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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
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PIV measurements in a shaken cylindrical bioreactor
W. Weheliye, M. Yianneskis and A. DucciDepartment of Mechanical
EngineeringUniversity College London, WC1E 7JE;
Corresponding author: [email protected]
Abstract: The flow dynamics in a 100 mm cylindrical shaken
bioreactor is investigated in this study. The freesurface
oscillations induced by the orbital motion of the shaker table
represent an issue that has to be addressed toobtain accurate PIV
measurements. A preliminary study was carried out to identify the
range of angular positions,φ, of the bioreactor along its circular
orbit that are not affected by optical distortion of the camera
field of view.For these phase angles standard PIV adaptive
correlation algorithms were employed to determine the variation
ofthe velocity field when a mask was employed to limit the analysis
only in the fluid region below the free surface.The free surface
profile was identified by image processing and mathematical and
statistical tools. The resultsshow that variation of the velocity
profiles for masked and unmasked data processing conditions affects
only afew points in close proximity of the free surface. Estimates
of the free surface interfacial area and detailedcharacterisation
of the phase averaged velocity fields are obtained for different
combination of Froude number, Fr,non-dimensional liquid height,
h/di and ratio of orbital to bioreactor diameters, do/di.
Keywords: Shaken bioreactor, free surface, PIV, mixing.
1. IntroductionIn recent years microscale bioprocess technology
has been employed in the early stage of bioprocessdevelopment (i.e.
microbial fermentation, bioconversion and recovery techniques),
before the developedprocess is implemented in a large scale
industrial stirred tank. One approach relies on the use ofmicrowell
plates where complete mixing is achieved by shaking rather than
stirring. However, despitethe extended use of shaken bioreactors
(flask and microwells), “probably less than 2% of the
publicationdealing with engineering aspects of bioreactors are
dedicated to shaken bioreactors” (Büchs, 2001).Büchs (2001)
concluded that, despite the extended use of shaken bioreactors,
their importance isunderestimated by biochemical engineers. A
reason for this is that shaken bioreactors are commonlyused in the
early stage of bioprocess development with the microbiologist being
the most importantprofessional figure in this phase. Biochemical
engineering aspects are generally considered in the lastphase of
the process development, which is mainly implemented in stirred
tank reactors.
The complexity of the problem is further increased by
considering that the few works in the literatureoften deal with
systems operating at very different initial conditions, with
filling volumes varying from25 ml to 495 l, orbital diameters of
15-100 mm, shaker rotational speed of 50-1000 rpm as well as
beingrelated to very different configurations, with or without
baffles and different wall/bottom geometries,microwells and
cylindrical vessels, thus reducing the possibility to correlate the
results of the differentstudies. This lack of knowledge poses two
main problems to the biochemical engineering community:
Processes developed in shaken bioreactors cannot be fully
characterized, undermining theirreproducibility; and
Operating conditions in shaken bioreactors cannot be properly
correlated with and scaled to thoseachievable in industrial
reactors, usually stirred tanks, for which a vast amount of data
exist inthe literature.
An understanding of the flow dynamics of free surface phenomena
is of significant importance for awide variety of engineering
applications (Hirsa et al. 2001). With substantial advances in
fluidmeasurement techniques in recent years, particle image
velocimetry is now capable of measuring fluidvelocity at a
sufficient resolution to determine the structure of vortices and
turbulence in many flowsincluding flows with a free surface. For
example, Dong et al. (1997) applied PIV techniques to studyflow
structure near the bow of a ship model subjected to a surface wave,
while Yeung et al. (1996)measured the flow generated by a plate
undergoing forced harmonic roll motion at the free surface
usingPIV. This study will be the first to apply the PIV technique
to study the flow field in a shaken bioreactor.
mailto:[email protected]
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Flow visualisation in shaken bioreactors was carried out by
Büchs et al. (2001) who were the first toidentify the so called
“out-of-phase” phenomenon. This phenomenon is characterised by an
amount ofliquid not following the movement of the shaking table,
thus reducing the volumetric powerconsumption, mixing and the
gas/liquid mass transfer. However the flow dynamics in shaken
bioreactorshas mainly been studied using Computational Fluid
Dynamics (CFD). Kim and Kizito (2009) carried outnumerical
simulations and experimental observations in order to characterise
the flow in a cylindricalbioreactor. Their simulations were only
limited to a configuration with fixed orbital and cylindricalvessel
diameters, whilst Zhang et al. (2005, 2008) investigated by
numerical simulation the flowdynamics in Erlenmeyer flask and
different microwells (of 24 and 96 l capacity). They presented
thevariation of several engineering parameters such as the
volumetric power consumption, interfacial areaand the mass transfer
coefficient with increasing shaker frequencies, N, and orbital
diameter, do.Furthermore, Discacciati et al. (2012) developed a
numerical method to determine the shape of the freesurface and to
estimate the shear stresses in a cylindrical bioreactor.
The objectives of the current work are twofold: assessing to
what extent the optical distortiondetermined by the free surface
affect the accuracy of PIV measurements, and characterising the
flowoccurring inside a cylindrical shaken bioreactor by means of
phase-resolved measurements for differentoperating conditions.
2. Material and MethodsThe 2D PIV system employed comprised a
continuous diode laser, a mirror, a Dantec intensified highspeed
camera and a cylindrical bioreactor rig, all of which were rigidly
mounted on a Lab LS-X Kühnershaker table. Schematic diagrams of the
PIV system set up for measurements on vertical and horizontalplanes
are provided in Figures 1 (a) and (b), respectively. The
cylindrical bioreactor was made ofpolished borosilicate glass, and
to minimise refraction it was encased in a square trough. To
obtainoptical access to the bioreactor from the bottom, the base of
the cylinder was made of acrylic plastic.The inner diameter of the
cylinder, di, was 100 mm, with a height of 250 mm and wall
thickness of 5mm. The laser employed was a continuous green diode
laser with a wavelength of 532 nm and an outputpower of 300 mW. A
cylindrical lens was mounted in front of the laser to create a
laser light sheet ofapproximately 1 mm thickness. Depending on the
measurement being carried out, two different mirrorswere used. The
first rectangular mirror was used to deflect the horizontal laser
plane of 90o andilluminate the vertical plane of measurement that
bisects the cylinder into two halves (see Figure 1 a).The second
circular mirror was used when the camera was positioned underneath
the laser and allowedto have optical access from the bottom window
of the bioreactor when measurement on horizontalplanes were carried
out (see Figure 1 b). A magnetic encoder was coupled to the Kühner
shaker table todetermine the angular position of the tray at any
instant throughout its orbital trajectory. The origin ofthe phase
angular coordinate, φ, was set when the tray reached its position
furthest to the left along itsclockwise circular orbit when seen
from above. Experiments were carried out for an orbital diameter,
do= 25 mm. Silver coated hollow spherical particles of 10 μm
diameter were used to identify at each phase angle the position of
the free surface, while for the PIV measurements it was preferred
to use 50 μm rhodamine particles, because they allowed to minimise
reflections at the walls and at the free surface.For the latter
case an orange filter with cut-off wavelength of 570 nm was mounted
on the 45 mmcamera lens. The three issues that needed to be
addressed to obtain the required data are considered inthe
following sections.
2.1 Free surface optical distortionDuring the early stage of the
research it was found that the free surface oscillations caused
major opticaldistortions for certain range of phase angle, φ. This
is well illustrated in Figures 2 (a-d). For phase anglesin the
range φ=180o-360o, there is no optical distortion and the image is
uniformly illuminated (Figure 2a). As shown in Figure 2 (b) for
this range of angles the highest side of the free surface is on the
sameside as the PIV camera. In this case light travelling along
paths A and B in Figure 2 (b) crosses the samepercentage of media
(air and water) between the camera and the focal plane. On the
contrary, when
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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
3
phase angles φ 180o. This de-magnification effect can be
explained byconsidering Figure 2 (d), and the different media
crossed by the camera light when travelling along pathsA or B. It
should be noted that for φ 420. This occurs since the flow
fieldunder the free surface has a “noisy texture” due to the
presence of the seeding particles, while the imagetexture above the
free surface is characterised by a nearly uniform black intensity.
As a consequence thestandard deviation below the free surface
(higher y values) is greater than the standard deviation abovethe
free surface (lower y values). The y coordinate associated to the
sharp increase in the standarddeviation is related to the presence
of the free surface, and can be used to identify the local free
surfaceheight. The same procedure is repeated for each horizontal
coordinate x until the entire free surfaceprofile is determined. A
representation of the free surface profile obtained with the
described procedureis illustrated in Figure 3 (c). The third step
involves a local regression method that is applied to smooththe
free surface line and improve its detection. A mask is then applied
to each raw image and all pixelsabove the free surface profile are
converted into black (Figure 3 d).
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2.3. Masked and unmasked PIV imagesAn analysis was carried out
to determine to what extent using a mask can affect/improve the
velocityfield determined by the PIV adaptive correlation algorithm.
Figures 4 (a) and (b) show a comparison ofthe axial profiles of the
velocity magnitude when the velocity field was obtained with and
withoutmasking for two different radial positions r/di=0.25 and
0.38, respectively. It can be noted from bothplots that near the
centre and bottom of the cylinder no difference is observed between
the velocitymagnitude profiles for the unmasked and masked PIV
images. However near the free surface adifference between the
velocity magnitudes for masked and unmasked conditions is present.
Themaximum discrepancy obtained for the velocity magnitude profile
at a radial position r/di=0.25 is 25%while at a radial position of
r/di=0.38 a discrepancy of 12% is observed. It should be noted that
thehighest errors of the velocity magnitude profiles are only
observed for a few points in close proximity ofthe free surface.
Thus masking is recommended before the PIV adaptive correlation
algorithm is carriedon the images.
Finally due to the rotational nature of the flow considered, an
analysis was necessary with regards to thethree velocity components
and their magnitude to establish which velocity component is
dominant indifferent regions of the cylinder and therefore to
determine the optimal PIV time delay to fully resolvethe flow.
Since the majority of the results shown are based on a phase angle
of φ = 0o, the dominantvelocity component in this phase is Uθ. Thus
the time delay between the images, ∆T=10 ms, has to besmall enough
to prevent the seeding particles from moving out of the plane of
focus.
3. Results and discussion
3.1 Measurement of the interfacial areaThe size of the
interfacial area is a very important parameter in mixing operations
where aeration/oxygenation of the shaken bioreactor is required.
The variation of the interfacial area, Ia, with increasingFroude
number, Fr, is investigated in this section, where Fr is defined in
equation 2.
ଶݎܨ ൌ ቀଶሺగேሻమௗ
ቁ (2)
and g is the gravitational acceleration. The 3D reconstruction
of the free surface shown Figure 5 (a) wasobtained by azimuthally
stacking the different free surface profiles measured at each phase
angle φ. Theinterfacial area was estimated by a trapezoidal
integration of the different points comprising the freesurface. An
alternative method is to derive an analytical method based on the
assumption that the freesurface is an inclined ellipse (see
equation 3).
ܫ ൌ ݀ଶ గ
ସ
ଵ
ୡ୭ୱ�ሺఏሻ(3)
Where:
ߠ ൌ ݃ݐ ିଵቀο
ௗቁן� ݃ݐ� ିଵ(ݎܨଶ) (4)
Where is the free surface difference and di is the inner
diameter of the cylinder. Thus an alternativemethod to analytically
estimate the interfacial area consisted in using equation (5),
which is valid at lowFr, when the free surface profile at φ= 0o is
an inclined line and the free surface can be approximated byan
ellipse.
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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
5
ܫ ൌ ݀ߨ
4ඥ(∆ℎ)ଶ ሺ݀ )ଶ
(5)
ܫ ൌ ݀ଶߨ
4ඥ(ͳǤͶݎܨଶ)ଶ + 1
Figures 5 (b) and (c) show a comparison between the analytical
and measured interfacial areas obtainedfor two different orbital
diameters do/di=0.25 and do/di=0.5 respectively. For both orbital
diameters theanalytical and measured estimates of the interfacial
area show a relatively good agreement for Fr
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3.3 Horizontal plane flow field measurementsThe measurements
presented in this section were carried out with optical access from
the bottom of thecylinder, using the system configuration shown in
Figure 1 (b). Figures 7 (a) and (b) show the contourplots of the
axial vorticity, ωz, and the velocity vector fields at three
different planes for differentoperating conditions with fluid
height and shaking frequency being h/di=0.7; N=70 rpm and
h/di=0.3,N=130 rpm, respectively. For h/di=0.7 and N=70 rpm (Fr
2=0.068), three different horizontal planes areconsidered: two
in the diffusion zone at an elevation z/di=0.1,0.35 and one in the
convection zone atz/di=0.6. In the diffusion zone (z/di=0.1) the
flow is dominated by solid body rotation with an axialvortex
clearly in evidence near the centre of the cylinder. On the
contrary in the convection zone(z/di=0.6) the flow is characterised
by two streams of opposite direction emanating and merging at
twopoints denoted as A and B in Figure 7 (a). The variation of the
angle, ∆α, between the lines joining the stagnation points to
centre of the cylinder, was analysed for increasing N and it was
found that ∆α was proportional to the average diameters of the two
azimuthal vortices described in Figure 6. Furthermore ath/di=0.3
and N=130 rpm (Fr2=0.24), the out-of-phase condition is induced in
the bioreactor (Figure 7 b):the two stagnation points disappear and
a vertical-axis vortex is formed on one side of the bioreactor.
The extent to which the flow is out of phase can be determined
by estimating ∆β, the angle defined bythe direction of the
centrifugal acceleration for the phase condition considered (a
horizontal line for φ =0o) and the direction of the line joining
the bioreactor and vortex centres. For the condition of Figure 7the
out-of-phase angle was found to be ∆β = 20o. It is worth to remark
that this angle was found to beindependent of the phase angle
considered, as it is evident from Figure 8 (a-c) where the velocity
fieldson a horizontal plane were obtained for φ = 0o, 90 o and 180
o. From Figure 8 it can be concluded that thevertical vortex
precesses around the cylinder axis as the bioreactor proceeds along
its orbit.
The “out-of-phase” phenomenon was further investigated by
conducting image analysis of the variationfor different phase
angles φ of the height, hf, of the point of the free surface
profile on the left wall of thebioreactor (Figure 9 a).
Measurements of hf were carried for the following operating
conditions: h/di=0.3,0o < φ < 400o, and N=60 rpm, 90 rpm, 120
rpm and 130 rpm. The variation of hf/hfmax with φ is shown inFigure
9 (b), where hfmax is the maximum value of hf . For N=60 rpm and 90
rpm hf/hfmax is maximum(hf/hfmax=1) for φ=0
o, which means that the free surface is in phase with the
orbital movement of theshaken bioreactor. At high shaking
frequencies, N=120 rpm and 130 rpm, the maximum value of hf
wasfound at φ = 15o and 20o, respectively. Thus for increasing N
the free surface is out-of-phase with theorbital movement of the
shaken bioreactor. These results are in agreement with those
obtained from thePIV measurements of horizontal planes.
ConclusionsAn overview of the flow configuration and the
measurement methodology employed for thecharacterisation of the
flows in shaken reactors was provided. The PIV magnification
problem near thefree surface which occurs for phase angles 0o
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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
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ReferenceBüchs J, Maier U, Milbradt C, and Zoels B (2000). Power
consumption in shaking flasks on rotaryshaking machines: II.
Nondimensional description of specific power consumption and flow
regimes inunbaffled flasks at elevated liquid viscosity. Biotechnol
Bioeng 68:594–601.Büchs J (2001). Introduction to advantages and
problems of shaken cultures. Biochem. Eng. J 7:91 – 98.Discacciati
M, Hacker D, Quarteroni A, Quinodoz S, Tissot S and Wurm F (2012).
Numerical simulationof orbitally shaken viscous fluids with free
surface. Int. J. Numer. Meth. Fluids. doi: 10.1002/fld.3658.Dong R,
Katz J, and Huang T (1997). On the structure of bow waves on ship
model. Flui.Mechan. J346:77-115.Hirsa A, Vogel M and Gayton J
(2001). Digital particle velocimetry technique for free-surface
boundarylayer measurements: Application to vortex pair
interactions. Exp.Fluids 31:127-139.Kim H and Kizito P (2009).
Stirring free surface flows due to horizontal circulatory
oscillationof partially filled container. Chem. Eng. Commun 11:
1300–1321.Tissot S, Farhat M, Hacker D, Anderlei T and Kühner M
(2010). Determination of a scale up factor frommixing time studies
in orbitally shaken bioreactors. Biochem Eng J 52: 181–186.Yeung R,
Cermelli C and Liao S. Vorticity fields due to rolling bodies in a
free surface-experiment andtheory, Proceedings, 21st Symposium on
Naval Hydrodynamics, Trondheim, Norway, June, 1996.Zhang H,
Williams-Dalson W, Keshavarz-Moore E, and Ayazi-Shamlou P (2005).
Computational fluiddynamics (CFD) analysis of mixing and gas liquid
mass transfer in shake flasks. Biotechnol.
Appl.Biochem.41:1–8.Zhang H, Lamping S, Pickering S, Lye G, and
Ayazi-Shamlou P (2008). Engineering characterisation ofa single
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40: 138–149.
(a)(b)
Figure 1: PIV set-up configurations used to measure the
velocities on a: (a) vertical; (b) horizontal plane.
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(a) (b)
(c) (d)Figure 2: Examples of optical distortion and associated
schematic diagram of the relative position of the freesurface with
respect to the camera set up for different phase angles. (a) φ=90o,
No optical distortion is presentthe image; (b) φ=90o, schematic
diagram of camera and free surface relative positions for
distortion condition;(c) φ=270o, No optical distortion is present
the image; (d) φ=270o, schematic diagram of camera and free
surfacerelative positions for distorted condition.
(a) (b)
(c) (d)Figure 3: (a) Original image of the free surface; (b) A
graph of the standard deviation againsty-distance at a generic
horizontal coordinate x; (c) The detected surface is shown in the
form of raw data; (d)The masked image.
A B
C
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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
9
(a)
(b) (c)
Figure 5: (a) 3D reconstruction of the free surface; (b)
Variation of the interfacial area Ia with increasing Fr2 for
do=2.5 cm; (c) Variation of Ia with Fr2 for do=5 cm.
(a) (b)Figure 4: Velocity profile, |U|, at different radial
position for φ=0o, h/di=0.5, do/di=0.25, N=90 rpm: (a)r/di=0.25;
(b) r/di=0.38.
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(a) (b)
(c) (d)Figure 6: Phase-resolved vector fields and contour plots
of the tangential component of the vorticity, ωθ, for increasing
N(do/di=0.25, φ=0
o): (a) N=70 rpm and h/di=0.5; (b) N=90 rpm and h/di=0.5; (c)
N=110 rpm and h/di=0.5; (d) N=90 rpm andh/di=0.3.
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16th Int Symp on Applications of Laser Techniques to Fluid
MechanicsLisbon, Portugal, 09-12 July, 2012
11
(a) (b)
Figure 7: Phase-resolved vector fields and contour plots of the
axial component of the vorticity, ωz, for increasing N
(do/di=0.25,φ=0o): (a) N=70 rpm and h/di=0.7; (b) N=130 rpm and
h/di=0.3.
A
B
∆α
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(a)
(b) (c)Figure 8: Phase-resolved vector fields for h/di=0.3 with
N=130 rpm: (a) φ = 0
o; (b) φ = 90o; (c) φ = 180o.
Figure 9: (a) Definition of the fluid liquid height hf being
measured; (b) Variation of hf/hfmax with φ.
