Understanding bubble hydrodynamics in bubble columns

Experimental Thermal and Fluid Science 45 (2013) 63–74

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Understanding bubble hydrodynamics in bubble columns Amir Sheikhi 1, Rahmat Sotudeh-Gharebagh ⇑, Reza Zarghami, Navid Mostoufi, Mehrdad Alfi Multiphase 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 2012 Received in revised form 19 July 2012 Accepted 9 October 2012 Available online 30 October 2012 Keywords: Gas–liquid column Hydrodynamics Vibration inspection Pressure fluctuations Frequency analysis Wavelet transform

a b s t r a c t Compared to conventional gas–liquid bubble columns, gas–liquid columns including both gas and liquid flows have been investigated less due to their complex hydrodynamics and operational difficulties. In this study, simultaneous non-intrusive methods of column shell vibration and pressure fluctuation measurements were coupled with direct photography and image analysis for bubble characterization. Various statistical and frequency analyses were conducted on the acceleration and pressure fluctuations signals to determine their capability of interpreting bubble behavior inside the column. The standard deviation of 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 all studied gas and liquid velocities while vibration and pressure fluctuations kurtosis could only detect the main transition point of the column at a moderate liquid velocity. It was found that besides regular statistical methods, the energy of pressure signals could predict bubble regime transition points successfully. While vibration-based inspection showed more sensitivity to bubble size distribution (similar to the standard deviation of pressure signals), frequency analysis on pressure signals proved to be a strong representative of bubble Sauter mean diameter alteration by liquid flow variation at constant gas velocities. Moreover, by means of energy-based discrete wavelet transformation, we defined the exact pathway of various sub-signal gradual evolutions throughout a wide range of operating conditions of gas and liquid velocities and captured regime transition points accordingly. The proposed methods in this work can be used for non-intrusive hydrodynamic characterization in industrial bubble columns. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Gas–liquid contactors are widely used in various industries such as chemical [1–4], biochemical, biotechnology [5–7], biomedical [8], petrochemical and refining [9,10], environmental, separation and purification [11–18], nanotechnology [19,20] and gas processing industries [21–23]. Among such contactors, bubble columns, with or without liquid flow, are of a considerable importance in numerous process units. Industrial plants which are dealing with physical [24] and/or chemical interactions between gas and liquid phases as well as gas–liquid–solid [25] contactors profit from the ease of construction [26], high interfacial area and consequently high mass [27] and heat [28] transfer rates, stable temperature [29], the ease of energy providence and the high liquid hold up [30] of bubble columns [31]. Successful design, operation, scales up and optimization of bubble columns highly depends on the hydrodynamics of such ⇑ Corresponding author. Tel.: +98 21 6697 6863; fax: +98 21 6646 1024. E-mail addresses: [email protected] (A. Sheikhi), [email protected] (R. Sotudeh-Gharebagh). 1 Present address: Chemical Engineering Department, McGill University, Montreal, Quebec H3A 0C5, Canada. 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.10.008

contactors. Although various theoretical efforts to model twophase gas–liquid contactors have been undertaken [32–38], new experimental approaches for hydrodynamic inspections are of great interests in industrial and R&D communities. Wall pressure fluctuations were used to study the effect of various sparger geometries on bubble flow regimes in bubble columns [39]. Flow pattern and structure were investigated by means of pressure fluctuations combined with particle image velocimetry [40]. Chaotic behavior of bubbles were studied using pressure signals and laser-phototransistor [41]. Also, bubbling-to-jetting regime transition was investigated by plenum pressure fluctuations monitoring [42]. Turbulence in the heterogeneous bubble regime was characterized by chaos analysis on pressure fluctuations [43]. Simonnet et al. studied the drag coefficient on the gas bubble swarm using laser Doppler velocimetry [44]. Harteveld et al. [45] and Olmos et al. [46] used laser Doppler anemometry for the accurate estimation of turbulence power spectra and flow regime transition identification, respectively. Magnetic resonance imaging was utilized to characterize hydrodynamics of opaque multiphase systems such as slurry bubble columns [47]. Also, particle image velocimetry was found to be able to define bubble velocity and flow regimes inside a two-phase gas–liquid column [48–50]. Similar advanced, non-intrusive but expensive methods, such as

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Nomenclature ak An CWT de dm,j dM,j dS Dk X(f) DWT E Ea ED f i k K n nj

approximation sub-signal amplitude in a time series at a certain frequency of fn (kPa or m/s2) continuous wavelet transform equivalent bubble diameter (m) minor length (smallest Feret diameter) of bubbles (m) major length (largest Feret diameter) of bubbles (m) Sauter mean diameter of bubbles (m) detail sub-signal discrete Fourier transform discrete wavelet transform energy of PSDF (kPa2 or m2/s4) energy of approximation sub-signal coefficient (kPa2 or m2/s4) energy of detail sub-signal coefficient (kPa2 or m2/s4) desired frequency (Hz) imaginary unit sub-signal number kurtosis or the forth moment counter bubble number with equivalent diameter of de,j

computer-automated radioactive particle tracking [51], computed tomography [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 measurement and analysis of vibrations in both time [55] and frequency [56] domains to characterize the hydrodynamics of gas–solid fluidized beds. They were able to define main transition points inside the bed as well as bubble behavior using regular signal processing methods. Sheikhi et al. [57] have shown that vibration inspection can also be used as a reliable method for the hydrodynamic characterization of liquid–solid fluidized beds. They predicted minimum liquid-fluidization and solid-regime transition conditions. Yet, no effort has been made to characterize gas–liquid contactors by means of simultaneous vibration and pressure fluctuations analyses. The aim of this work is a critical comparative study on the applicability of vibration and pressure fluctuation signal processing for the hydrodynamic characterization of bubble behavior inside bubble columns. Electrical signals obtained from vibration inspection and pressure fluctuations were processed in time and frequency domains and the extracted information were used to determine the hydrodynamic state of a bubble column at a wide range of industrial gas–liquid two-phase reactor operating conditions.

2. Materials and methods

N L p Pxx Pxxn PSDF q S t Ug Ul v xn

data point number in a sample segment (window) number in a time series indicating pressure fluctuation experiments average power spectrum (kPa2/Hz or m2/s4 Hz) power spectrum for each segment (kPa2/Hz or m2/s4 Hz) power spectral density function (kPa2/Hz or m2/s4 Hz) time-lag coefficient skewness or the third moment time (s) gas velocity (m/s) liquid velocity (m/s) indicating vibration (acceleration) experiments time series data (kPa or m/s2)

Greek symbols d scale factor r standard deviation s shift factor w mother wavelet function

with a triangular pitch, followed by a 0.0003 m mesh screen. The upper section of the bed (gas–liquid disengagement zone) was set 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, two DJB accelerometers with sensitivities of 100 mV/ms2 were used in the experiments. The cut off frequency was set to 65 kHz to prevent data loss in the vibration signals. At each run, the data were recorded for 30 s. Two accelerometers were glued to 0.045 m and 0.135 m above the distributor on the outer surface of the column wall. To ensure the reproducibility of the data, each test was conducted 2–3 times, randomly. The analog signals produced by accelerometers were converted to digital signals and recorded by a B&K PULSE system using 3560 type hardware. The frequency of external noise sources was identified and eliminated from bed vibration signals by low-pass and high-pass filters. To measure pressure fluctuations, a piezoresistive absolute pressure transducer (Kobold, SEN-3248(B075)) was installed at the height of 0.135 m above the gas–liquid distributor and opposite to the accelerometer to avoid probable conflicts. The pressure fluctuations were recorded by a data acquisition system (Advantech PCI-1712L) with a frequency of 400 Hz for 163.84 s. The frequency of sampling for both acceleration and pressure was set in a way that satisfies the Shanon–Nyquist criterion by being greater than 2 times the maximum frequency within the spectrum [55,57].

2.1. Experimental set-up 2.3. Image acquisition and analysis The bubble column used in this study was made of a 2 m height Plexiglas column with an inner diameter of 0.09 m, presented in Fig. 1. Air at ambient temperature, produced by a compressor, was introduced into the 0.1 m high gas–liquid engagement section from the bottom of the bed using a cylindrical porous ceramic air sparger with a 0.03 m diameter and 0.085 m length consisting of 0.0001 m pores. Tap water, as the continuous phase, was pumped into the engagement section. Engagement section was filled with 0.01 m glass beads for better mixing of air and water. The mixture of gas and liquid was then sent into the bed through a perforated plate distributor including 110 holes of 0.3 cm-diameter, placed

To obtain bubble size distribution and equivalent bubble size at each operating condition, a photographic technique was used. Bubble images were photographed using a digital CCD camera (Canon PowerShot-SI3) at a height of 0.135 m above the gas–liquid distributor to ensure the elimination of initial liquid jetting effect. Images of 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 ruler was placed inside the column at the focal distance of camera to determine the real bubble size. Finally, the equivalent size of bub-

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Disengagement section

Gas vent Column liquid recycle Gas bubbles

Liquid flow meters

Liquid phase

Sampling taps Diffuser paper

CCD camera Pump recycle

Water reservoir

Halogen lamp

Gas-liquid distributor

Air

Pump Glass beads Gas sparger Water drain

Engagement section

Fig. 1. The schematic of the two-phase gas–liquid column.

bles, defined as an equivalent sphere diameter with the same volume as the bubble, was calculated. The bubble size change at constant gas and various liquid velocities was investigated by the direct photography of bubbles at the location of pressure measurements. The Sauter mean diameter of bubbles was calculated from: N X 3 nj de;j

dS ¼

j¼1 N X 2 nj de;j

ð1Þ

parameters were used to analyze the signals in the time domain. Standard deviation is a measure of the data set dispersion from its mean and is defined as follows:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u 1 X r¼t ðxi  xÞ2 n  1 i¼1 where the mean value is calculated from:

x ¼

j¼1

in which the bubble equivalent diameter can be calculated using:

de;j

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 ¼ dM;j  dm;j

3. Data treatment methods Vibration and pressure fluctuation signals were analyzed in both time and frequency domains as described below. Statistical

n 1X xi n i¼1

ð4Þ

Skewness is a measure of symmetry, or more precisely lack of symmetry, in the distribution of a signal:

ð2Þ

where dM,j and dm,j are the large and small diameters of oval-shaped bubbles.

ð3Þ

n X ðxi  xÞ3

S¼

i¼1

ðn  1Þr3

ð5Þ

Negative or positive values for the skewness indicate that data are skewed left or right, respectively. Kurtosis is defined as the degree of the peakedness of data and is a criterion whether the distribution is flat or peaked relative to the normal distribution, defined as:

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A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74 n X ðxi  xÞ4

K¼

i¼1

ð6Þ

ðn  1Þr4

Kurtosis is a measure of the relative concentration (flatness or peakedness) of data in the center of a frequency distribution relative to the tails, when compared with a normal distribution (which has a kurtosis of 3). Fourier analysis is an extremely useful tool in frequency domain for data analysis. Fourier analysis decomposes a signal into its constituent sinusoids of different frequencies and is performed using the discrete Fourier transform (DFT). The estimated Fourier transform, X(f), of a measured time series, xn, consisting of N points is equal to [58]:

Xðf Þ ¼

N X

ð7Þ

in which f and i are frequency and the complex number, respectively. If N is a power of 2, then Eq. (7) represents the fast Fourier algorithm, which is an efficient algorithm for computing the discrete Fourier transform (DFT) of a sequence. The power spectrum of a signal which represents the contribution of each frequency in the spectrum to the power of the overall signal can be estimated from the magnitude of X(f) squared. The variance of such an estimation of the power spectrum does not decrease with an increase of N. To decrease the variance, the signal is repeatedly divided into windows, and an average of the power spectrum within the windows is used to obtain an estimate for the power spectrum (the Welsh method of power spectrum estimation). However, the decrease of samples within the windows gives poor frequency resolution. Hence, an appropriate window width should be chosen to get a satisfactory trade-off between frequency resolution and variance [58]. Using Hann window and without any overlap between windows, the averaged power spectrum becomes [58]: L 1X Pn ðf Þ L n¼1 xx

ð8Þ

Nf N X X jxn j2  Pxx ðf Þ i¼1

Z

xn W

t  q  2k 2k

! dt

Afterwards, by screening the signals via pairs of low-pass and high-pass filters, known as quadrature mirror filters [56,59], it is decomposed into its constituents. Each decomposition step makes the time resolution half and doubles the frequency resolution. The constituent sub-signals, known as decomposed signals, are called detail (D) and approximation (a) sub-signals. The main signal is a linear superposition of the sub-signals:

Z

Also, the energy of sub-signals can be utilized as a good representative of each decomposed signal: N X jak ðtÞj2

Eak ¼

ð13Þ

t¼1

EDk ¼

N X jDk ðtÞj2

ð14Þ

t¼1

Accordingly, the original signal energy is obtained based on the energy conservation of WT on orthogonal constituents [56]:

E¼

N k X X jxn j2 ¼ Eak þ EDj t¼1

ð15Þ

j¼1

Similar to the signal itself, the energy of main signal is a linear superposition of sub-signal energies. To utilize the WT, a wavelet function should be selected based on the signal reconstruction error. Such error was calculated for a random signal, and the secondorder Daubechies wavelet (db2) was found to have the lowest reconstruction error. Therefore it was chosen for the wavelet analyses.

Two completely-different-in-nature responses of a bubble column to its internal hydrodynamic alterations, namely column shell vibration and local pressure fluctuations, are processed by means of statistical and frequency-based analyses, and the results are summarized below. 4.1. Statistical analyses

where Nf is the number of points in the frequency domain. On one hand, a trade-off between the window size and frequency resolution always happens when using short-time Fourier transform. On the other hand, the acquired signals show an unsteady and non-regular pattern at different time intervals, e.g., unsteady impulses and amplitude patterns. Therefore, a mathematical method is required to extract information from the signals based on several window sizes through the time. This is needed to achieve the highest possible time–frequency resolution. The continuous wavelet transform, CWT, is introduced as [56]: 1

ð12Þ

ð9Þ

k¼1

CWTðs; dÞ ¼ d 2

ð11Þ

4. Results and discussion

where L is the number of windows and Pnxx ðf Þ is the power spectrum estimate of each window. The energy of a signal, squared sum of amplitudes, can be defined in the frequency domain by Parseval’s theorem:

E¼

1 DWTðk; qÞ ¼ qffiffiffiffiffiffiffiffi j2k j

xn ’ ak ðtÞ þ D1 ðtÞ þ    þ Dk1 ðtÞ þ Dk ðtÞ xn expð2pinf Þ

n¼1

Pxx ðf Þ ¼

overcome this difficulty, discrete wavelet transform [56], DWT, selects the so-called coefficients based on the power of positions and scales dyadic:

  ts xn W dt d

ð10Þ

Using a non-fixed window width, the wavelet transform (WT) offers accurate frequency-based information at both high and low frequencies. Here, the challenge is to define the time and scale coefficients by time, which needs a huge computational effort. To

To investigate the capability of shell vibration in capturing the effect of gas and liquid velocities variations on the hydrodynamics, first, the statistical characteristics of acceleration signals were examined. Fig. 2a presents vibration standard deviation versus liquid velocity. The effect of liquid velocity, at constant gas velocities, on the standard deviation of column vibration signals is shown in Fig. 2a. While at higher gas velocities (e.g., Ug = 0.05 m/s compared to Ug = 0.02 m/s), a significant shift in the standard deviation of shell vibration is observed due to average bubble size increase inside the column, no remarkable change in the trend of curves can be seen at each constant gas velocity. The presence of larger bubbles at higher gas velocities is also proved in gas–liquid air–water bubble columns [60]. However, bubble size in bubble columns is a function of not only gas velocity, but also distributor geometry [60] and column characteristics [61], which does not allow a general and unique conclusion on bubble behavior to be made. This is an important point to consider that in contrast to

A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74

67

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 one transition 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.

gas-filled media [55,56], the standard deviation of vibrations in a liquid-filled column cannot significantly show slight changes in the bubble size. However, slight changes in these curves can be categorized in three various behaviors: (a) At a high gas velocity (Ug = 0.05 m/s), by increasing the liquid velocity, bubbles experience four main governing regimes of coalesced bubble flow, discrete bubble flow and again coalesced flow, and finally discrete bubbles. Accordingly, there are two regime transition points of coalesced bubbles flow-to-discrete flow transition (1st point corresponds to minimum r value at Ul = 0.006 m/s), and again coalesced bubbles flow-to-discrete flow transition (2nd point at maximum r value where Ul = 0.03 m/s). The second point (i.e., discrete-coalesced-discrete bubble transition), compared to the first point (i.e., coalesced-discretecoalesced bubble transition), can be considered as the main transition point. Based on the comprehensive regime transition map for two-phase air–water systems with the flow of both liquid and gas, provided by Zhang et al. [62], such a triple effect of liquid flow on the bubble behavior in gas–liquid contactors operated at high Ug was observed by the gradual increasing of liquid velocity. At extremely low liquid and high gas velocities (corresponding to relatively large bubbles, i.e., coalesced bubble flow), in the so-called gas-dominant regime, liquid shear has no significant effect on gas bubbles [63]. By increasing the liquid velocity, relatively smaller bubbles are formed due to an increased shear on the bubbles at the time of bubble formation on the sparger pores. This leads to the presence of discrete bubble inside the column (Ul = 0.006 m/s) [62]. Further increase in the liquid velocity helps bubbles coalesce together and form larger slugs (6 mm/s < Ul < 3 cm/s). However, high shear exerted on slugs at higher liquid velocities (Ul > 3 cm/s) tears bubbles apart and form relatively smaller and discrete bubbles which is consistent with what is reported by Zhang et al. [62]. This is shown schematically in Fig. 2b. (b) At lower gas velocities (Ug = 0.03–0.04 m/s), no slug is seen and bubbles tend to change their regime from coalesced to discrete 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 bubbles at 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 larger bubbles at higher gas velocities. This is explained by relatively lower drag force exerted on small bubbles compared to larger ones. After a certain critical bubble size (greater than 1.5–2.5 mm) [64], exerted drag on bubbles decreases by the decrease in the bubble size. This is the main reason for the low influence of liquid flow on the bubbles in the discrete-bubble regime. Two other statistical characteristics of vibration signals were also studied: third and fourth central moments (skewness and kurtosis, respectively). The skewness of vibration signals at three gas velocities of 0.05, 0.03, and 0.02 m/s is shown in Fig. 3. Starting from the lowest liquid velocity, first, the skewness is increasing, then it decreases, and finally, based on the gas velocity, whether it increases (at high gas velocities, 0.05 and 0.03 m/s) or becomes a plateau (at a low gas velocity, 0.02 m/s). It can be seen in this figure that at high gas velocities, the skewness of vibration signals predicts the first regime-change point by a change in sign. However, at all conditions, it is able to approximate the coalescing-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 signals against the liquid velocity at constant gas velocities is presented in Fig. 4. At low liquid velocities, by increase in liquid velocity, kurtosis shows several fluctuations. However, at intermediate liquid velocities, depending on gas velocity, it may reach a maximum value (at high gas velocities, 0.05 and 0.03 m/s) or reach a plateau (at a low gas velocity of 0.02 m/s). While the kurtosis of vibration at low liquid velocities cannot predict the bubble behavior due to sever fluctuations, it shows to be a good predictor of coalescingto-disintegrating bubble transition velocity by a significant rise around the regime transition point. At the regime transition point, signals are more peaked because of steady bubble coalescence and breakup rates. A distribution with a steep peak (kurtosis > 0)

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A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74

Coalesced to Discrete (Second Transition) Coalesced to Discrete (First Transition)

Bubble size

Coalesced Bubbles Small Discrete Bubbles

Large Bubbles

Discrete Bubbles

Ul 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).

0.025 Ug=0.05 m/s Ug=0.03 m/s Ug=0.02 m/s

0.02 0.015

Sv

0.01 0.005 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

-0.005 -0.01

U l (m/s) Fig. 3. The skewness of vibration fluctuations in the gas–liquid two-phase column. Transition points are illustrated by the circles.

3.6

and can produce uniform bubbles sizes. It should be noted that changes in bubble size occur dynamically in the whole bed, and vibration signals are influenced by the whole vibration of shell. Therefore, some statistical analyses on vibration signals may not be able to predict the bubble size pathway at low liquid velocities. To compare the extracted information from the vibration signals of the bed with local pressure fluctuation measurements, pressure fluctuation signals were also acquired. The standard deviation of pressure fluctuations is shown in Fig. 5. Two distinct regions can be recognized in this figure: (1) rising and (2) falling of standard deviation versus liquid velocity. These two regions fade away by decreasing the gas velocity due to the less influence (lower drag coefficient) of liquid velocity on small (discrete) bubbles inside the bed. The increase in the standard deviation of pressure fluctuations is attributed to the increase of bubble size. This trend has also been observed in gas–solid fluidized beds [58]. The effect of liquid velocity at low liquid velocities, corresponding to low shears exerted on the bubbles, helps bubbles coalesce (region 1) while after the regime transition point to disintegrating bubbles, which is around Ul = 0.03 m/s for the local studied place, the high shear tears the bubbles apart and decreases the average local bubble size.

Ug=0.05 m/s Ug=0.03 m/s Ug=0.02 m/s

3.55

0.25

3.5

Ug=0.01 m/s

3.45 3.4 3.35 3.3 3.25 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ul (m/s)

of pressure fluctuations (kPa)

Kv

Ug=0.02 m/s 0.2

Ug=0.03 m/s Ug=0.04 m/s Ug=0.05 m/s

0.15

1 2

0.1

0.05

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

means bubbles with sizes around average bubble size are much more (in population) than smaller and larger ones. A larger kurtosis means 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

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ul (m/s) Fig. 5. The standard deviation of pressure fluctuations, obtained at a height of 0.135 m above the distributor, in the gas–liquid two-phase column. Dashed line shows the main transition in bubble behavior.

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A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74

0.4 0.2 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Sp

-0.2 -0.4 -0.6 -0.8 Ug=0.05 m/s Ug=0.03 m/s Ug=0.02 m/s

-1 -1.2

U l (m/s) Fig. 6. The skewness of pressure fluctuations, obtained at a height of 0.135 m above the distributor, in the gas–liquid two-phase column. The circles show transition points.

7 Ug=0.05 m/s Ug=0.03 m/s Ug=0.02 m/s

6 5 4

Kp

This is in agreement with the results obtained from the shell vibration inspection (both are showing a liquid velocity around 0.03 m/s as the second bubble regime transition point: Figs. 2a and 5). The skewness of pressure fluctuations at three sample gas velocities, Ug = 0.05, 0.03, 0.02 m/s, is shown in Fig. 6. Depending on the gas velocity, pressure fluctuations skewness starts with a rising (at a high gas velocity of 0.05 m/s) or a flat region (at lower gas velocities, 0.03 and 0.02 m/s). It, then, experiences a minimum value at intermediate liquid velocities. Compared to the vibration signals, at high gas velocities, pressure skewness shows two regime transitions by a maximum value (at Ul = 0.007 m/s), corresponding to the coalesced-to-discrete bubble transition, followed by a minimum value (at Ul = 0.03 m/s), which is related to the occurrence of disintegrating bubbles. It is noticeable that the skewness of vibration signals indicates the first transition point by a maximum value followed by a local minimum value while no minimum value is seen in the pressure fluctuation skewness. Both vibration and pressure signals show the main transition point, which is the main coalescing-to-disintegrating bubble flow, by their minimum values. The evolution of pressure fluctuations kurtosis at constant gas velocities by increasing liquid velocity is illustrated in Fig. 7. Based on this figure, at all gas velocities, kurtosis starts with a flat region and then increases only at two highest gas velocities of 0.05 and 0.03 m/s. Finally, it reaches a plateau at all gas velocities. It is obvious that similar to vibration fluctuations, the kurtosis of pressure fluctuations can only catch the main regime transition, i.e., the coalescing-to-disintegrating bubble flow by its maximum value at intermediate liquid velocities. It is worth noting that it is not possible to detect the first transition point based on the trend of kurtosis, whether by using vibration or pressure fluctuation signals. Also, the predicted values can be considered as good estimations of the regime alteration point, which contain almost 25% error compared to the real regime transition point. In this case, the kurtosis of vibration signals can predict the change in the bubble behavior at the main transition point more accurately than that of pressure fluctuations. Such applicability is mainly due to the overall sensing capability of vibration inspection analysis rather than the local one of pressure fluctuations. Bubble size distributions at various operating conditions are presented in Fig. 8a–c. As can be seen in Fig. 8a, at a high gas velocity of 0.05 m/s, an increase in liquid velocity results in the widest bubble size distribution at the regime transition point (Ul = 0.03 m/s). This is the effect of liquid velocity on the bubble coalescence before the main regime transition point, which was

3 2 1 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ul (m/s) Fig. 7. The kurtosis of pressure fluctuations, obtained at a height of 0.135 m above the distributor, in the gas–liquid two-phase column. The main transition is shown by the circle.

observed as the minimum value of vibration and pressure fluctuations skewness (Figs. 3 and 6, respectively), as well as the maximum values of their kurtosis (Figs. 4 and 7, respectively). Afterwards, increasing the liquid velocity, and consequently increasing the liquid shear exerted on the bubbles, decreases the bubble size and makes the bubble-size distribution narrower (Fig. 8a at Ul = 0.05 m/s). Such decrease in bubble size is clear in the decreasing manner of pressure fluctuation standard deviation after the main regime transition point at Ul = 0.03 m/s. The wideness of the bubble size distribution at the main regime transition point (Ul = 0.03 m/s) decreases by decreasing the gas velocity to 0.03 m/s (Fig. 8b) because bubbles become more uniform at lower gas velocities and the influence of liquid shear becomes less significant. The decrease of the distribution width in both Fig. 8a and b at high liquid velocities after the main transition point (Ul = 0.03 m/s) is due to a decrease in equivalent bubble size because of induced bubble breakage. This is in agreement with the level off in the pressure signals standard deviation (Fig. 5). Comparing Figures. in 8c reveals 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) at Ug = 0.02 m/s is seen in the curves. The bubble size change at constant gas and various liquid velocities was investigated by direct photography of bubbles at the location of pressure measurements. The results of bubble size characterization as well as error bars (for three sets of photography at each condition) are illustrated in Fig. 9. As can be seen in this figure, bubble size is firstly increasing by an increase in liquid velocity and finally is decreasing. However, such trend is more obvious at higher gas velocities due to much sensible bubble size alterations. The trend of bubble size variation by the increase of liquid velocity at constant gas velocities is the same as that predicted by the standard deviation of pressure fluctuations. Although the effect of liquid velocity on bubbles at low liquid velocities could not be caught, the main local transition point of the system at moderate liquid velocities was observed. To investigate the applicability of pressure fluctuation signals energy in bubble characterization, at three constant gas velocities of 0.05, 0.03, and 0.02 m/s, the signal energy was calculated and presented in Fig. 10. This figure shows the trend of pressure signal energy by increasing liquid velocity at constant gas velocities. Gas velocities are selected with the same logic as the previous discussion on having various possible bubble regimes. At a high gas velocity of 0.05 m/s in Fig. 10, an increase in liquid velocity, firstly, resulted in a decrease in signal energies showing that the prevailing structures inside the bed have relatively lower energies. This

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means that bubbles are becoming smaller. The first transition point at such a high gas velocity of 0.05 m/s is occurring at the minimum value of pressure fluctuation energies around Ul = 0.006 m/s. Afterwards, the trend of signal energies is the same for Ug = 0.05 and 0.03 m/s; first it increases with an increase in liquid velocity due to the increase of bubble size, which is in agreement with bubble Sauter mean diameter trend presented in Fig. 9, and then decreases due to bubble breakage. The maximum value of pressure fluctuation energies is corresponding to the main regime transition of

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Fig. 10. The energy of pressure signals at constant gas velocities.

column (at Ul = 0.03 m/s). No sensible change in pressure signal energies is seen at a low gas velocity of 0.02 m/s showing no obvious regime transition inside the bed. This is also consistent with Fig. 9, which is presenting the equivalent bubble diameter pathways at certain liquid velocities and constant gas velocities. 4.2. Frequency-based analyses Vibration and pressure signals were decomposed in the frequency domain to investigate the effect of change in the bubble

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A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74

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Ug = 0.03 m/s 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.

size on the power of frequency spectra. Through such analyses, it is possible to observe the effect of two important hydrodynamic properties of the column, i.e., bubble size distribution and regime transition. Fig. 11a–c illustrates the power spectra of 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 velocity, the PSDF was studied, and it was found that transition from coalesced to discrete flow is manifested in the shape of the PSDF. At Ul = 0.003 m/s (Fig. 11a1) the power spectrum is relatively high in value and narrow in distribution with a tendency towards low frequencies (dominant peak at around 750 Hz). This can be attributed to coalesced (large) bubbles with close sizes at lower 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) bubbles at lower frequencies. In addition, there are smaller bubbles with larger frequencies. Afterwards, by increasing the liquid velocity from Ul = 0.006 m/s (Fig. 11a2) to Ul = 0.03 m/s (Fig. 11a6), PSDFs have dominant peak at lower frequencies showing increased bubble sizes. This is in agreement with bubble Sauter mean diameter growth (Fig. 9) up to the main transition point to disintegrating bubbles at around 0.03 m/s of liquid velocities. Finally, at high liquid velocities (Fig. 11a7) PSDF shows the occurrence of small bubbles at large frequencies. At Ug = 0.03 m/s, although no sensible change in PSDFs is seen at low liquid velocities (Fig. 11b1–b3), the same trend as Fig. 11a is seen at the transition point to discrete bubble flow (Fig. 11b4–b7). Narrow peaks in the PSDFs at Ug = 0.02 m/s

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(Fig. 11c1–c7) are observed corresponding to a narrow bubblesize distribution. At such condition, liquid flow has a faded effect on bubbles throughout the column. It is noteworthy that at high liquid velocities, the bubble-breaking effect of liquid can still be seen (Fig. 11c7). To obtain the detailed pathway of different structures (bubble behavior) inside the bed, wavelet analysis on pressure fluctuations was applied. The number of decomposition levels was set to be eight in order to have nine decomposed sub-signals (a8 as the low-frequency representative and D1–8 as high-frequency representatives). Fig. 12a–c shows the multi-resolution-analysis subsignal energies by increasing liquid velocities at constant gas velocities of 0.05, 0.03, and 0.02 m/s, respectively. At a high gas velocity of 0.05 m/s, Fig. 12a, the dominant peak of sub-signal energies is on D5 at low liquid velocities (e.g., 0.003 m/s). By an increase in liquid velocity to 0.006 m/s, the curve is shifted to the left indicating that the energies of fine (detail) sub-signals (corresponding to highly-oscillating small bubbles) are prevailing those of coarse scales (relevant to larger bubbles). This is due to the increase in bubble size up to the first regime transition point, pointed as number 1 in Fig. 12a. As it is seen in Fig. 12a, by further increase in liquid velocity, the peak of sub-signal energies is shifting to the right, shown with number 2, and then starts increasing its portion in the total energy (see number 4 in Fig. 12a). This is basically because of an increase in bubble size up to the second bubble-regime transition point at Ul = 0.03 m/s. In fact, by the increase of bubble size, low-oscillating bubbles are formed, which results in the decrease of fine-scale sub-signal energies (corresponding to high oscillations), and the increase of low-frequency sub-signal energies (coarse sub-signals). After the main bubble-regime transition point at 0.03 m/s of liquid velocity, bubbles are being torn apart manifested in the descended peak (see number 5 in Fig. 12a) at D6 and increase in fine-scale sub-signal energies due to the occurrence of relatively smaller bubbles. Interestingly, further increase in liquid velocity to 0.07 m/s shifts the peak to D4 (arrow number 6 in Fig. 12a), just the same as the condition of bed at the beginning of bed operation at low liquid velocities. However, at high liquid velocities 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) is concluded based on the comparison of coarse sub-signal energies at these two conditions. This is in accordance with bubble size measurements obtained by photography, i.e., Fig. 9. Decreasing the gas velocity to 0.03 m/s, the energy of whole multi-resolution-analysis sub-signal spectra was calculated. Fig. 12b presents the energy portion change of various sub-signals by increasing liquid velocity at a constant gas velocity of 0.03 m/s. The bed is starting with a dominant peak of sub-signal energies at D4 at low liquid velocities. This peak is vanishing by an increase in liquid velocities giving rise to ascending peaks at D6. Finally, the peaks at D6 start descending by further increase in liquid velocities (Ul > 0.03 m/s) resulting in ascending peaks at D4. Such trend is in full accordance with the so-called one regime transition point at moderate gas velocities (e.g., 0.03 m/s). Starting from a very low liquid velocity, by increasing liquid velocity, bubbles are coalescing together up to the regime transition point at 0.03 m/s of liquid velocity. Such coalescing behavior enhanced by liquid velocity is causing the energy of fine-scale sub-signals to decrease and the energy of coarse-scale sub-signals to increase (arrows number 1 and 2 in Fig. 12b) due to the occurrence of relatively low-oscillating bubbles (large bubbles). After the regime transition point, a high shear exerted on bubbles by liquid phase is breaking the bubbles, which leads to the presence of smaller bubbles with higher energies in their fine-scale subsignals due to rising with higher oscillating frequencies (arrow number 3 on Fig. 12b). Further decrease of gas velocity to 0.02 m/s results in sub-signal energy spectra shown in Fig. 12c. This figure is illustrating the multi-resolution-analysis sub-signal energy portion by changing liquid velocity at a constant gas velocity of 0.02 m/s. As can be seen in this figure, no distinguishable manner can be found due to the lack of any sensible regime transition at low gas velocities. However, the overall effect of liquid velocity on bubble size is started by a decrease in peaks at D6 at low liquid velocities and ended at relatively higher fine-scale energies (e.g., D3, D4, and D5) at a high liquid velocity of 0.07 m/s showing the slight effect of liquid shear on bubbles with the same trend as that of Ug = 0.03 m/s.

A. Sheikhi et al. / Experimental Thermal and Fluid Science 45 (2013) 63–74

45 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

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velocity and one main and one faded transition points at moderate and low gas velocities, respectively, were detected by liquid velocity variations. Statistical and frequency-based approaches were used to exploit information from the vibration and pressure signals. Different operating modes at various operating gas velocities were detected by the standard deviation of vibration signals. However, compared to pressure fluctuations, the standard deviation of vibration signals was less sensitive to the effect of liquid flow on the bubble size. The skewness of both vibration and pressure fluctuations showed a good sensitivity to regime transition points while vibrations were more successful than pressure fluctuations in determining the first transition point. The kurtosis of vibrations was found to be more reliable in detecting the transition points compared to pressure fluctuations. Also, pressure fluctuation energies proved to be a simple, yet trustable way of treating signals to define bubble behavior inside the column. Furthermore, analyzing the signals in the frequency domain suggested the pathway of bubble behavior alteration based on their size at different operating conditions of gas and liquid velocities. The energy of various multi-resolution-analysis sub-signals showed to be an accurate representative of bubble gradual change inside the column. Accordingly, it was shown that at high gas velocities, a shift to the left in subsignal energy spectra defined the first bubble transition point while a gradual descend in the peaks at D5 sub-signals and ascend in D6 sub-signals with their corresponding effect on the whole energy portion spectra captured the second regime transition point. At moderate gas velocities, a gradual shift from D4 to D6 up to the main regime transition point and then a reverse-back shift from D6 to D4 detected the transition liquid velocity correctly. The photographs of bubbles were used to observe the bubble behavior at different operating conditions. These observations were shown to be consistent with the results extracted from the signal processing methods. The results of this study are suggested to be used in non-invasive characterization of industrial gas-liquid processes, especially, those being operated at sever temperature and pressure conditions. Acknowledgement The authors would like to thank Noise, Vibration, and Acoustics (NVA) Lab., School of Mechanical Engineering, College of Engineering, University of Tehran for their help in data acquisition. References

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(c) Ug = 0.02 m/s Fig. 12. The energy of multi-resolution-analysis sub-signals obtained at constant gas and variable liquid velocities by wavelet analysis.

5. Conclusion Novel non-intrusive measurements, namely the vibration (acceleration) of bed shell as an inspection tool, as well as corresponding signal processing methods for hydrodynamic characterization of a two-phase gas–liquid column with both gas and liquid flows were introduced. Two transition points at a high gas

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