Cans Pasteurization

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Simulation of heat transfer for solidliquid food mixtures in cansand model validation under pasteurization conditions

Selin Kzltas, Ferruh Erdogdu *, T. Koray Palazoglu

Department of Food Engineering (Gda Mhendisligi Blm), University of Mersin, 33343 iftlikky-Mersin, Turkey

a r t i c l e i n f o

Article history:Received 10 March 2009

Received in revised form 28 October 2009

Accepted 29 October 2009

Available online 4 November 2009

Keywords:

Canning

Solidliquid food mixtures

CFD

Heat transfer

Natural convection

a b s t r a c t

During processing of canned mixtures of solidliquid foods, conduction and convection occur simulta-neously. The literature lacks in a complete simulation study where a large number of solids are dispersed

in the liquid phase, e.g. canned peas. Therefore, the objectives of this study were to determine tempera-ture changes inside a can containing solidliquid food mixtures. For this purpose, dispersed stationary

solids (canned peas in water) in a 2D (axi-symmetrical) configuration were applied. Ansys V11 (AnsysInc., Canonsburg, PA) was used to solve continuity, energy and momentum equations. For experiments,

canned pea samples were prepared in 500 g cans, and heating process was conducted in a retort underpasteurization conditions at 98C. Temperature changes were measured using needle type thermocou-

ples, and simulation results were validated against experimental data. This study is expected to be a sig-nificant contribution to the literature for further optimization studies and to form basis of an industrial

project to improve canning process of solidliquid mixtures.2009 Elsevier Ltd. All rights reserved.

1. Introduction

Heat transfer studies in foods are of greater importance since

thermal processing is the most common technique used for preser-vation of foods. Thermal processing is the critical control point toensure safety and a critical unit operation to maximize process effi-ciency (Weng, 2005). Aseptic processing and canning are used in

food processing for this purpose. Although aseptic processing gainsimportance with recent developments, canning still provides a uni-versal and economic method (Weng, 2005). Process efficiency isdetermined using analytical and numerical solutions of partial dif-

ferential equations governing the process, and there has been anincreasing interest in using new process modeling and calculationmethods in canning industry (Weng, 2005). Heat transfer modes ina canned food are conduction for solid foods, natural convection

especially for low viscosity liquid foods, convection plus conduc-tion for liquid foods with solid particles and convection followedby conduction for liquid foods containing starch or high viscositymodifiers (Chen and Ramaswamy, 2007).

To determine process efficiency for conduction heating, solutionof energy equation is required while energy, momentum and con-tinuity equations should be solved for convection.Datta and Teixe-ira (1988)were first to develop numerical predictions of transient

temperature and velocity profiles of a can filled with water. Then,

simulations of viscous liquid foods in cans were done by Kumaret al. (1990) and Kumar and Bhattacharta (1991). Upon introduc-

tion of computational fluid dynamics (CFD) programs and fastercomputing abilities, simulation studies for natural convectionheating have been conducted for different processing conditions

(Abdul Ghani et al., 1999, 2002; Farid and Abdul Ghani, 2004; Chenet al., 2005; Sriwattanayotin et al., 2006; Varma and Kannan,2006). Besides solid and liquid products, mixtures of solidliquidfoods are also processed in cans. Processing time for these cases

can be determined assuming solidliquid mixture heats up by con-duction ignoring natural convection effects. This leads to heatingtimes much longer than required with over-processed products.For the case of agitation, spatial variation of liquid temperature

can be ignored assuming a lumped parameter model (Lenz andLund, 1978; Datta and Teixeira, 1988). For process simulation ofsolidliquid mixtures,Lenz and Lund (1978) applied heat transfercoefficient between liquid and particles to determine the transient

temperature change of the particles where it was assumed that theliquid temperature change could be described with the lumpedmodel. Heat transfer coefficient approach was later justified byRamaswamy et al. (1982).Lekwauva and Hayakawa (1986)devel-

oped a model for temperature prediction of particleliquidmixtures solving overall heat balance equations for spherical,cylindrical and oblate spheroidal-shaped particles. Agarwal(1988)proposed a model, based on a boundary-layer formulation

for individual particles in a sphere assemble, to provide a relationbetween heat transfer characteristics and hydrodynamics of multi-particle systems. Chinesta et al. (2002) used a homogenized

0260-8774/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.jfoodeng.2009.10.042

* Corresponding author. Tel.: +90 324 361 0001x7199; fax: +90 324 361 0032.

E-mail addresses: [email protected], [email protected] (F.

Erdogdu).

Journal of Food Engineering 97 (2010) 449456

Contents lists available at ScienceDirect

Journal of Food Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j f o o d e n g
http://dx.doi.org/10.1016/j.jfoodeng.2009.10.042mailto:[email protected]:[email protected]://www.sciencedirect.com/science/journal/02608774http://www.elsevier.com/locate/jfoodenghttp://www.elsevier.com/locate/jfoodenghttp://www.sciencedirect.com/science/journal/02608774mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.jfoodeng.2009.10.042


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thermal conduction model for particulate foods assessing the ef-fects of particles spatial distribution and differences in thermal

conductivities.Abdul Ghani and Farid (2006) verified the effect ofnatural convection on heating process of solidliquid food mix-tures (pine-apple slices in a model liquid) indicating that naturalconvection effects in the liquid played a significant role in the evo-

lution of temperature. Abdul Ghani and Farid (2007) simulated

temperature distribution within beef fat and water mixture duringhigh pressure compression. Rabiey et al. (2007) simulated tran-sient temperature and fluid flow during natural convection heating

of a cylindrical can containing nine large spherical particles in amodel liquid. The latter two studies used CFD approaches for calcu-lations and concluded that solid particles influenced the buoyancywhich drove the flow.

The literature still lacks in a complete simulation study for pre-dicting temperature changes of solidliquid mixtures where solidsare randomly dispersed in the liquid phase, e.g. canned peas.

Therefore, the objective of this study is to determine temperaturechanges inside a can containing solidliquid food mixtures duringthermal processing and verify simulation results with experiments.

2. Materials and methods

To accomplish the stated objectives, canned pea samples were

used. Simulations were accomplished using Ansys V11 (AnsysInc., Canonsburg, PA), and simulations results were compared withthe experimental results for validation.

2.1. Experimental methodology

Canned peas, representing the solidliquid mixtures, were usedfor experimental measurement of temperature changes. For this

purpose, canned peas were purchased from a local store. Thesecans were opened, and weights of liquid (water) and solid (peas)portions were determined. The objective to use water for filling li-

quid was to apply temperature variable thermo-physical proper-ties in the simulations. However, to demonstrate the effect ofthis assumption, experiments were also carried out where the fill-ing was done directly with the liquid obtained from the purchasedcans. The dry matter of the filling material was 3.5%, and the heat-

ing rates were similar compared the cases where the water as thefilling liquid was used. Diameters of peas were also measured(7.3 mm), and they were filled back in empty cans (500 g; #1;73 mm in diameter 110 mm in length). Needle type thermocou-

ples were located on the side of the cans using ring gaskets andlocking-receptacles. One thermocouple was inserted in a peas cen-ter located at the cans geometrical center while another one was

off-center to measure water temperature change (82 mm frombottom and 12 mm from central line). Then, the cans were tightly

seamed (MAC-230, Umar Makina Sanayii, _Istanbul, TR) after filling.Due to tightly-packed configuration of the cans constituents, pos-

sible thermocouple conduction errors were assumed to be negligi-ble. For each thermocouple, different cans were used to minimizethermocouple heating effects on velocity profiles of water andtherefore on temperature changes due to natural convection. As re-

ported by Kannan and Sandaka (2008), disturbed temperaturevelocity fields might result in difficulties in accurate measurementof temperature, and these effects might not be quantified eitherexperimentally or analytically. Ten experiments were conducted,

and average values of temperature change with standard devia-tions were reported. Heating experiments were carried out in boil-ing water (98 C) in a vertical retort (OMS Lab 20, OsmanlMakina, Balkesir, TR), and temperature changes were recorded

using a Keithley 2700 DMM (coupled with Keithley 7700.20CHmultiplexer, Keithley Instruments, Cleveland, OH, USA) data acqui-

sition system. After each experiment was conducted, cans wereopened and checked to assure that the thermocouple inside thepea was not disturbed. For the cases when the thermocouple wasdisturbed, the data was discarded.

2.2. Simulations

As stated in Section 1; continuity, energy and momentum equa-tions (NavierStokes equations) need to be solved when naturalconvection heating was involved. Eqs. (1)(4) show the NavierStokes equations in cylindrical coordinates. The angular directionequations were not involved since an axi-symmetric approach

was applied in this study.

Continuity equation:

1

r @

@rr qf vr

@

@rqf vz 0 1

Fig. 1. Arrangement of solids in the 2D axi-symmetric arrangement (left hand sideis center line).

450 S. Kzltas et al./ Journal of Food Engineering 97 (2010) 449456


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Energy equation:

@T

@t vr

@T

@r vz

@T

@z

kfqf cpf

1

r @

@r r

@T

@r

@2T

@z2

" # 2

Momentum equation in the radial direction:

qf @vr

@t vr

@vr

@r vz

@vr

@z

@P

@r l

@

@r

1

r @

@rr vr

@2vr

@z2

" # 3

Momentum equation in the vertical direction:

qf @vz

@t vr

@vz

@r vz

@vz

@z

@P

@z l

1

r @

@r r

@vz

@r

@2vz

@z2

" # qf g 4

where Tis temperature (K),Pis pressure (Pa),tis heating time (s),g

is gravitational acceleration (9.81 m/s2), l is dynamic viscosity(Pa s), kf, qfand cpfare the thermal conductivity (W/m K), density(kg/m3) and specific heat (J/kg K) of the fluid (water) and vrandvzare the velocity components (m/s) in radial and vertical direc-

tions, respectively. Ansys V11 (Ansys Inc., Canonsburg, PA) was

used to solve the NavierStokes equations to simulate the heattransfer in both liquid and solid phases. For this purpose, Ansys-

Flotran module was applied with the following parameters andassumptions:

Fig. 2. Torus volume approach applied using the axi-symmetry.

Table 1

Temperature-variable thermo-physical properties of water applied in the simulations

(engel, 2007).

Temperature (K) Density

(kg/m3)

Viscosity

(Pa s)

Thermal

conductivity

(W/m K)

Specific heat

(J/kg K)

293.15 998 0.001002 0.598 4182

313.15 992.1 0.000653 0.631 4179

333.15 983.3 0.000467 0.654 4185

353.15 971.8 0.000355 0.670 4197

373.15 957.9 0.000282 0.679 4217

393.15 943.4 0.000232 0.683 4244

Fig. 3. (a) Mesh structure applied in the simulation (right hand side is can wall);and (b) nodes at particle surfaces and between the particles.

S. Kzltas et al./ Journal of Food Engineering 97 (2010) 449456 451


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Solid phase (peas) was assumed to be stationary, a perfectsphere shape and uniformly distributed in the can.

To reduce the problem from 3D to 2D for a vertical can,axi-symmetrical analysis has been applied. With this approach,computation time was reduced considerably since there wasno need to define the nodes in the angular direction. The dis-

tance between the spheres was 0.5 mm, and the circles on the

vertical center line were half in area since they will result in acomplete sphere when the 2D axi-symmetrical shape is com-pleted to the 3D.

To locate the stationary solids in the water, the porosity value ofthe can constituents (ratio of the water volume to the volume ofcan; 35% 2.0%) was chosen to be target value. For this pur-pose, required diameters of solids were estimated to be

7.5 mm. Based on different pre-trials, 65 solids, arranged asshown inFig. 1, resulted in the target porosity value with theirtorus volumes when the 2D shape was completed to 3D

(Fig. 2; completed shape of the assumed axi-symmetricalsituation resulted in torus-shaped volumes uniformly distrib-uted in the water).

0.5 mm distance between the particles was due to the problems

faced during meshing the fluid phase. There were restrictions inmeshing abilities to let numerous particles touch each otherwhile meshing. Since meshing was not possible for that kindof approach, a certain space (0.5 mm) between the particles

was assumed. Including head space in the model would result in the require-

ment of the analysis of airwater interface problem with addi-tional complexities in the problem. Erdogdu et al. (2009)

neglected the effect of air space for comparison of natural con-vection and conduction heating processes in cans, and thisassumption was shown not to affect the simulation results.

In the 2D axi-symmetric configurations, number of nodes were

over 60,000. In the Ansys-Flotran module, Collocated Galerkin advection

scheme was used to get a convergent solution in a straight for-

ward fashion for solution of momentum, pressure and tempera-ture variable as reported in ANSYS help.

Modified inertial relaxation parameter was set to 1 to preventpossible spurious oscillations in the fluid phase and resultingconvergence difficulties in the solutions.

Three dimensional matrix algorithm (TDMA) was used to solve

velocity and temperature changes while preconditioned conju-gate gradient method (PCGM) was applied to solve pressurechanges.

Time step was progressively increased from 0.001 to 0.05 s inthe first 120 s of heating; it was specified based on the resultsof pre-runs. Then, it was again progressively increased to 0.1

(for 120240 s of heating) and 0.25 s (for 240360 s of heating)during the run. It was important to note that a higher number ofiterations were required in the Ansys-Flotran module toimprove the accuracy due to lower viscosity of water. A similarcomment was also noted by Abdul Ghani et al. (1999). This was

especially significant at the initial stages of heating to solve themomentum equations for correct velocity profiles.

Literature-reported values for thermo-physical properties (ther-

mal conductivity, k= 0.5 W/m K; specific heat,cp = 3057 J/kg K,and density, q = 1062 kg/m3) of the solid phase (peas) were used

(Garrote et al., 2006, 2008) in the simulations. Since the heattransfer in peas were in conduction mode, variation in thermal

diffusivity value a kqcp

was assumed to be negligible even

though thermo-physical properties of the liquid phase were

applied ad as a function of temperature as explained below. Temperature dependent thermo-physical properties of liquid

phase (water), as applied in the simulations, are reported inTable 1. Water density, with all the other properties, wereassumed to be the function of temperature to account the natu-ral convection.

Meshing was implemented with a very fine grid at the vicinity ofcan walls, particle surfaces and between the particles toaccurately resolve velocities and temperatures near the surfaces.Velocity and temperature gradients were expected to be rela-

tively higher especially at the can walls due to higher tempera-ture difference at the initial steps of the analysis. While Fig. 3ashows the mesh structure applied in the simulation, Fig. 3bshows the nodes at particle surfaces and between the particles.

Initial temperature of the system was 27 1C (based on theexperiments) while the medium temperature was boiling water(98 C) with infinite heat transfer coefficient assumption. Since

the cans were immersed in boiling water, a high heat transfercoefficient with a very low thermal resistance of the can walls

Fig. 4. Movement of liquid phase adjacent to can wall due to buoyancy effects (right hand side is can side wall).



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was assumed. Therefore, constant surface temperature as athermal boundary condition was applied in the simulations

assuming that surface temperature reaches medium tempera-ture immediately and stayed constant. Validity of this assump-tion was shown byErdogdu et al. (2009).

No-slip condition was applied at the can walls and particle

(sphere) surfaces.

Liquid phase inside the can was assumed to be initially at restwith the given uniform initial temperature. Laminar flow mode was assumed to occur through the whole

heating process. This resulted in oscillations in the first few sec-onds of the simulations. Since the oscillations did not continue,turbulent flow mode was not required to apply, and the oscilla-

tions that occurred were just neglected. Further information onthis issue was given byErdogdu et al. (2009).

Calculations were carried out on an Intel Pentium QuadCore,2.4 GHz with 8 GbyteRAM PCrunningon Windows XP64 bitedition.

3. Results and discussion

When a fluid is subjected to a rapid temperature increase adja-cent to a solid wall, part of the fluid in the wall vicinity expands

resulting in an increase in the local pressure with significant effectsin heat transfer due to thermal buoyancy effects in a gravitationalforce field (Aktas and Farouk, 2003). In a similar way, during

Fig. 5. Velocity profile of the liquid phase at 30 s of the process at the vicinity of can wall and between the particles.



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thermal processing of solidliquid mixtures in cans, water adjacentto the can walls receives the heat resulting in expanding and get-

ting a lower density while the liquid away from the walls stay atlower temperature. This leads to development of an upward buoy-ancy force with a motion due to density differences. This move-ment also carries the colder fluid upward by viscous drag. The

fluid flowing upward is deflected by top surface of the can and

starts moving in radial direction by getting heavier and startingto move downwards. Fig. 4 shows this movement. As the liquiddescends, its temperature decreases upon mixing with colder lay-

ers, and a new cycle starts from bottom. These changes create a re-circulating flow increasing the rate of heat transfer. When there aresolid impermeable particles distributed in the fluid, velocity pro-files change due to the heat exchange and surface deflections while

the flow is slowly through the stack of solid particles.Fig. 5showsthe evolved velocity profiles on vicinity of can wall and between

the particles at 30 s of the process. Confined natural convectionis related to RayleighBenard problem where the hot fluid expands

and produces an unstable density gradient in the fluid layer at thebottom (Vargas et al., 2002). The slowest heating zone, a criticalparameter in estimating process efficiency, between geometriccenter and bottom of the can with formation of Benard convective

cells is shown in Fig. 6a and b. When the effect of natural

convection heating is pronounced, thermal stratification is also ob-served (Fig. 6a and b) based on the fluid movement due to buoy-ancy effects explained above.

Figs. 7 and 8 show the comparison of simulation results withthe experimental data obtained from cans heated in boiling waterunder pasteurization conditions (at 98 C) for peas located at thecan geometric center and off-center water temperature (82 mm

from bottom and 12 mm from central line). As seen in thesefigures, simulation results agreed well with the experimental data

Fig. 6. Temperature contours at 30 and 300 s of the process (left hand side is center line); (a)t= 30 s; and (b) t= 300 s.



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validating the given 2D assumption to simplify the canned solidliquid mixture. Based on these figures, however, center peatemperature seemed to be over-estimated (the differences wereless than 2 C in the worst case) and water temperature to be un-

der-estimated (the differences were less than 5 C in the worst case)at the processing time of 3050 s. This possibly implies that naturalconvection between particles and liquid phase was over-estimatedin the simulations. It is suspected that due the assumption of thin

film water between the particles, natural convection effects mightbe over-estimated as a result of faster liquid phase movement be-tween the particles, and this might result in higher heat fluxes be-

tween the solid and liquid phases leading to the higher estimatedtemperature in the simulations. For the case of liquid temperature,

the thermocouple location was in the upper side of the cans as ex-plained in the methods. Since, in the upper side of the cans, vorti-

ces, recirculation and the natural convection currents were densercompared to the other regions, these kinds of differences were ex-pected to be. In addition, thermocouple conduction errors shouldalso be noted.

As indicated, experimental validation of the simulation was car-ried out in boiling water under pasteurization conditions (at98 C). Hence, simulation results should be used with cautionwhile extending to the sterilization conditions.

For further development of the simulation model, use of 3Dgeometry with a packing optimization algorithm which will leadto locating homogeneous spherical particles inside a cylindricalcan might be used. Mueller (2005) described the details of a

numerical packing algorithm using a sequential technique to packspheres in cylinders. Using such an algorithm with a CFD program

is expected to improve the heat transfer model for solidfluid mix-tures used in this study. Due to the complexity of the requirement

for solutions of continuity, energy and momentum equations in thesolidliquid mixture systems, porous media approaches mighthave been considered for the solution. Influence of porosity on nat-ural convective flow and heat transfer was reported to be signifi-

cant in fluid saturated porous media (Nithiarasu et al., 1998). For

this approach, the given system could be considered as a porousmedia involving small pores where the fluid flow becomes mostlyoutside the solid (Datta, 2007). However, as stated byDatta (2007),

an exact manner should refer to the solution velocity distributionof the fluid in the void space of the solidfluid mixture using theNavierStokes equations even though higher number of calcula-tions is required (Xu and Jiang, 2008).Xu and Jiang (2008)also pre-

sents considering limited number of identical particles as theporous media for various arrangements to solve the NavierStokesequations.

4. Conclusions and suggestions

In this study, simulation of heat transfer in canned solidliquid

mixtures was carried out applying a CFD methodology. The axi-symmetric assumption, leading to the formation of torus volumesof solid phase inside the liquid reduced the problem from 3D to 2Dwithout affecting the results significantly, and the simulationswere validated by experiments. This part might be especially sig-

nificant for further optimization studies. So far in the literature,optimization of heat transfer in solidliquid food products, whereheat transfer occurs by natural convection and conduction heatingsimultaneously, has not been reported probably due to the require-

ment of extensive CPU usage, very dense computations for deter-mining temperature distribution. Alvarez-Wazquez and Martinez(1999) described the optimal control of natural convection incanned foods from a mathematical point of view. The 2D assump-

tion might help in reducing the computational requirements and

developments of optimization models for canned solidliquid foodmixtures. Canned solidliquid mixtures are usually processed inagitated retorts where heat transfer is easily influenced by particle

to fluid relative motion (Meng and Ramaswamy, 2007a). Excellentexperimental studies were reported in the literature (Meng andRamaswamy, 2007a,b, 2009). Simulation of thermal processingfor this case becomes an important task for process design and

control. Based on the results of this study, applying a CFD method-ology for a heat transfer study in an agitated retort might also becarried out including the particles movement in the filling liquidwhere a 3D modeling should be done since the 2D assumption sce-

nario will not hold.

Acknowledgement

This research was supported by the Scientific and Technical Re-search Council of Turkey, project no: 107O619 (TOVAG-Agricul-

ture, Forestry and Veterinary Research Grant Committee).

References

Abdul Ghani, A.G., Farid, M.M., 2006. Using the computational fluid dynamics toanalyze the thermal sterilization of solidliquid food mixture in cans.Innovative Food Science and Emerging Technologies 7, 5561.

Abdul Ghani, A.G., Farid, M.M., 2007. Numerical simulation of solidliquid foodmixture in a high pressure processing unit using computational fluid dynamics.Journal of Food Engineering 80, 10311042.

Abdul Ghani, A.G., Farid, M.M., Chen, X.D., Richards, P., 1999. Numerical simulationof natural convection heating of canned food by computational fluid dynamics.Journal of Food Engineering 41, 5564.

Abdul Ghani, A.G., Farid, M.M., Chen, X.D., 2002. Numerical simulation of transient

temperature and velocity profiles in a horizontal can during sterilization usingcomputational fluid dynamics. Journal of Food Engineering 51, 7783.

0

20

40

60

80

100

0 60 120 180 240 300 360

TIme (s)

CenterPeaTemperature(C)

Center Pea Temp.SD

Simulation

Fig. 7. Comparison of simulation results with experimental data for pea located at

the can geometric center.

0

20

40

60

80

100

120

0 60 120 180 240 300 360

Time (s)

WaterTemperature

(C)

Water Temp. SD

Simulation

Fig. 8. Comparison of simulation results with experimental data for off-center

water temperature (82 mm from bottom and 12 mm from central line).



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