FEDSM DEVELOPMENT OF A NEAR REAL-TIME INSTRUMENT FOR NUCLEI MEASUREMENT: THE ABS ACOUSTIC BUBBLE SPECTROMETER

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1 Proceedings of FEDSM 3 International Symposium on Cavitation Inception, 4TH ASME_JSME Joint Fluids Engineering Conference Honolulu, Hawaii, USA, July 6-1, 3 FEDSM DEVELOPMENT OF A NEAR REAL-TIME INSTRUMENT FOR NUCLEI MEASUREMENT: THE ABS ACOUSTIC BUBBLE SPECTROMETER Georges L. Chahine DYNAFLOW, INC. glchahine@dynaflow-inc.com Kenneth M. Kalumuck DYNAFLOW, INC. ken@dynaflow-inc.com 161-J Iron Bridge Road, Jessup, MD 794 Tel: Fax: ABSTRACT The ABS Acoustic Bubble Spectrometer (ABS) is an acoustics based device that measures bubble size distributions and void fractions in liquids using the properties of acoustic wave propagation through a two-phase medium. The ABS is PC-based and uses software that controls signal generation, detection and signal processing through data boards and two hydrophones. The data is processed and analyzed utilizing inverse problem solution algorithms to obtain the bubble size distribution. All physical, experimental, and analytical parameters are input by the user via a series of dialog boxes. The results are displayed graphically by the interface in real time and can also be stored or printed. In this paper we describe the method and present validation experiments that compare bubble distributions and void fraction results of ABS measurements with optical measurements in the laboratory. The two methods give very close results with the ABS possessing the significant advantage of enabling near real-time measurements with the potential to become an on-line measuring device. Keywords: Bubble Nuclei, Cavitation Inception, Bubble Size Distribution, Acoustic Waves NOMENCLATURE A attenuation of acoustic wave, equation (9) a bubble radius b damping constant c l sound speed in the pure liquid c m sound speed in the bubbly mixture D bubble gas thermal diffusivity k 1, k kernels of the integral dispersion relations N(a) bubble density function p bubble pressure at equilibrium p v liquid vapor pressure u, v real and imaginary parts of the sound speed ratio, equation (6) γ bubble gas specific heat ratio ρ liquid density µ liquid dyanmic viscosity σ surface tension ϖ bubble natural frequency ϖ acoustic wave frequency INTRODUCTION Cavitation inception in a liquid is due to the explosive growth of microscopic bubbles or nuclei initially present in the liquid when the local pressure drops below a critical value. Therefore, determination (and control when possible) of the number and size of these nuclei is important for controlled cavitation inception studies. This has resulted in many studies and technical approaches to measure the properties of the tested waters in terms of their nuclei content. These have included optical studies (photography, holography, and scattering techniques), acoustical studies, electrical impedance tomography, and cavitation susceptibility meters [1-11]. Unfortunately, measurements obtained with different methods often vary widely, and each method has its own significant strengths and weaknesses. Acoustical methods rely on the fact that bubbles have a strong effect on the propagation of acoustic waves, and the acoustical cross-section of a bubble is three to four orders of magnitude greater than its geometrical crosssection. Many studies including [1-13] developed equations for acoustic wave propagation through a bubble laden liquid. These have resulted in integral relationships between acoustic wave attenuation and phase velocity for a given bubble population. The ABS Acoustic Bubble Spectrometer (ABS) is based on exploiting the results of these studies. 1 Copyright 3 by ASME

2 The ABS extracts the bubble population from acoustic measurements made at several frequencies. It is a PC-based instrument, which includes a set of two hydrophones or transducers connected to a set of computer boards resident on a personal computer (Figure 1). Data boards control signal generation by the first hydrophone and signal reception by the second hydrophone. Short monochromatic bursts of sound at different frequencies are generated by the transmitting hydrophone and received by the second hydrophone after passage through the interrogated liquid. These signals are processed utilizing inverse method software algorithms to obtain the bubble size distribution from the attenuation and phase velocities of the acoustic waves. Measurements are controlled with the aid of a user-friendly Graphical User Interface (GUI). All physical, experimental, and analytical parameters are input by the user via a series of dialog boxes. The results are displayed graphically by the interface in real time and can also be stored or printed. In this paper we describe the method, its application in the ABS instrument and some validation measurements. Figure 1. Picture of a portable PC-Based ABS Acoustic Bubble Spectrometer and accompanying hydrophones in a tank to test a new bubble generator.. BACKGROUND OF THE METHOD The bubble size distribution in a liquid can be characterized by the bubble density function, N(a), defined as a N( a) da = Total Number of bubbles per unit volume, (1) a1 where a is the bubble radius. If the liquid is subjected to an acoustic wave of pulsation ϖ, the bubbles present in the liquid oscillate in response to the acoustic excitation and thus extract and re-radiate energy into the liquid. Each bubble acts as an oscillator with a natural frequency ϖ, p pv + σ / a σ ϖ = ( ), R Φ () ρa ap and a damping constant b that depends upon the imposed frequency ϖ and the bubble radius, a, p a b = µ ϖ ( ). ρa + I ρa Φ + (3) c l R ( Φ) and I( Φ) are the real and imaginary parts of Φ, 3γ Φ=, 1/ 1/ 1 3( γ 1) iχ( i/ χ) coth ( i/ χ) 1 (4) D χ =. ϖ a p is the ambient pressure, pv is the liquid vapor pressure, σ is the surface tension parameter, p is the bubble pressure at equilibrium, µ is the liquid dynamic viscosity, and γ and D are respectively the bubble gas specific heat ratio and thermal diffusivity. The complex sound speed, c m, in the mixture is then related to the sound speed in the liquid, c l, by: a cl an( a) = 1+ 4 π da, c (5) ϖ ( a) ϖ + ib( a) ϖ m a1 where i is the imaginary unit. Replacing in (5) ϖ and b with their expressions (,3) we obtain, with cl u iv, c = (6) m the following dispersion relations: where ahigh k1( a, ϖ ) N( a) da= u v 1; alow ahigh alow k ( a, ϖ ) N( a) da = uv,. ( ϖ ϖ ) ( ) + a k1 =, ϖ ϖ 4b ϖ bϖ a k =. ϖ ϖ + 4b ϖ ( ) The quantities u and v may be obtained by measuring the phase velocity c m and the attenuation A of the wave in the bubbly liquid, where A is given in db per unit length by: ϖ v A= log 1 e. (9) cl The ABS software is designed to analyze the emitted and received signals and deduce from these measurement u and v. An inverse method solution is then used to deduce the bubble size distribution from the knowledge of u and v for all the emitted waves frequencies. (7) (8) Copyright 3 by ASME

3 Figure. Graphical User Interface for experiment set-up and acoustic waves emission. THE ABS MEASUREMENT TECHNIQUE Measurement Procedures The ABS Acoustic Bubble Spectrometer is based on using the measurement of the quantities u and v described above to determine the bubble distribution. The ABS extracts the bubble population from measurements of the acoustic phase velocity c m and attenuation A made at several insonifying frequencies. Presently, the device uses a set of two hydrophones connected to data acquisition and control boards resident on a personal computer. Procedures with more hydrophones are being considered for increased precision. We are also considering setups with a single emitter-receiver hydrophone. In order to enable such a configuration, we need to be able to generate reflected acoustic signals that are much stronger than any background noise. In its present set-up the ABS uses two hydrophones facing each other and the measurements are conducted for a straight acoustic path. The user inputs a series of interrogating frequencies to cover the range of expected bubble sizes, as well as the number of acoustic periods to compose each acoustic burst (see Figure ). Even though the ABS inverse method procedure accounts for the fact that each bubble contributes acoustically at all frequencies as expressed in the relations (8,9), selection of the interrogation frequencies to be comparable to the resonance frequencies of the expected bubble sizes is helpful. The following approximate equation of Equation () can be used for these frequencies for experiments conducted at atmospheric pressures, 3.3 f( khz). amm ( ) (1) The ABS software uses this user input to generate electric signals to send to a function generator board to send strong electric signals of the required voltage to the emitting hydrophone. Short monochromatic bursts of sound are thus generated by the transmitting hydrophone and received by the second hydrophone after passage through the bubbly liquid. The signals emitted by the first hydrophone cross the liquid containing the bubbles and arrive at the second hydrophone located at a distance d after a time delay t. This is shown for various frequencies in the ABS screen shot of Figure 3, where the emitted signals are in blue and the amplified received signals are in red. The effective sound speed at each frequency can be obtained from this delay using: d cl. (11) t The distance between the two hydrophones is input by the user in the Signals Characteristics interface, while t is computed by the ABS software Signal reception from the second hydrophone is achieved using a data acquisition board. The sampling rate of this data acquisition board is very important and directly impacts the performance of the ABS. It determines the precision of the measurements, and the highest value of the acoustic frequency that can be measured and thus the smallest size of the bubbles that can be detected. The sampling rate is also a user input in the Signals Characteristics interface (Fig. ). In the present implementation of the ABS one of two types of acquisition boards is optionally selected: a 1.M Hz maximum sampling rate card and a. MHz maximum sampling card. The emitted and received signals are processed and analyzed utilizing software algorithms we have developed to obtain the attenuation and phase velocities of the acoustic waves, and, from these, the bubble size distribution. The time delay, t, is obtained using cross-correlation computations between the emitted and the received signal. Measurements are conducted with the aid of a Graphical User Interface, where all experimental (Figure ), physical (see Figure 3), and analytical parameters are input by the user via a series of dialog boxes. Both raw and processed data from experiments can be saved to disk for future use. The results are displayed graphically by the interface in real time (see Figure 4) and can also be stored or printed. The PC and its resident signal generation and data acquisition hardware synchronize and control the measurements and perform the data analysis. A sketch of the procedure is shown in Figure 5. Acoustic Probes The present ABS system uses piezoelectric hydrophones that are made to specifications for the user application from flat sensitive piezo element sheets. The size of the hydrophone determines its range as well as its maximum and minimum frequencies. The larger the size, the stronger are the emitted and received signals for a given voltage excitation, and also the lower is the lowest frequency than the hydrophone can emit and receive. Typical values of the frequency range for a x cm hydrophone element are 1 khz through 5 KHz. In this case the system can easily measure bubbles between 5 µm and 5 µm. Presently three types of hydrophone configurations have been used and extensively tested (see Figure 6): 3 Copyright 3 by ASME

4 Figure 3. Graphical User Interface for the physical parameters of the experiment. a. Hydrophones embedded in the flat walls of the experimental facility. This is an excellent configuration when possible, since it results in a non-intrusive measurement and satisfies the requirement of direct path between emitter and receiver. In this case the measurement provides an average value of bubble size distribution in the volume comprised between the two sensing elements. An additional advantage of this configuration is its minimization of wall reflection. However, one has to be very careful in insulating the hydrophones from the facility walls to avoid measurement of wall vibration as well as the presence of a direct path through the facility walls between the two hydrophones. Figure 7, further discussed below, shows a picture of an actual implementation of this setup. b. Hydrophones embedded in the circular walls of the test section. This is also a very good configuration. It results in a non-intrusive measurement and satisfies the requirement of direct path between emitter and receiver. It could be used in a bypass section of a cavitation tunnel flow and can be combined with other measurement techniques. In this configuration provision of a flush surface in the cylinder and insulating the hydrophones from the facility walls to avoid measurement of wall vibration as well as the presence of a direct path through the facility walls between the two hydrophones is essential. This can be achieved by special fabrication of the hydrophones to fit in the designed cylindrical tubes. Figure 8 shows a picture of an actual implementation of this setup. c. Hydrophones submerged in the test section. This configuration is intrusive, but can be effectively used where the above two configurations are not practical. In this case one can measure local distributions in the absence of significant local flow or when the hydrophones are faired to minimize interference with the basic flow. The user can also use other types of transducers and hydrophones available. Figure 4. Screen shot of the ABS raw signals display showing an example of the transmitted and received signals in the presence of bubbles. Figure 3. Sketch of the ABS Acoustic Bubble Spectrometer method. 4 Copyright 3 by ASME

5 Reference Data A key user-friendly feature of the present ABS system is the fact that it does not require separate calibration of the measuring system (i.e. hydrophones, liquid, experimental setup). Instead, we have adopted a procedure, which consists in enabling the user, to conduct a reference experiment in the same geometrical set-up in which the experimental study will be conducted. In this reference configuration, the user selects an experimental condition, in which nuclei presence is minimized (it is difficult if not impossible to totally eliminate the nuclei). Under this condition, e.g. highest level of degassing of the experimental facility, an original experiment is conducted covering the full range of emission frequencies. Both emitted and received signals are then stored by the ABS system, once the user has selected the option Generate Reference Data in Figure (or in the corresponding shortcut icon in the main software GUI). The ABS software then computes the reference u and v curves with which to compare the curves obtained during actual testing. The advantage of such an approach is that a) it does not require any assumptions on the propagation of the emitted sound waves (i.e. planar, spherical, etc.), b) it corrects for any modifications of the hydrophones response function under the geometrical constraints of the experimental set-up, and c) it does not require explicit knowledge of the response functions of the two hydrophones but rather accounts implicitly for these. An additional new feature of the ABS, aimed at minimizing experimental errors, consists of averaging multiple measurements if so requested by the user. When this choice is made by entering the number of requested repetitions in the experimental set-up dialogue box of Figure, Multiple Tests, the ABS performs the number of tests requested, stores the results in the computer memory then uses the average of all the data to perform the inverse problem analysis and deduce the bubble size distribution. Inverse Problem Solution Once a series of measurements of sound speed and attenuations in the bubbly medium is accomplished at a set of frequencies covering the range of interest, the inverse problem consists of the determination of the bubble size distribution corresponding to these measurements. Such an inverse problem is difficult to solve and is usually ill-posed, that is small variations in the measured quantities may result in large variations in the sought distribution. Since experiments are prone to measurement errors and numerical computations are subject to round off and other errors, this can result in the solution oscillating wildly when refining discretization until finally the solution has little relation to the original data. It is thus necessary to regularize the problem. We have solved this issue using constrained optimization methods [11,14-17]. Physical constraints are imposed in order to enable solution of the ill-posed problem, and the parameters of the computed distribution are specified. These include imposing limits on the minimum and maximum expected bubble sizes (radii) and the number of discrete sizes to compute. Also, upper bounds on both the total bubble surface area and total bubble volume per unit volume of the measurement region are also specified here. These are utilized as constraints in the inverse problem solution algorithm, and are usually set to large positive values. (a) (b) Emitting Transducer Receiving Transducer (c) Hydrophones Insulation Figure 4. Sketch of present hydrophone configurations: a) embedded in flat experimental facility walls, b) embedded in cylindrical bypass or experimental facility walls, c) streamlined hydrophone in experimental facility. Figure 5. Photograph of the test section and the divergence area of the flow. In this case the flow was directed downward. 5 Copyright 3 by ASME

6 Air/Water Mixing Tank Air Injection Transducers Water shear Microporous Tube Figure 6. Picture of a cylindrical pipe equipped with two ABS transducers embedded flush in the cylindrical walls. Test Section High Speed Video camera VALIDATION EXPERIMENTS Experimental Setup Over the last few years we have conducted many experiments to validate and improve the accuracy of the ABS Acoustic Bubble Spectrometer [18-]. These experiments have consisted mainly of using electrolysis bubbles, microporous tubes, hypodermic needles and injected bubbles by various means in an otherwise quiescent container [18-]. We have also considered the case of bubbles generated by a water jet impacting in on a free surface [1]. We present here one of the latest validation test in which a controlled bubble distribution was generated then measured both with the ABS Acoustic Bubble Spectrometer and with High Speed microphotography []. Emitting Transducer Receiving Transducer Figure 7. The Experimental Settings display: Physical Constraints page. Pump ABS Figure 8. Sketch of the experimental setup for the ABS Acoustic Bubble Spectrometer validation studies. The experimental set-up used was designed to enable simultaneous acoustic and optical measurements of the liquid domain and to enable validation of the ABS in the case of a flowing bubbly liquid. Figure 1 shows a sketch of the set-up. A micro-porous tube is used to inject air bubbles into a cm 3 Plexiglas mixing chamber. Water is injected at various speeds in a second tube enclosing the microporous tube and is used to shear off the bubbles ejecting from the micropores resulting into smaller sized bubbles [3]. The water / bubble mixture is drawn through a 5 mm pipe into a cm 3 Plexiglas test section. The bubbly medium is then guided through a gentle 3-degree angle divergent section of length 15 cm from the 5 mm pipe into the test section. Downstream of the test section a variable speed pump takes the laminar parallel flow in the test section from the suction port through the test section and back into the mixing chamber through the shearing water injection tube surrounding the microporous tube. Two flat piezoelectric hydrophones of 5 5 cm active area are embedded in polyurethane for waterproofing and mounted in two sides of the test section, and are insulated acoustically from the structure by cork layers. One of the transducers acts as the emitter side of the ABS system while the other one acts as the receiver. The other two sides of the Plexiglas test section are used for optical observation. A Redlake high-speed video camera with a macroscopic lens is used to take a series of pictures of the bubble distribution as a function of time. These images are then analyzed semi-automatically using the data analysis system of the video-camera. Usually, 5 such frames were analyzed to provide one data point; all bubbles in focus are measured and counted to generate a bar chart of the bubble size distribution. 6 Copyright 3 by ASME

7 The bubbles are then grouped in bins that correspond to those obtained with the ABS analysis in order to enable a side-byside comparison. The video image is a quasi-d representation of the real 3D bubbly flow field. However, it has volume information through the depth of field of the lens / optical field considered. Objects will appear in focus within a certain depth, ±δ, of the focus plane. δ is measured initially in the same facility using a thin wire. In order to compute the number of bubbles of a given size in a unit volume, we use the fact that the counted and measured bubbles were observed in a volume of size δwh, where w and h are the width and height of the optical measurement volume. Number per cm ABS 8%waterFlow 3% Air Test 1 Test Test 3 Test Bubble Radius, µm Figure 1. Illustration of the degree of variation in the bubble size distribution in the measurement volume using one measurement each time with the ABS Acoustic Bubble Spectrometer (Similar results are obtained with the microphotography). Figure 11. Screen shot of the ABS graphical user interface showing, for one of the case studies reported here, the sound speed ratio, u, and the attenuation ratio, v, defined above in Equation (6). Also shown is the resulting bubble size distribution after solution of the inverse problem by the ABS software. This results in an unavoidable large difference between the measurement volumes of the two methods, about 19 cm 3 for the ABS and about 5 mm 3 for the microphotography. The second difference is the duration of the measurement, which is less than a second for the ABS ( 1 ms) and a few minutes for the video photography. Figure 1 shows a typical example of the data obtained when the measurements are done several times under the same conditions within a few minutes apart. It is quite obvious that on the local level, the details of the bubble size distribution spectra (number of bubbles in a unit volume of a given size) change significantly between one measurement and the next despite appearance to the contrary to the naked eye. However, the overall trend does not change much. Figure 13 shows a comparison between the ABS and the photographic results where an average was made over six ABS computations and six video photo analyses of images each. Here, we can see that the two methods give very close results, even though no attempt was made to adjust any of the measurement parameters such as the value used for the depth of field or the intensity level selected to decide if an image was in focus or not. In general, the number of bubbles of a given size measured with the ABS also appears to be quite close to optical observations. Discrepancies are definitely within the margin of variation in the results of each of the observation method. They are related to actual variations in the bubble population and not so much due to errors in either of the measurement methods. Figure 14 shows the effect of doubling the amount of air injected into the mixing chamber. As measured directly with the video photography and indirectly with the Acoustic Bubble Spectrometer, this results in a modification of the shape of the bubble size distribution. Instead of a simple peak in the distribution, we observe that two peaks are formed on each side of the previous one. This is a result of the complex interaction between the injected air stream from the micropores and the shearing action of the surrounding water flow. It is quite encouraging that both methods captured the same trend and again appear to give close result within the variations of the experimental bubble/liquid distribution. Number per cm ABS Average 6 tests Photos Average 13 frames Bubble Radius, µm Figure 13. Comparison between ABS measurements and micro video photography averaging six repetitions. 7 Copyright 3 by ASME

8 Number per cm Bubblr Radius, µm ABS 3% max air Photo 3% max air ABS 6% max air Photo 6% max air Figure 14. Sensitivity of the bubble size distribution measurements to a doubling in the flow rate of air through the DynaPerm microporous tube. In order to test the system when there are two very different peaks in the bubble size distribution, the position of the air generator was deliberately misplaced in order to force some large bubbles to be directly injected into the suction end upstream of the test section. Figure 15, shows the resulting ABS determined bubble sizes and the direct optical measurements. Again we can see a very good correspondence between the two methods in the detected bubble sizes, with discrepancies in the bubble number in the same range as the repetition error in the experimental realization of the same bubble / liquid configuration. Number per cm Bubble Radius, µm H.S.VIDEO ABS Figure 15. Bubble size distribution in a condition where large bubbles were injected into the test section. Comparison between ABS results and video photography analysis. CONCLUSIONS After several years of development, the ABS Acoustic Bubble Spectrometer has become a reliable and user-friendly instrument for bubble size distribution measurement in a liquid. Since bubble size distribution can play an important factor in cavitation studies especially in cavitation inception. It is very useful to be able to characterize the liquid studied for its properties not only in terms of overall air content or dissolved oxygen but also in terms of the actual detail of the bubble size distribution. The ABS Acoustic Bubble Spectrometer appears to have important advantages that make it a useful instrument. It allows near real time on line measurement of the bubble size density. It can be designed to be non-intrusive, when the experimental set-up enables one to locate the transducers in the walls of the test section. It has the advantage of being able to examine a large volume of the liquid if necessary. The system, previously tested successfully using synthetic data, and in complex configuration, provides very satisfactory results when compared with a direct and simple but time consuming method such as microphotography. Both ways of measuring the bubble size distributions give very close results in terms of the bubble sizes present. Differences in the numbers of bubbles of a given size are comparable to the scatter in experimental data for each method. An additional advantage of the ABS method is its flexibility and adaptability to hardware improvements. Limitations now are due to the limitations in the frequency responses of the hydrophones and in the data acquisition rates of the PC Cards. Improvement in the existing capabilities of the industry can be rapidly implemented in the modular system. Input from users in terms of necessary improvements as well as suggestions for additional flexibility and features are responsible for many of the features presently in the system as well as for many of those planned for future development. ACKNOWLEDGMENTS The ABS Acoustic Bubble Spectrometer was initially developed under SBIR Phase I and Phase II grants from the National Science Foundation. We are most grateful to that support. Many people at DYNAFLOW contributed in several ways to further developments. Several customers have made significant and welcomed suggestions for improvement of the system. We are very grateful for their support and will always try our best to be responsive to their needs. REFERENCES 1. N. Breitz and H. Medwin, Instrumentation for in situ acoustical measurements of bubble spectra under breaking waves, J. Acoust. Soc. Am., 86, , F. MacIntyre, On reconciling optical and acoustical bubble spectra in the mixed layer, in Oceanic Whitecaps, edited by E.C. Monahan and G. Macniocaill, Reidell, New York, 75-94, D.M. Oldenziel, A new instrument in cavitation research: the cavitation susceptibility meter, J. Fluids Engr., 14, , S. Vagle and D.M. Farmer, The measurement of Bubble- Size Distributions by Acoustical Backscatter, J. Atmos. Ocean. Tech., 9, , M. L. Billet, Cavitation nuclei measurements a review, ASME Cavitation and Multiphase Flow Forum, FED-vol 3, June T. Ohern, J. Torczynski, S. Tassin, S. Ceccio, G. Chahine, R. Duraiswami, and K. Sarkar, Development of an Electrical Impedance Tomography System for an Air- Water Vertical Bubble Column, Proceedings, Forum on Measurement Techniques in Multiphase Flows, ASME IMEC&E, C.-T. Hsiao, G. Chahine & N. Gumerov, An efficient electrical impedance tomography software combining boundary element method and genetic algorithm, OptiCON'99 Optimization Software, Methods, and 8 Copyright 3 by ASME

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