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KINETICS, CATALYSIS, AND REACTION ENGINEERING Mapping of Acoustic Streaming in Sonochemical Reactors Ajay Kumar, Parag R. Gogate, and Aniruddha B. Pandit* Chemical Engineering Department, Institute of Chemical Technology, UniVersity of Mumbai, Matunga, Mumabi-400019, India
Acoustic streaming is an important phenomenon observed in sonochemical reactors controlling the physical effects due to the cavitation. Not many efforts are observed, however, in exact quantification of the generated liquid circulation currents, experimentally or theoretically. The present work has been directed at quantifying the liquid circulation velocity using laser Doppler anemometry (LDA) and particle image velocimetry (PIV) techniques and establishing its dependency on the location in the reactor and the power dissipation levels. The measurements reported in the work are useful in understanding the flow distribution in the sonochemical reactor and can aid in strategic placement of the reactants in zones of maximum cavitational intensity as well as in strategic placement of process-intensifying parameters such as flow distributors and multiple transducers for eliminating zones with minimal cavitational activity. Theoretical analysis has also been carried out to compare the actual values of velocity measured using the two optical techniques. It has been observed that the liquid circulation currents are at a maximum near the transducer and secondary currents are generated at the reactor wall and the bottom. It has also been shown that the usefulness of ultrasonic horn-type reactors is restricted to a small size of reactors. 1. Introduction Ultrasound-based chemical and physical transformations are becoming popular for research investigations because of the wide range of applications in various fields such as chemical synthesis, wastewater treatment, biotechnology, polymer engineering, micromixing, homogenization, emulsification, crystallization, extraction, filtration, etc.1-5 Sonochemical reactors of different types and scales have been widely used for laboratory/ pilot-scale investigations, though successful industrial-scale exploitation is still lacking. The spectacular effects of acoustic cavitation may be attributed to its chemical or mechanical effects or to both simultaneously. The chemical effects of ultrasound are due to the implosion of microbubbles, generating free radicals that are highly reactive, leading to a series of different reactions. Mechanical effects are caused by shock waves formed during symmetric cavity collapse or by microjets formed during asymmetric cavity collapse. When ultrasound passes through the liquid, acoustic streaming is generated as a result of the sound pressure field and continuous generation/collapse of the cavities in the system. In the case of sonochemical reactors, absorption of the ultrasonic wave during its propagation in the cavitating liquid is responsible for an energy gradient (in the form of pressure potential) that induces a macroscopic liquid flow described as acoustic streaming. Acoustic streaming including associated turbulence is perhaps the main cause for the observed physical effects due to cavitation. Thus, the quantification of acoustic streaming is an important step in the overall design methodology for sonochemical reactors. The first theoretical analysis of acoustic streaming phenomena was accomplished by Rayleigh.6 More investigations in the * To whom correspondence should be addressed. Phone: 91 22 24145616. Fax: 91 22 24145614. E-mail:
[email protected] theory were carried out by Schlichting,7 Nyborg,8 and Lighthill,9 where emphasis was laid on the fundamental role of dissipation of the acoustic energy in the form of the changing of the gradients in the momentum flux. Jackson and Nyborg10 have also investigated acoustic streaming induced by sonic longitudinal vibration. Boluriaan and Morris11 have also written an indepth review on the basic aspects of acoustic streaming. On the basis of the careful analysis of these reviews and other literature, it can be said that exact quantification of the streaming velocity at different locations in a low-frequency ultrasound reactor and its dependency on the measurement technique is perhaps lacking. Such an analysis will also be helpful in understanding the flow distribution in the sonochemical reactor and would be helpful in devising scale-up methodologies for relative locations of the transducers and the reactants. The main objective of the paper is to identify the distribution of the cavitational activity and energy-dissipation patterns in sonochemical reactors. The criteria used for this mapping exercise is the measurement of local liquid circulation velocity using two different techniques of fluid velocity measurement. Among the different available techniques for flow measurement, optical techniques are considered to be more efficient. This is because they are capable of acquiring data at a high rate and, at the same time, not creating any flow disturbance, unlike the methods involving probes. Campbell et al.12 recently reviewed the details of the application of laser Doppler anemometry (LDA) and particle image velocimetry (PIV) techniques for the measurement of sound and acoustic streaming. Special attention has been paid to analysis of LDA signals including the Hilbert transform, which enables amplitude information to be obtained about various frequency components of a signal and wavelet analysis, which allows nonstationary signals to be accurately analyzed. Apart from identifying the flow distribution in sonochemical reactors as discussed earlier, an attempt has also been made in
10.1021/ie060575q CCC: $37.00 © 2007 American Chemical Society Published on Web 05/11/2007
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Figure 1. Experimental setup for LDA experiments.
this work to compare two optical techniques, namely, LDA and PIV, in ultrasound reactors. The aim was to check the dependency of the spatial distribution of the circulation velocity on the type of measurement techniques, if any, as sometimes the results obtained from sophisticated techniques are not always easy to interpret because they are not explicit in nature. 2. Experimental Work In the present work, flow patterns in an ultrasonic horn-type of reactor (frequency of 20 kHz, power in the range 3-70 W, horn tip with diameter 0.013 m inserted to a depth of 20 mm in the liquid vessel) have been studied by LDA and PIV techniques. LDA measures the velocity of a moving object by illuminating it using laser light and measuring the Doppler shift of the light scattered by the moving object, whereas PIV enables the measurement of instantaneous velocities in a two-dimensional plane of a fluid flow. 2.1. LDA Measurements. A two-dimensional LDA was used to measure the velocities in an ultrasound reactor. The light source was an argon-ion laser. Beams from the argon-ion laser passed the transmitting and focusing optics to intersect and form a measuring volume within a cylindrical vessel (diameter ) 0.135 m, height of the liquid in the reactor ) 0.15 m), immersed in a square tank filled with water to minimize optical distortion. The probe volume was positioned at the desired point with the help of a manual traversing system. The receiving optics with photo detectors was operated in a forward-scattering manner. A Burst spectrum analyzer (BSA) was used to convert analog signals from the receiving optics into Doppler frequencies and velocities. The Burst signal analyzer uses frequency-domain burst detection to convert the analog signal to instantaneous velocity measurements. The effects of signal sampling rate and sample size on the reproducibility of velocity measurements were investigated. An average validated sample size of 20 000 was obtained at an average data rate of 1 kHz. The schematic diagram of the experimental setup used is shown in Figure 1. In all the experiments, tap water was used as a working fluid. No additional tracer particles were used in this experiment. 2.2. PIV Measurements. The PIV measurements were made using a double-pulsed Minilite Nd:YAG laser that has a variable frequency between 1 and 15 Hz and a wavelength of 532 nm. A black-and-white charge-coupled device (CCD) camera (Kodak) was used to record simultaneous images of the flow in laserilluminated plane. A Masterbox links the lasers, camera, and computer, and allows several operating parameters to be optimized. The experimental setup of PIV-based investigations is shown in Figure 2. Experiments were performed in a cylindrical reactor of diameter 0.2 m and liquid height 0.5 m. The liquid phase was seeded using 30 µm hollow glass particles implanted with fluorescent rhodamine dye (Dantec). These particles diffuse light at a wavelength of 575 nm, which is greater than the wavelength of the light diffused by the air bubbles (550 nm). A filter is fitted to the camera, which enables
Figure 2. Experimental setup: (1) double-pulsed Nd:Yag laser source, (2) optics, (3) lens, (4) laser sheet, (5) ultrasonic horn reactor, (6) Masterbox, (7) computer, (8) CCD camera.
only the light with a wavelength greater than 550 nm to be captured. Images are acquired with different exposure time delay, depending on the ultrasonic power used. In order to calculate a mean velocity vector field from instantaneous data points in the PIV technique, the instantaneous data population must be of a number that is statistically significant. In this study, the number of instantaneous data points used to calculate the average velocity field was determined by following the mean velocity at a given point (r, z) over the time interval of 500 µs. The location of the point (r, z) is close to the horn tip, in an area where velocity gradients are highest. Variation in the axial mean velocity with respect to the number of images for different dissipation powers has been investigated with an aim of optimizing the number of images to be captured. It has been observed that constant axial mean velocities are obtained after averaging about 300 image pairs. So, all the further experiments have been done with 400 image pairs. The objective of measurements is to investigate the velocity in the axial and radial directions in a fixed-geometry ultrasonic reactor. The dependency of the liquid circulation velocities on the ultrasonic power dissipation in the system has also been investigated. Measurements have been carried out at different locations (away from the horn tip in axial as well as radial directions) in the reactor so as to investigate the spatial distribution of the mean liquid velocity. The trends obtained with the two measurement techniques have been compared so as to check the dependency of the spatial distribution of the mean liquid velocity on the type of measurement technique, if any. 3. Results and Discussion 3.1. Comparison of Velocity Profiles using LDA and PIV Techniques. Vector diagrams showing velocity profiles from LDA and PIV measurements are given in Figures 3 and 4, respectively. From Figure 3, it can be observed that there is an entrainment of liquid toward the center due to high liquid velocity generated near the tip of the oscillating horn and also due to an existing high-pressure gradient. This is the reason for the formation of the secondary circulation cell. Also, near the bottom, a second circulation cell is formed due to the occurrence of flow reversal at the base of the reactor. Formation of circulation cells in the system leads to more uniform distribution of the cavitational activity in the reactor. Figure 4, which shows the PIV results, clearly indicates the presence of a central downward flowing liquid jet similar to a plunging liquid jet reactor. It has been observed that the jet gradually expands from
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Figure 5. Radial profile of axial mean velocity at different powers in LDA.
Figure 3. Vector diagram showing velocity profile from LDA measurements for acoustic power of 70 W. Figure 6. Radial profile of axial mean velocity at different powers in PIV.
Figure 4. Vector diagram showing velocity profile from PIV measurements for acoustic power of 63 W.
the face of the horn to the bottom of the reactor. It has also been observed that the velocity is almost zero in most other parts of the reactor. In this case, there is no flow reversal occurring due to a relatively larger size of reactor compared to the reactor used in the LDA measurement (Figure 3). Thus, it means that the performance of the sonochemical reactors based on a single transducer will be strongly dependent on the relative dimensions of the transducer and the reactor. The bigger the reactor, the larger is the number of zones with very low or no
cavitational activity and, hence, the cavitational performance for a reactor as a whole will be poor. Radial profiles of axial mean velocities near the horn at different powers are shown in Figures 5 and 6 for LDA and PIV techniques, respectively. The negative sign depicts the direction of velocity from the horn tip to the bottom of the reactor. It has been observed that the mean fluid circulation velocity decreases with an increase in the radial distance (toward the wall). The trend is similar to that reported in the literature using other mapping techniques such as measurement of the rate of the chemical reaction or quantifying the local pressure.13 It has also been observed that velocity marginally increases near the wall when measured using LDA. It may also be due to the flow reversal or some error in the measurements for a nearwall position. Further, with an increase in the ultrasonic power dissipation, the mean velocity at a particular location also increases continuously over the range of power dissipation used in the work, indicating that enhanced power dissipation leads to the intensification of the acoustic streaming and also possibly of the cavitational activity. Radial profiles of radial mean velocities near the horn at different powers are shown in Figures 7 and 8 for LDA and PIV techniques, respectively. It has been observed that the nature of the variation in the radial velocity with location is similar for both measurement techniques, though the magnitude is different in the two cases, which has been explained later. Further, the circulation velocity increases with an increase in the power dissipation, which is similar to a reported increase in the cavitational activity with the power dissipation as measured using chemical reactions.13 3.2. Estimation of Mean Circulation Velocity through Mixing Time (θmix). The mixing time (θmix) was measured using two conductivity probes located at various positions so as to represent all the regions of the vessel. Experiments were
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Figure 7. Radial profile of radial mean velocity at different powers in LDA.
Figure 10. Comparison of theoretical and measured velocities (max) by LDA, PIV, and with mixing time techniques.
where T is the diameter of the beaker and Z is the height of the liquid in the beaker. It is assumed that a minimum five circulations are required for calculating time required for 95% mixing.14 So the average liquid circulation velocity (Vc) is calculated as
Vc ) minimum number of circulations for mixing (≈5) × loop length/θmix (2)
Figure 8. Radial profile of radial mean velocity at different powers in PIV.
Figure 9. Schematic representation of horn movements for the estimation of theoretical velocity.
performed in a cylindrical reactor of diameter 0.2 m and liquid height 0.5 m. Probe 1 was located near the bottom of the reactor and 10 mm away from the vessel wall. Probe 2 was located near (below) the horn tip and 10 mm away from the vessel wall. Sodium chloride solution (2 M) was used as a tracer. An impulse input of tracer (1% of reactor volume) was injected on the liquid surface, 10 mm away from wall, which was diagonally opposite to the location of probe 2. Data acquisition was continued for a sufficient length of time so as to allow for closer approach to the steady state in the concentration profiles. The mixing time was estimated for each of the probes as the time required to attain a final concentration within (2% of the final average concentration. Final mixing time was obtained as the average of all the mixing times indicated by the two probes. In order to estimate liquid circulation velocity, the maximum distance traveled by a liquid packet during one circulation, i.e., loop length, should be considered. The loop length (L) is taken as
L ) T + 2Z
(1)
It is possible to estimate the mean acoustic streaming velocity with the use of the above formula. The logic and the reasoning behind the successful use of the above formula have been discussed by Vichare et al.15 3.3. Theoretical Prediction of Velocity. For the validity of the absolute values of velocity obtained with both techniques, the theoretical maximum liquid circulation velocity has been estimated based on the following assumptions: (1) The horn tip oscillates in simple harmonic motion, so it starts with velocity zero at time t ) 0 and reaches a maximum velocity at half the amplitude in time t ) 0.25/f and again reaches zero velocity at maximum amplitude (a), i.e., at the end of the forward stroke, the time taken for the forward stroke is 0.5/f, i.e., the time taken for one forward cycle. (2) There is no slip between the horn surface and the liquid, i.e., liquid is always attached to the tip at least in the forward stroke till the point of maximum velocity. (3) Acceleration and deceleration during one oscillation cycle is uniform. A schematic representation of the movement of the horn with respect to time is shown in Figure 9. The stepwise procedure for the estimation of maximum velocity has been given in Appendix A, whereas a specific example showing the detailed calculations has been given in Appendix B. The variation of the maximum velocity with power dissipation has been reported in Table 1. 3.4. Comparison between Experimental and Predicted Velocities. Figure 10 shows the comparison between the estimated velocity based on theoretical analysis as described earlier and the experimental values (LDA and PIV values) with different ultrasonic powers. It has been observed that, at low dissipated power, the estimated and the measured velocities are similar, but at higher dissipated power, i.e., >25-30 W, the measured velocity tends to deviate from the theoretical velocity; at the highest power dissipation levels, it is almost 3 times more
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Table 1. Theoretical Estimated Values of Parameters in Ultrasonic Reactor dissipated power (W)
I (W/m2)
a (µm)
S (µm)
ac (m/s2)
velocity max (m/s)
2.40 4.80 5.85 7.20 10.20 16.50 18.24 23.40 30.72 33.60 44.16 62.88
21 238 42 477 51 769 63 716 90 265 146 017 161 415 207 079 271 858 297 345 390 796 556 460
1.19 1.68 1.85 2.06 2.45 3.12 3.28 3.71 4.25 4.45 5.10 6.09
0.59 0.84 0.92 1.03 1.22 1.56 1.64 1.85 2.12 2.22 2.55 3.04
9642 13636 15053 16700 19877 25281 26580 30106 34495 36076 41358 49352
0.10 0.15 0.16 0.19 0.22 0.28 0.29 0.33 0.38 0.40 0.45 0.54
than the theoretical velocity. This can possibly be attributed to the presence of intense cavitation at higher power dissipation levels, creating a significant pressure gradient and secondary flow, enhancing the unidirectional velocity. The contribution of cavitational collapse to the acoustic streaming is not considered in the theoretical analysis, but in reality, the contribution appears to be much higher at higher power dissipation levels. This difference at higher power dissipation levels merits further investigation and demands a better theoretical model to predict acoustic streaming. It has also been found that the measured velocity by LDA is always higher as compared that by the PIV technique. It may be possible that the difference between the velocities measured using LDA and PIV is due to the seeding particles used in the later case. The seeding particles that are used in the PIV experiments are assumed to be naturally buoyant, but their density is significantly higher when compared to the dust in the tap water used in the LDA experiments. A small slip due to higher particle inertia in the case of the PIV measurement could be responsible for this observed difference. Estimated mean velocity through mixing time is smaller compared to all methods, but these are comparatively nearer to the predicted values. This difference can be attributed to the fact that the velocity estimated on the basis of the mixing time is the average velocity (combined effect of the circulation currents generated in the system considering both radial as well as axial components), whereas the theoretically estimated velocity and velocity measured using optical techniques gives the maximum radial/axial velocity existing in the system. It should also be noted that the model used here for predicting the theoretical velocity is a simplistic one and also the number of data points available for comparison are not enough for generalization of the reports. More work is indeed required for a large-scale reactor (with a sufficient number of data points) along the directions presented in the present work before generalized results in terms of dependency of the circulation velocity on different operating parameters and locations can be established. 4. Conclusions The trends in the variation of the liquid circulation velocity due to acoustic streaming with the two measurement techniques are quite similar, though the actual values are higher in the case of LDA as compared to the PIV technique. The velocity increases near the wall and also at the bottom in a small reactor due to the flow reversal, which increases the extent of mixing in the reactor. Thus, it can be said that single transducer type reactors are more suited for small-size vessels. The liquid circulation velocity increases with an increase in the power
dissipation levels over the entire range studied in the work. It has been observed that, at low dissipated power, the theoretical and measured velocities are almost identical, but at higher power dissipation levels, the measured velocity is much higher than the theoretical velocity, which reveals the contribution of the collapsing cavities to the acoustic streaming phenomena. Estimated mean velocity through mixing time is comparatively nearer to predicted values. The unique work presented here offers a real contribution to the quantification of liquid circulation velocities, both experimentally and on the basis of theoretical modeling, and should be useful in establishing sound design strategies for sonochemical reactors. Appendix A The estimation of actual power dissipation in the system has been determined by monitoring temperature rise (calorimetric method), and hence, the intensity of sound (I) can be estimated with the use of the following formula.
intensity (I) ) dissipated power in the system/ cross-sectional area of horn tip (3) The Amplitude for oscillation has been calculated using the formula
I ) 0.5Fc(a2ω2)
(4)
where I is intensity, c is the velocity of sound, a is the amplitude, and ω is the angular frequency of oscillation. By Newton’s law of motion, we can find the acceleration of the tip (ac)
S ) ut + 0.5act2
(5)
where S ) distance traveled by tip ) a/2, u ) initial velocity of tip ) 0, ac ) acceleration of tip, and t ) time ) 0.25/f. At time t ) 0, u ) u0 ) 0. Again we know that
V ) u + a ct
(6)
Here, V is the maximum velocity (Vmax) of the horn tip at distance a/2. So,
Vmax ) act (since u ) 0). Appendix B The following is an example with power dissipation ) 7.2 W. From eq 3,
I ) 63 716.82 W/m2 (dia ) 0.013 m) From eq 4,
a ) 2.061 µm Again from eq 5,
S ) ut + 0.5act2
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where S is the distance traveled by the tip, where the tip has a maximum velocity. So, S ) a/2 ) 1.0309 µm, u ) initial velocity of the tip, ac ) acceleration of the tip, t ) time ) 0.25/f, u ) u0 ) 0. So, putting all these values in eq 5, we get
ac ) 2S/t2 ) 16 700 m/s2 Then from eq 6,
Vmax ) act ) 0.19 m/s Literature Cited (1) Lindley, J.; Mason, T. J. Use of ultrasound in chemical synthesis. Chem. Soc. ReV. 1987, 16, 275. (2) Mason, T. J. Practical Sonochemistry: User’s Guide in Chemistry and Chemical Engineering; Ellis Horwood Series in Organic Chemistry; Chichester, U.K., 1992. (3) Keil, F. J.; Swamy, K. M. Reactors for Sonochemical Engineerings Present Status. ReV. Chem. Eng. 1999, 15, 85. (4) Luche, J. L. Synthetic organic chemistry; Plenum Press: New York, 1999.
(5) Gogate, P. R. Cavitation: An auxiliary technique in waste water treatment schemes. AdV. EnViron. Res. 2002, 6, 329. (6) Rayleigh, L. Theory of sound; Dover publication: New York, 1945. (7) Schlichting, H. Boundary layer theory; McGraw-Hill: New York, 1955. (8) Nyborg, W. L. J. Acoustic Soc. Am. 1958, 30 (4), 329. (9) Lighthill, J. J. Sound Vibration 1978, 61 (3), 391. (10) Jackson, F. J.; Nyborg, W. L. J. Acoustic Soc. Am. 1960, 32 (11), 1387. (11) Boluriaan, S.; Morris, P. J. Acoustic Streaming: From Rayleigh to today. Int. J. Aeroacoustics 2003, 2, 255. (12) Campbell, M.; Cosgrove, J. A.; Greated, C. A.; Jack, S.; Rockliff, D. Review of LDA and PIV applied to the measurement of sound and acoustic streaming. Opt. Laser Technol. 2000, 32, 629. (13) Gogate, P. R.; Tatake, P. A.; Kanthale, P. M.; Pandit, A. B. Mapping of sonochemical reactors: Review, analysis and experimental verification. AIChE J. 2002, 48 (7), 1542. (14) Pandit, A. B.; Joshi, J. B. Mixing in mechanically agitated gasliquid contactors, bubble columns and modified bubble columns. Chem. Eng. Sci. 1983, 38 (8), 1189. (15) Vichare, N. P.; Gogate, P. R.; Dindore, V. Y.; Pandit, A. B. Mixing time analysis of a sonochemical reactor Ultrason. Sonochem. 2001, 8, 23.
ReceiVed for reView May 9, 2006 ReVised manuscript receiVed March 27, 2007 Accepted April 10, 2007 IE060575Q
