understanding bubble hydrodynamics in bubble columns
TRANSCRIPT
Experimental Thermal and Fluid Science 45 (2013) 63–74
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Experimental Thermal and Fluid Science
journal homepage: www.elsevier .com/locate /et fs
Understanding bubble hydrodynamics in bubble columns
Amir Sheikhi 1, Rahmat Sotudeh-Gharebagh ⇑, Reza Zarghami, Navid Mostoufi, Mehrdad AlfiMultiphase Systems Research Lab., Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563,Tehran, Iran
a r t i c l e i n f o
Article history:Received 31 March 2012Received in revised form 19 July 2012Accepted 9 October 2012Available online 30 October 2012
Keywords:Gas–liquid columnHydrodynamicsVibration inspectionPressure fluctuationsFrequency analysisWavelet transform
0894-1777/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.expthermflusci.2012.10.00
⇑ Corresponding author. Tel.: +98 21 6697 6863; faE-mail addresses: [email protected] (A
(R. Sotudeh-Gharebagh).1 Present address: Chemical Engineering Departmen
Quebec H3A 0C5, Canada.
a b s t r a c t
Compared to conventional gas–liquid bubble columns, gas–liquid columns including both gas and liquidflows have been investigated less due to their complex hydrodynamics and operational difficulties. In thisstudy, simultaneous non-intrusive methods of column shell vibration and pressure fluctuation measure-ments were coupled with direct photography and image analysis for bubble characterization. Various sta-tistical and frequency analyses were conducted on the acceleration and pressure fluctuations signals todetermine their capability of interpreting bubble behavior inside the column. The standard deviationof vibration signals showed less sensitivity to bubble behavior compared to that of pressure fluctuations.The skewness of vibration and pressure fluctuations could detect bubble regime transition points at allstudied gas and liquid velocities while vibration and pressure fluctuations kurtosis could only detectthe main transition point of the column at a moderate liquid velocity. It was found that besides regularstatistical methods, the energy of pressure signals could predict bubble regime transition points success-fully. While vibration-based inspection showed more sensitivity to bubble size distribution (similar tothe standard deviation of pressure signals), frequency analysis on pressure signals proved to be a strongrepresentative of bubble Sauter mean diameter alteration by liquid flow variation at constant gas veloc-ities. Moreover, by means of energy-based discrete wavelet transformation, we defined the exact path-way of various sub-signal gradual evolutions throughout a wide range of operating conditions of gasand liquid velocities and captured regime transition points accordingly. The proposed methods in thiswork can be used for non-intrusive hydrodynamic characterization in industrial bubble columns.
� 2012 Elsevier Inc. All rights reserved.
1. Introduction
Gas–liquid contactors are widely used in various industriessuch as chemical [1–4], biochemical, biotechnology [5–7], biomed-ical [8], petrochemical and refining [9,10], environmental, separa-tion and purification [11–18], nanotechnology [19,20] and gasprocessing industries [21–23]. Among such contactors, bubble col-umns, with or without liquid flow, are of a considerable impor-tance in numerous process units. Industrial plants which aredealing with physical [24] and/or chemical interactions betweengas and liquid phases as well as gas–liquid–solid [25] contactorsprofit from the ease of construction [26], high interfacial areaand consequently high mass [27] and heat [28] transfer rates, sta-ble temperature [29], the ease of energy providence and the highliquid hold up [30] of bubble columns [31].
Successful design, operation, scales up and optimization ofbubble columns highly depends on the hydrodynamics of such
ll rights reserved.8
x: +98 21 6646 1024.. Sheikhi), [email protected]
t, McGill University, Montreal,
contactors. Although various theoretical efforts to model two-phase gas–liquid contactors have been undertaken [32–38], newexperimental approaches for hydrodynamic inspections are ofgreat interests in industrial and R&D communities. Wall pressurefluctuations were used to study the effect of various sparger geom-etries on bubble flow regimes in bubble columns [39]. Flow patternand structure were investigated by means of pressure fluctua-tions combined with particle image velocimetry [40]. Chaoticbehavior of bubbles were studied using pressure signals andlaser-phototransistor [41]. Also, bubbling-to-jetting regime transi-tion was investigated by plenum pressure fluctuations monitoring[42]. Turbulence in the heterogeneous bubble regime was charac-terized by chaos analysis on pressure fluctuations [43].
Simonnet et al. studied the drag coefficient on the gas bubbleswarm using laser Doppler velocimetry [44]. Harteveld et al. [45]and Olmos et al. [46] used laser Doppler anemometry for the accu-rate estimation of turbulence power spectra and flow regime tran-sition identification, respectively. Magnetic resonance imaging wasutilized to characterize hydrodynamics of opaque multiphase sys-tems such as slurry bubble columns [47]. Also, particle imagevelocimetry was found to be able to define bubble velocity andflow regimes inside a two-phase gas–liquid column [48–50].Similar advanced, non-intrusive but expensive methods, such as
Nomenclature
ak approximation sub-signalAn amplitude in a time series at a certain frequency of fn
(kPa or m/s2)CWT continuous wavelet transformde equivalent bubble diameter (m)dm,j minor length (smallest Feret diameter) of bubbles (m)dM,j major length (largest Feret diameter) of bubbles (m)dS Sauter mean diameter of bubbles (m)Dk detail sub-signalX(f) discrete Fourier transformDWT discrete wavelet transformE energy of PSDF (kPa2 or m2/s4)Ea energy of approximation sub-signal coefficient (kPa2 or
m2/s4)ED energy of detail sub-signal coefficient (kPa2 or m2/s4)f desired frequency (Hz)i imaginary unitk sub-signal numberK kurtosis or the forth momentn counternj bubble number with equivalent diameter of de,j
N data point number in a sampleL segment (window) number in a time seriesp indicating pressure fluctuation experimentsPxx average power spectrum (kPa2/Hz or m2/s4 Hz)Pxx
n power spectrum for each segment (kPa2/Hz or m2/s4 Hz)PSDF power spectral density function (kPa2/Hz or m2/s4 Hz)q time-lag coefficientS skewness or the third momentt time (s)Ug gas velocity (m/s)Ul liquid velocity (m/s)v indicating vibration (acceleration) experimentsxn time series data (kPa or m/s2)
Greek symbolsd scale factorr standard deviations shift factorw mother wavelet function
64 A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74
computer-automated radioactive particle tracking [51], computedtomography [52], electrical resistance [53] and capacitance [54]tomography have also been used by a variety of researchers.
Recently, Abbasi et al. suggested the non-intrusive measure-ment and analysis of vibrations in both time [55] and frequency[56] domains to characterize the hydrodynamics of gas–solid fluid-ized beds. They were able to define main transition points insidethe bed as well as bubble behavior using regular signal processingmethods. Sheikhi et al. [57] have shown that vibration inspectioncan also be used as a reliable method for the hydrodynamic char-acterization of liquid–solid fluidized beds. They predicted mini-mum liquid-fluidization and solid-regime transition conditions.Yet, no effort has been made to characterize gas–liquid contactorsby means of simultaneous vibration and pressure fluctuationsanalyses. The aim of this work is a critical comparative study onthe applicability of vibration and pressure fluctuation signal pro-cessing for the hydrodynamic characterization of bubble behaviorinside bubble columns. Electrical signals obtained from vibrationinspection and pressure fluctuations were processed in time andfrequency domains and the extracted information were used todetermine the hydrodynamic state of a bubble column at a widerange of industrial gas–liquid two-phase reactor operatingconditions.
2. Materials and methods
2.1. Experimental set-up
The bubble column used in this study was made of a 2 m heightPlexiglas column with an inner diameter of 0.09 m, presented inFig. 1. Air at ambient temperature, produced by a compressor,was introduced into the 0.1 m high gas–liquid engagement sectionfrom the bottom of the bed using a cylindrical porous ceramic airsparger with a 0.03 m diameter and 0.085 m length consisting of0.0001 m pores. Tap water, as the continuous phase, was pumpedinto the engagement section. Engagement section was filled with0.01 m glass beads for better mixing of air and water. The mixtureof gas and liquid was then sent into the bed through a perforatedplate distributor including 110 holes of 0.3 cm-diameter, placed
with a triangular pitch, followed by a 0.0003 m mesh screen. Theupper section of the bed (gas–liquid disengagement zone) wasset to vent the air into the atmosphere and circulate the water.
2.2. Vibration and pressure fluctuation signal acquisition
For the non-intrusive vibration inspection of the column, twoDJB accelerometers with sensitivities of 100 mV/ms�2 were usedin the experiments. The cut off frequency was set to 65 kHz to pre-vent data loss in the vibration signals. At each run, the data wererecorded for 30 s. Two accelerometers were glued to 0.045 m and0.135 m above the distributor on the outer surface of the columnwall. To ensure the reproducibility of the data, each test was con-ducted 2–3 times, randomly. The analog signals produced by accel-erometers were converted to digital signals and recorded by a B&KPULSE system using 3560 type hardware. The frequency of externalnoise sources was identified and eliminated from bed vibration sig-nals by low-pass and high-pass filters.
To measure pressure fluctuations, a piezoresistive absolutepressure transducer (Kobold, SEN-3248(B075)) was installed atthe height of 0.135 m above the gas–liquid distributor and oppo-site to the accelerometer to avoid probable conflicts. The pressurefluctuations were recorded by a data acquisition system (Advan-tech PCI-1712L) with a frequency of 400 Hz for 163.84 s. The fre-quency of sampling for both acceleration and pressure was set ina way that satisfies the Shanon–Nyquist criterion by being greaterthan 2 times the maximum frequency within the spectrum [55,57].
2.3. Image acquisition and analysis
To obtain bubble size distribution and equivalent bubble size ateach operating condition, a photographic technique was used. Bub-ble images were photographed using a digital CCD camera (CanonPowerShot-SI3) at a height of 0.135 m above the gas–liquid distrib-utor to ensure the elimination of initial liquid jetting effect. Imagesof not less than 250 bubbles were analyzed to determine small(minor) and large (major) bubble diameters (Feret diameters),and bubble size distribution at various operating conditions. A ru-ler was placed inside the column at the focal distance of camera todetermine the real bubble size. Finally, the equivalent size of bub-
Diffuser paper
CCD camera
Halogen lamp
Water drain
Liquid phase
Air
Liquid flow
meters
Disengagement section
Gas vent
Column liquid recycle
Water reservoir
Pump recycle
Pump
Sampling taps
Gas bubbles
Glass beads
Engagement section
Gas sparger
Gas-liquid distributor
Fig. 1. The schematic of the two-phase gas–liquid column.
A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 65
bles, defined as an equivalent sphere diameter with the same vol-ume as the bubble, was calculated. The bubble size change at con-stant gas and various liquid velocities was investigated by thedirect photography of bubbles at the location of pressure measure-ments. The Sauter mean diameter of bubbles was calculated from:
dS ¼
XN
j¼1
njd3e;j
XN
j¼1
njd2e;j
ð1Þ
in which the bubble equivalent diameter can be calculated using:
de;j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2
M;j � dm;j3q
ð2Þ
where dM,j and dm,j are the large and small diameters of oval-shapedbubbles.
3. Data treatment methods
Vibration and pressure fluctuation signals were analyzed inboth time and frequency domains as described below. Statistical
parameters were used to analyze the signals in the time domain.Standard deviation is a measure of the data set dispersion fromits mean and is defined as follows:
r ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
n� 1
Xn
i¼1
ðxi � �xÞ2vuut ð3Þ
where the mean value is calculated from:
�x ¼ 1n
Xn
i¼1
xi ð4Þ
Skewness is a measure of symmetry, or more precisely lack ofsymmetry, in the distribution of a signal:
S ¼
Xn
i¼1
ðxi � �xÞ3
ðn� 1Þr3 ð5Þ
Negative or positive values for the skewness indicate that dataare skewed left or right, respectively.
Kurtosis is defined as the degree of the peakedness of data andis a criterion whether the distribution is flat or peaked relative tothe normal distribution, defined as:
66 A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74
K ¼
Xn
i¼1
ðxi � �xÞ4
ðn� 1Þr4 ð6Þ
Kurtosis is a measure of the relative concentration (flatness orpeakedness) of data in the center of a frequency distribution rela-tive to the tails, when compared with a normal distribution (whichhas a kurtosis of 3).
Fourier analysis is an extremely useful tool in frequency domainfor data analysis. Fourier analysis decomposes a signal into its con-stituent sinusoids of different frequencies and is performed usingthe discrete Fourier transform (DFT). The estimated Fourier trans-form, X(f), of a measured time series, xn, consisting of N points isequal to [58]:
Xðf Þ ¼XN
n¼1
xn expð�2pinf Þ ð7Þ
in which f and i are frequency and the complex number, respec-tively. If N is a power of 2, then Eq. (7) represents the fast Fourieralgorithm, which is an efficient algorithm for computing the dis-crete Fourier transform (DFT) of a sequence.
The power spectrum of a signal which represents the contribu-tion of each frequency in the spectrum to the power of the overallsignal can be estimated from the magnitude of X(f) squared. Thevariance of such an estimation of the power spectrum does not de-crease with an increase of N. To decrease the variance, the signal isrepeatedly divided into windows, and an average of the powerspectrum within the windows is used to obtain an estimate forthe power spectrum (the Welsh method of power spectrum esti-mation). However, the decrease of samples within the windowsgives poor frequency resolution. Hence, an appropriate windowwidth should be chosen to get a satisfactory trade-off between fre-quency resolution and variance [58].
Using Hann window and without any overlap between win-dows, the averaged power spectrum becomes [58]:
Pxxðf Þ ¼1L
XL
n¼1
Pnxxðf Þ ð8Þ
where L is the number of windows and Pnxxðf Þ is the power spectrum
estimate of each window.The energy of a signal, squared sum of amplitudes, can be de-
fined in the frequency domain by Parseval’s theorem:
E ¼XN
i¼1
jxnj2 �XNf
k¼1
Pxxðf Þ ð9Þ
where Nf is the number of points in the frequency domain.On one hand, a trade-off between the window size and fre-
quency resolution always happens when using short-time Fouriertransform. On the other hand, the acquired signals show an unstea-dy and non-regular pattern at different time intervals, e.g., unstea-dy impulses and amplitude patterns. Therefore, a mathematicalmethod is required to extract information from the signals basedon several window sizes through the time. This is needed toachieve the highest possible time–frequency resolution.
The continuous wavelet transform, CWT, is introduced as [56]:
CWTðs; dÞ ¼ d�12
ZxnW
t � sd
� �dt ð10Þ
Using a non-fixed window width, the wavelet transform (WT)offers accurate frequency-based information at both high andlow frequencies. Here, the challenge is to define the time and scalecoefficients by time, which needs a huge computational effort. To
overcome this difficulty, discrete wavelet transform [56], DWT, se-lects the so-called coefficients based on the power of positions andscales dyadic:
DWTðk; qÞ ¼ 1ffiffiffiffiffiffiffiffij2kj
q ZxnW
t � q � 2k
2k
!dt ð11Þ
Afterwards, by screening the signals via pairs of low-pass andhigh-pass filters, known as quadrature mirror filters [56,59], it isdecomposed into its constituents. Each decomposition step makesthe time resolution half and doubles the frequency resolution. Theconstituent sub-signals, known as decomposed signals, are calleddetail (D) and approximation (a) sub-signals. The main signal is alinear superposition of the sub-signals:
xn ’ akðtÞ þ D1ðtÞ þ � � � þ Dk�1ðtÞ þ DkðtÞ ð12Þ
Also, the energy of sub-signals can be utilized as a good repre-sentative of each decomposed signal:
Eak ¼
XN
t¼1
jakðtÞj2 ð13Þ
EDk ¼
XN
t¼1
jDkðtÞj2 ð14Þ
Accordingly, the original signal energy is obtained based on theenergy conservation of WT on orthogonal constituents [56]:
E ¼XN
t¼1
jxnj2 ¼ Eak þ
Xk
j¼1
EDj ð15Þ
Similar to the signal itself, the energy of main signal is a linearsuperposition of sub-signal energies. To utilize the WT, a waveletfunction should be selected based on the signal reconstruction er-ror. Such error was calculated for a random signal, and the second-order Daubechies wavelet (db2) was found to have the lowestreconstruction error. Therefore it was chosen for the waveletanalyses.
4. Results and discussion
Two completely-different-in-nature responses of a bubble col-umn to its internal hydrodynamic alterations, namely column shellvibration and local pressure fluctuations, are processed by meansof statistical and frequency-based analyses, and the results aresummarized below.
4.1. Statistical analyses
To investigate the capability of shell vibration in capturing theeffect of gas and liquid velocities variations on the hydrodynamics,first, the statistical characteristics of acceleration signals wereexamined. Fig. 2a presents vibration standard deviation versus li-quid velocity. The effect of liquid velocity, at constant gas veloci-ties, on the standard deviation of column vibration signals isshown in Fig. 2a. While at higher gas velocities (e.g., Ug = 0.05 m/scompared to Ug = 0.02 m/s), a significant shift in the standard devi-ation of shell vibration is observed due to average bubble sizeincrease inside the column, no remarkable change in the trend ofcurves can be seen at each constant gas velocity. The presence oflarger bubbles at higher gas velocities is also proved in gas–liquidair–water bubble columns [60]. However, bubble size in bubblecolumns is a function of not only gas velocity, but also distributorgeometry [60] and column characteristics [61], which does not al-low a general and unique conclusion on bubble behavior to bemade. This is an important point to consider that in contrast to
Fig. 2a. The standard deviation of vibration fluctuations in the gas–liquid two-phase column; a, b and c are different hydrodynamic behavior regions. While two and onetransition points are seen in regions a and b, respectively, no obvious regime transition can be elucidated from region c. The first transition point is enlarged besides the y-axis,shown by an asterisk.
A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 67
gas-filled media [55,56], the standard deviation of vibrations in aliquid-filled column cannot significantly show slight changes inthe bubble size. However, slight changes in these curves can be cat-egorized in three various behaviors:
(a) At a high gas velocity (Ug = 0.05 m/s), by increasing theliquid velocity, bubbles experience four main governingregimes of coalesced bubble flow, discrete bubble flow andagain coalesced flow, and finally discrete bubbles. Accord-ingly, there are two regime transition points of coalescedbubbles flow-to-discrete flow transition (1st point corre-sponds to minimum r value at Ul = 0.006 m/s), and againcoalesced bubbles flow-to-discrete flow transition (2nd
point at maximum r value where Ul = 0.03 m/s). The secondpoint (i.e., discrete-coalesced-discrete bubble transition),compared to the first point (i.e., coalesced-discrete-coalesced bubble transition), can be considered as the maintransition point. Based on the comprehensive regime transi-tion map for two-phase air–water systems with the flow ofboth liquid and gas, provided by Zhang et al. [62], such a tri-ple effect of liquid flow on the bubble behavior in gas–liquidcontactors operated at high Ug was observed by the gradualincreasing of liquid velocity. At extremely low liquid andhigh gas velocities (corresponding to relatively large bub-bles, i.e., coalesced bubble flow), in the so-called gas-domi-nant regime, liquid shear has no significant effect on gasbubbles [63]. By increasing the liquid velocity, relativelysmaller bubbles are formed due to an increased shear onthe bubbles at the time of bubble formation on the spargerpores. This leads to the presence of discrete bubble insidethe column (Ul = 0.006 m/s) [62]. Further increase in theliquid velocity helps bubbles coalesce together and form lar-ger slugs (6 mm/s < Ul < 3 cm/s). However, high shearexerted on slugs at higher liquid velocities (Ul > 3 cm/s) tearsbubbles apart and form relatively smaller and discrete bub-bles which is consistent with what is reported by Zhanget al. [62]. This is shown schematically in Fig. 2b.
(b) At lower gas velocities (Ug = 0.03–0.04 m/s), no slug is seenand bubbles tend to change their regime from coalesced todiscrete by the high liquid shear at high liquid velocities.Still, a low liquid velocity results in the increase of bubble
size due to prevailing coalescing mechanism over breakage.This is called the dual effect of liquid velocity on gas bubblesat moderate gas velocities.
(c) When the gas velocity is considerably low (Ug < 0.02 m/s),gas bubbles are small and more uniform in size. Therefore,they are not affected by the liquid velocity as much as largerbubbles at higher gas velocities. This is explained by rela-tively lower drag force exerted on small bubbles comparedto larger ones. After a certain critical bubble size (greaterthan 1.5–2.5 mm) [64], exerted drag on bubbles decreasesby the decrease in the bubble size. This is the main reasonfor the low influence of liquid flow on the bubbles in the dis-crete-bubble regime.
Two other statistical characteristics of vibration signals werealso studied: third and fourth central moments (skewness and kur-tosis, respectively). The skewness of vibration signals at three gasvelocities of 0.05, 0.03, and 0.02 m/s is shown in Fig. 3. Startingfrom the lowest liquid velocity, first, the skewness is increasing,then it decreases, and finally, based on the gas velocity, whetherit increases (at high gas velocities, 0.05 and 0.03 m/s) or becomesa plateau (at a low gas velocity, 0.02 m/s). It can be seen in thisfigure that at high gas velocities, the skewness of vibration signalspredicts the first regime-change point by a change in sign.However, at all conditions, it is able to approximate the coalesc-ing-to-disintegrating bubble regime transition by its local minima.No local minimum can be seen at low gas velocities (Ug = 0.02 m/s),which is due to no sensible change in the bubble behavior.
The fourth central moment (kurtosis) of vibration signalsagainst the liquid velocity at constant gas velocities is presentedin Fig. 4. At low liquid velocities, by increase in liquid velocity, kur-tosis shows several fluctuations. However, at intermediate liquidvelocities, depending on gas velocity, it may reach a maximum va-lue (at high gas velocities, 0.05 and 0.03 m/s) or reach a plateau (ata low gas velocity of 0.02 m/s). While the kurtosis of vibration atlow liquid velocities cannot predict the bubble behavior due tosever fluctuations, it shows to be a good predictor of coalescing-to-disintegrating bubble transition velocity by a significant risearound the regime transition point. At the regime transition point,signals are more peaked because of steady bubble coalescence andbreakup rates. A distribution with a steep peak (kurtosis > 0)
Coalesced to Discrete
(First Transition)
Coalesced to Discrete
(Second Transition)
Large Bubbles Small Discrete Bubbles
Coalesced Bubbles
Discrete Bubbles
Ul
Bubble size
Fig. 2b. The schematic of bubble size evolution pathway in the gas–liquid two-phase column at a high gas velocity (corresponding to case a in Fig. 2a).
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ul (m/s)
S v
Ug=0.05 m/s
Ug=0.03 m/s
Ug=0.02 m/s
Fig. 3. The skewness of vibration fluctuations in the gas–liquid two-phase column.Transition points are illustrated by the circles.
3.25
3.3
3.35
3.4
3.45
3.5
3.55
3.6
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ul (m/s)
Kv
Ug=0.05 m/s
Ug=0.03 m/s
Ug=0.02 m/s
Fig. 4. The kurtosis of vibration fluctuations in the gas–liquid two-phase column.The circle indicated the main transition point at high and moderate gas velocities.
0
0.05
0.1
0.15
0.2
0.25
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ul (m/s)
Ug=0.01 m/s
Ug=0.02 m/s
Ug=0.03 m/s
Ug=0.04 m/s
Ug=0.05 m/s1
2
of p
ress
ure
fluc
tuat
ions
(kP
a)
Fig. 5. The standard deviation of pressure fluctuations, obtained at a height of0.135 m above the distributor, in the gas–liquid two-phase column. Dashed lineshows the main transition in bubble behavior.
68 A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74
means bubbles with sizes around average bubble size are muchmore (in population) than smaller and larger ones. A larger kurtosismeans small and large bubbles are less than average bubble sizes.This happens when bubble coalescence (high gas velocity effect)and breakage (liquid shear effect) are in equilibrium condition
and can produce uniform bubbles sizes. It should be noted thatchanges in bubble size occur dynamically in the whole bed, andvibration signals are influenced by the whole vibration of shell.Therefore, some statistical analyses on vibration signals may notbe able to predict the bubble size pathway at low liquid velocities.
To compare the extracted information from the vibration sig-nals of the bed with local pressure fluctuation measurements, pres-sure fluctuation signals were also acquired. The standard deviationof pressure fluctuations is shown in Fig. 5. Two distinct regions canbe recognized in this figure: (1) rising and (2) falling of standarddeviation versus liquid velocity. These two regions fade away bydecreasing the gas velocity due to the less influence (lower dragcoefficient) of liquid velocity on small (discrete) bubbles insidethe bed. The increase in the standard deviation of pressure fluctu-ations is attributed to the increase of bubble size. This trend hasalso been observed in gas–solid fluidized beds [58]. The effect of li-quid velocity at low liquid velocities, corresponding to low shearsexerted on the bubbles, helps bubbles coalesce (region 1) whileafter the regime transition point to disintegrating bubbles, whichis around Ul = 0.03 m/s for the local studied place, the high sheartears the bubbles apart and decreases the average local bubble size.
0
1
2
3
4
5
6
7
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08Ul (m/s)
Kp
Ug=0.05 m/s
Ug=0.03 m/s
Ug=0.02 m/s
Fig. 7. The kurtosis of pressure fluctuations, obtained at a height of 0.135 m abovethe distributor, in the gas–liquid two-phase column. The main transition is shownby the circle.
A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 69
This is in agreement with the results obtained from the shell vibra-tion inspection (both are showing a liquid velocity around 0.03 m/sas the second bubble regime transition point: Figs. 2a and 5).
The skewness of pressure fluctuations at three sample gasvelocities, Ug = 0.05, 0.03, 0.02 m/s, is shown in Fig. 6. Dependingon the gas velocity, pressure fluctuations skewness starts with arising (at a high gas velocity of 0.05 m/s) or a flat region (at lowergas velocities, 0.03 and 0.02 m/s). It, then, experiences a minimumvalue at intermediate liquid velocities. Compared to the vibrationsignals, at high gas velocities, pressure skewness shows two re-gime transitions by a maximum value (at Ul = 0.007 m/s), corre-sponding to the coalesced-to-discrete bubble transition, followedby a minimum value (at Ul = 0.03 m/s), which is related to theoccurrence of disintegrating bubbles. It is noticeable that the skew-ness of vibration signals indicates the first transition point by amaximum value followed by a local minimum value while no min-imum value is seen in the pressure fluctuation skewness. Bothvibration and pressure signals show the main transition point,which is the main coalescing-to-disintegrating bubble flow, bytheir minimum values.
The evolution of pressure fluctuations kurtosis at constant gasvelocities by increasing liquid velocity is illustrated in Fig. 7. Basedon this figure, at all gas velocities, kurtosis starts with a flat regionand then increases only at two highest gas velocities of 0.05 and0.03 m/s. Finally, it reaches a plateau at all gas velocities. It is obvi-ous that similar to vibration fluctuations, the kurtosis of pressurefluctuations can only catch the main regime transition, i.e., the coa-lescing-to-disintegrating bubble flow by its maximum value atintermediate liquid velocities. It is worth noting that it is not pos-sible to detect the first transition point based on the trend of kur-tosis, whether by using vibration or pressure fluctuation signals.Also, the predicted values can be considered as good estimationsof the regime alteration point, which contain almost 25% errorcompared to the real regime transition point. In this case, the kur-tosis of vibration signals can predict the change in the bubblebehavior at the main transition point more accurately than thatof pressure fluctuations. Such applicability is mainly due to theoverall sensing capability of vibration inspection analysis ratherthan the local one of pressure fluctuations.
Bubble size distributions at various operating conditions arepresented in Fig. 8a–c. As can be seen in Fig. 8a, at a high gas veloc-ity of 0.05 m/s, an increase in liquid velocity results in the widestbubble size distribution at the regime transition point(Ul = 0.03 m/s). This is the effect of liquid velocity on the bubblecoalescence before the main regime transition point, which was
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ul (m/s)
S p
Ug=0.05 m/s
Ug=0.03 m/s
Ug=0.02 m/s
Fig. 6. The skewness of pressure fluctuations, obtained at a height of 0.135 m abovethe distributor, in the gas–liquid two-phase column. The circles show transitionpoints.
observed as the minimum value of vibration and pressure fluctua-tions skewness (Figs. 3 and 6, respectively), as well as the maxi-mum values of their kurtosis (Figs. 4 and 7, respectively).Afterwards, increasing the liquid velocity, and consequentlyincreasing the liquid shear exerted on the bubbles, decreases thebubble size and makes the bubble-size distribution narrower(Fig. 8a at Ul = 0.05 m/s). Such decrease in bubble size is clear inthe decreasing manner of pressure fluctuation standard deviationafter the main regime transition point at Ul = 0.03 m/s. The wide-ness of the bubble size distribution at the main regime transitionpoint (Ul = 0.03 m/s) decreases by decreasing the gas velocity to0.03 m/s (Fig. 8b) because bubbles become more uniform at lowergas velocities and the influence of liquid shear becomes less signif-icant. The decrease of the distribution width in both Fig. 8a and b athigh liquid velocities after the main transition point (Ul = 0.03 m/s)is due to a decrease in equivalent bubble size because of inducedbubble breakage. This is in agreement with the level off in the pres-sure signals standard deviation (Fig. 5). Comparing Figures. in 8creveals that smaller bubbles are less influenced by the liquid shear.However, a smooth effect of liquid velocity on the bubble size (i.e.,a smooth change in their size distribution at Ul > 0.03 m/s) atUg = 0.02 m/s is seen in the curves.
The bubble size change at constant gas and various liquid veloc-ities was investigated by direct photography of bubbles at the loca-tion of pressure measurements. The results of bubble sizecharacterization as well as error bars (for three sets of photographyat each condition) are illustrated in Fig. 9. As can be seen in this fig-ure, bubble size is firstly increasing by an increase in liquid velocityand finally is decreasing. However, such trend is more obvious athigher gas velocities due to much sensible bubble size alterations.The trend of bubble size variation by the increase of liquid velocityat constant gas velocities is the same as that predicted by the stan-dard deviation of pressure fluctuations. Although the effect of li-quid velocity on bubbles at low liquid velocities could not becaught, the main local transition point of the system at moderateliquid velocities was observed.
To investigate the applicability of pressure fluctuation signalsenergy in bubble characterization, at three constant gas velocitiesof 0.05, 0.03, and 0.02 m/s, the signal energy was calculated andpresented in Fig. 10. This figure shows the trend of pressure signalenergy by increasing liquid velocity at constant gas velocities. Gasvelocities are selected with the same logic as the previous discus-sion on having various possible bubble regimes. At a high gasvelocity of 0.05 m/s in Fig. 10, an increase in liquid velocity, firstly,resulted in a decrease in signal energies showing that the prevail-ing structures inside the bed have relatively lower energies. This
0
0.05
0.1
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0.25
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0 5 10 15 20
0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20
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0 5 10 15 20 0 5 10 15 20 0 5 10 15 20
de (mm)
de (mm)
de (mm)
de (mm)
de (mm)
de (mm)
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tion
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tion
Ul = 0.004 m/s Ul = 0.02 m/s Ul = 0.03 m/s Ul = 0.05 m/s
(a) Ug = 0.05 m/s
0
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tion
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ber
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ctio
n
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ber
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tion
Ul = 0.004 m/s Ul = 0.02 m/s Ul = 0.03 m/s Ul = 0.05 m/s
(b) Ug = 0.03 m/s
0
0.05
0.1
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tion
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umbe
r fr
acti
on
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ber
frac
tion
lU = 0.004 m/s lU = 0.02 m/s lU = 0.03 m/s Ul = 0.05 m/s
(c) Ug = 0.02 m/s
Fig. 8. Bubble size distribution at constant gas and variable liquid velocities acquired by image analysis after photography at a height of 0.135 m above the distributor.
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
0 0.01 0.02 0.03 0.04 0.05 0.06Ul (m/s)
d S (
mm
)
Ug=0.02 m/s
Ug=0.03 m/s
Ug=0.05 m/s
Fig. 9. Bubble Sauter mean diameter, obtained at a height of 0.135 m above thedistributor, in the gas–liquid two-phase column.
0
50
100
150
200
250
300
350
400
450
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08U l (m/s)
E (
kPa2 )
Ug=0.02 m/s
Ug=0.03 m/s
Ug=0.05 m/s
Fig. 10. The energy of pressure signals at constant gas velocities.
70 A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74
means that bubbles are becoming smaller. The first transition pointat such a high gas velocity of 0.05 m/s is occurring at the minimumvalue of pressure fluctuation energies around Ul = 0.006 m/s. After-wards, the trend of signal energies is the same for Ug = 0.05 and0.03 m/s; first it increases with an increase in liquid velocity dueto the increase of bubble size, which is in agreement with bubbleSauter mean diameter trend presented in Fig. 9, and then decreasesdue to bubble breakage. The maximum value of pressure fluctua-tion energies is corresponding to the main regime transition of
column (at Ul = 0.03 m/s). No sensible change in pressure signalenergies is seen at a low gas velocity of 0.02 m/s showing no obvi-ous regime transition inside the bed. This is also consistent withFig. 9, which is presenting the equivalent bubble diameter path-ways at certain liquid velocities and constant gas velocities.
4.2. Frequency-based analyses
Vibration and pressure signals were decomposed in the fre-quency domain to investigate the effect of change in the bubble
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f (Hz)
f (Hz) f (Hz) f (Hz) f (Hz)
PSD
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f (Hz)
PSD
F (
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(a1) Ul = 0.003 m/s (a2) Ul= 0.006 m/s (a3) Ul = 0.008 m/s
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z)
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F (
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4 .Hz)
(a4) Ul = 0.015 m/s l(a5) U = 0.02 m/s (a6) Ul = 0.03 m/s (a7) Ul = 0.05 m/s
Ug = 0.05 m/s
(b1) Ul = 0.003 m/s (b2) Ul= 0.006 m/s (b3) Ul= 0.008 m/s
(b4) Ul = 0.015 m/s (b5) Ul= 0.02 m/s (b6) Ul= 0.03 m/s (b7)Ul= 0.05 m/s
Ug = 0.03 m/s
0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000
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F (
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4 .Hz)
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F (
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F (
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4 .Hz)
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PSD
F (
m2 /s
4 .Hz)
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18P
SDF
(m
2 /s4 .H
z)
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
Fig. 11. The power spectral density function of vibration signals, obtained at a height of 0.135 m above the distributor, in the gas–liquid two-phase column at Ug = 0.05, 0.03,and 0.02 m/s.
A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 71
size on the power of frequency spectra. Through such analyses,it is possible to observe the effect of two important hydrody-namic properties of the column, i.e., bubble size distributionand regime transition. Fig. 11a–c illustrates the power spectraof vibration signals at constant gas velocities of 0.05 m/s,0.03 m/s and 0.02 m/s, respectively. At each gas and liquid veloc-ity, the PSDF was studied, and it was found that transition fromcoalesced to discrete flow is manifested in the shape of thePSDF. At Ul = 0.003 m/s (Fig. 11a1) the power spectrum is rela-tively high in value and narrow in distribution with a tendencytowards low frequencies (dominant peak at around 750 Hz). Thiscan be attributed to coalesced (large) bubbles with close sizes atlower frequencies. By increasing the liquid velocity to 0.006 m/s(Fig. 11a2), the PSDF becomes wider with lower values. At
0.006 m/s there are fewer numbers of coalesced (large) bubblesat lower frequencies. In addition, there are smaller bubbles withlarger frequencies. Afterwards, by increasing the liquid velocityfrom Ul = 0.006 m/s (Fig. 11a2) to Ul = 0.03 m/s (Fig. 11a6), PSDFshave dominant peak at lower frequencies showing increasedbubble sizes. This is in agreement with bubble Sauter meandiameter growth (Fig. 9) up to the main transition point to dis-integrating bubbles at around 0.03 m/s of liquid velocities. Final-ly, at high liquid velocities (Fig. 11a7) PSDF shows theoccurrence of small bubbles at large frequencies. AtUg = 0.03 m/s, although no sensible change in PSDFs is seen atlow liquid velocities (Fig. 11b1–b3), the same trend as Fig. 11ais seen at the transition point to discrete bubble flow(Fig. 11b4–b7). Narrow peaks in the PSDFs at Ug = 0.02 m/s
(c1) Ul= 0.003 m/s (c2) Ul= 0.006 m/s (c3) Ul= 0.008 m/s
(c4) Ul= 0.015 m/s (c5) Ul= 0.02 m/s (c6) Ul= 0.03 m/s (c7) Ul= 0.05 m/s
Ug = 0.02 m/s
0
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4
6
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18
PSD
F (
m2 /s
4 .Hz)
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PSD
F (
m2 /s
4 .Hz)
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PSD
F (
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f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)
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PSD
F (
m2 /s
4 .Hz)
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PSD
F (
m2 /s
4 .Hz)
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PSD
F (
m2 /s
4 .Hz)
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
f (Hz)0 2000 4000 6000 8000 10000
0
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18
PSD
F (
m2 /s
4 .Hz)
Fig. 11. (continued)
72 A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74
(Fig. 11c1–c7) are observed corresponding to a narrow bubble-size distribution. At such condition, liquid flow has a faded effecton bubbles throughout the column. It is noteworthy that at highliquid velocities, the bubble-breaking effect of liquid can still beseen (Fig. 11c7).
To obtain the detailed pathway of different structures (bubblebehavior) inside the bed, wavelet analysis on pressure fluctuationswas applied. The number of decomposition levels was set to beeight in order to have nine decomposed sub-signals (a8 as thelow-frequency representative and D1–8 as high-frequency repre-sentatives). Fig. 12a–c shows the multi-resolution-analysis sub-signal energies by increasing liquid velocities at constant gasvelocities of 0.05, 0.03, and 0.02 m/s, respectively. At a high gasvelocity of 0.05 m/s, Fig. 12a, the dominant peak of sub-signalenergies is on D5 at low liquid velocities (e.g., 0.003 m/s). By an in-crease in liquid velocity to 0.006 m/s, the curve is shifted to the leftindicating that the energies of fine (detail) sub-signals (corre-sponding to highly-oscillating small bubbles) are prevailing thoseof coarse scales (relevant to larger bubbles). This is due to the in-crease in bubble size up to the first regime transition point, pointedas number 1 in Fig. 12a. As it is seen in Fig. 12a, by further increasein liquid velocity, the peak of sub-signal energies is shifting to theright, shown with number 2, and then starts increasing its portionin the total energy (see number 4 in Fig. 12a). This is basically be-cause of an increase in bubble size up to the second bubble-regimetransition point at Ul = 0.03 m/s. In fact, by the increase of bubblesize, low-oscillating bubbles are formed, which results in the de-crease of fine-scale sub-signal energies (corresponding to highoscillations), and the increase of low-frequency sub-signal energies(coarse sub-signals). After the main bubble-regime transition pointat 0.03 m/s of liquid velocity, bubbles are being torn apart mani-fested in the descended peak (see number 5 in Fig. 12a) at D6
and increase in fine-scale sub-signal energies due to the occur-rence of relatively smaller bubbles. Interestingly, further increasein liquid velocity to 0.07 m/s shifts the peak to D4 (arrow number6 in Fig. 12a), just the same as the condition of bed at the beginningof bed operation at low liquid velocities. However, at high liquidvelocities of 0.05 and 0.07 m/s, the presence of relatively larger
bubbles compared to very low liquid velocities (e.g., 0.003 m/s) isconcluded based on the comparison of coarse sub-signal energiesat these two conditions. This is in accordance with bubble sizemeasurements obtained by photography, i.e., Fig. 9.
Decreasing the gas velocity to 0.03 m/s, the energy of wholemulti-resolution-analysis sub-signal spectra was calculated.Fig. 12b presents the energy portion change of various sub-sig-nals by increasing liquid velocity at a constant gas velocity of0.03 m/s. The bed is starting with a dominant peak of sub-signalenergies at D4 at low liquid velocities. This peak is vanishing byan increase in liquid velocities giving rise to ascending peaks atD6. Finally, the peaks at D6 start descending by further increasein liquid velocities (Ul > 0.03 m/s) resulting in ascending peaksat D4. Such trend is in full accordance with the so-called one re-gime transition point at moderate gas velocities (e.g., 0.03 m/s).Starting from a very low liquid velocity, by increasing liquidvelocity, bubbles are coalescing together up to the regime transi-tion point at 0.03 m/s of liquid velocity. Such coalescing behaviorenhanced by liquid velocity is causing the energy of fine-scalesub-signals to decrease and the energy of coarse-scale sub-signalsto increase (arrows number 1 and 2 in Fig. 12b) due to the occur-rence of relatively low-oscillating bubbles (large bubbles). Afterthe regime transition point, a high shear exerted on bubbles byliquid phase is breaking the bubbles, which leads to the presenceof smaller bubbles with higher energies in their fine-scale sub-signals due to rising with higher oscillating frequencies (arrownumber 3 on Fig. 12b).
Further decrease of gas velocity to 0.02 m/s results in sub-signalenergy spectra shown in Fig. 12c. This figure is illustrating the mul-ti-resolution-analysis sub-signal energy portion by changing liquidvelocity at a constant gas velocity of 0.02 m/s. As can be seen inthis figure, no distinguishable manner can be found due to the lackof any sensible regime transition at low gas velocities. However,the overall effect of liquid velocity on bubble size is started by a de-crease in peaks at D6 at low liquid velocities and ended at relativelyhigher fine-scale energies (e.g., D3, D4, and D5) at a high liquidvelocity of 0.07 m/s showing the slight effect of liquid shear onbubbles with the same trend as that of Ug = 0.03 m/s.
0
5
10
15
20
25
30
35
40
45
D1 D2 D3 D4 D5 D6 D7 D8 a8
Multi-resolution-analysis sub-signals
Ek (
%)
Ul=0.003 m/s
Ul=0.006 m/s
Ul=0.008 m/s
Ul=0.015 m/s
Ul=0.02 m/s
Ul=0.03 m/s
Ul=0.05 m/s
Ul=0.07 m/s
6
5 4
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1
(a) Ug = 0.05 m/s
0
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D1 D2 D3 D4 D5 D6 D7 D8 a8
Multi-resolution-analysis sub-signals
Ek
(%
)
Ul=0.003 m/s
Ul=0.006 m/s
Ul=0.008 m/s
Ul=0.015 m/s
Ul=0.02 m/s
Ul=0.03 m/s
Ul=0.05 m/s
Ul=0.07 m/s
3
2 1
(b) Ug = 0.03 m/s
0
5
10
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30
D1 D2 D3 D4 D5 D6 D7 D8 a8
Multi-resolution-analysis sub-signals
Ek
(%)
Ul=0.003 m/sUl=0.006 m/sUl=0.008 m/sUl=0.015 m/sUl=0.02 m/sUl=0.03 m/sUl=0.05 m/sUl=0.07 m/s
(c) Ug = 0.02 m/s
Fig. 12. The energy of multi-resolution-analysis sub-signals obtained at constantgas and variable liquid velocities by wavelet analysis.
A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 73
5. Conclusion
Novel non-intrusive measurements, namely the vibration(acceleration) of bed shell as an inspection tool, as well as corre-sponding signal processing methods for hydrodynamic character-ization of a two-phase gas–liquid column with both gas andliquid flows were introduced. Two transition points at a high gas
velocity and one main and one faded transition points at moderateand low gas velocities, respectively, were detected by liquid veloc-ity variations. Statistical and frequency-based approaches wereused to exploit information from the vibration and pressure sig-nals. Different operating modes at various operating gas velocitieswere detected by the standard deviation of vibration signals. How-ever, compared to pressure fluctuations, the standard deviation ofvibration signals was less sensitive to the effect of liquid flow onthe bubble size. The skewness of both vibration and pressure fluc-tuations showed a good sensitivity to regime transition pointswhile vibrations were more successful than pressure fluctuationsin determining the first transition point. The kurtosis of vibrationswas found to be more reliable in detecting the transition pointscompared to pressure fluctuations. Also, pressure fluctuation ener-gies proved to be a simple, yet trustable way of treating signals todefine bubble behavior inside the column. Furthermore, analyzingthe signals in the frequency domain suggested the pathway of bub-ble behavior alteration based on their size at different operatingconditions of gas and liquid velocities. The energy of various mul-ti-resolution-analysis sub-signals showed to be an accurate repre-sentative of bubble gradual change inside the column. Accordingly,it was shown that at high gas velocities, a shift to the left in sub-signal energy spectra defined the first bubble transition pointwhile a gradual descend in the peaks at D5 sub-signals and ascendin D6 sub-signals with their corresponding effect on the whole en-ergy portion spectra captured the second regime transition point.At moderate gas velocities, a gradual shift from D4 to D6 up tothe main regime transition point and then a reverse-back shiftfrom D6 to D4 detected the transition liquid velocity correctly.The photographs of bubbles were used to observe the bubblebehavior at different operating conditions. These observationswere shown to be consistent with the results extracted from thesignal processing methods. The results of this study are suggestedto be used in non-invasive characterization of industrial gas-liquidprocesses, especially, those being operated at sever temperatureand pressure conditions.
Acknowledgement
The authors would like to thank Noise, Vibration, and Acoustics(NVA) Lab., School of Mechanical Engineering, College of Engineer-ing, University of Tehran for their help in data acquisition.
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