Visualisation of three-dimensional flows in rotating cans using positron emission particle tracking...

Journal of Food Engineering 60 (2003) 229–240

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Visualisation of three-dimensional flows in rotating cansusing positron emission particle tracking (PEPT)

P.W. Cox a, S. Bakalis a, H. Ismail a, R. Forster b, D.J. Parker b, P.J. Fryer a,*

a Centre for Formulation Engineering, School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UKb Positron Imaging Centre, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Received 16 August 2002; accepted 15 January 2003

Abstract

The flow of foods in cans is critical in determining process times and thus product quality. The flow of liquids has been followed

in axially rotated metal food cans using positron emission particle tracking. The technique involved placing a small (�600 lm)

isokinetic radioactive tracer into a container and following its movement with a positron sensitive camera. The small size of the

tracer, as well as the ability of the emitted gamma rays to penetrate both opaque fluids and considerable thicknesses metal (�10 cm)

make the method ideal for studying fluid flows inside real equipment. The method enables a spatial resolution of close to one

millimetre and a time resolution of a millisecond. Flows have been studied in axially rotated cans filled with Newtonian liquids of

differing viscosities and a varying amount of headspace. The inclusion of a headspace in a can caused the flow within the two-phase

system of a viscous solution to become inherently three-dimensional with a regular period of circulation and flow trajectory.

� 2003 Elsevier Ltd. All rights reserved.

1. Introduction

Thermal processing of canned foodstuffs is a com-

monplace activity. Canning has been the focus of in-

tensive study for many years and remains a significant

processing operation. Enhancing heating rates would be

extremely useful as the size of the pack makes it difficult

to heat or cool quickly and therefore reducing thequality of the product. Understanding the relationship

between the heating rate and the flow patterns in the can

would be valuable. Within solid products heat transfer is

by conduction alone and the rate of heating, and

therefore process efficacy, may adequately be modelled

by techniques such as finite element analysis (e.g., see

Bakalis, Cox, & Fryer, 2001). However, where liquid

products or solids within a liquid matrix, are heated,natural convective currents and fluid mixing augment

the thermal penetration from the heated wall to the bulk

liquid phase. The use of forced convection methods

(such as rotary retorts) is designed to increase the rate of

mixing in the liquid and may further raise the rate of

thermal penetration (e.g., see Roa, Cooley, Anathes-

* Corresponding author. Tel.: +44-121-414-5451; fax: +44-121-414-

5324.

E-mail address: [email protected] (P.J. Fryer).

0260-8774/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0260-8774(03)00042-6

waran, & Ennis, 1985). A commonly applied mechanism

to achieve rates of thermal penetration faster than by

conduction alone is to roll cans during heating. Con-

tainers may either be rotated axially or longitudinally to

increase the flow of liquids and therefore heat penetra-

tion within the container. Considerable efforts have been

applied to estimate heat transfer rates in axially rotating

cans, for instance Deniston, Hassan, and Merson (1987).However, studies of the variations of fluid and particle

velocities inside cans has received less attention and little

consideration has been given to the mixing properties of

the fluids within the cans during processing. Even more

so, only empirical observations have been made of the

effect of the headspaces commonly included in com-

mercially produced cans (such as Berry & Bradshaw,

1980; Berry & Kohnhorst, 1985; Berry, Savage, & Pflug,1979).

Statically heated canned liquid products and natural

convection during cooking have been considered and

modelled by a number of workers (including Abdul

Ghani, Farid, Chen, & Richards, 1999; Datta & Teixe-

ira, 1988; Kumar & Bhattacharya, 1991) suggesting that

during heating hot, more buoyant, liquid rises at the can

walls and descends at the can centre, with a subsequentdisplacement of the slowest heating zone away from the

geometric centre of the can. However, if the container is

mail to: [email protected]

230 P.W. Cox et al. / Journal of Food Engineering 60 (2003) 229–240

agitated, either axially or end over end, the effect ofgravitation or gravity-induced convection of the hot

buoyant liquid is lost.

Tattiykul, Roa, and Datta (2001) have evaluated the

loss of gravitational reference using a finite element

simulation. When revolved rapidly enough an axially

rotated can displays a different mode of heat transfer.

The complex convection loops described by Kumar and

Bhattacharya (1991) and Abdul Ghani et al. (1999) arereplaced by a stratified temperature gradient, which is

distributed symmetrically around the axis of rotation

(Tattiykul et al., 2001).

Not surprisingly many studies of the heat transfer

rates within rotated cans filled with rheologically com-

plex liquids have been made (e.g., Berry & Bradshaw,

1980; Berry et al., 1979). The complexity of the problem

is increased by the incorporation of particles (e.g.,Deniston et al., 1987; Merson & Storoforos, 1990).

Deniston et al. (1987) considered that a full numerical

solution for describing the motion of food particles

within rotated heated cans to be a remote possibility;

over a decade later, little progress has been made on

the problem. Merson and Storoforos (1990) estimated

heat transfer using tethered particles that incorporated

transducers, it was felt that this may not provide asuitable method of investigating heat penetration in

complex fluid/particle arrangements because of the

tethered particle affected the fluid flow it was intended to

study.

Many authors have provided dimensional analysis

solutions of heat penetration in such situations. Di-

mensionless groups such as the Nusselt (d=k), Prandtl

(v=a), Biot (hd=k), Reynolds (qxd2=2l) and Froude(x2d=4g) have been used to describe and correlate heat

transfer data from experimental results (e.g., Deniston

et al., 1987). However, only the radial dimension is con-

sidered, if any in the dimensionless groups used to des-

cribe heat transfer and no account of fluid mixing, by

any mechanism, is made. Stoforos and Merson (1992)

followed the trajectories of large Teflon spheres in sili-

cone oil and, although their findings were only qualita-tive, a variety of particle paths could be seen; albeit only

considered in one viewing plane. Merson and Storoforos

(1990) proposed various typical cases to describe the

motion of the liquid and liquid/particle systems. Their

paper considered two extremes of fluid motion: either (i)

the can rotated and imparted no force to the liquid, so

the fluid remained stationary, or (ii) a solid body rota-

tion was established within a fully filled can so that therotational speed of the fluid at a given radius r is given

by Eq. (1).

uðrÞ ¼ 2pNr ð1Þ

where u is the fluid velocity, N the can rotational speed

(revolutions per second).

However, the mode of fluid flow was not quantifiedsave for simple descriptions (rotating, still and co-

rotating).

One other complexity in the commercial canning

process is a headspace in the can (i.e. the presence of an

air bubble with air either incorporated deliberately or

degassed from the liquid). Although common within

industrial practices, the effect of headspaces in cans is

rarely considered. This extends the experimental systemsto two or more phases (i.e. liquid/air or liquid/particle/

air systems). Berry and Bradshaw (1980) suggest that

industrial canning practices may make it impossible to

produce a canned product without a headspace, either

intentionally or by its thermal generation as the heated

products degas. Berry et al. (1979) and Berry and

Kohnhorst (1985) examined the effects that the inclusion

of headspaces in canned viscous liquid products mighthave by examining the can heating curves. Increasing

the headspace in canned cream style corn dramatically

increased thermal penetration. Berry et al. (1979) con-

cluded that the headspace volume was the most critical

processing parameter; with the size of the head-

space bubble providing a correlating parameter for heat

transfer studies. Berry and Bradshaw (1980) also pro-

posed that the headspace bubble moved, via centripetalforces, through the product and so increased mixing and

therefore heat transfer.

Experimental studies of in-can mixing have been

restricted to model transparent systems. The behaviour

of opaque fluids inside metal cans is difficult to follow.

In the work presented here fluid flow trajectories have

been followed in rotating metal cans containing vis-

cous Newtonian solutions. The rates of rotation, fluidviscosity and headspace volumes have been used as

variable parameters and the fluid flow observed within

metal cans using positron emission particle tracking

(PEPT). Parker, Broadbent, Fowles, Hawkesworth,

and McNeil (1993) described the use of PEPT for vi-

sualisation studies within metal pilot scale equipment.

Such equipment need not be transparent as for visual

observations and need not be metal free as withmagnetic resonance imaging experiments (e.g., Reyes,

Lafi, & Saloner, 1998). The PEPT tracer positions are

rapidly calculated by multiple triangulations and are

highly resolved in three dimensions this enables the

PEPT camera to record the trajectories of particles

that are sufficiently small and insufficiently dense as to

be considered isokinetic with most viscous fluid flows.

The spatially and temporally accurate data allows theposition and velocity of the fluid to be found. In the

context of axially rolled cans the penetrative capabili-

ties of the PEPT system made it ideal for studying

fluid flow and velocity fields within opaque fluids and

metal containers. The aim of this paper is to demon-

strate the validity of the method and to identify flow

patterns.

x

y

z

Can centre plane

Axis of rotation

Fig. 1. Geometry of the can, with axis labels.

P.W. Cox et al. / Journal of Food Engineering 60 (2003) 229–240 231

2. Materials and methods

2.1. Cans and liquids

The metal cans used throughout this study were

supplied by a commercial cannery and measured 119

mm high with a diameter of 100 mm. After filling the

cans were sealed using a hand-operated seamer. Head-

space volumes were calculated as mass fractions ofliquid removed from brimful cans.

Initial experiments used water, but the sedimentation

velocity of the tracers in water was found to be ca. 1.2

mm/s. Subsequent experiments used cans filled with

sucrose solutions made from commercially available

syrup. The syrup was diluted with water to give two

solutions with viscosities of 4.85 and 13.90 mPa s at 20

�C respectively. In either solution no particle sedimen-tation was observed tracers were isokinetic with the

flow. The cans were rotated on a horizontal tube roller

at 12 and 24 rpm. All experiments were performed at

ambient temperatures.

A Perspex replica of the cans used for the PEPT ex-

periments was constructed. This was used for visuali-

sation studies of the position of the headspace, and

verification of the flow patterns indicated by the PEPTtracers.

2.2. Positron emission particle tracking

PEPT tracers were prepared by bombarding water in

the Birmingham �in-house� cyclotron to make the ap-

propriate tracer: 16O + 3He ¼ 18F + neutron. 18F decays

by positron emission with a half-life of �110 min. Theradioactive water was absorbed into 600 lm ion ex-

change beads, which were then coated with paint to

prevent leakage of the 18F. Annihilation of the positron

generated by the decay results in the emission of back-

to-back 511 keV c-rays, which can be detected. The 180�separation of the emitted c-rays allow the position of the

tracer to be estimated by regression of the multiple c-ray

trajectories recorded by the Birmingham positron ca-mera (see, e.g., Ding, Seville, Forster, & Parker, 2001;

Parker et al., 1993).

The School of Physics at the University of Birming-

ham have written several computer programs for the

visualisation of PEPT data:

(i) Particle tracking program data may be presented as

x, y, or z motion components against time (see Fig.2).

(ii) Relative occupancies within specific regions may be

shown as x=y, x=z and y=z slices with values colour

coded.

(iii) Animated trajectories may be drawn, once more as

x=y, x=z and y=z slices, and the motion of the parti-

cle observed.

For the situations encountered here the existing

program was not suitable for routinely examining the

tracer trajectories. An isometric plotting program was

developed using the Matlab technical computing envi-ronment which projected particle trajectories as a

moving point followed by a line within a rotatable,

three-dimensional, virtual space. Raw data files pro-

duced by the PEPT camera contain ASCII data columns

of time and ðx; y; zÞ positions and thus can be used fur-

ther examination. Typically the data were smoothed to

remove noise by applying a median filter (taking the

median average over every five points). Other datatransformations are described below.

In Figs. 2–8 and 10–13 all the position values refer to

the position of the can within the positron camera. Al-

though, values are similar between experiments they are

not the same and positional definitions will be given in

each instance. Fig. 1 shows the geometry of the cans

with each axis position and the direction of rotation

marked.

3. Results

3.1. Flow patterns without headspaces

Initial experiments used cans that were filled com-

pletely. In this case the tracer trajectories followed

circles within the can. Fig. 2 shows the x, y, z and

time traces for 13.90 mPa s solution in a fully filled can.With all of the liquids examined, in fully filled cans the

tracer particles followed essentially circular trajectories

throughout the experiments. The frequency of rotation

of the can is the same as that of the tracer the slight

variations of amplitude seen in the x=y plots is the result

of slight variations in the rollers. Very slow motion

along the length of the can was observed but the amount

of movement was much less than below, where air isintroduced as a headspace. Calculation of velocity pro-

files for the experiments was performed with Matlab.

Velocity components could be extracted for each of the

Fig. 2. Trajectories for a fully filled can containing 13.90 mPa s syrup: z value shows movement along the can, whilst x and y show rotation. It should

be noted that the migration in the z direction i.e. can length is much smaller and slower than in the examples shown in Figs. 6 and 7.


velocity components i.e. x, y and z. With the full can the

experiment ran for 1750 s in which a 0.03 m migration

was observed in that time, an average rate of 10�4 m/s.

When the x and y rotation velocities are plotted as a

function of radius they show that the fully filled can doesrotate as a solid body as shown by Fig. 3a. A regression

of these points is shown in addition to the theoretical

velocities calculated by Eq. (2).

u ¼ umax

rR

ð2Þ

where u is the fluid velocity, umax the velocity at the can

periphery, r the radius for the measurement and R the

can radius.

Comparison of the velocities of the particle and the

calculated solid body rotation velocities showed a close

correlation albeit over a narrow range of radii as the

particle showed little axial movement.

3.2. Flow patterns with headspaces

A second series of experiments were carried out where

a headspace was introduced in to the can during the

filling stage (typically 5%, 10% and 20% air contents).

Here the flow patterns within the cans was significantly

different to those of the full cans. For the experimental

conditions considered here the headspace was never

significantly displaced from the top of the can duringrotation. The effect of the headspace in a can caused the

tracer particles to follow a ‘‘D’’ shaped trajectory as

they passed under and around the bubble as can be seen

in Fig. 4. The presence of the headspace acts to make the

flow significantly three-dimensional. The position of the

headspace and the general flow pattern of the liquids

were observed within a Perspex replica can using similar

solutions to those used in the PEPT experiments as theposition of the headspace could only be inferred, (albeit

correctly), from the PEPT experiments. Visual obser-

vations confirmed that the headspace remained at the

top of the can, regardless of the rotation speed (up to 24

rpm), and had a ‘‘D’’ shaped profile (Fig. 4). The bubble

position was heeled over from the can top due to the

rotation of the container and the leading edge of the

bubble also had a slight D profile to it. Flow patternsobservations in the Perspex can were made using non-

Fig. 3. (a) Relation ship between radius and rotational velocity (uy)

with a fully filled can containing 13.90 mPa s syrup with no headspace.

(b) Relation ship between radius and rotational velocity (uy) with a

fully filled can containing 13.90 mPa s syrup with a 10% headspace.

Fig. 4. A typical �D� shaped trajectory of the tracer particle passing

close to the headspace (20% headspace volume, 20 s of data recording

shown). The inset figure shows the direction of rotation.

Fig. 5. Three-dimensional flow with a 13.90 mPa s solution with a 5%

headspace at 24 rpm The longitudinal axis of the can lies along the Zaxis of the graph. The inset figure shows the direction of rotation.


radioactive PEPT particles and food dye flow followers;

it was possible to confirm that the three-dimensional

flow patterns established themselves. It was not possible

to follow the details of such flows.

The trajectory deformation seen in Fig. 4 persistedacross the radius of the can, irrespective of the tracer

position. With the test materials used here, even with the

small 5% headspaces, where the D shape of the trajec-

tory was less pronounced, the flow was inherently three-

dimensional. This was rapidly established and persisted

with a regular periodicity. For example, Fig. 5 shows

part of the tracer particle trajectory for the 13.90 mPa s

solution with a 5% headspace at 24 rpm: fluid flowsslowly away from the centre plane (ca. x ¼ 370 mm,

y ¼ 290 mm, z ¼ 240 mm in Fig. 5) at a high radius and

then returns more quickly at a radius much close to the

axis of rotation (ca. y ¼ 330 mm). Fig. 6 shows the x, y, ztraces for the experiment shown in Fig. 5; the z direction

shows clear periodicity, as does the radial position.

Although the period of axial movement is apparent in

Fig. 6 the flow pattern is much more stable and pro-

nounced at higher headspace volumes. Fig. 7 shows the

x, y, z chart for the 13.90 mPa s solution at 24 rpm (as in

Fig. 6) except the headspace had been increased to 10%.

This experiment showed a very regular period of ap-

proximately 150 s, whereas the period for the 5%

headspace, was on average both smaller and less regular.

The corresponding three-dimensional view for this ex-

periment is shown in Fig. 7. Note that in this case thetracer travelled close to the wall of the can and appear to

rotate above the headspace (see Fig. 8) presumably

within a fluid layer carried on the can wall. However,

Fig. 6. Three-dimensional flow with a 13.90 mPa s solution with a 5% headspace at 24 rpm.


this did not appear to affect the procession of the tracer

through the can. Where the three-dimensional flow es-

tablished itself the flow pattern was symmetrical either

side of a perpendicular to the mid line axis of the can

(can centre plane in Fig. 1). A two-compartment flow

regime was produced, one in each end of the can.

The typical particle route for the three-dimensionalmixing was for the same for all the circumstances exa-

mined (i.e. as shown in Figs. 5 and 8). Fig. 9 shows the

typical particle route diagrammatically. From the centre

of the can the particle would spin out at high radius

towards the can periphery and move, close to the exte-

rior wall, to the can end. Here the particle changes di-

rection, spinning in rapidly towards the axis of rotation.

At some radius the flow changes direction and the par-ticle then moves rapidly in the z direction towards the

can centre. Similar observations were made at different

rates of revolution and with the 4.85 mPa s solutions.

With the lower viscosity solutions, similar results were

seen; except the periodicity was longer and not as re-

gular. Not all the data is shown here. Fig. 10 does show

one experiment with 4.85 mPa s solution, 10% headspace

at 24 rpm; there is still flow but the movement in the zdirection is uneven.

In all cases, as shown in Figs. 5 and 8, the migration

from can centre to can end takes many revolutions, as

does the reduction in orbit radius at the can end.

However, the return from the can end to the centre is a

much more rapid process. The velocities of the particlesand fluid are discussed more fully later. The variation

in relative velocity is illustrated by Figs. 11–13 where

the return velocity (from can end to centre represented

here as negative velocities) is on average higher than

the outward procession. Examination of Fig. 5 shows

that:

• The procession from can centre (z � 245 mm) to thecan end (z � 285 mm) requires approximately 25

revolutions (�1 min).

• The radial reduction from the can periphery to the

centre at the can end takes approximately 10 revolu-

tions (�25 s).

• And the return of the particle to the can centre

required only 7 revolutions (�18 s).

Fig. 7. Three-dimensional flow with a 13.90 mPa s solution with a 10% headspace at 24 rpm.

Fig. 8. Three-dimensional flow with a 13.90 mPa s solution with a 10%

headspace at 24 rpm.

Fig. 9. A schematic representation of the two compartment three-

dimensional flow within the rotating cans.


Similarly with Fig. 8 the time constants are approxi-

mately (i) 30 s from the can centre to the end, (ii) �43 s

to move from the can periphery to the axis of rotation

and (iii) 18 s to return to the centre. The residence time

at the can axis of rotation is thus less than 20% of the

circulation period.

Fig. 10. The trajectories for a 4.85 mPa s solution at 24 rpm with a 10% headspace.


Data for the radial velocity from the headspace

containing cans with a headspace was compared with

the theoretical equation (Eq. (2)) no correlation to solid

body rotation was found (see Fig. 3b). Indeed, Fig. 12

shows the variation of tracer velocity in the z direction–

uz––along the length of the can against a can diameter

and it can be clearly seen to be non-linear.

4. Discussion

Figs. 5–8 demonstrate the different rates of motion

seen within the three-dimensional flows encountered.

Fig. 7 particularly shows that regular periods of move-

ment can be established within the containers. Here the

average period for procession through the can was in the

order of 110 s per migration.

Although liquid viscosity is important in the

establishment of the three-dimensional flow patternsobserved for the high viscosity solutions it is felt that

the shape of the headspace bubble and not its volume

or the liquid viscosity, which establishes and maintains

of the flow regime. The bubble although displaced

over by the rotating fluid, does not change shape with

respect to the fluid flowing past it. The D profile to

the leading edge of the bubble causes fluid to be

diverted axially as it passes close to the leading edge

(in addition to any compression of the liquid passing

beneath the bubble and can wall). Fig. 4 shows asmall segment of an experiment with a large 20%

headspace and clearly illustrates the change in trajec-

tory of the particle as it passes close to the headspace.

The net effect of the small changes in the fluid ele-

ments trajectory, caused by the shape of the essentially

inflexible headspace bubble, creates the three-dimen-

sional flows observed. The solution viscosity and

headspace volume only appear to affect the rate ofmixing and thus the periodicity of the motion. Fig. 5

shows various aspects of the fluid flow in the cans.

Where z is close to the can centre (240 mm) the D

shape of the bubble can be seen to affect the fluid

across the can radius, whereas as the particle pro-

gresses towards the can end (z increases) the particle

then moves to the can periphery.

Fig. 11. Transverse section velocity profiles for 13.9 mPa s solution at 24 rpm with 10% headspace: velocities are positive towards the end of the can

and negative towards the central plane (indicated on the inset figure). The inset figure shows the xy planes at which the profiles were made.


4.1. Velocity field in the can

The rotated can demonstrates a constrained fluid flow

with the fluid recirculating when the outward flow

reaches the can end. Using programs written within the

Matlab environment the data from a 13.9 mPa s solution

at 24 rpm and 10% headspace was examined more rigo-rously to try and deduce the relative velocities of the

tracer particles (ux, uy, uz) and then to estimate the fluid

velocity throughout the can. To do this hypothetical

planes (0.05 mm wide) were constructed through the can

(longitudinally and transversely). Such a hypothetical

plane acts as a window; as a particle path crosses the

window its position is recorded in three dimensions. The

position of the particle was then retrieved from the data

2000 time points later, i.e. 2 s. The long time delay

helped to remove noise from the data caused by the

volume of uncertainty surrounding a tracer position due

to the resolving capability of the PEPT camera, i.e. �1mm. Although the time delay between points is rela-

tively long i.e. 80% of a full rotation at 24 rpm, only the

axial velocity of the particle along the length of the can

(uz) is of interest; the radial velocities ux and uy are

overwhelmingly functions of radius and rotation speed

Fig. 12. Plot of all the uz data along a longitudinal section of the data

shown in Fig. 11. The figure shows the variation in z velocity (uz) as a

function of z, i.e. for different xy planes (the sectioning plane is shown

in the inset figure). As in Fig. 11 the velocities are positive towards the

end of the can and negative towards the central plane.

Fig. 13. The data from Fig. 11 was replotted (plus one extra point)

using a graphically fitted cubic spline against a reduced radius esti-

mation. This is to indicate the underlying fluid velocities within the

whole can. The horizontal lines indicate individual data points and the

vertical curves indicate the variation from the zero velocity (vertical

straight lines). The can positions for the data were as follows: A; 245

mm (can centre plane), B; 250 mm, C; 260 mm, D; 270 mm, and E; 279

mm (can end). The velocity variations are positive left to right from the

can centre to the can end and negative for the return path.


(see Eq. (1)). From the two positions of the particle thevelocity vectors for the particle in the z direction (at the

data window) may be calculated.

Fig. 11 shows the result of performing the data ma-

nipulations using transverse sections at various positions

along the can length (z direction). Fig. 11 shows the

particle velocity (uz) where z ¼ 279 mm is close to the

can end, Fig. 11A; and z ¼ 245 mm is at the can centre

line, Fig. 11D, (the flow is symmetrical about the cancentral plane). The two other plots in Fig. 11B and C are

at points between the two extremes of the can end and

centre, all the graphs illustrates plots of y (can height)

against uz, similar graphs could be obtained by plotting

x (can width) against uz. These graphs show the tracer

velocity in the z direction (uz) at all radii at each selected

location and although the data demonstrates the vari-

ance of flow in the outward and return directions (uz isboth positive and negative). However, visualisation of

the rates of fluid motion in three-dimensions is difficult

to perceive, although the reversing of the flow direction

at the can end is apparent (Fig. 10A). Using a similar

process to that shown in Fig. 11, Fig. 12 shows the re-

sults for a longitudinal section, i.e. along the y axis, of

the same data set. Fig. 12 demonstrates the relative ve-

locities of the fluid (the tracer is considered isokinetic)along the can length i.e. the z direction. Once more

valuable information is present, but again the true three-

dimensional aspects of the fluid motion are difficult to

perceive. Similarly, Fig. 12 could equally have been

produced from a y versus uz data set.

To elucidate the bulk flow velocities within the can

more clearly a cubic spline was graphically fitted to the

data shown in Fig. 13 (an additional point was alsoexamined). The radial dimensions, i.e. x and y were re-

duced to a single dimension by Eq. (3):

R ¼ x2 þ y2 ð3Þ

where R is the reduced radius and x and y the radial

positions of the particle.

In Fig. 12 the cubic spline has smoothed the data to

indicate the bulk flow; however, once more the flow

behaviour remains difficult to perceive. At positions A–

C in Fig. 12 the bulk of the flow is away from the can

centre, however, flow in the opposite direction must

exist to maintain the volume of the can. The subtlety ofthis behaviour is difficult to describe as an overall flow

map as bulk examinations of the fluid may mask the

fluid movements that PEPT has shown i.e. within the

constrained system presented here there in no net flow.

However, it was possible to combine together all

of the data obtained from the various sections. When

combined and interpolated to form a virtual volume the

data produced a more complete picture of the movementand relative velocities of the fluid within the rotated

cans. With such a virtual data volume the interpolated

data could be represented in three dimensions with the


colour representing the relative fluid velocities and theinterpolated data volume viewed isometrically with

dissecting planes were at any x or y plane position.

However, data representations made in this manner are

very complex and such Figs. are unsuitable for publi-

cation. However, when viewed as rotating objects within

a virtual system it could be seen more clearly that at the

can centre fluid moves in the positive direction towards

the can end. In the virtual data volume all of the relativefluid motions within the cans could be discerned and the

symmetrical nature of the two compartments is also

appreciated, for reference the process is shown sche-

matically in Fig. 9.

4.2. Relevance to the heated case

The motion of the fluid in a can may be considered

in the context of thermal treatment of foodstuffs.

Clearly within fully filled cans the rate of heat transfer

will primarily remain a function of can radius and

thermal conductivity (Fig. 2) as the liquid positionshows little variance with time. However, the ex-

perimental results imply that when a headspace is in-

troduced, especially for the viscous liquid systems

examined here, the three-dimensionality of the liquid

flow may have marked implications for heat transfer.

Empirically, fluid elements that traverse from the can

centre to the can end close to the wall would be

rapidly heated at the hot surface, the hot liquid maythen be transported to the can centre via the three-

dimensional flow patterns observed. Undoubtedly the

rate of heat transfer will be augmented by this. Other

experiments using can centre thermocouples have

shown this for other viscous fluids (data not shown).

Additionally, the relative duration of fluid at different

loci within the can will also help to augment the

heating rate. The longitudinal velocity (uz) of the fluidat the can periphery is lower than that at the centre

(see Figs. 11–13) with the higher fluid motion rates at

the centre helping to transfer the hot fluid throughout

the can volume. It might also be expected that the

mixing regime in the viscous liquids would persist

through the heating and cooling cycles of can pro-

cessing, although liquid viscosity diminishes with in-

creased temperature, as the range of fluid viscositiesthat have so far demonstrated the three-dimensional

flows is large i.e. almost 10 mPa s difference between

the solutions tested. Therefore, it is reasonable to ex-

pect the fluid to remain viscous enough through out a

thermal cycle to maintain the headspace shape and

exhibit the flow and therefore maintain the enhanced

higher rate of heat transfer. Although only the data

for Newtonian fluids are presented here similar effectshave been observed for other viscous fluids; i.e. shear

thinning and fluids with a yield stress. Further work to

demonstrate this is under way.

5. Conclusions

PEPT has been used to follow isokinetic flow tracers

inside sealed metal rotated cans. Filled cans show liquid

velocities from Eq. (1). Whereas, with cans with a

headspace a three-dimensional fluid flow regime was

seen whose velocity field could not be adequately des-

cribed by the same equation. The establishment of the

three-dimensional flow patterns within the axially ro-tating can is of great importance when considering heat

treatment regimes for canned liquid products. It is be-

lieved that it is the shape of the bubble that gives rise to

the three-dimensional mixing rather than the rheological

characteristics of the fluids. The use of PEPT for �in-

container� flow following has proved highly effective and

clearly demonstrates the potential for exploring complex

flow patterns within real situations. As well as providinga visualisation tool for fluid flows the use of PEPT may

also offers important information about convective

modes of heat transfer in complex products. Efforts are

now under way to model the three-dimensional mixing

regime and to elucidate its effects upon heat transfer.

Acknowledgements

This research was funded by the MAFF Advancedand Hygienic Food Manufacturing Link scheme

AFM113. Thanks to Paul Young of Stratford Foods

Ltd. for supplying the cans and seamer.

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