre, (c) yolk shifted towards the top of the egg. Process conditions for all caseswere: Ti = (24.5 ± 0.2) ◦C; T∞ = (59.4 ± 0.2) ◦C (Denys et al., 2007).

Recent studies have focused on the fact that inadequate cool-ing of eggs before storage as improper cooling can lead to growthof pathogenic bacteria such as Salmonella Enteritidis (SE). Thecooling rate of an egg, which depends on several factors, suchas cooling air temperature, initial egg temperature, air velocityinside the chiller, type of packaging material, and location ofthe egg inside the chamber, has been recently investigated us-ing CFD (Kumar et al., 2009). During the research work theauthors (Kumar et al., 2009) compared simulated and experi-mental values of the egg center temperature at various boundaryconditions, and found good agreement with root mean squarederror ranging from 0.23◦C to 0.37◦C. It is assumed that futurework will use predicted egg temperatures from the heat trans-fer model as an input to a microbial growth model to estimatethe potential growth of Salmonella spp. during egg cooling forassessing food safety. CFD modelling has also been used to pre-dict the decontamination period for intact eggs contaminated bySalmonella spp. Results from the model, together with the mi-crobial results on experimentally inoculated eggs, suggests theapplication of the hot air treatment on eggs before packaging isuseful in reaching approximately 90% reduction of S.Enteritidispopulation (Pasquali et al., 2010).

Plate Heat Exchangers for Milk Processing

The development of CFD models in recent years has con-tributed to the significant progress made in understanding of

the thermal-hydraulics of heat exchangers (Grijspeerdt et al.2005; Jun and Puri, 2005). It has been shown that the plategeometry can influence fouling rates, and so CFD models ofPHE thermal-hydraulics can bring about significant benefits forsystem optimization (Park et al., 2004). Many CFD studies ofPHEs exist, and have presented different techniques for geome-try optimization, that is, corrugation shape, or the optimizationof other process parameters, that is, inlet and outlet positions andPHE-product temperature differences (Grijspeerdt et al. 2005;Jun and Puri, 2005; Kenneth, 2004). Grijspeerdt et al. (2005)investigated the effect of large temperature differences betweenthe product and the PHE, and noted that the larger the differ-ence is, the greater the opportunity for fouling. Nema and Datta(2006) proposed a model to predict the fouling thickness and themilk outlet temperature in a helical triple tube heat exchanger asa function of temperature and shear stress on the surface of theheat exchanger. For this analogy to work, the milk outlet tem-perature was determined from the simulations, and the foulingthickness was determined based on the enthalpy balance and as-suming a constant heat flux across the heat exchanger wall leadto a dimensionless fouling factor in the form of a Biot number.

On the other hand, Jun and Puri (2005) were the first to cou-ple a fouling model with a three-dimensional thermal-hydraulicmodel within CFD simulations. Figure 3 shows a closer viewof the area most prone to fouling in the channel (Jun and Puri,2007). The figure shows that there occurs less fouling whenthe flow stream passes through the narrow gap between two

260 T. NORTON ET AL.

Figure 3 Simulated fouling profiles of fluid milk in the corner of channel (Source: Jun and Puri, 2007). (Color figure available online.)

corrugated plates. This is due to the increase of flow rate, whichis governed by the Bernoulli equation. However, a thicker layerof potential milk fouling can be observed inside the corrugationwhere there might occur the entrapment of milk proteins due toeddy or reverse flows. Also in their study, Jun and Puri investi-gated the influence of various PHE designs on fouling rates, fromthose typically used in the dairy industry to those used in theautomobile industry. They concluded that employing the latterPHE design in milk processing could decrease fouling (that is,deposited mass) by a factor of 10, compared to the current sys-tem under the identical energy basis. However, Grijspeerdt et al.(2007) noted a problem with this coupled model, namely thatthe deposition scheme did not include a recalculation area, platedimensions and the heat transfer characteristics, even though,strictly speaking, this would be necessary. More recently, DeBonis and Ruocco (2009) employed a thermal-hydraulic cou-pled with a fouling kinetics model in a similar fashion to Junand Puri (2007). De Bonis and Ruocco (2009) found that foulingformation was strictly dependent upon the wall temperature dis-tribution, and that local flow deceleration favoured solid deposi-tion by inhibiting shear stress and increasing wall temperature.They concluded that by using local species concentration, ve-locity, and temperature new corrugation shapes and orientationsthat minimize fouling can be designed and implemented.

Plate Heat Exchangers for Yoghurt Processing

Fernandes et al. (2005; 2006) studied the cooling of stirredyoghurt in PHEs with CFD simulations in order to investigatethe thermal-hydraulic phenomena involved in the problem. Theymodelled the rheological behavior of yoghurt via a Herschel-Bulkley model, with temperature influence on viscosity being

accounted for through Arrhenius-type behavior. As well as ac-counting for this rheological behavior, they also provided a highlevel of precision in the PHE geometrical design and the imposedboundary conditions. During the course of these studies, it wasfound that due to the higher Prandtl numbers and shear thinningeffects provided by the yoghurt, the Nusselt number of the fullydeveloped flows were found to be more than ten times higherthan those of water. This result presented a substantial thermal-hydraulic performance enhancement in comparison with thatfrom Newtonian fluids (Maia et al., 2007). Furthermore, it wasshown that PHEs with high corrugation angles may provide bet-ter opportunities for the gel structure breakdown desired duringthe production stage of stirred yoghurt. Regarding stirred yo-ghurt flow behavior, some other studies have been publishedwhere both experimental and simulation results were reported(Fernandes et al., 2005; Mullineux and Simmons, 2007). Afonsoet al. (2003) where they conducted a CFD study to obtain corre-lations for the determination of convective heat transfer coeffi-cients of stirred yoghurt during the cooling stage in a plate heatexchanger, taking into account its rheological features. Despitemodelling simplifications good agreement between measure-ments and predictions owing to the prevailing effects of thehigh viscosity of stirred yoghurt, that is, the corrugated surfacesdid not seem to cause significant perturbations in the flow de-velopment in their particular case. Recently, Fernandes et al.(2008) conducted simulations of laminar flows of Newtonianand power-law fluids through cross-corrugated chevron-typeplate heat exchangers (PHEs) as a function of the geometryof the channels. Due to the geometrical complexity of the cross-corrugated chevron-type PHEs passages the authors found itdifficult to predict the apparent viscosity observed during theflow of shear-thinning fluids, unless the generalized viscosityconcept was used. Using this concept, the authors showed that

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the flow index behavior influences the velocity profiles and themagnitude of the average interstitial velocity.

Dehydration

Fluidized Bed Drying

Spouted beds are a type of fluidized bed dryer commonlyfound in the food industry, in which heat is transferred from agas to the fluidized particle. These beds are suitable for industrialunit-operations that handle heavy, coarse, sticky, or irregularlyshaped particles through a circulatory flow pattern (Mathur andEpstein, 1974). Spouted beds have had many applications indrying of foods, such as for drying of grains (Madhiyanon et al.,2002), diced apples (Feng and Tang, 1998), etc. Because of thecomplex interactions that occur, empirical correlations are onlyvalid for a certain range of conditions, and CFD simulations havebeen the only means of providing accurate information on theflow phenomena. However, similar to other drying applications,difficulties exist in modelling the interactions between the solidand liquid phases, as well as limitations in computing power, andconsequently only a limited number of CFD simulations exist.To simulate the drying of agricultural products, various differ-ent approaches can be taken, that is, a single grain approach, aEulerian-Eulerian approach, or discrete-element particle (DEM)approach. In the DEM model, two techniques can be used to sim-ulate the drying of granular foods, that is, a soft sphere modeland a hard sphere model. In the soft sphere model, the interactionforces using multiple particle-particle or particle-wall contactscan be predicted, whereas in the hard sphere model, it is onlypossible to compute the instantaneous change in particle ve-locity through particle collision (Li et al., 2010). However, thecomputational demand rises strongly with the number of tracedparticles, which limits its applicability.

The single grain approach is when the drying of a represen-tative grain is modelled. Using this approach Markowski et al.(2009) undertook an experimental and theoretical investigationto determine the drying characteristics of barley grain dried inspouted-bed dryer, where the influence of the shape of a solidapplied during modeling on the determined diffusivity of barleywas studied. The finite element method was used to solve theequations applied in the barley drying process. The optimizationtechniques were applied to determine moisture diffusivity usingan inverse modelling approach. Their results showed that whenmodelling drying of grain, the assumed geometry of a solid is ofa fundamental importance as it has a direct influence on mois-ture diffusivity. From this it was also shown that using sphericalgeometry for modelling drying processes of grain is faulty ifhigh accuracy of the results is expected from the modelling.

The Eulerian-Eulerian approach offers the most efficient wayof representing the two phases in this type of system, when con-sidering the present levels of computer power and the largenumber of granules (grain) in a typical system, and consequen-tially its use has been preferred over discrete methods by someresearchers. Moreover, using the Eulerian-Eulerian approach

the momentum exchange can be accurately simulated betweencomponents of the fluid–solid type mix on the dynamics ofthe spouted bed and height of the fountain characteristic for flu-idized dryers (Sobieski, 2009). Assarie et al. (2007) developed atwo-dimensional mathematical model for batch drying based onthe Eulerian- Eulerian approach to simulate the drying processof wheat particles (0.15 m internal diameter) in a fluidized beddryer. The authors stated that their model was able to simulatethe drying phenomenon, showing the influence of the mois-ture content in the solid phase on this phenomenon. Szafranand Kmiec (2004) also used this approach, via the multifluidgranular kinetic model of Gidaspow et al. (1992) and the k–ε

model, in their CFD simulations of the transport mechanismsin the spouted bed. Many physical mechanisms needed to beaccounted for in the CFD model, as not only did the transport ofthe mass continuum, that is, granular phase, need to be solved,but so did the inter-phase moisture transport. Using the appropri-ate mass flux equations, which were derived from the diffusionmodel of Crank (1975), the drying period was predicted in eachmesh element without the use of the critical moisture content;this represented a considerable boost in accuracy. This accu-racy was borne out in the mass flux computations; however, theheat-transfer rate was under-predicted, when compared to exper-imental results. An analysis of the transport mechanisms showedthat fluctuations in airflow had an influence on the instantaneousdistributions of the grain, air temperatures, and the local mois-ture content, but not on the mean mass-averaged values. In fact itwas shown that the internal mass transfer resistance and the masstransfer depended on the zone of the dryer which the grain waspositioned during the process. In a more recent study, Zhonghuaand Mujumdar (2007) adopted a similar method to Szafran andKmiec (2004) when they computed the numerical simulation ofa spouted bed dryer. While no experimental validation was usedfor the drying predictions, their predictions provided a quali-tative estimate for the drying kinetics in spouted beds, and areimportant information for the scale-up and process design ofspouted bed dryers (Jamaleddine and Ray, 2010).

A major difficulty encountered in modelling spouted bed dry-ers has been the excessive computing times required to simulateonly a fraction of the drying process. For example, owing to thesmall time-steps required to resolve the instabilities in the flowregime, it would take a two-dimensional CFD simulation almostone year to simulate one hour of drying (Szafran and Kmiec,2005). That being said, studies have shown that the results fromCFD simulations can be transformed into time-independentdata, extrapolated, and then transformed back to time-dependantdata so that the mass flow rate over the full drying period canbe quantified (Szafran and Kmiec, 2005). Using this method,good agreement was found with the important phase of drying,which makes this technique an important consideration whenundertaking such simulations, as system design or optimizationmay then be realized in reasonable time-frames. Recently Liet al. (2010) have simulated the bubbling flow in a 2D pulsedfluidized bed using a Eulerian-Eulerian modelling approach.With this model they found that the flow instabilities and

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pressure drop inside the fluidized bed were mainly caused bythe formation and motion of air bubbles, with a low frequencypulsating inlet flow causing intermittent fluidization, whereashigh frequency of 40 Hz results in a normal fluidization.Numerical results improve the understanding of the pulsedfluidization. Recent CFD work in fluidization during drying hasfocused on the design of an efficient gas distribution system fora fluidized bed dryer (Jangam et al., 2009); the influence of adraft tube on the fluid dynamics of a spouted bed (Neto et al.,2008) as well as the development of an accurate online modelwhich can be used to control the fluidized-bed drying processes(Wang et al., 2008). For more innovative applications of CFDfor fluidized bed analysis and design the readers are referred tothe recent specialized review of Tarek and Ray (2010).

Spray Drying

Spray drying is another traditional drying technique and isused to derive powders from products, with its main objec-tive being to create a product that is easy to store, handle, andtransport. As pointed out by Fletcher et al. (2006), an impor-tant requirement of the spray dryer operation is to avoid highlyunsteady flows as these can cause deposition of partially driedproduct on the wall, resulting in a build up of crust, which isliable to catch fire due to over-heating. As the phenomenolog-ical aspects of spray dryers are highly three-dimensional andreliant on flow patterns, empirical techniques cannot providethe means of analyzing effects of chamber geometry or operat-ing parameters. Therefore, CFD has been a necessary requisitefor accurate spray dryer modelling, and has been employed forover ten years now (Langrish and Fletcher, 2003).

The use of CFD in spray drying has been comprehensivelyreviewed in recent years, and for interested readers the articlesof Langrish and Fletcher (2003) and Fletcher et al. (2006) pro-vide a good understanding of the topic. It is important to notethat most CFD of spray dryers use the Eulerian-Lagrangian ap-proach, which, as discussed above, demands a large amountof storage, if the numbers of particles/droplets being modelledare great. Moreover, when large-scale systems need to be mod-elled, enhancing efficiency by parallel processing via domaindecomposition would be difficult, as particles will not remainin the one domain (Fletcher et al., 2006). Even though suchdifficulties are obviated with the Eulerian-Eulerian approach,many disadvantages exist, such as the loss of the time historyof individual particles, the difficulty of modelling turbulent dis-persion and the inability to model interacting jets, with someof these problems sharing common ground with fluidized bedmodelling. However, in phenomena unrelated to fluidized bedapplications, the Eulerian-Lagrangian approach permits reason-able predictions of drying rate, particle-wall depositions, andparticle agglomeration, whereas comparable applications usingthe Eulerian-Eulerian approach are limited. Lagrangian particletracking will remain a key feature of spray dryer modelling intothe future as it allows the modeller to gain understanding ofparticle histories such as, velocity, temperature, residence time,

and the particle impact position are important to design andoperating spray drying, which is important given that the finalproduct quality is depending on these particle histories. For acomprehensive review on the CFD simulation of particle histo-ries during spray drying the reader is referred to Kuriakose andAnandharamakrishnan (2010).

One of the big difficulties when using CFD software packagesin spray dryer modelling is that, owing to the presence of bothsolid and fluid, the mass transport limitations within a dropletcannot be easily taken into account, and therefore submodelsmust be included to do so; and for accurate solutions these mustbe used alongside many other submodels that account for otherphenomological aspects (Straatsma et al., 2007). In a recentstudy by Straatsma et al. (2007), submodels for mass trans-port, inter-particle collision, agglomeration, thermal reactions,and stickiness were implemented with an Eulerian-Lagrangianmodel of an industrial dryer. The CFD simulations allowed theauthors (Straatsma et al., 2007) to assess the agglomeration sizeof the particles and the stickiness of the particles colliding witheach other and with the wall, and as a consequence allowed thefouling liability of the dryer to be evaluated. Recently, Woo et al.(2009) investigated the effect of chamber aspect ratio and oper-ating conditions on flow stability in spray dryers, observing thata large expansion ratio produces a more stable flow due to thelimitations of the jet fluctuations by outer geometry constriction.Mujumdar et al. (2010) have recently presented an overview ofthe recent advances in spray-drying, where they discussed issuesincluding recent predictive studies on predicted effects of inno-vative chamber geometry, reduced pressure operation, operationin low dew-point air, and superheated steam.

Forced-Convection Drying

Impinging jets are regularly used to dry food products inthe food industry. Consequently, numerous investigations havenumerically studied the heat and mass transfer characteristics ofthese applications. Many of these studies examine the influenceof turbulence models (Seyedein et al., 1994; Ashforth-Frost andJambunathan, 1996), or the shape of the impinging jet (Zhaoet al., 2004), on Nusselt number distribution over the productsurface. However, limited CFD studies that consider the coupledheat and mass transfer during drying exist.

Because of the complex geometry usually encountered indrying applications, theoretical studies are often not applicable,and to obtain the spatial distribution of transfer coefficients withreasonable accuracy it is necessary to solve the Navier-Stokesequations in the product surroundings. From the distributionof transfer coefficients, the correct temperature and moistureprofiles within the product can be predicted, so that the dryingprocess can be optimized. Kaya et al. (2007) used this approachwith CFD to determine the transfer coefficients, and then theheat and mass transfer within the food was simulated with anexternal programme. In a later study Kaya et al. (2008) used asimilar CFD approach to find out the optimum inlet and out-let configurations and locations for a dryer containing a moist

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 263

object. This approach was also recently used to investigate theeffects of confined flow on the hydrodynamic, thermal, and masstransfer characteristics of a circular cylinder and the interrela-tion of these mechanisms are investigated numerically (Ozalpaand Dincer, 2010). However, it is also possible to do this withinthe CFD package by determining the heat transfer coefficientwith Eq. (7), and the mass transfer with the Lewis relation,once a transient solution is performed. Such a technique wasused by Suresh et al. (2001) in CFD simulations of the con-jugate heat and mass transfer through a block immersed in aboundary layer flow. Conjugate heat and mass flux can alsobe determined with the help of empirically correlations of thetransfer coefficients; however, these may not always be adequate(Zheng et al., 2007).

Fully coupled CFD solutions of heat and mass transfer in bothsolid and fluid phases also exist. De Bonis and Ruocco (2007)numerically modelled the heat and mass transfer in a food slabby an impinging heated air jet using time-dependent governingequations for a dilute-mixture, via two-dimensional CFD sim-ulations. The specific exchange configuration they consideredwas a thin baking product and the focus was on residual localwater activity. Later De Bonis and Ruocco (2008), extendedtheir approach by employing a finite-element CFD approach tothe drying of a vegetable substrate. Residual water and temper-ature fields were computed locally within the substrate, whenthis interacts with a forced, laminar air flow. They described theevaporation kinetics as a first-order Arrhenius-type reaction andfound strong process heterogeneity in moisture and tempera-ture gradients. This kinetic representation was included to solvefor transient, two-dimensional flow, temperature, and moisturefields. Realistic transfer exchanges were inherently consideredthat vary with process time and surface location, eliminating theneed for empirical heat and mass transfer (averaged) coefficientsevaluation. A more advanced coupling procedure was presentedby Erriguible et al. (2005; 2006), who explicitly accounted forthe movement of bound water, free water, and vapor throughthe porous solid. They noted increase in the prediction accu-racy when compared to those made via the use of heat transfercoefficients in the literature.

Cooking

Natural Convection Ovens

Electric ovens are commonly used household appliances thatrely on conjugate thermal exchange to produce the desired cook-ing effect in a foodstuff. For that reason, CFD is an appropriatetool to quantify the internal thermal field and mass transfer, bothof which are important for robust design and performance. Natu-ral convection is dominant in these ovens when it is produced bya source below the product (bake mode), with a source above theproduct driving radiative heat transfer (broil mode). Abrahamand Sparrow (2003) used CFD to model the flow-field in an elec-tric oven on baking mode with isothermal sidewalls, employingtemperature boundary conditions consistent with experimental

measurements. These simulations allowed insight into the rel-evant contributions of convective and radiative heat transfer tobe gained, as well as determining the accuracy of predictionsmade by simple elementary surface correlations. Predictionswere obtained with a steady-state solver and the solutions werethen used as input into a quasi-steady model to permit the time-wise temperature variation of the foodstuff to be analyzed fromwhich excellent agreement between experimental and numer-ical results was achieved. Abraham and Sparrow (2003) alsofound that for a blackened thermal load radiative heat transfercontributed to 72% of the total heat transfer, whereas this was8% when the load was reflective. Heat flux distribution on thelower and upper surfaces varied as a function of contributionsfrom temperature difference between the oven and the product,alongside that from the buoyant plume emanating from the heatsource. From this, it was noted that steady-state heat transfercould be obtained at the top surface, whereas the under-surfacewas highly unsteady. More recently, Mondal and Datta (2010)developed a 2D CFD model for crustless bread, where they com-puted the heat and mass transfer during baking. It was found thatthe simulated model was able to predict very well the pattern oftemperature and moisture profile during bread baking process.

A thorough investigation into the thermal profile of an elec-trical oven, operated under both broil and bake modes, wascompleted by Mistry et al. (2006). The solution first obtainedfrom the steady-state analysis yielded a flow-field, which op-posed that evident from experimental observation. This wasaddressed by imposing an artificial, that is, a “numerical,” ventsuction pressure, the value of which was tweaked until ther-mal field predictions corresponded with experimental measure-ments. Full cycling times, employing intermittent ON/OFF op-eration of heaters, were also simulated for both the broil andbake cycles. From the comparison of predictions, the broil cyclewas confirmed to be less efficient, with a notable heterogeneityin temperature profile, owing to temperature stratification; thisunderscored the fact that the main thermal exchange in this cyclewas due to radiation.

In more recent investigations, Navaneethakrishnan et al.(2007) completed CFD solutions of a 2-D steady-state naturalconvection heating oven, and Chhanwal et al. (2010) developeda CFD model for the electrical heating domestic bread bakingoven CFD coupled with different radiation models. The simu-lations of Chhanwal et al. (2010) showed that the electric ovenattained uniformity of heating in twenty minutes (pre-heatingcycle) and with the slowest heating zone being present near theoven wall due to the lower air flow pattern.

Forced Convection Ovens

Over the years, forced convection ovens have been developedinto two types of systems which operate in very distinct andseparate ways. First, the conventional forced convection ovenuses a fan to develop high-velocity convection currents aroundthe enclosed foodstuffs, which enhances the rate of heat transfer,and permits faster cooking of the products. The second type

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of forced convection oven permits the use of impinging jets toprovide the main thermal exchange. The physics associated withthis type of oven has a direct relationship with air impingementdrying; thus, it is easy to see why its correct utilisation in theindustry can provide high levels of efficiency.

Verboven et al. (2000a) developed a CFD model of an empty,isothermal forced-convection oven, in which numerous sub-models were incorporated, including those describing the air-flow through the heating coils and fan, alongside swirl in theflow regime added by the fan. Due to the complexity of theflow dynamics involved in the oven, a detailed validation ex-ercise was performed. An important outcome of the study wasthe observation that the swirl model was a necessary requisitefor accurate quantitative results, as the swirl actually improvesthe airflow rate whilst having no direct effect on the mechan-ical energy balance. In a later study they conducted a CFDinvestigation into the temperature and airflow distribution in thesame oven during operation cycle, loaded with product (Ver-boven et al., 2000b). Prior to the CFD modelling a lumped FEMmodel of heat transfer within a food was designed to calculatethe appropriate heat sources and boundary conditions, whichwere then applied in the CFD model. The prediction errors av-eraged to 4.6◦C for the entire cavity at the end of the warm-upstage, with this reducing to 3.4◦C at the end of the process asthe variability in the system levelled out. As expected, the prod-ucts subject to the highest heat transfer were situated closest tothe fan where they experienced uniform high velocity air flow.Unfortunately, the CFD predictions of the surface heat transfercoefficients were grossly under-predicted, and were attributedto the inaccuracy of the wall functions calculations. However, inorder to circumvent these errors, Verboven et al. (2000b) usedthe local turbulence intensity and Reynolds number, obtainedfrom the CFD model, to compute the heat transfer coefficients.The correlation derived alongside other published numericallyderived correlations are summarized in Table 2.

Recently, Smolka et al. (2010) presented an experimentallyvalidated 3-D CFD analysis of the flow and thermal processesin a laboratory drying oven with a forced air circulation froma rotating fan. Because the numerical results show very goodagreement with the measured values, a number of new devicemodifications were simulated to improve temperature unifor-mity within the chamber of the device.

Application of CFD in jet impingement oven systems pro-vides detailed understanding of the effect of different oven ge-ometries as well as object geometries on the system perfor-mance. A full three-dimensional CFD model of a multiple jetimpingement oven was developed by Kocer and Karwe (2005).Convection and conduction heat transfer were coupled. How-ever, as the thermal exchange was a result of jet impingementonly, radiation was ignored with small compromise of accuracy.Moisture transfer was not considered. Kocer and Karwe (2005)then determined a correlation for the average Nusselt numberin terms of the Reynolds number for multiple jets impingingon the surface of a cylindrical model cookie, which indicatedthe strong dependence of surface heat transfer coefficient on

velocity of the jet. In another CFD study of multiple jets flows,(Olsson et al., 2005) the airflow and thermal exchange charac-teristics cylinders were found to be dependent on the distanceand opening between the jets. At larger distances between thejets, more entrainment of air between the jets occurred, whereasfor smaller spacing between the jets, the entrainment was sup-pressed, almost no air exited through the opening between thejets, and the flow between the cylinders were almost stagnant.

Commercial Baking Ovens

For the bakery industry, it is necessary to maintain consis-tency in product quality throughout processing. This requiresquality-conscious control strategies to be implemented (DeVries et al., 1995) which should permit the adjustment of pro-cess parameters in response to disturbances, such as a change inthe oven load. The successful implementation of such controlstrategies has been the long term goal of process modelling viaCFD for some time now (Zhou and Therdthai, 2007). The toneof the first studies with this aim was set out by Therdthai et al.(2003), who solved the two-dimensional flow and temperaturefield in conventional “u-turn” bread baking oven. They usedthe simulations to provide information for temperature control,as well as for control sensor position. However, a number ofsimplifications limited the veracity of the model, with regardsto its representation of the physical process. For example, asteady-state flow regime was assumed, even though the processis inherently transient. Furthermore, the contribution from ra-diative heat transfer was ignored, despite the fact that this modesignificantly influences thermal exchange. These assumptionswere, however, addressed in a subsequent publication, in whicha full three-dimensional model was built, using a moving gridtechnique, to simulate the transient baking process (Therdthaiet al., 2004a). Radiative heat transfer was also incorporated.The authors (Therdthai et al., 2002) used mathematical models,which they had developed in a previous study, in conjunctionwith the CFD results to predict the quality attributes of bread.Using both sets of predictions they provided recommendationsto reduce energy use during the process, whilst not compromis-ing bread quality. More specifically, with reference to Fig. 4, thepropositions were that the duct temperature in zones 1, 3, and 4should be reduced by about 10◦C so that the tin temperature inzones 1 and 3 would decrease, thereby reducing weight-loss inthis zone. At the same time, their observations showed that theflow rate of the convection fan in zone 3 should be increased bydoubling it throughput, so that the tin temperatures in zones 2and 4 could be maintained at high levels. This optimization waspredicted to produce a weight loss of 7.95%, with the lightnessvalues of the crust color on the top, bottom, and side of the loafbeing around L-values of 50.68, 55.34, and 72.34, respectively.

Later a starch gelatinization model, based on simple first-order kinetics, was incorporated to examine the effects of theoptimized operation on dough gelatinization (Therdthai et al.,2004b). The rate of gelatinization was notably slower for thebread baked using the optimized conditions, especially in zone 3,

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Table 2 Correlations for surface heat transfer heat coefficients developed from CFD models predictions

Authors Process Turbulence model Correlation developed Comments

Verboven et al. (2000b) Heating of food inforced convectionoven

Std. k-ε NuNu0

= 1 + 0.088T uRe1/2

where,Nu0 = 0.245Re1/2

Due to inaccuracies with wallfunctions the correlation was notdeveloped using turbulencevalues from the free-stream

Abraham and Sparrow (2003) Oven heating ofrectangular food in anatural convectionoven

Spalart-Allmaras Developed quasi-steady model to predicttemperature evolution of solid food.

Reasonable agreement withper-surface heat transfercoefficients was found forsurfaces were steady heattransfer was predicted

Ollson et al. (2004) Jet impingement heatingof cylindrical foodplaced on flat surface

SST (Shear StressTransport) k-ω

Num = 0.14Re0.65(H/d)−0.077(d/D)0.32 The heat transfer rate was found tobe higher on the top of theproduct and in the wake, lowerin the separation point and theback of the cylinder.

Kocer and Karwe (2005) Multiple jetimpingement heatingof cylindrical food(cookie) placed incenter of oven

Std. k-ε Nu = 0.58Re0.375 Predictions showed a strongdependence between the surfaceheat transfer coefficients and airvelocity, whereas they werealmost independent oftemperature.

Nitin et al. (2006) Jet impingement heatingof cylindrical foodplaced on flat surface

Std. k-ε Nu = 0.000348Re0.78(d/D

)0.65Predictions were found to depend

on the geometry of the modelobject and jet flow field in theoven.

as a result of reduction in energy supplied to this zone. However,the gelatinization gradually picked up and reached a maximumgelatinization extent at the end of the baking process. Otherinvestigations have sought to assess and quantify the robustnessof CFD models to changes in the physical properties of breadduring the baking process (Wong et al., 2006). Wong et al. (2006)developed simple mathematical models, which described thechanges in the temperature profiles as a function of the changesin the physical properties.

Recent CFD modelling studies of the bread baking processhave looked at the two-dimensional physical representation,coupling convection and radiative heat transfer via discrete or-dinate (DO) model (Wong et al., 2007a). Moreover, the density,heat capacity, and thermal conductivity were allowed to varywith temperature. However, some discrepancies between pre-dictions and measurements of the actual baking process werefound, especially of those comparisons made at the dough cen-ter, which were probably caused by no modelling of the moisturetransport in the dough and evaporation kinetics. Moreover, theconfining effect afforded by the two-dimensional model wasseen to cause lack of correspondence in the validation study.Comparisons were also made with the three-dimensional modelof Therdthai et al. (2004a), from which it was summarized thatthe two-dimensional model provided better predictions in themoving sensors. Most notably CFD predicted that at full ovencondition the temperature readings from the stationary sensorsoscillated in association with the movement of dough/breadalong the travelling track owing to the reduced temperature gra-dient in the region around the sensors and bread surface. In a laterstudy proportional–integral (PI) controllers were incorporated

to the existing 2D CFD model and the feasibility of establishinga framework that is capable of integrating a process controllerwith a CFD model was assessed (Wong et al., 2007b). This studycomprises the long term objective of process modelling in thebakery industry, in which a dual-mode controller was designedto suit different processing conditions, which were simulatedto provide satisfactory control in the presence of disturbancesand set-point changes. From the study it was shown how thepreheating stage could be removed under controlled conditions,which retained the quality characteristics of the bread whilstsaving energy. More recently, Boulet et al. (2010) modelled abakery pilot oven using CFD where the movement of the prod-uct through the oven was considered. Overall, the authors foundgood agreement with experimental data even though problem-atic areas were noted when trying to characterize the influenceof wall temperature on radiation.

Microwave Ovens

Microwave ovens are commonly used appliances in thehome. Heat and mass transfer in these appliances have beenmodelled using CFD. Unfortunately, the coupled problem ofelectromagnetic, heat transfer and airflow has not yet beensolved with the CFD approach, as commercially available fi-nite volume codes are not amenable for electromagnetic mod-elling. In the first CFD study of this nature, Verboven et al.(2003) numerically solved the flow around a product of uniformsurface temperature, under both natural and forced convectionconditions, in order to observe the phenomenological aspectsin the solution field. The combination of natural and forced

266 T. NORTON ET AL.

Figure 4 The industrial bread baking oven; (a) schematic and (b) simulations results (Therdthai et al., 2004a). (Color figure available online.)

convection typically experienced in microwave ovens was mod-elled and the local heat transfer coefficients were computed.The study showed that, for the typical flow rates experiencedin the oven, there was an overall increase in heat and masstransfer coefficient when compared to purely natural or forcedconvection situations. However, the mass transfer coefficient

was not high enough to avoid the development of sogginess.To reduce sogginess, it was suggested that optimal placementof inlets and outlets, alongside optimizing fan design would berequired.

Even though commercial CFD codes may not be suitable formultiphysics problem including electromagnetic radiation, such

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 267

Figure 5 Air flow pattern (left) and temperature field (right) in a microwave cavity for different air velocity magnitudes. Temperatures are plotted for range from20◦C (white) to 40◦C (black) on a vertical cross section through the cavity (Verboven et al., 2007). (Color figure available online.)

268 T. NORTON ET AL.

coupling can be accomplished. Perre and Turner (1999) coupledheat and mass transfer with Maxwell’s equations and the dielec-tric properties, which varied as a function of both on temperatureand moisture, so that the drying of wood could be quantified.As mentioned above, such coupling in food simulations hasrequired synergy between different numerical approaches. Forexample, a weak coupling between a finite elements model forelectromagnetic radiation and a CFD model has been achievedby Verboven et al. (2007), via surface heat transfer coefficients,in a jet impingement microwave oven (Fig. 5). An example offull coupling between the calculations of heat and mass trans-fer and electromagnetic radiation has been achieved by Dincovet al. (2002), who mapped the (moisture and temperature de-pendent) porous media dielectric properties from the CFD meshonto the electromagnetic finite difference mesh and then mappedthe microwave heating function from the electromagnetic finitedifference mesh onto the CFD mesh. Using this specializedcoupling algorithm, Dincov et al. (2002) modelled the phasechange that accompanies the temperature increase during mi-crowave heating. The elevated internal temperatures coupledwith the increase in internal vapor pressure were seen to drivethe liquid from the medium quickly and efficiently. It was alsoseen that, because liquid water is the most active component inabsorbing microwaves, the energy absorption is reduced duringthe process.

The CFD solution to the fully coupled microwave and con-vection heating problem has been presented by Marra et al.(2010). The model was validated against available experimen-tal data for heat transfer and moisture transfer occurring ina food slab. Then process duration and working air veloc-ity were varied to assess the ability of the model to predictheat and mass transfer for configurations closer to those foundin the industrial framework. The simulation showed that heatand mass transfer will vary with the sample thickness, due tothe dependence of shape and intensity of the volumetric heat-ing distribution on geometry, when the substrate is exposedto MWs.

Far-Infrared Heating

Postharvest heat treatments have become increasingly pop-ular to control insect pests, prevent fungal spoilage, and af-fect the ripening of fruits and vegetables (Marquenie et al.,2003). Far infrared radiation (FIR) heating technology is usefulfor these purposes because it can achieve contactless heating(Tanaka et al., 2007). Tanaka et al. (2007) performed advanced3D thermal radiation calculations to assess the quality and effi-ciency of FIR heating for postharvest treatments of fruits. It wasshown that the proposed CFD based method was a powerful toolto evaluate in a fast and comprehensive way complex heatingconfigurations that include radiation, convection, and conduc-tion. However, the authors also found that the FIR method wasfound inferior to water bath heating in terms of efficiency anduniformity.

MODELLING EMERGING THERMAL TECHNOLOGIESWITH CFD

High Pressure Thermal Processing

High pressure processing (HPP) is a novel food processingmethod which has shown great potential in the food industry.During compression/decompression phases the internal energyof a high pressure processing system changes, resulting in heattransfer between the internal system and its boundaries. Thesethermal-hydraulic characteristics were studied with CFD byHartmann (2002) the technique was deemed necessary in gain-ing thorough understanding of the phenomena inherent in HPP,especially when the scale-up phenomena need to be analyzed(e.g., layout and design of high pressure devices, packages,etc.) (Hartmann, 2002). Hartmann and Delgado (2002) usedCFD and dimensional analyses to determine the time-scales ofconvection, conduction, and bacterial inactivation, the relativevalues of which contribute to the efficiency and uniformity ofconditions during HPP. Conductive and convective time-scaleswere directly compared to the inactivation time-scale in orderto provide a picture of the thermal-hydraulic phenomena in theHP vessel during bacterial inactivation. The results showed thatpilot-scale systems exhibited a larger convection time-scale thanthe inactivation time-scale, and that the intensive fluid motionand convective heat transfer resulted in homogenous bacterialinactivation. Furthermore, the simulations of industrial scaledsystems showed greater efficiency in bacterial inactivation asthe compression heating subsisted for greater time periods whencompared to smaller laboratory systems. Other CFD simulationsshowed that the thermal properties of the HP vessel boundarieshave considerable influence on the uniformity of the process,and insulated material promoted the most effective conditions(Hartmann et al., 2004). As well as this, the insulated vesselwas found to increase the efficiency of the HPP by 40%. ACFD and dimensionless analysis of the convective heat transfermechanisms in liquid foods systems under pressure was alsoperformed by Kowalczyk and Delgado (2007) who advised thatHP systems with a characteristic dimension of 1 m alongsidea low viscous medium should be used to avoid heterogeneousprocessing of the product.

CFD studies have also provided solutions to the thermal-hydraulic phenomena in HPP systems containing packagedUHT (Ultra High Temperature) milk (Hartmann et al., 2003),packaged enzyme mixture (Hartmann and Delgado, 2003), solidbeef fat (Abdul Ghani and Farid, 2007), and solid food analoguematerial (Otero et al., 2007) (e.g., tylose with similar propertiesto meat, and agar with similar properties to water). In both inves-tigations (Hartmann et al., 2003; Hartmann and Delgado, 2003)the most significant results showed strong coupling betweenconcentrations of the surviving micro-organisms and the spatialdistribution of the food package in the HP vessel, owing to theinhomogeneous temperature field. A low conductive packagematerial was also found to improve the uniformity of processingby preserving the elevated temperature level within the package

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 269

throughout the pressurization phase; an average difference ofabout two log reductions was found per 10 fold increase inthe package thermal conductivity. The two-dimensional CFDsimulations of Otero et al. (2007) found that the filling ratio ofthe HP vessel played a major role in process uniformity, withconvective currents having least effect on heat transfer whenthis ratio is large. Otero et al. (2007) also showed that by an-ticipating the temperature increase resulting from compressionheating and by allowing the pressure transmitting medium tosupply the appropriate quantity of heat, the uniformity of HPPwas enhanced when both large and small sample ratios wereused. More recently, Abdul Ghani and Farid (2007) used three-dimensional CFD simulations to illustrate both convective andconductive heat transfer in a HPP system loaded with pieces ofsolid beef fat. The simulation showed a greater adiabatic heatingin the beef fat than the pressure transmitting medium owing tothe greater compression heating coefficient used in this case.

Ohmic Heating

The basic principle of ohmic heating is that electrical energyis converted to thermal energy within a conductor. In food pro-cessing, foodstuffs act as the conductor. The main advantage ofohmic heating is that, because heating occurs by internal energygeneration within the conductor, this processing method leadsitself to even distribution of temperatures within the food, and itdoes not depend on heat transfer mechanisms (Jun and Sastry,2005). Jun and Sastry (2005) were the first to model the ohmicheating process, with the aim to enhance heating techniques foruse by cabin crews during long-term space missions. They de-veloped a two-dimensional transient model, for chicken noodlesoup (assumed single phase) and black beans, under the ohmicheating process, by solving the electric field via the Laplaceequation. From this solution the internal heat generation wasobtained, which was added as a source to the Fourier equation,and was then numerically solved by the CFD code. Electricalconductivity was allowed to vary as a function of temperature.The CFD model was able to predict regions of electric fieldovershoot in the food, as well as the non-uniformities in thepredicted thermal field. Moreover, they noted that as the elec-trode got wider, the cold zone area developed in the middleof the packaging diminished to a minimum and then appearedand grew at the corners of the packaging, clearly illustratingthe existence of a threshold value for electrode size optimiza-tion. They later expanded the model so that a three-dimensionalrepresentation of pouched tomato soup could be simulated (Junand Sastry, 2007), in which they found the electric field strengthnear the edges of electrodes to overshoot as it got close to themaximum value, as predicted by their first model. On the otherhand, the food between the V-shaped electrodes experienced aweak electric field strength, which gave rise to cold zones inthe food. Jun and Sastry (2007) recognized that the presenceof these cold zones merited further research on pouches viamodelling and package redesign.

Marra et al. (2009) developed a CFD model to quantifythe ohmic heating effects within a model solid food system,which they then used to optimize heat distribution within thefoodstuff in order to evaluate the main parameters affectingthe system. Their results showed that heat loss occurs to thecell wall and electrode surfaces could be reduced by improv-ing the system design. It was also found that the temperaturegradients that were established in the proximity of the outercurved surface exhibited colder areas at junctions of electrodeswith lateral sample surface. However, as noted by Shim et al.(2010) former CFD modelling however, the majority of CFDmodels for multiphase food mixture have dealt with a sin-gle solid particle system surrounded by liquid fluid, which isover-simplified and far from the reality. Therefore, Shim et al.(2010) conducted CFD simulation of the thermodynamic per-formances of the multi-component food mixture in an ohmicheating system in order to predict realistic hot and cold spotsin the processed food, thereby preventing less conductive foodparticles from being under-processed. While the model was suc-cessfully validated, it was only developed in 2D; therefore, theflow regime with moving particle orientation inside the fieldstrength distribution is crucial and could not be interpretedin three-dimensions. The authors proposed that a future 3Dmodel should be developed and should be capable of addressingthe particles concentration and orientation in a continuous flowsystem.

CHALLENGES FACE THE USE OF CFD IN THERMALPROCESS MODELLING

Improving the Efficiency of the Solution Process

As can be seen above, the physical mechanisms that gov-ern thermal processes generally include any combination offluid flow, heat, mass, and scalar transport. As CFD involvesthe modelling of such mechanisms, which mostly occur ondifferent timescales, the temporal accuracy, and stability ofa solution is usually bounded by the ability of the model tocapture the mechanism that is the quickest to occur. This isdone through time stepping, which has therefore to be opti-mized during model development. The time-step must be smallenough to resolve the frequencies of importance during a tran-sient process. To do this an appropriate characteristic lengthand velocity of the problem is necessary, which can be ob-tained from non-dimensional numbers such as the Stroudalnumber, from experimental data, or from experience. For exam-ple, when Szafran and Kmiec (2005) developed a CFD modelof a spouted bed dryer, they found that extremely small time-steps of the order of 1 × 10−4 were required to resolve theinstabilities in the flow regime as well as the circulation ofphases. However, this meant that a year of computation wouldresult in a solution for only one hour of drying. Such a timeframe is excessive by any length of the imagination, and over-coming this difficulty required considerable insight into the

270 T. NORTON ET AL.

physical process. To do so, Szafran and Kmiec (2005) trans-formed the process from time-dependent into time-independent,from which drying curves could be developed, as describedabove.

Insight into the numerical abilities of CFD packages is alsoimportant if one needs to solve the problems of excessive com-puting times. Taking the parallelization features of commercialCFD codes as an example, these can allow a solution to beformed quicker, via domain decomposition, as long as the com-puting power is available and Lagrangian particle tracking is notemployed. Alongside this, the solving techniques employed incommercial CFD codes have also been found to play a majorrole in efficiency. Fletcher et al. (2006) noted how segregatedsolvers and coupled solvers can bring different attributes to so-lution progression, and found that owing to the reduced levelsof “random noise” introduced, the coupled solver permitted ahigh level of control over the solution process, allowing efficientand accurate predictions of the transient evolution of the flowinstability in a spray dryer, when compared to the segregatedsolver.

Simplifying the geometrical representation of CFD modelscan also cut down on both pre-processing and solving time. Thetwo-dimensional modelling technique assumes that the lengthof a system is much greater than its other two dimensions, andthat the process flow is normal to this length. As the effects of theconfining geometry are essentially disregarded, accurate judge-ment of whether the process is amenable to the two-dimensionalassumption is required.

CFD and Controlling Thermal Processing

All thermal processes in the food industry are performedunder controlled conditions. Unfortunately, due to the non-linearity of the transport-phenomena, CFD techniques are notyet amenable to the on-line control of thermal processes, andreduced order models which use statistical data to manipulatethe process variables via controlled inputs are more appropriate.However, this does not mean that the actions of a control systemcannot by modelled by CFD. Wong et al. (2007b) have beenthe first to implement a control system within a CFD model, inorder to simulate its performance. Such abilities undoubtedlyprovide benefits during the pre-design or optimization stages ofsystem development.

However, research and technology has not yet reached thelevel where low-order and CFD models can be combined toeffect control with accuracy during industrial thermal process-ing. This type of synergism would provide benefits in situationswhere accurate experiential readings, which act as the input tothe control system, may not be representative of the total sys-tem, that is, aseptic processing of non-homogeneous food. Inthis instance, the use of CFD to generate the time-series datacould be a viable alternative. However, more research is neededbefore such approaches can be applied.

Turbulence

One of the main issues faced by the food industry over thelast two decades is the fact that most turbulence models haveshown to be application specific. At the present time, there aremany turbulence models available; however, until a completeturbulence model capable of predicting the average field of allturbulent flows is developed the CFD optimization of manythermal processes will be hampered. The reason is that in everyapplication many different turbulence models must be applieduntil the one that gives the best predictions is found. The clos-est to the complete turbulence model thus far is LES, whichuses the instantaneous Navier-Stokes equations to model largescale eddies, with smaller scales solved with a subgrid model.However, using this model demands large amounts of computerresources, which may not be presently achievable.

For many cases, the k-ε model and its variants has proved tobe successful in applications involving swirling flow regimes,once the mesh is considerably fine. This is because when themesh is very fine, the k–ε model performs like the subgrid modelof a LES, and handles small-scale turbulence, while the largestscales are solved by the transient treatment of the averagedequations. In practice, therefore, most of the important energy-carrying eddies can be solved by this means. However, k–ε

models have lacked performance when predicting impingingflows, or inflows with large adverse pressure gradients. In suchinstance models like the k-ω or LES should be considered moreclosely.

Boundary Conditions

In CFD simulations, the boundary conditions must be ade-quately matched to the physical parameters of the process, withthe precision of similarity being conditioned by the mechanismunder study and the level of accuracy required. Even when thisis done, CFD solution still may not be a correct physical rep-resentation of the physical system. This was shown by Mistryet al. (2006), who found that an artificial pressure differentialwas required to predict the correct flow patterns in an oven,which was heated by natural convection. Such results suggestthe importance of sensitivity analysis studies alongside experi-mental measurements in the early stages of model development.Sensitivity analyses are also necessary for turbulence modelspecification, or turbulence model tuning via inlet conditions,and for CFD model simplification.

CONCLUSIONS

CFD has played an active part in the design of thermal pro-cesses for over a decade now. In recent years simulations havereached higher levels of sophistication, as application specificmodels can be incorporated into the software with ease, viauser defined files. The importance of maintaining a high level

RECENT ADVANCES IN COMPUTATIONAL FLUID DYNAMICS 271

of accuracy via circumspect choices made during model devel-opment is evident from the reviewed studies, as many studiesprovide detailed validation exercises. Undoubtedly, with currentcomputing power progressing unrelentingly, it is conceivablethat CFD will continue to provide explanations for transport phe-nomena, leading to better design of thermal processes in the foodindustry.

NOMENCLATURE

A = area (m2)C = water concentration (mol m−3)Cμ = empirical turbulence model constantcp = specific heat capacity (W kg−1 K−1)d = width of jet (m)D = width of cylinder (m)g = acceleration due to gravity (m s−2)M = Molecular weight (kg kmol−1)Nu = Nusselt numberp = pressure (Pa)R = gas constant (J kmol−1 K−1)Re = Reynolds numberk = turbulent kinetic energy (m2 s−2)sT = thermal sink or source (W m−3)sc = concentration sink or source (mol m−3)T = temperature (K)t = time (s)U = velocity component (m s−1)V = volume (m3)−→v i = velocity component (m s−1)x = Cartesian coordinates (m)Greek Lettersρ = density (kg m−3)μ = dynamic viscosity (kg m−1 s−1)β = thermal expansion coefficient (K−1)λ = thermal conductivity (W m−1 K−1)α = water molar latent heat of vaporization,

(J mol−1)ε = turbulent dissipation rate (m2 s−3)φ = the transported quantity� = diffusion coefficient of transported variableϑ = the diffusivity of the mass component

in the fluid (m2 s−1)ω = specific dissipation (s−1)μt = turbulent viscosity (kg m−1 s−1)Subscriptsi = Cartesian coordinate indexbf = bulk fluids = surfaceV = mesh element volumeA = area of mesh elementm = mean0 = with no turbulence

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