Chemical Engineering Science 94 (2013) 20–29

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Science

0009-25

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Development of an image measurement technique for sizedistribution in dense bubbly flows

Y.M. Lau, N.G. Deen n, J.A.M. Kuipers

Multiphase Reactors Group, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven,

The Netherlands

H I G H L I G H T S

G R A P H I C A L A

c An image analysis method is devel-oped to obtain the bubble size dis-tribution in dense bubbly flow.

c Synthetic images of dense bubblyflows are used to evaluate theerrors of the method.

c The developed method is applied tomeasure the BSD in a pseudo-2Dbubble column.

09/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.ces.2013.02.043

esponding author. Tel.: þ31 40 247 3681; fax

ail address: N.G.Deen@tue.nl (N.G. Deen).

B S T R A C T

a r t i c l e i n f o

Article history:

Received 27 November 2012

Received in revised form

13 February 2013

Accepted 15 February 2013Available online 28 February 2013

Keywords:

Bubble columns

Digital image analysis

Fluid mechanics

Gas–liquid flow

Multiphase flow

Multiphase reactors

a b s t r a c t

Present work describes the development of a non-intrusive image analysis technique to measure the

bubble size distribution in bubbly flows. Generally image analysis methods for bubble characterization

in bubbly flows are suitable at low void fractions. These methods depend mainly on the appropriate

thresholding/conversion of the image into a binary image, dividing liquid and bubble objects. Clusters

of overlapping bubbles are discarded using the criteria of a shape factor, thus leaving only solitary

bubbles within an image. When the void fraction is low, the amount of discarded bubble data is very

small compared with the obtained solitary bubble data. For bubbly flows with larger void fractions, the

discarded data of overlapping/clustering bubbles is considerable. In this work the overlapping clusters

are passed through a watershedding algorithm in order to segment the groups of bubble object areas

into individual bubbles. The developed image algorithm is verified with synthetic bubble images and

applied for an actual system involving bubbly flow in a pseudo-2D bubble column.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Bubble columns are widely used in many industrial applications,e.g. Fischer–Tropsch process for hydrocarbon synthesis, hydrogena-tion of unsaturated oil, coal liquefaction, fermentation and wastewater treatment. Adequate control of these processes is essential inachieving successful operation. One of the important aspects is toquantify the bubble size distribution, which depends on the

ll rights reserved.

: þ31 40 247 5833.

coalescence and break-up of bubbles. These two processes aregenerally considered to be independent from one another and occurat different conditions. Collisions between bubbles could lead tocoalescence, depending on the local flow conditions and gas–liquidproperties, e.g. surfactants can act as coalescence inhibitors. On thecontrary, bubble break-up could be the result of the interaction withvortical flow structures (eddies), wake shear effects and bubbleinstabilities. The combination of coalescence and break-up of bubblesalong with other mentioned aspects determines the resulting bubblesize distribution (BSD) in a bubble column. However, it is verydifficult if not impossible to accurately measure BSD in industrialbubble columns. Therefore, lab-scale bubble columns are often

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–29 21

studied, where it is possible to measure BSD. Currently, there areseveral non-intrusive as well as intrusive methods that can be used tomeasure BSD. Intrusive methods employ, for instance, capillarysuction probes (CSP) (Barigou and Greaves, 1991; Laakkonen et al.,2005), conductivity probes (Liu and Bankoff, 1993), optical fibreprobes (Saberi et al., 1995) and wire-mesh sensors (Prasse, 2008).Non-intrusive methods include Phase Doppler Anemometry (PDA)(Laakkonen et al., 2005), Interferometric Particle Imaging (IPI) (Gloveret al., 1995) and Digital Image Analysis (DIA) (Honkanen et al., 2010;Laakkonen et al., 2005; Majumder et al., 2006). Non-intrusivemeasurement techniques are preferred over intrusive methods, sincethe flow conditions are not disturbed by the insertion of probes.Among these non-intrusive methods, DIA is a convenient technique,which can measure irregular-shaped/non-spherical bubbles accu-rately over a wide range of bubble sizes (Honkanen et al., 2005). Thisoptical technique has been used in many studies, ranging from flat-sided vessels (Unno and Inoue, 1980; Zhou et al., 1993) to agitatedvessels (Takahashi et al., 1992; Takahashi and Nienow, 1993; Bouaifiand Roustan, 1998; Hebrard et al., 2001; Machon et al., 1997; Gloveret al., 1995) for extraction of bubbles in a reservoir (Ahmed andJameson, 1985; de Rijk et al., 1994; Malysa et al., 1999; Chen et al.,2001; Yianatos et al., 2001; Grau and Heiskanen, 2002; Rodrigues andRubio, 2003). The limitations of this technique are obvious: atransparent wall as well as a transparent liquid is required and onlythe vicinity of the wall can be observed at high gas hold-up. If the gashold-up exceeds 1%, more than 40% of the bubbles are overlapping inthe image (Lecuona et al., 2000; Rodriguez-Rodriguez et al., 2003).This makes it very difficult to detect/recognize bubbles from thedigital image. One way to deal with overlapping bubbles is to ignorethem by a constraint condition. This condition can be, for instance,the sphericity/roundness (Bailey et al., 2005; Hernandez-Aguilar,2004) or the concavity index (Mena et al., 2005) to interpret anobject area as a bubble. The ignored overlapping bubbles can beintroduced to categorize classes by their complex shapes (Ferreiraet al., 2012). In another method, overlapping bubbles can be identifiedby an object recognition approach (Honkanen et al., 2005; Pla, 1996;Shen et al., 2000) by fitting an ellipsoidal shape to the object areas.Since large bubbles have more opportunities to overlap with otherbubbles, the latter method would be more suitable for the BSDestimation than the previous one. However, bubbles in most kinds ofequipment are not spherical/ellipsoidal and can vary widely in shape.

In the present work, we propose to use the watershed transfor-mation function (Meyer, 1994) to segment/separate the overlapping

Fig. 1. Image processing sequences to determine the bubble size distribution: (a) filte

bubbles I1-ðI2aþ I2bÞ, (c) segment the overlapping bubbles using the watershedding te

bubbles into individual bubble objects. In this image analysismethod, the overlapping bubbles are defined by a shape factor(sphericity/roundness) and the number of individual bubbles isdetermined by the number of recognized/detected inner bubbleholes. Bubble holes are the inner areas of bubbles, which have adifferent intensity than the background in a grayscale image.Synthetic images (with a single bubble or multiple bubbles) areused to evaluate/verify this method and to quantitatively analyzethe error in the BSD estimation. Finally, the image analysis methodis applied to estimate the BSD of true experimental images whichare obtained from a pseudo-2D bubble column.

2. Image analysis algorithm

2.1. Overview

The bubble properties that can be obtained from an image are theprojected area and shape. From these properties we can derivecentroids and the equivalent diameter. To acquire these values, anumber of operations (see overview in Fig. 1) are performed uponthe images to attribute individual pixels to bubbles. As shown in thefigure, the image analysis algorithm consists of four main subsequentoperations: (a) image filtering Io-I1, (b) separation of the bubbleobjects into solitary bubbles and overlapping bubbles I1-ðI2aþ I2bÞ,(c) application of the watershedding technique to segment theoverlapping bubbles I2b-I3 and (d) combination of the segmentedsolitary and overlapping bubbles’ images ðI2aþ I3Þ-I4. In the filteringstep (a), the high-speed camera image is passed through a number offilters as shown in Fig. 2. First the inhomogeneous backgroundillumination is corrected using local thresholding. Assuming thatthe background illumination is homogeneous in local areas of theoriginal image (Io), Io is divided in blocks and each block isindependently thresholded by employing the filter function pro-posed by Otsu (1979)

Ilocal thresholdði,jÞ ¼0 if Ioði,jÞ4 lOtsu

1 if Ioði,jÞr lOtsu

(ð1Þ

where lOtsu is the automatic threshold level. Then, Ilocal threshold issubtracted from Io to yield an image without background

Ibackground removed ¼ Io�Ilocal threshold ð2Þ

In the second step, the edges of the bubble objects in Ibackground removed

r original image Io-I1, (b) separate bubble objects into solitary and overlapping

chnique I2b-I3 and (d) combine the results ðI2aþ I3Þ-I4.

Fig. 2. Image filtering process.

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–2922

are highlighted using an edge detection algorithm proposed byCanny (1986) to enhance the distinction between bubbles andbackground

Iedge ¼ Ibackground removedþedgeðIbackground removedÞ ð3Þ

In the third step of the filtering process, Iedge is converted to a binaryimage using an appropriate threshold value lhistogram chosen from thehistogram of the image gray scales

I1ði,jÞ ¼0 if Iedgeði,jÞ4 lhistogram

1 if Iedgeði,jÞr lhistogram

(ð4Þ

Small white areas ðoAminÞ due to noise are removed and the filteringstep ends by filling the image regions and holes. After filtering, thebubble objects of the filtered image (I1) are separated in step (b) intosolitary bubbles and overlapping bubbles using the roundness toclassify the bubbles. The roundness is determined as follows:

Ro¼Sffiffiffiffiffiffiffiffiffi

4pAp ð5Þ

with S the object perimeter and A the area. Note that sphericalbubbles have a roundness of unity. Here, an object area is defined asa solitary bubble if Roo1:25. The actual value is found through trialand error due to the complex shape of the bubbles for the estimationof the BSD. The two resulting images are segmented independently.The image with the solitary bubbles (I2a) is segmented by labellingthe solitary areas, whereas the image with the overlapping bubbles(I2b) is segmented in step (c) using the watershed transformproposed by Meyer (1994). Principles of this transformation will beexplained in the next section. In the last step (d), both segmentedimages (I2aþ(I3)) are combined to yield an overall image (I4) withsolitary and separated overlapping bubbles. Finally, the area of pixelsof each bubble object is counted and converted from pixel to metricvalues using the magnification of the image. From the measuredarea, the equivalent diameter is calculated as follows:

de ¼

ffiffiffiffiffiffi4A

p

rð6Þ

2.2. Watershedding technique

The watershed transform is a region-based segmentationmethod coming from the field of mathematical morphology.Watershed transformation is easily explained by considering theanalogy with a water flooding process on a gray scale image (seeFig. 3). The gray scale image can be visualized as a topographicinterpretation of three dimensions i.e. two spatial coordinates andthe gray levels as the altitude. In the flooding process of thetopographic interpretation, three types of points are considered:such as (a) points belonging to a regional minimum; (b) points atwhich a drop of water, if placed at the location of any of thosepoints, would flow to reach a single minimum; and (c) points atwhich water would be equally likely to fall to more than one suchminimum. For a particular regional minimum, the set of pointssatisfying condition (b) is called the catchment basin of that

minimum. The points satisfying condition (c) form crest-lines onthe topographic surface and are termed as watershed lines or dividelines. When rising water in a distinct catchment basin is about tomerge, a dam is built to prevent the merging. The flooding willeventually reach a stage only when the top of dams is visible abovethe water line. The dam boundaries correspond to the divide lines ofthe watersheds or the boundary lines between overlapping bubbles.

The objective in segmenting the image with the overlappingbubbles is to find the watershed lines. Fig. 4 illustrates the process ofwatershedding of a group of overlapping bubbles. In the first stepthe original image (see Fig. 4(a)) is inverted. The background andsolitary bubbles are masked out (see Fig. 4(b)). Then, in the secondstep, the image is thresholded and cleaned to only keep the bubbleinner areas remaining in the image (see Fig. 4(c)). The thresholdvalue is chosen in between the intensity of the bubble outerinterface and the bubble inner area. These areas will function asthe regional minima in the watershedding process. Noted from theimage that three bubbles are detected. The bubble area borders (seeFig. 4(d)) are the outer boundaries of the catchment basins. Theseboundaries are generated by the gradient magnitude of the binaryimage I2b. Segmentation can proceed as depicted in Fig. 4(e). Fromthe local minimum, the entire topography is flooded from below byletting water rise through the minima uniformly forming catchmentbasins and creating watershed lines.

3. Verification of the measurement technique

3.1. Measurement errors

As in all experimental methods, errors are unavoidable in the useof the image measurement method to extract bubble characteristics.Besides the calibration errors of the experimental set-up and/orhardware imperfections, other causes of measurement errors in anactual image measurement of the bubble size distribution can bedistinguished as follows:

�

Imaging errors:

J Inhomogeneous background illumination causes intensitydifferences between image sections. The inhomogeneity iscancelled out by filtering the image using a combination oflocal and global thresholding.

J Bubble images are distorted by white image noise and/ornoise generated by bubbles, which are not located in thefocal plane of the high-speed camera. Noise is filtered out byremoving the small noise areas (Amin) from the image.

�

Filtering errors:

J Coupled to the inhomogeneous background illumination ofthe image, appropriate local and global thresholding para-meters must be chosen in order to filter out the background/

Figout

floo

Figand

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–29 23

liquid. If not, the final segmented image can yield too less ofdetected bubbles or the detected bubble sizes are too small.

J Inclusions of liquid areas in between clusters of bubbles canpass through the filtering step as bubble object areas. Appro-priate local and global thresholding values can minimize thenumber of these so-called ghost bubbles.

J Removal of the image noise through removal of the smallobject areas causes the image analysis method to be unableto detect bubble objects oAmin.

. 4., (c)

ded

. 3.(3)

�

Separation errors:

J Non-spherical bubbles can cause errors during the separationof the object areas into solitary and overlapping bubbleobjects, e.g. a non-spherical bubble can be interpreted as acluster of bubbles or a cluster of non-spherical bubbles can beinterpreted as one solitary bubble. This error is very difficult tominimize through the separation criteria and mainly dependson how distorted the shapes of the bubbles are in the image.

1

2

Example of the watershedding process: (a) a partial image with a group of three

thresholded image to acquire the bubble markers as local minima, (d) image w

image with three distinct bubbles.

Illustration of the watershed transformation in a two-dimensional plane: (1) star

dams or watershed lines are formed dividing the bubbles from each other.

�

3

bu

ith l

ting

Segmentation errors:

J Overlapping (partially/entirely) or clustering of bubbles can beassessed by the algorithm as one large bubble (undersegmen-tation) or as multiple smaller bubbles (oversegmentation).

J Noted that if a non-spherical object area is interpreted as acluster of bubbles, the watershedding technique (illustratedfor a cluster of three bubbles in Fig. 4) should have no problemto detect a single bubble provided that the inner bubble area iscleaned properly to show only one bubble.

J During the detection of the bubble inner areas within thegroup of overlapping bubbles, small areas can be eliminated.This leads to a lesser number of bubbles being detected andinaccurate object area division between the detected bubbles.

bble

ocal

from

�

Computational errors:

J Numerical error in calculating the bubble areas is due tothe sampling of the bubble image.

s, (b) inverted image with background and solitary bubble objects masked

minima and the border (gradient magnitude) of the bubble group, (e) the

the local minima of the bubbles, (2) the basins or bubble area are flooded

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–2924

3.2. Creating synthetic bubble images

The image analysis algorithm is written with the purpose tominimize the impact of the above-mentioned errors. To deter-mine the magnitude of errors made with the image analysis,synthetic bubble images of a known size are generated andprocessed by the image analysis algorithm. Creating such syn-thetic images requires the synthetic bubble to mimic the actualpixel intensity values as seen by the camera. The intensity profileof a bubble depends on the orientation and type of the lighting,the bubble shape and gas–liquid properties. Fig. 5(a) shows anexample of the intensity profile of a bubble of a true experiment.By analyzing the shape of this profile, bubbles can be drawn in thesynthetic images using similar characteristics (see Fig. 5(b)). Thefollowing functions are used to describe the intensity profile of abubble:

I¼min Iinnerbubble,9ðr�RÞ9

w

� �n !

for ðrrRÞ ð7Þ

I¼min Ibackground,9ðr�RÞ9

w

� �n !

for ðRorrRþwÞ ð8Þ

I¼ Ibackground for ðr4RÞ ð9Þ

with r¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx2þy2Þ

p, n¼2, w� 0:15R and the bubble radius equals

to Rþw. The coordinates x and y are defined by reference to thebubble centroid (x0,y0).

3.3. Error analysis

3.3.1. Single bubble size measurement

To quantify the errors of the image analysis technique, we startwith a synthetic image of a single bubble (see Fig. 5(b)). A circularshaped bubble is drawn with a specific diameter in pixels and itscentroid is placed in the middle of a pixel (0.5 pixel, 0.5 pixel).Subsequently new bubbles are generated with its centroid trans-lated with steps of 0.001 pixel in both x- and y-direction. For eachtranslation, the bubble equivalent diameter is calculated by the

Fig. 5. Grayscale intensity profile across the centerline o

image analysis algorithm and the error of the detected/calculatedbubble diameter is given in Fig. 6. The maximum and minimumerrors for small bubbles with pixel diameter of 10–30 pixels areestimated as þ2% and �6% respectively. In terms of the calcu-lated spherical bubble volume, the minimum and maximumerrors are þ5% and �16% respectively. For bubbles with adiameter 430 pixels, the error is between þ0.5% and �1% andthe calculated volumetric error is þ1% and �2%.

A rough estimate of the error is given as follows. Assumede ¼N pixels and an error of DN pixels. This gives A¼ ðp=4ÞN2 andAþDA¼ ðp=4ÞðNþDNÞ2. Thus, the relative error of area is calcu-lated by

erelA ¼

ðAþDAÞ�A

A¼

2DN

NþðDNÞ2

N2ð10Þ

For Nb1:

erelA �

2DN

Nð11Þ

And for the equivalent diameter (de ¼

ffiffiffiffi4Ap

qpixels), the relative

error is

erelde�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ

2DN

N

� �s�1 ð12Þ

With a maximum and minimum errors of DN¼ 71 pixel, therelative errors are erel

de�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið17 2

NÞ

q�1 and erel

A � 7 2N. These errors

are also shown in Fig. 6.

3.3.2. Bubble size distribution measurement

Following the analysis of the single bubble size measurement,synthetic images with a multiple number of bubbles are generated.These images can be drawn with bubbles with either a constantbubble or a wide bubble size distribution. The bubbles are drawnrandomly in a three-dimensional box (see Fig. 7), whereafter thethree-dimensional structure of the bubbles is projected onto a 2D-front plane to create a synthetic 2D-camera image.

Monodisperse distribution. Synthetic images with multiple bub-bles of a constant bubble diameter were generated (see Fig. 8). Inthis figure, the box depth is larger than the bubble diameter causing

f a bubble image: (a) experiment and (b) synthetic.

0 10 20 30 40 50 60 70 80 90 100−20

−15

−10

−5

0

5

10

bubble diameter [pixels]

diam

eter

cal

cula

tion

erro

r [%

]

0 10 20 30 40 50 60 70 80 90 100−20

−15

−10

−5

0

5

10

bubble diameter [pixels]

volu

me

calc

ulat

ion

erro

r [%

]

Fig. 6. Maxima and minima errors in the calculation of the bubble equivalent diameter (a) and the bubble volume (b) with the estimated error-lines (Eqs. (11) and (12)).

Fig. 7. Generated bubbles of a polydisperse BSD with an input gas hold-up of 0.05

within a box with a height�width�depth of 1024�1024�150 pixels.

Fig. 8. Synthetic image with a monodisperse bubble size distribution showing

overlapping bubbles within a box with a height�width�depth of 1024�1024

�150 pixels and an input gas hold-up of 0.05.

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–29 25

the appearing bubbles to overlap. Due to randomization of thebubble locations, some bubbles are clustered. For the verification ofbubble size measurement, synthetic images are created for a gashold-up (ag) of 0.05 with a constant bubble diameter of 30 pixels ina box of 1024�1024 pixels and depths of 1.0db, 2.5db and 5.0db.Using the image analysis algorithm, the resulting bubble sizedistributions are measured for the three depths and the probabilitydensity functions (PDFs) of the bubble size are illustrated in Fig. 9.For a depth equal to the initial bubble size, where no overlap ispossible, the resulting PDF is nearly identical to the initial PDF withsome small differences. These differences are due to the errors ofthe image analysis method, filtering and segmentation errors.Liquid inclusions between surrounding bubbles within a groupcan be detected as a bubble object through filtering, which in turncould result in segmentation errors of the bubble group. Byincreasing the image depth, partially overlapping bubbles occurand are detected as individual smaller bubbles. Another possibilityfor the occurrence of small bubbles is that the overlapping bubblesare oversegmented. This effect is amplified by increasing the depthof the image, since more overlapping of bubbles occur at the samegas hold-up. The amount of bubbles missed or partially detected isshown in Table 1, where the error of the calculated gas hold-up isgiven for the resulting PDFs.

Polydisperse distribution. For the creation of synthetic imageswith a polydisperse bubble size distribution, bubble sizes aregenerated that comply with a Rayleigh distribution

f ðdb;sÞ ¼db

s2eð�db=2s2Þ ð13Þ

with s¼ 0:12 pixels. This distribution is chosen based on pre-liminary BSD measurements within a pseudo-2D bubble columnto mimic an actual BSD. The generated bubbles are limited to amaximum bubble size of 60 pixels. The bubbles are drawn in asimilar box as for the monodisperse synthetic images. The boxdimensions are 1024�1024 pixels with depths of dmax, 2dmax and2:5dmax. The input gas hold-up values are 0.03, 0.05, 0.07, 0.09 and0.11. Fig. 10 shows one such generated polydisperse syntheticimage. The PDFs obtained after applying the image analysisalgorithm are shown in Fig. 11. In this figure, bubbles with adiameter o5 pixels are not detected due to the noise filtering ofthe images which removes small pixel areas. For each calculatedPDF, there are too few bubbles detected with a diameter smallerthan 12 pixels, too many bubbles with a diameter of 12–20 pixelsand the right number of bubbles with a diameter 420 pixels. Thedecrease in the presence of smaller bubbles and increase of largerbubbles are due to the overlapping effect, causing the algorithm

5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

diameter [pixels]

PD

F [−

]

input dbub= 30pixelsoutput, depth = dbuboutput, depth = 2.5dbuboutput, depth = 5dbub

Fig. 9. PDF for a monodisperse bubble size distribution with a gas hold-up of 0.05 as

input and its detected/calculated PDFs as output with three different depths (1.0db,

2.5db and 5.0db). The line of input dbub overlaps the line of output (depth ¼dbub).

Table 1Calculated gas hold-up error values from a monodisperse bubble size distribution

with db ¼ 30 pixels.

Image depth input ag (–) output ag (–) Error (%)

1.0db 0.0503 0.0492 2.19

2.5db 0.0502 0.0480 4.38

5.0db 0.0501 0.0412 17.73

Fig. 10. Synthetic image with a polydisperse bubble size distribution showing

overlapping bubbles.

0 10 20 30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

diameter [pixels]

PD

F [−

]

Rayleighαg=0.03

αg=0.05

αg=0.07

αg=0.09

αg=0.11

0 10 20 30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

diameter [pixels]

PD

F [−

]

Rayleighαg=0.03

αg=0.05

αg=0.07

αg=0.09

αg=0.11

Fig. 11. Input and output PDF for a polydisperse bubble size distribution with

depths of (a) D¼ 1:0dmax and (b) D¼ 2:5dmax for different initial gas hold-up values

(ag ¼ 0:03, 0.05, 0.07, 0.09 and 0.11).

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–2926

to recognize a group of small bubbles as one large bubble. Thiseffect is less apparent for an image depth equal to 60 pixels (seeFig. 11(a)), where the resulting PDF is approximately equal to theexact PDF. Increase of the image depth amplifies the effects bydetecting less smaller bubbles and more larger bubbles. Thiseffect is more profound due to the increase of the gas hold-up.

The calculated gas hold-up values from the detected bubblesare illustrated in Fig. 12 along with the related errors. From thisfigure, it is seen that the amount of bubbles missed for the imagedepth of D¼ 1:0dmax is the least due to the lesser space orpossibility for bubbles to overlap. Generally, the error increasesmodestly as the gas hold-up increases. As for the gas hold-up for

the image depths of 2:0dmax and 2:5dmax, the errors increase forinput gas hold-up range of 0.03–0.07. While it seems that theerrors reduce for input gas hold-up values 40:07, it does notmean that more bubbles are detected. The lesser error in thedetected gas hold-up is caused by an increase in the amount ofmisinterpretation of liquid inclusions between bubbles as bubblesitself. Thereby the detected bubbles’ volume is overestimated.This shows that although most errors of the image analysismethod are as much as possible eliminated, the results obtainedat high void fractions should be interpreted with care.

4. Application to bubbly flow in a pseudo two-dimensionalcolumn

4.1. Experimental set-up

To illustrate the application of the image analysis technique toa real bubbly flow, high-speed camera images obtained from apseudo-2D bubble column are used for processing. A schematicoverview of the bubble column is given in Fig. 13. The column is0.20 m wide, 0.03 m deep and 1.00 m high. The column is filled

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

input αg [−]

outp

ut α

g [−

]

depth = 1.0dmaxdepth = 1.67dmaxdepth = 2.0dmaxdepth = 2.5dmax

0 0.02 0.04 0.06 0.08 0.1 0.120

5

10

15

20

25

30

35

40

input αg [−]

erro

r out

put α

g [%

]

depth = 1.0dmaxdepth = 1.67dmaxdepth = 2.0dmaxdepth = 2.5dmax

Fig. 12. Calculated gas hold-up values (a) and the related error (b) from the PDFs

of the polydisperse synthetic images with different image depths.

Fig. 13. Schematic overview of the pseudo-2D bubble column set-up.

Fig. 14. High speed camera image obtained in the pseudo-2D bubble column at a

superficial gas velocity of 0.015 m/s with the encircled detected bubbles, solitary

(blue) and watershedded (red) bubble objects. The depth of the column is about

D¼ 6:5de and ag ¼ 0:068. (For interpretation of the references to color in this

figure caption, the reader is referred to the web version of this article.)

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–29 27

with distilled water and air is dispersed from the sparger at thebottom of the column. The sparger consists of 20 needles, alignedat the centreline with a pitch of 0.01 m. Each needle has an outerdiameter of 0.0013 m, an inner diameter of 0.001 m and is0.010 m elevated inside the column. Experiments are performedwith an initial liquid height of 0.60 m using a superficial gasvelocity of 0.015 m/s. The region of measurement is a 0.18 by0.18 m2 window that is positioned between approximately0.2 and 0.4 m from the bottom-plate (see Fig. 13). The magnifica-tion of the images is 0.1787 mm/pixel. Due to the image noisefiltering, the minimum detectable diameter of a solitary bubble isapproximately 0.9 mm, while the smaller bubbles can still bedetected through the watershedding technique. A total number of5000 images are recorded at a frequency of 50 Hz.

4.2. Results

Fig. 14 shows an image obtained from the experiments alongwith the detected bubble objects. From visual observation of suchimages, it can be seen that the limitation of the minimumdetectable db does not play a significant role in the currentconfiguration.

The bubble size distribution resulting from the image analysiswith watershedding is presented in terms of a PDF of the equivalent

bubble diameters shown by the solid line in Fig. 15(a). It can beseen that there are two groups of bubbles: small bubbles with apeak at approximately 2.1 mm and large bubbles with a peak atapproximately 4.9 mm. These two groups indicate the occurrenceof an equilibrium between coalescence and break-up of bubbles.Any minor adjustment of the system variables can result in a shiftor change of the PDF.

To compare the effect of the watershedding step in the analysis,the result without watershedding is shown by the dashed line inFig. 15(a). The peaks of the two bubble groups remain at the samepositions when watershedding is applied, but the distinctionbetween the peaks is less clear. Most importantly is that withoutthe watershedding algorithm, a large amount of data is discarded.The amount of discarded data can be quantified by comparing the

0 2 4 6 8 10 12 14 160

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

diameter [mm]

PD

F [−

]

With watershedWithout watershed

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

3 x 105

diameter [mm]

Num

ber o

f bub

bles

[−]

With watershedWithout watershed

Fig. 15. PDF of the image analysis algorithm with/without watershedding (a) and the actual number of bubble counts (b).

Y.M. Lau et al. / Chemical Engineering Science 94 (2013) 20–2928

number of bubble counts of the two bubble size distributions inFig. 15(b) or by comparing the gas hold-up values. The integral gashold-up values are calculated using the bubble size distributionPDF and compared with the value calculated from the expansionheight given by

ag ¼hf�h0

hfð14Þ

with hf the aerated height and h0 the initial liquid height. For thePDF with and without watershedding, the obtained gas hold-upsare respectively 0.047 and 0.0044. Compared with the true gashold-up of 0.068, the amount of data loss or undetected bubbles isapproximately 31% with the use of watershedding and 94%without.

5. Conclusions

An image measurement technique was developed to charac-terize the bubble size distribution in dense bubbly flows. Tradi-tionally, image analysis methods for bubbly flows with low voidfractions mainly depend on thresholding the grayscale image to abinary image. Thereby the information of overlapping bubbles isdiscarded on the basis of the roundness shape factor. In this paperwe used a watershedding algorithm on the discarded bubblegroups to extract extra data from the image. Synthetic bubbleimages with monodisperse and polydisperse distributions werecreated and used for the verification of the image measurementtechnique. Though the accuracy of the image measurementmethod declines with increasing gas hold-up and/or image depthas shown in the verification process, it provides a robust mea-surement of the bubble size distribution in dense bubbly flows.

The method was illustrated on the basis of true experimentalimages. It was found that the two bubble groups are detected.This is also observed by only taking the solitary bubbles intoaccount, hereby discarding a large amount of data containingoverlapping bubbles. Clusters of bubbles can be segmented intoindividual bubbles with minimum data loss, but with the possi-bility of oversegmentation (interpreting a non-bubble object areaor partial bubble object area as a bubble). Note that, overlappingbubbles are always a cause of incomplete bubble information,since only a portion of the bubbles appear in the image. Apartfrom the limit of detecting tiny bubbles due to the image noisefiltering, the resulting PDF does provide a reliable measure of thebubble size distribution within pseudo-2D bubble columns.

Acknowledgements

This project is part of the Industrial Partnership Program‘‘Fundamentals of Heterogeneous Bubbly Flow’’, which is fundedby FOM, AkzoNobel, DSM, Shell and TataSteel.

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