Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 9.1.3 - The quantification of bubble size distributions using ultra-fast MRI
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 Material Information
Title: 9.1.3 - The quantification of bubble size distributions using ultra-fast MRI Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tayler, A.B.
Holland, D.J.
Sederman, A.J.
Gladden, L.F.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: bubbly flow
bubble size distribution
MRI
 Notes
Abstract: Bubble size distributions (BSD) for dispersed bubbly flow in a vertical column have been measured using ultra-fast 2D magnetic resonance imaging (MRI) for the first time. A single-shot spiral trajectory echo planar imaging (sEPI) protocol was selected due to its high time resolution (images were acquired in 13.8 ms) and robustness to flow artefacts. To overcome the inherent low resolution of this fast scanning technique a methodology was developed to permit the measurement of bubble size from signal intensity. The technique was validated in comparison to photography for a low voidage ( = 1.6%) system of air bubbles in 0.1 g L −1 sodium dodecyl sulfate solution. It was also demonstrated at the point were optical bubble sizing becomes problematic ( = 3.5%) and on a high voidage system ( = 34.7%). Thus, MRI was found to enable the non-invasive measurement of BSD beyond that possible by other means. The measurement of velocity fields in the presence of bubbly flow using sEPI was also demonstrated.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00216
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 913-Tayler-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


The quantification of bubble size distributions using ultra-fast MRI


A.B. Tayler, D.J. Holland, A.J. Sederman and L.F. Gladden

Department of Chemical Engineering and Biotechnology, University of Cambridge,
Pembroke Street, Cambridge CB2 3RA, United Kingdom.
abt31 @Ocam.ac.uk
Keywords: Bubbly flow, bubble size distribution, MRI




Abstract

Bubble size distributions (BSD) for dispersed bubbly flow in a vertical column have been measured using ultra-fast
2D magnetic resonance imaging (MRI) for the first time. A single-shot spiral trajectory echo planar imaging (sEPI)
protocol was selected due to its high time resolution (images were acquired in 13.8 ms) and robustness to flow
artefacts. To overcome the inherent low resolution of this fast scanning technique a methodology was developed
to permit the measurement of bubble size from signal intensity. The technique was validated in comparison to
photography for a low voidage (e 1..' system of air bubbles in 0.1 g L 1 sodium dodecyl sulfate solution. It was
also demonstrated at the point were optical bubble sizing becomes problematic ( = 3.5' and on a high voidage
system (c = 34.7'. ,. Thus, MRI was found to enable the non-invasive measurement of BSD beyond that possible by
other means. The measurement of velocity fields in the presence of bubbly flow using sEPI was also demonstrated.


Nomenclature

Roman symbols
Eo E6tvds number (4. A., b/Ta)
9 acceleration due to gravity (m s 1)
rb spherically equivalent bubble radius (mm)
rp projected equivalent bubble radius (mm)
M Morton number (gp4 Ap/p2r3)
Sbub signal in bubble region (bubble image) (a.u.)
Sref signal in bubble region (reference image)(a.u.)
V volume of voxel (mm3)

Greek symbols
a aspect ratio
S voidage
p density (kgm-3)
a surface tension (Nm 1)


Introduction

The accurate experimental measurement of bubble size
distributions (BSD) for bubbly flow systems has proved
an elusive goal for the multiphase processes community.
Bubbly flow describes the relatively homogeneous dis-
tribution of gas throughout a liquid as fine bubbles, and
is commonly encountered in both natural and industrial


systems. In particular, bubbly flows frequently occur in
oil transportation, nuclear cooling systems, mineral sep-
aration, metal purification and gas-liquid chemical re-
actors. Quantification of bubble size is of fundamental
importance for the design and operation of these sys-
tems. Much difficulty has been had, however, in obtain-
ing an accurate measurement of BSD. Bubbly flows are
most often optically opaque by virtue of the varying re-
fractive index of the two heavily mixed phases, which
defeats optical bubble sizing methods at all but the low-
est of void fractions. Further, the gas-liquid interface
is so highly sensitive to the presence of invasive probes
that confidence is undermined in measurements obtained
by such means. These complications have spawned a
variety of innovative, non-invasive measurements tech-
niques for BSD. In particular, acoustic measurements
(Leighton 1994) and laser Doppler anemometry (Kulka-
ri et al. 2004) have met with some success, although
are limited in respect to the range of bubble sizes and
voidages to which they are applicable.
The present work is concerned with the measurement
of BSD using magnetic resonance imaging (MRI). Most
previous applications of MRI to bubbly flow in the liter-
ature focus upon obtaining either temporally or spatially
averaged measurements, and do not present the 'snap-
shot' style images necessary to resolve individual bub-
bles (see for example the work of Sankey et al. (2009)).











This is principally because MRI is conventionally con-
sidered a slow measurement technique, with only low
resolution images able to be acquired within a millisec-
ond scale timeframe. If, however, such images yield suf-
ficient information for the measurement of bubble size
then MRI may prove an excellent tool for the obser-
vation of gas-liquid flows due to its non-invasive, non-
optically based nature. We currently explore the use of
one of the fastest known full-Fourier MRI protocols, spi-
ral echo planar imaging (sEPI) (Ahn et al. 1986), which
is capable of acquiring 64 x 64 images in approximately
10 20 ms (depending on hardware). We seek to validate
this technique as a potential tool for the measurement of
BSD, and to explore its potential for application to the
characterisation of bubbly flow.


Theoretical

No comprehensive review of the theory of NMR and
MRI is herein attempted. The interested reader is re-
ferred to standard texts such as Callaghan (1991) or
Levitt (2001). The MRI scan protocol employed herein,
spiral EPI (sEPI), was selected for its high time resolu-
tion and its robustness to flow artefacts (Nishimura et al.
1995). While single-shot, ultrafast MRI techniques such
as sEPI are principally limited to the acquisition of low
resolution images, the quantitative nature of the MRI
signal provides extra information that enables the accu-
rate measurement of bubble size. If a bubble is wholly
contained within the slice of excited fluid during the ac-
quisition time, the signal discrepancy in the region of a
bubble, relative to a reference image in which no bubbles
are present, will be directly proportional to the volume
of the bubble. Thus, the spherically equivalent bubble
radius may be calculated as:


rb 3 b 1 Sb (1)
47r Sref )

where V is the volume of the fluid voxels contained
in the region of an identified bubble, Sbub is the signal
present in this region for the image containing the bub-
ble and Sref is the signal present for the reference image.
Clearly this method of bubble sizing is dependent upon
the measured signal remaining quantative. A demon-
stration the sEPI produces maintains quantitivity even in
the presence of high shear rates shall be published else-
where.
Prior to the extraction of bubble size as described
above, it is necessary to segment the image into pro-
jected bubble shapes. This process will also allow an
apparent radius of the projected bubble radius, rp, to
be quantified. Many techniques exist in the literature
for the identification of shapes within an image. The


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


present system is somewhat complicated by the rela-
tively low signal-to-noise ratio associated with fast MRI
techniques. In such cases, the application of a Hough-
type shape searching procedure is often most effective
(Petrou and Bosdogianni 1999). The present data were
prepared by subtraction of a reference dataset obtained
with the column filled with solution, prior to applica-
tion of an edge extraction procedure. Bubbles were then
identified by two dimensional cross-correlation with
template images (circles of varying diameter) to pro-
duce a correlation map in which the local maxima rep-
resent the locations most likely to contain a bubble.
This process was then followed by an iterative greedy-
type algorithm for selection of maxima from the cross-
correlogram. That is, maxima in the correlation map
may be identified firstly by locating a global maximum,
which represents the size and location of the most-likely
bubble. The region containing this bubble may then be
removed from the original data and the cross-correlation
recalculated. The global maximum of this new correla-
tion map represents the next most likely bubble present
in the original data. By iterating in this fashion until
some threshold is reached (a minimum correlation coef-
ficient of 0.7 was found adequate for the present dataset)
all bubbles were accurately identified. The iterative-
subtraction process was noted to be particularly robust
to regions of densely clustered bubbles, where ambigu-
ity in peak positions in the correlogram is progressively
reduced as each bubble is identified and removed.
A potential source of error in these measurements is
the inclusion of bubbles which leave the excited slice
during acquisition or that are part-contained during ex-
citation. In such cases the apparent aspect ratio, a, pro-
vides a useful insight for data filtering. The aspect ratio
may be calculated as:


For low Morton number bubbles (M < 10 6), such as
those examined herein, rising in a surfactant contami-
nated liquid the aspect ratio may be estimated by the
correlation of Wellek et al. (1966):


1 + 0.163Eo0.757
where the E6tv6s number is defined as:

S4gpr2
Eo b


where g is acceleration due to gravity, Ap is the density
difference between the gas and liquid, and a is surface
tension. Clift et al. (1978) discuss similar correlations
for other systems. Thus, by comparing aspect ratios


3()
rb











determined experimentally, and discarding those bub-
bles which show a significant disparity from the correla-
tion (> _".' difference was deemed appropriate for the
present dataset), the influence of bubbles part-included
in the slice may be minimised.
For the above measurement of bubble size to be valid,
the thickness of the excited slice of fluid must be large
enough to ensure that the bubbles will be wholly con-
tained within the slice for the duration of the imaging
sequence. Adopting an estimate of bubble slip velocity
of 30 cm s 1 (conservative for bubbles of radius 1-5 mm
(Clift et al. 1978)), this distance is equivalent to a bub-
ble rise of 4.5 mm of the course of an approximately
15 ms acquisition time. Thus the minimum slice thick-
ness used must be at least 4.5 mm. Additionally, care
must be taken to ensure that the slice excitation profile is
rectangular, such that the signal loss due to the presence
of a bubble is independent of the longitudinal position
of the bubble within the excited slice.


Experimental

In the selection of bubble column size we were limited
by the physical restrictions of the bore of our magnet. To
this end, a 31 mm inside diameter Perspex column was
used. Bubbles were generated by sparging air through
an aquarium airstone. sEPI images were acquired for
gas flow rates of 100 ml min 1, 200 ml min 1 and
1 L min 1. The gas flow-rate was controlled using an
Omega FMA3206ST mass flow meter. To demonstrate
the usefulness of sEPI in velocimetry of bubbly flows,
images were also acquired with velocity encoding ap-
plied in the axial direction. The liquid phase in all ex-
periments was a 0.1 g L 1 sodium dodecyl sulfate (SDS)
solution doped with 16.5 mM dysprosium chloride. This
dopant was necessary to ensure that the magnetic sus-
ceptibility of the solution is identical to that of air, which
precludes the occurrence of off-resonance artifacts in the
MRI images. Surface tension measurements were per-
formed on this solution using a Dataphysics OCA 15+
goniometer, and it was found that the inclusion of such
a small quantity of paramagnetic salt has a negligible ef-
fect upon surface tension. The voidage of each flow-rate
was determined by a pulse-acquire experiment. Pho-
tographs were taken at each gas-fraction using a Canon
Powershot A630.
sEPI images were acquired on a Bruker AV-400 ul-
trashield spectrometer operating at a proton resonance
frequency of 400.25 MHz. This apparatus is fitted with
a 3-axis gradient system capable of a maximum mag-
netic field strength of 0.29 T m 1. A 38 mm diame-
ter birdcage coil was used for r.f. excitation, and subse-
quently, signal reception. Images were acquired at a res-


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


solution of 500/mx 500pm. Images were acquired fol-
lowing a single slice-selective spin-echo, and traversing
reciprocal space in a 'spiral-out' trajectory determined
using the algorithm of Glover (1999). A Mao refocus-
ing pulse (Mao et al. 1988) was used to generate a 5 mm
thick rectangular excitation profile. A velocity compen-
sated spoiler gradient was included around the refocus-
ing pulse (Pope and Yao 1993), simultaneously to the
slice selection gradient, which was also velocity com-
pensated. When velocity encoding was applied, it was
done so simultaneously to slice refocusing and velocity
compensation. The velocity encoding time was 416/s,
with a flow contrast time of 1.24 ms, and a gradient
strength of 0.073 T m 1. The total time for each im-
age acquisition was 13.8 ms. Images were reconstructed
using a non-uniform fast-Fourier transform (Fessler and
Sutton 2003).



Results

Bubbly flow at a range of gas-fractions has been imaged
using MRI and BSDs extracted from these data. The
voidage in each system was determined experimentally
by obtaining the quotient of the total NMR signal loss
in the presence of bubbly flow and the signal present for
a single phase system. In order to validate the results
produced by the MRI technique, it was first applied to
a low (c 1. .'. voidage system and compared with
bubble sizes measured optically. An example sEPI
image and a photograph of this system are given in
Figure 1 a i) and ii), respectively, and a comparison of
the BSD extracted from each is given in iii) (presented
as spherically equivalent radii). As expected, the pro-
duced size distributions are approximately log-normal
in form, with good agreement evident between the
two techniques. The mean bubble radius present is
0.85 mm, with a standard deviation of 0.21 mm. Note
that in order to calculate a spherically equivalent radius
from the photographs, it was necessary to assume that
the bubbles maintain fore-aft symmetry, and that the
projected major and minor axes are representative of
the true axes of the bubble (i.e. that the influence of
bubble orientation is negligible). The gas flow rate in
these images was 100 ml min 1. As the voidage in
the pipe is increased, the accurate optical measurement
of bubble size in the bulk becomes difficult as bubble
overlap events in the data become more frequent. We
judge that the system becomes prohibitively occluded
at a voidage of approximately 3.5% (equivalent to a gas
flow rate of 200 ml min 1). Figure 1 b) shows sEPI and
photographic images of the system in this condition,
together with a BSD produced from the MRI data. The
mean bubble size and distribution of bubbles increase







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010





iii)


S0.3

S0.2


0 0.5 1 1.5 2 2.5 3
Bubble radius (mm)


0 0.5 1 1.5 2 2.5
Bubble radius (mm)


S0.3

0.2
I a


0 0.5 1 1.5 2 2.5 3
Bubble radius (mm)


Figure 1: A comparison of i) sEPI images and ii) photographs with iii) bubble sizes distributions (given as spherically
equivalent radii extracted from MRI data (0) and optically where possible (A). Also shown are log-normal
distributions fitted to the data. Three voidages were examined: a) c = 1. .'. b) c = 3.5%, the limit of optical
sizing, and c) c = 34.7%, the highest voidage attainable in the present system prior to the transition to slug
flow. The field of view of the MRI images is 35mm x 35mm, and 40mm x 45mm for the photos.


only slightly for the higher voidage system despite the
number of bubbles almost doubling (from an average of
22 bubbles per image for the low voidage case to 38 for
the present system).
To demonstrate the utility of the MRI technique in
high voidage systems, images were also acquired with
a gas flow rate of 1 L min 1 (equivalent to a voidage of
34.7'. i These data are shown in Figure 1 c). While it
is clear that the bulk flow is now completely optically
concealed, individual bubbles may still be clearly
resolved in the MRI data. From the BSD it is clear


that the mean bubble size has increased to 1.2 mm, and
that the distribution of sizes is much larger (standard
deviation of 0.31 mm). Additionally, the data appear
more normally distributed, suggesting that bubble
breakup and coalescence may now be significant factors
in the system. This voidage represents the highest we
were able to attain for stable discrete bubbly flow, with
higher gas flow rates leading to periodic slug formation.
By measuring bubble size from signal intensity
rather than some projected shape, many complications
that afflict other measurement techniques are entirely







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


14.5


-14.5


Figure 2: i) Intensity and ii) velocity images acquired for bubbly flow at gas-fractions a) = 3.5% and b) = 34.7%.
The bubble driven upward conveyance of fluid at the centre of the column may be observed in a), and
multiphase induced turbulence is evident in b). The field of these images is 35mm x 35mm


avoided. Obtaining the true shape of bubbles from
2D projections (i.e. photographs, X-ray) is a problem
which has long been acknowledged (Lunde and Perkins
1998), and obtaining a representative measurement
of size from techniques which only measure a chord
length is the subject of ongoing research (Kulkarni et al.
2004). To the best of the author's knowledge, no other
experimental technique is capable of obtaining bulk
measurements in the presence of gas-fractions as high
as those demonstrated here.
In addition to spatial encoding with MRI, it is possible
to precondition the signal phase with a velocity sensitive
component. By incorporating this velocity encoding
into sEPI, it is possible to attain 2D velocity maps in
the presence of bubbly flow. Example axial velocity
images for the 3.5% and 34.7% voidage systems are
given in Figure 2. Intensity images (reconstructed from
the same data) are also presented. Full details of the
implementation of this technique and a demonstration
of the quantative nature of the results shall be published
elsewhere. From the velocity image for the low voidage
system, it is clear that fluid is being conveyed up the
column by swarms of bubbles, while downward flow


occurs in areas of relative bubble sparsity (predomi-
nantly at the edges of the column). Conversely, the
high voidage system appears more heavily mixed, and
is highly turbulent. The net velocity in each of these
images is approximately zero, as one would expect from
conservation of mass as applied to the liquid phase. This
technique also enables the measurement of fluid velocity
in previously inaccessible opaque systems. The highest
voidage system from which velocity measurements have
previously been made is that of Mudde et al. (1997) who
examined gas fractions up to -".'. using LDA. Their
sampling rate, however, decreased exponentially due to
intervening bubbles interfering with the measurement
as they focused their laser on regions deeper into the
column. By obtaining measurements with a non-optical
method, such as MRI, these complications are entirely
avoided. If the flow patterns and onset of multiphase
induced turbulence may be thus characterized, the better
design and operation of gas-liquid operations will be
enabled.











Conclusions

Bubbly flow has been imaged using ultrafast MRI for
the first time. A procedure for accurately determining
the spherically equivalent radius of bubbles from the sig-
nal level present in MRI images was developed, and im-
plemented for images acquiring using the sEPI scanning
protocol. Images were acquired in 13.8 ms. The veracity
of the MRI measurements was validated in comparison
to optical measurements of a low voidage (e 1. '.'
system consisting of air bubbles in 0.1 g L 1 SDS solu-
tion. The technique was also demonstrated at the limit
of optical measurement (e 3.5' .1 and at the highest
gas-fraction for which dispersed bubbly flow was still
achievable (e = 34.7'. i The latter represents the high-
est voidage for which bulk bubble sizes have been mea-
sured to date. As expected, the mean bubble size in-
creased with increasing gas-flowrate, and the distribu-
tion of sizes was seen to widen for the high voidage
system. Lastly, a velocity sensitive variant of sEPI was
applied to bubbly flow, and quantitative velocity maps
were extracted for low and high voidage systems.


Acknowledgements

The authors wish to thank the EPSRC for support under
the Grant EP/F047991/1 and Microsoft Research Cam-
bridge. Bruce Lee of the University of Newcastle, Aus-
tralia, is thanked for performing the surface tension mea-
surements. ABT would like to thank the Cambridge
Commonwealth Trust and Trinity College, Cambridge
for financial support.

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ICMF 2010, Tampa, FL, May 30 -June 4, 2010


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