WO2001079829A1

WO2001079829A1 - Bubble acoustics

Info

Publication number: WO2001079829A1
Application number: PCT/AU2001/000420
Authority: WO
Inventors: Richard Manasseh; John Laurence Davy; Ian Clarence Shepherd
Original assignee: Commonwealth Scientific And Industrial Research Organisation
Priority date: 2000-04-14
Filing date: 2001-04-11
Publication date: 2001-10-25
Also published as: AUPQ689900A0

Abstract

A method of investigating a characteristic of a bubble is disclosed in a fluid in which the bubble is introduced or produced. The method includes the steps of obtaining an acoustic signal from the fluid, representing an acoustic signature of the bubble, and identifying a time reference representing a beginning of the acoustic signature. The method further includes analysing a time parameter of at least one signal period associated with the acoustic signature subsequent to the time reference, and obtaining the characteristic of the bubble from the time parameter. Preferably, the time parameter is associated with the first signal period or part thereof subsequent to the time reference.

Description

BUBBLE ACOUSTICS Field of Invention

The present invention relates to bubble acoustics, and in particular concerns a method for investigating bubble characteristics in a fluid system. The invention has application in a number of industries in which gases are injected into fluids. One application is in the field of wastewater treatment systems, in which the effectiveness of the aeration processes depends on the characteristics of the bubbles introduced into the system (such as their size, shape and distribution). Other industrial fluid systems to which the present invention may be applied include metals smelting in which gases are injected; minerals processing involving aeration or flotation; food processing, in particular extrusion of highly expanded food products; biotechnology involving aeration; and medicine, in particular the detection of bubble contaminants introduced into blood during cardiopulmonary or dialysis procedures.

Background of the Invention

Measurement of bubble size distributions continues to be a problem for many systems. Moreover, in many industrial aeration systems high temperatures, pressures and the opacity of the fluids preclude any form of optical, chemical or electrical measurement, while internal techniques such as tomography cannot usefully reflect the physics of gas-liquid flow. Bubbles of gas (often air) are introduced into many industrial and environmental flows to promote some chemical or biological reaction. Aeration (or 'sparging') systems are found in the chemical, minerals-processing, biotechnology and pyrometallurgy industries, and in food, beverage and wastewater processing. Aeration is the pumping or sparging of bubbles into liquid, often with mechanical stirring to break up and distribute the bubbles. Aeration typically supplies the gas needed for a chemical reaction in a liquid, or the oxygen demanded by organisms in bio- engineering. Bubbles are also widely used in chemical and metallurgical engineering to drive recirculating and mixing flows in reactors. In some cases, mechanical stirring is too harsh for delicate crystals or biological cells, so bubbles do the job. Often, a small bubble size is ideal to maximise mass transfer, while a larger bubble size is needed to maximise recirculation and mixing. In many cases, the bubble size distribution is a vital control on the rate of gas-liquid mass transfer. In other cases, bubbles of a certain size are a nuisance that must be removed. In the environment, entrapment of bubbles of varying sizes by breaking waves is a mechanism by which oceans absorb 'greenhouse' gases.

For tests on industrial aeration equipment, standard instruments are available that measure the void fraction. A sharp-tipped probe registers a binary change in conductivity or refractive index as it pierces a bubble. Clearly, the time- averaged signal from such instruments will represent the local void fraction. However, inferring the bubble size distribution from void-fraction probes requires many problematic assumptions; not least is the assumption that the bubble is not distorted as it hits the probe.

In the laboratory, bubble sizing has generally relied on high-speed photography. More recently, holography and novel video techniques have been applied. High-speed photography requires expensive equipment and materials. For given optics, the spatial resolution of high-speed film is generally inferior to video, which is in turn inferior to 35 mm film. Moreover, visual techniques are often not suitable for a plant environment, where liquids may be opaque or visualization of the flow impossible. Even in laboratory models, the presence of particles in a bubbly flow may preclude the use of visual techniques. Significant voidage may also obscure the internal details, making visual techniques unworkable.

The production of an acoustic signal by bubbles was first studied by Minnaert, M.; "On musical air bubbles and the sound of running water". Phil. Mag. 16 1933, p. 235-248. Bubbles produce an acoustic signal owing to compression of the gas in the bubble. The compression can be caused by the recoil of the bubble neck on formation, or by deformation of the bubble during its motion, although the precise mechanism of either process is still the subject of research. It has been suggested that the sound spectrum produced by bubbles in the environment could be used to calculate the bubble size spectrum (Leighton, T.G. & Walton, A.J.; "An experimental study of the sound emitted by gas bubbles in a liquid". Eur. J. Phys. 8, 1987, p. 98-104).

Minnaert showed that under adiabatic conditions, the frequency of the acoustic signal is directly related to the bubble size according to

where / is the frequency in Hz, P_∞ is the absolute liquid pressure, γ is the ratio of specific heats for the gas, p is the liquid density and R₀ is the bubble radius.

It may at first seem surprising that surface tension is not involved, but it can be shown that this is a second-order effect (Longuet-Higgins, M.S., Kerman, B.R.,

Lunde, K.; "The release of air bubbles from an underwater nozzle", J. Fluid

Mech. 230, 1991 , p.365-390). The bubble only rises a few bubble diameters during the production of the acoustic pulse. Hence P_∞ may be considered constant to within a few tenths of a percent. If the liquid is water and is not too deep, Poo is little changed from atmospheric pressure; for diatomic gases like air, the factor in equation (1 ) multiplying the 1/P₀ is roughly 3. Hence bubbles 1 mm in radius emit a 3 kHz signal; bubbles 3 mm in radius emit a 1 kHz signal. These frequencies are generally much higher than mechanical and turbulent noises in a stirred-tank system.

The existence of an acoustic signal leads to a number of potential experimental techniques. The 'natural' acoustic emissions of a bubbly flow can be used to deduce the bubble size distribution. This could be seen as 'passive' bubble sizing. It is also possible to insonate a bubbly flow and infer the bubble sizes. This could be seen as 'active' bubble sizing and requires relatively complex, specialised equipment and sophisticated analysis. The passive acoustic signal can also be used as a trigger to enable accurate, high-resolution photography of the bubbles, providing a second check on the bubble size. However, work to date on bubble acoustics has mostly investigated the signals produced by small, single bubbles. As bubbles rise they are distorted by hydrodynamic forces. These shape distortions alter the frequency. It has been shown that the frequency may be corrected for prolate and oblate spheroidal bubbles (Strasberg, M. "The pulsation frequency of nonspherical gas bubbles in liquid". J. Acoustical Soc. of America 25(3), 1953, p. 536-537). Furthermore, the shape distortions themselves induce acoustic oscillations by nonlinear parametric resonances (Longuet-Higgins, M.S.; "Monopole emission of sound by asymmetric bubble oscillations. Part 1. Normal modes", J. Fluid Mech. 201 , 1989, p. 525-541). As the air-flow rate increases, the bubbling rate increases. The bubbling rate could be considered 'high' once bubbles begin to collide. As the bubbling rate increases, bubbles also become larger and more distorted and begin to affect each other. Under these conditions, the relationship of equation (1 ) will break down. A small-amplitude correction to the basic frequency will no longer be possible.

Several studies have been made of acoustic spectra in bubbly flows. Pandit et al. took acoustic data from a turbulent jet containing bubbles (Pandit, A.B., Varley, J., Thorpe, R.B., Davidson, J.F.; "Measurement of bubble size distribution: an acoustic technique". Chem. Eng. Sci. 47 (5), 1992, p.1079- 1089). They found that the sound-pressure power spectrum could be related directly to the bubble size distribution. The mean bubble size compared reasonably with photographic estimates. However, in estimating the bubble- size distributions, they relied on the assumption of uniform turbulence in the flow exciting bubble-acoustic oscillations. Their bubbles were in the range 0.1 to 1 mm.

Further, Hsi et al. studied sound spectra in a stirred tank (Hsi, R., Tay, M., Bukur, D., Tatterson, G.B., Morrison, G.; "Sound spectra of gas dispersion in an agitated tank". Chem. Eng. J. 31 , 1985, p. 153-161 ). They focused on lower frequencies (below 1 kHz). They associated the low-frequency sound with the formation of air cavities behind the impeller blades, flooding of the rotor with air and with large (tens of mm) bubbles. Boyd & Varley measured a wider spectrum of sounds in a stirred tank, and obtained a fair comparison between acoustic- and photographically-measured bubble-size distributions (J.W.R. Boyd and J. Varley, "Sound Measurement as a Means of Gas-Bubble Sizing in Aerated

Agitated Tanks". AIChE Journal, August 1998, Vol. 44, No.8, P1731 - 1739).

Nevertheless, they noted that further work is required on the causes of bubble sound in this system, before the technique can be universally applied.

An object of the present invention is to improve the information available from bubble acoustic sensing techniques. The invention arises out of work carried out by the inventors in investigations directed towards an understanding of bubble sounds when bubbles are continuously produced from a nozzle or from any continuous source.

Summary of Invention

According to the invention there is provided a method of investigating a characteristic of a bubble in a fluid in which said bubble is introduced or produced, including the steps of :

(a) obtaining an acoustic signal from said fluid, representing an acoustic signature of said bubble;

(b) identifying a time reference representing a beginning of said acoustic signature;

(c) analysing a time parameter of at least one signal period associated with said acoustic signature subsequent to said time reference; and

(d) obtaining the characteristic of said bubble from said time parameter.

Unlike all previous bubble acoustic techniques, which address the full frequency response of the bubble acoustic pulse signature and analyse the signature over the whole of, or at least most of, its duration, the method of the invention looks at only a brief window in the time signature. Clearly this involves the acquisition and analysis of significantly less data then would otherwise be required, but surprisingly the inventors have found that focussing the analysis on this time window can provide useful estimates of certain bubble characteristics. In effect, this windowing technique results in a signal spectrum having far more clearly defined peaks than would otherwise be available. It is suggested by the inventors that this is due to the fact that the bubble is not a linear oscillator when rapidly produced.

Importantly, the technique of the invention requires significantly less data to be captured than hitherto necessary, and far less data processing is needed to then analyse this data. This method therefore enables real-time bubble analysis to be performed at practical bubbling rates with far less processing power than conventional bubble acoustic techniques.

Preferably, no more than the first five acoustic signal periods are analysed. In a preferred embodiment, only the first acoustic signal period is analysed, the time parameter being the duration t of this period. In some practical systems eg. in which many signals are superimposed, in high temperature or in viscous liquids, the first acoustic signal period may be the only period available for analysis. The time parameter may be associated with the first zero-crossing of the acoustic signal. The beginning of said bubble acoustic pulse signature may be determined by using a triggering signal level, while may be preselected or set by the system itself.

The invention has particular application to estimation of bubble size. In one form of the invention, the bubble size is estimated from the equation:

Where only the first acoustic signal period (t) is used, then f = t

Alternatively, a Fourier transform method may be used for the analysis if the first few acoustic periods are to be considered. Other analysis techniques include wavelet transforms and Hubert transforms. In another application, the technique of the invention may be applied to estimation of void fraction.

Preferably, the technique of the invention is applied at a plurality of different locations in the fluid system to provide a representation of the distribution of the bubble characteristic.

Where the invention involves the introduction of bubbles into the fluid system, the method may include the step of controlling the introduction of bubbles dependent on the bubble characteristic estimated.

Such a feedback system can be used to adjust bubble size as required for optimal gas-liquid mass transfer, for example. In one exemplary application, to wastewater diffusers, the bubble size produced by some such diffusers is thought to increase significantly after a short period of use, reducing the oxygen transfer efficiency. This may be caused by fouling, changes in the water composition or a drop in air flow which allows some diffuser pores to become clogged.

It is to be noted that the bubble acoustic pulse signature may be produced by formation of the bubble, related to compression of the gas in the bubble caused by recoil of the bubble neck on formation. Alternatively, the bubble acoustic pulse signature may be produced during progress of the bubble once produced such as by coalescence or by breaking up, or by the impact of fluid turbulence on the bubble.

Alternatively, the bubble acoustic signature may be produced in response to an interrogation or input signal, such as an acoustic signal, intentionally applied to the fluid system. Such an "active" bubble acoustic system relies on the fact that bubbles tend to respond to the interrogation or input signal by resonating.

It is also to be noted that the bubble signatures when bubbles are produced continuously appear different to those when the bubbles vibrate in isolation. In a preferred from, the method of the present invention may be applied to a stirred tank in which bubbles are introduced.

In broad terms, the present invention may provide an acoustic technique for bubble sizing which can be applied at practical bubbling rates. Nonlinear effects during the bubble rise alter the frequency, but a spectral measure of bubble frequency can be related to the radius of the bubble just on formation, provided allowances are made for the frequency changes. As explained in detail below, the best match to a photographically-measured bubble radius is obtained when a 'frequency' based on the first period of acoustic oscillation is used. The results imply that the best technique is to capture individual bubble pulses and analyse them separately, rather than measuring overall spectra. Moreover, the first, or at most only the first few cycles of the pulses, preferably should be analysed.

As detailed further in the following description, tests conducted on a sparged stirred tank obtained a realistic distribution of mean bubble size with location in the tank. Moreover, it is also possible to obtain a reasonable distribution of average void fraction using the acoustic technique.

The bubble characteristic obtained by analysing the time parameter may be further processed using an error correction algorithm to increase the accuracy of results obtained using the present method. The inventor has found that a particularly suitable error correction algorithm involves a method including the further steps of :

(a) measuring a first and a second signal period associated with the acoustic signal subsequent to the reference;

(b) comparing the magnitude of the first and second periods; and

(c) if the magnitude of the first period is greater than the magnitude of the second period, disregarding the characteristic obtained from the time parameter.

This correction algorithm improves accuracy in determining the bubble characteristic by eliminating bubble characteristic data in situations where erroneous data is more likely to be collected. Inaccuracy may occur in situations such as where there has been an imperfect formation of the bubble or an imperfect acoustic signal due to superposition of a number of acoustic pulses.

The signal period may be measured in any suitable manner and by any suitable means. In one form the signal period may be determined by the separation between successive valleys in the acoustic signal. In another form the signal period may be determined by a zero crossing of the acoustic signal.

According to a further aspect of the invention, there is provided an apparatus for investigating a characteristic of a bubble in a fluid in which said bubble is introduced or produced, said apparatus including : means for obtaining an acoustic signal from said fluid representing an acoustic signature of said bubble; means for identifying a time reference representing a beginning of said acoustic signature; means for analysing a time parameter of at least one signal period associated with said acoustic signature subsequent to said time reference; and means for obtaining the characteristic of said bubble from said time parameter.

The time parameter may be associated with no more than the first five signal periods subsequent to the time reference. Preferably, the time parameter may be associated with the first signal period or part thereof subsequent to the time reference.

in a particularly preferred form of the present invention the characteristic may be determined at two or more locations in the fluid to provide an estimation of distribution of the obtained characteristic.

The characteristic of the bubble in the fluid may be determined in a system in which a plurality of bubbles is introduced. Where a plurality of bubbles is introduced, a preferred form the apparatus may include means for controlling introduction of the bubbles in response to the obtained characteristics. Alternatively, the apparatus may include means for controlling introduction of the bubbles in response to the estimation of distribution of the obtained characteristics.

The acoustic signature may be determined by passively monitoring the sound emitted by the bubble. The acoustic signature may also be produced in response to an interrogation signal.

The bubble characteristic may include the size of the or each bubble in the fluid. It may also include the void fraction of the or each bubble in the fluid.

In a particularly preferred form the apparatus may include an error correction means. A particularly suitable error correction means includes : means for measuring a first and a second signal period associated with the acoustic signal subsequent to the time reference; means for comparing the magnitude of the first and second periods; and means for disregarding the characteristic obtained from the time parameter when the magnitude of the first period is greater than the magnitude of the second period.

The analysing means may be provided in any suitable manner and by any suitable means. Preferably the analysing means includes a Fourier transform.

Because the method of the present invention can operate with relatively brief acoustic signatures or signal periods, the rate at which valid bubble pulses are detected can be counted. This may provide useful statistical data on the bubbles enabling vigorous comparisons to be made at different locations and times, using for example, 95% statistical confidence intervals.

Brief Description of the Drawings The invention will now be described in more detail with reference to the experimental studies carried out by the inventors. Reference is made to the accompanying figures, in which :

Figure 1 schematically illustrates the equipment set-up for continuous sparging tests;

Figure 2 shows the acoustic pulse from the formation of a single bubble;

Figure 3 shows the acoustic spectrum from the formation of single bubbles;

Figure 4 shows photographic frames illustrating the bubble formation sequence; Figure 5 is a graph representing the bubble radius versus the spectra-peak frequency for different nozzles;

Figure 6 is a graph showing the bubble radius versus the reciprocal of the first acoustic pulse period;

Figure 7 shows a comparison of the bubble radii as measured acoustically and optically;

Figure 8 represents the airflow reconstructed from measurements of bubble frequency and bubbling rate versus calibrated air flow;

Figure 9 shows the continuous spectrum from a stirred, sparged tank;

Figure 10 shows the windowed spectrum from the stirred, sparged tank; Figure 11 shows the distribution of average bubble-size in the stirred, sparged tank using an FFT method;

Figure 12 shows the distribution of average bubble-size in the stirred, sparged tank using the first period method of the invention; and

Figure 13 represents the acoustically estimated void fraction in the stirred, sparged tank.

Detailed Description of the Invention

Bubble Acoustic Calibrations

Bubble-acoustic calibrations were carried out on a single stream of continuously-sparged bubbles. Bubbles were produced from vertical-axis nozzles with internal diameters of 0.3, 0.5, 1.0, 2.0 and 4.0 mm. All nozzles were machined to maintain their internal edges as sharp as possible. This ensured a known contact radius for the forming bubble. The bubbles were produced in pressure-controlled mode with the exception of the bubbles from the smallest nozzle, which was produced in volume-controlled mode. Bubbles were produced at a depth of 0.238 ± 0.0005 m in a box 23 cm square. A schematic of the equipment set-up is shown in Figure 1. Results

A typical acoustic pulse from a single bubble is shown in Figure 2, the bubble formed from an internal-diameter 4 mm nozzle submerged in water. It was measured using an underwater hydrophone (Bruel & Kjaer type 8103) near the bubble release point. Tests determined that the presence of the hydrophone did not alter the bubble dynamics or acoustic signal. The bubbling rate was 12 Hz and the acoustic frequency about 980 Hz. The labels A-F are centred at the times corresponding to the photographic frames (a) to (f) in Figure 4. The corresponding spectrum, averaged over 30 bubbles, shows a clear peak at the bubble frequency (Figure 3). The relevant part of the spectrum (below 2500 Hz) for a single bubble is virtually identical. After passing through filters (pass band 600 Hz-3 kHz) and a variable-delay trigger, the acoustic pulse was used to fire a strobe that enabled high-resolution photographs to be taken using a 35 mm camera (Figure 4). Such photographs, which are accurately related to the phase of the acoustic pulse, were used to calibrate the frequency-derived bubble sizes.

The photographs depict the progress of a single bubble formed from the internal-diameter 4mm nozzle submerged in water. Breaking of the neck occurs at t = 0; times measured to ± 0.2 ms. a: -2.0 ms; b: -0.5 ms; c: 2.0 ms; d: 5.0 ms; e: 14.0 ms; d: 18.0 ms. The sequence is produced by the acoustic triggering technique, and hence the images are not of the same bubble. However, it can be demonstrated that bubbling is completely repeatable at this air flow rate. To be compared precisely, the frequency measurement must be made at the same time as the optical measurement. This is because the frequency alters with time owing to the nonlinear factors already mentioned. Generally, the frequency reduces with time. Hence, the frequency of the peak in a spectrum of the entire acoustic pulse, such as Figure 3, will be lower than the frequency for the first few periods of acoustic oscillation. As a result, the radius of a bubble assumed to be spherical and calculated using the spectral peak will be an overestimate of the bubble radius just after release. This effect can be seen by comparing Figures 5 and 6, in both of which R_p is the photographically- measured radius. Spectra were averaged over 30 ensembles; photographic radii are half the bubble-image's minor axis. Errors in photographic measurements range from 1 % for larger bubbles to 4% for smaller bubbles. Five different nozzle sizes are used, denoted by different symbols. In Figure 5 the frequency of the spectral peak is used to calculate the bubble radius Ro_sp via equation (1 ). In Figure 6 the 'frequency' used to calculate the bubble radius Rθ_fp is in fact the reciprocal of the period of the first acoustic oscillation. For all but the highest air flow rates measured, the bubble production and acoustic oscillation are so regular that this first period can be measured with an error less than 1 %. It can be seen that the smaller bubbles are closest to ideal; for these, nonlinear errors due to distortions are minimal.

The photographic measurements have random errors of up to 4% for smaller bubbles. Optical measurements are also subject to systematic errors of interpretation. For example, it is never certain precisely where the bubble rim is, and systematic errors arise especially for the smaller nozzle size because the image of the nozzle tip is used as the datum scaling dimension. Although the bubble is close to spherical at the instant the photograph was taken, there is still an eccentricity. Major and minor axes of the bubble were measured and the photographic radii R_p were calculated as an equivalent spherical radius using R_p = e^llid_mmor /2, (2)

where e = d_majoJd_mmor is the eccentricity and d_major and d_mιnor are the measured major and minor axis lengths. The eccentricity is at most 10% so this correction accounts for less than 3%. Optical measurements should not be regarded as the 'true' or 'datum' bubble- size; in effect, figure 6 is a comparison of two techniques for measuring bubble- size, one optical and one acoustic. As a further check, bubble-sizing software was run on digitized bubble images to provide software-estimated radius R_s, which was compared with the acoustic measurements Rθf_P. Figure 7 shows that the software and acoustic data agree well for the 4.0 and 6.0 mm nozzles, but the acoustic estimate overpredicts the software estimate (or the software underpredicts the acoustic estimate) for smaller nozzles. The difference between the nozzles is likely to be due to differing degrees of bubble distortion.

The bubble first-period 'frequency' was used to calculate the bubble volume using equation (1 ), which together with the bubbling rate can be used to reconstruct the air flow rate through the nozzle. Comparing this with the known flow rate obtained from a calibration gives a useful check of the accuracy of the acoustic technique. This is shown in Figure 8, which represents the flow through the nozzle re-constructed from measurements of bubble frequency and bubbling rate, V_b, versus calibrated air flow rate, V, for the internal-diameter 4 mm nozzle submerged in water.

The agreement on air flow rate appears better than that on bubble radius alone. This is because the air flow rate is the product of bubble volume and bubbling rate. As the air flow rate increases, the bubbling rate increases much more than bubble volume, hence errors on bubble volume become proportionately smaller. As before, the volume is calculated as 4/3πr³e, where e is the eccentricity and r is the minor-axis radius, using estimates of the bubble eccentricity gained from photographic work.

The agreement is good and linear up to a limit which corresponds to the beginning of bubble pairing. Here, the bubble just formed collides with the bubble immediately above. Under some circumstances the bubbles can coalesce, however in this experiment surface tension is sufficiently low to prevent coalescence. The implications of this work and the basis of the present invention is that, surprisingly, rather than taking overall spectra, individual bubble pulses should be stored and analysed separately. In particular, the earliest cycles of the bubble pulse will yield the most accurate data.

Tests on a stirred, sparged tank

Equipment, tests and procedure

Tests of the bubble-acoustic technique were performed on a model of an actual tank used in industry, which modelled a tank from the Becher process employed in the production of titanium dioxide. Most aeration tanks used in industry have a similar schematic form: a cylindrical tank, stirred by an impeller on the centreline and close to the bottom, and fitted with four vertical baffles to present swirling of the bulk of the flow. The tank held 20 litres of tap water, and its diameter was 290 mm. It was made of clear acrylic and was surrounded by a clear water-filled box; thus, some visualization of the flow was possible. The speed of the impeller, a Rushton turbine of diameter D = 131 mm, was held at 250 RPM. Air is sparged in below the turbine disc and hence gets distributed by the turbine's action. The principle of the Rushton turbine is the formation of low-pressure regions in the trailing vortices behind each blade. These low- pressure regions attract air into them and form cavities that shed continuous streams of bubbles.

To facilitate measurements at many points in the tank, the probe pivoted about a point movable vertically, while the tank was rotatable through 90°C about its axis. Probe and tank motion were controlled by a computer, as was data recording.

An air flow rate of Q = 1.6 litre s^"1 was used. The fluid height was 267 mm. For these parameters, the Flow number, defined as

F, = Q (3)

ND³ was 0.027, while a Froude number defined as

N²D

F. = (4) g

was 9.16. For these parameters, the bubbles form structures known as 'vortex cavities' behind each blade of the Rushton turbine.

The acoustic equipment used was similar to that shown in Figure 1.

Following on from the findings of the experimental calibration work detailed above, only the information contained in the earliest stages of each acoustic pulse was to be considered in yielding accurate information on the bubble size. Therefore, the following 'windowing' procedure was adopted:

1. The signal was observed with various trigger settings and at various probe locations. By trial and error, a trigger level was established manually, such that only pulses corresponding to clear bubble signals were captured. For most of the experiments reported here, this trigger level corresponded to a sound pressure of 186.2 Pa at the hydrophone location.

2. This trigger level was then set, together with a capture time of 15 ms, on the digital oscilloscope, which was controlled by the PC. This capture time was enough to obtain several cycles of acoustic oscillation after the initial sharp rise of the pulse, but no more. Because the actual acquisition was done by the oscilloscope, then transferred over a serial line to the PC, the minimum time t_st0re required to store one pulse was about 1.97 s, much longer than the 15 ms capture time. 3. The system was left to capture n = 100 pulses. These were stored individually, together with data on the time it took to capture each pulse.

As a test, a spectrum was obtained when the data was analysed continuously, with no reckoning if a bubble pulse was present or not. The intention was to compare this spectrum with that obtained with the triggering method. The signal was low-pass filtered at the charge amplifier with a 10 kHz cut-off and then high-pass filtered with a 500 Hz cut-off. To ensure exactly the same data were analysed by the two techniques, it was recorded on Digital Audio Tape by a DAT recorder (Sony TCD D7) which has a digitising rate of 44 kHz, and this data was played back through the two techniques. Figure 9 shows the acoustic spectrum at one point in the tank, when the data were analysed continuously. A digital oscilloscope (HP 35670A) was set to 1600 lines resolution (4096 points) and a span of 12.8 kHz, which corresponds to a sample length of 125 ms. Hence 2224 averaged samples of this data covers 278 s. These 2224 samples took 280 s; thus the data coverage was effectively continuous. Only the part of the spectrum below 3 kHz is shown in Figure 9, since there is no significant signal power about 3 kHz. Checks for liaising were performed by resampling the data at up to 104 kHz. The mean of the 2224 averaged spectra is the central curve in Figure 9; the two bounding curves represent 95% statistical confidence limits. The sharp drop-off in signal power at 500 Hz is due to the high-pass filtering applied to the signal. The signal power falls quickly until about 2 kHz and it tails off gradually above 2.5 kHz.

The spectrum obtained by the windowing technique detailed above using the same (HP 35670A) digital oscilloscope is shown in Figure 10. Here a trigger was set with a level corresponding to sound a pressure of 186.2 Pa at the hydrophone location (roughly 40% of the typical peak signal). Data were captured for 15.6 ms and zero-padded out to 125 ms. The spectra were taken at the same resolution (1600 lines) as for the continuous analysis, giving the same frequency span of 12.8 kHz. The spectra from 100 windowed samples were averaged. Figure 10 thus represents considerably less data than Figure 9 (100/2224 is less than 5%). The 95% confidence limits bounding the averaged curve are therefore broader. It is clear that the windowing technique results in a much peakier spectrum. Individual sub-peaks that may correspond to features of the bubble-size distribution are apparent. This information has been lost from the continuous spectrum, clearly demonstrating the significant advantage of the technique of the present invention.

The windowing technique focuses the analysis on the first few cycles after a peak in signal intensity. Since the loudest sounds in this system are made by bubbles, the windowing technique focuses the analysis on the first few cycles of bubble-acoustic oscillation, which as previously explained gives the best estimate of bubble-size. Clearly, however, a window selected by a signal-level trigger biases the analysis towards bubbles that are large and very close to the hydrophone, because the sound pressure falls off both with distance and bubble-size. Additionally, the technique tends to bias the analysis towards bubbles excited to a higher amplitude.

The same trigger level was used both near to and far away from the turbine. Close to the turbine-blade tips, bubbles are produced continually from the cavities behind the blades and loud bubble pulses occur virtually continuously. The trigger level setting was such that at these locations, the time spent waiting for a suitably loud bubble pulse was virtually zero. However, in regions of the tank far from the bubble-formation zones, bubble pulses loud enough to be captured were rare. In some locations the system waited half an hour to obtain 100 pulses, while close to the turbine the time to obtain 100 pulses tended to the minimum of 1.97 s.

Data recording commenced with the probe pivoted to the setting closest to the vertical and the probe at the lowest sampling point.

The probe was then progressively raised through the higher levels, waiting at each until all the required data had been obtained. After the probe recorded the upper-most position, the tank was rotated 5° and the above sequence repeated. Results - spatial distribution of bubble-sizes

Figures 11 , 12 and 13 show results of the acoustic technique in the model stirred sparged tank. The plane shown cuts a diameter through the tank intersecting a pair of baffles. The probe-traversing system described above resulted in data on a grid of 14 points across the diameter and 13 points in the vertical; and there were 7 such planes cutting progressively smaller chords of the tank, the plane shown being the one with the most data. The data have been bilinearly interpolated within the pixel corresponding to each measurement location to give a continuous effect, but no additional data smoothing or spatial filtering has been performed. The significant asymmetry is due to the presence of baffles in the tank coupled with the swirling nature of the flow. The impeller was turning clockwise, viewed from above.

Figure 11 shows the distribution of average bubble-sizes, obtained through a windowed spectrum, calculated in the same way as that of Figure 10. In fact, Figure 10 is the data from the point at the bottom row of the tank and just to the left to the white 'danger zone' surrounding the impeller in Figure 11. Figure 10, of course, shows the average of 100 windowed spectra. To get an average bubble-size at each point, the mean frequency of spectra such as that of Figure 10, were calculated from 4096-point FFTs over 125 ms, and the bubble-size calculated from this frequency simply by using equation (1 ). It would also be possible to obtain a distribution of bubble-size at each point, following a procedure such as that described by Pandit et al (1992), referenced above, but the aim here is simply to see how the bubble-size varies with location in the tank.

Figure 12 shows the distribution of average bubble-sizes calculated from the first period alone, as described in the description of the calibration work above. The general pattern is very similar; only, as expected, the bubble-sizes are somewhat smaller. The similarity of the pattern is evidence that the bubble- acoustic technique is quite robust: quite different analysis techniques will give similar results. In both Figures 1 and 12, the zone of largest bubbles is found above the impeller and a 'chimney' of large bubbles rises up the tank centre to the surface. This can be explained, given an understanding of the typical flow in such tanks. The impeller creates a toroidal vortex that sends small, newly-formed bubbles radially outwards. On reaching the wall, some bubbles are recirculated inwards and downwards. Because they are moving against their buoyancy, these bubbles are the slowest moving, and thus have the greatest opportunity to coalesce. The result is a zone of large bubbles above the impeller. These large bubbles get sucked into the impeller blades, forming the two 'legs' in the pattern (really a cone in three dimensions).

Estimate of void-fraction distribution

While the spatial distribution of bubble-size is important, it is equally important for mass-transfer applications to know the distribution of void fraction or the population density of bubbles. In general, the acoustic technique cannot directly provide this information; however, we may be able to estimate the void fraction, employing some assumptions based on the use of the windowing technique.

It can be shown that instantaneous sound pressure p(t) produced by a single bubble is given by

where the bubble is undergoing adiabatic compressions, f is the bubble's natural frequency given by equation (1 ), r is the distance from the bubble and the time-dependent factor X(t) is given by

(Pandit et al, 1992, as referenced above), where R(t) is the instantaneous value of the bubble's radius as it oscillates about its equilibrium radius R₀.

Unfortunately, we do not know what the function R_c R(t) is in general; this requires knowledge of the phenomena distorting the bubble, which may well be different for different-sized bubbles. In a generally turbulent flow where energy is present at a wide range of length scales, it may be valid to assume that R_c R(t) is the same for all bubble-sizes; this was assumed by Pandit et al (1992) for their turbulent jet. It is unlikely the same assumption can be made in all regions of the more complex stirred tank. Nevertheless, near the impeller tips, the sounds recorded are those of bubbles being formed. Bubble formation causes distortions to the bubble shape that are self-similar for bubbles 2-8 mm in diameter, so there may be some validity for the assumption of self-similar R_/R(t) in this zone.

In a system where R_c/R(t) is self-similar, the peak value of X(t) would be independent of bubble-size, so the peak value p of p(t) from equation (5) would be given by

P = kR₀- /r\ (7)

where k is a constant, since Mf ² ∞ R₀ ² from equation (1 ). When individual bubble pulses are captured with the use of a fixed trigger level (hence a fixed p, say p_trig ), a bubble of given size R₀ will be detected by the system provided its centre is within a critical radius r_c of the hydrophone, given by

r„ = R o - (8)

In other words, if we accept the assumption of self-similar bubble distortions, a bubble twice as big will be detected twice as far away from the same trigger level. Furthermore, if the windowing period is sufficiently brief, it may be possible to assume that only the actual bubble detected is within the critical radius during the windowing period. The probability that two bubbles coexist within the critical radius during the windowing period is considered negligible. Therefore, the instantaneous void fraction (during the windowing period) is given by the ratio of the bubble volume to the volume within the critical radius (plus a bubble radius),

a = R '

(9) fc +Λ

neglecting the volume occupied by the hydrophone itself. Since from equation (8) r_c °c R₀, the conclusion is that the instantaneous void fraction α is a constant. Rather than guessing the constant k, which depends on the unknown R_o/R(t), it was determined from the experiments of the calibration work detailed above for bubbles of the size range found in the stirred tank.

For present purposes, the intention is not to accurately quantify α but to use the fact that α may be considered constant to determine the relative spatial distribution of void fraction.

It should be noted in passing that for some experiments, the trigger level was set sufficiently high so that α= 0.13 or roughly 1/8; thus, r_c R₀ and the bubble had to be virtually touching the hydrophone for it to be detected. In this case any error in assuming the bubble detected is the only bubble within the critical radius is virtually eliminated. (Although to be precise when such 'close-range' measurements are being made, the volume of the hydrophone itself should be included). Hence, by estimating the 'instantaneous' void fraction in this way, it is possible to make the hydrophone function virtually as an electrical or optical void-fraction probe - without having to pierce the bubble. Of course, because the volume of the hydrophone (a cylinder about 25 mm long and 9.5 mm in diameter) is much greater than the volume of the tip of a typical void-fraction probe, the spatial resolution is much poorer, but is still good for testing most industrial systems. For most of the present experiments, α was 0.39.

To estimate the average void fraction, it remains to calculate the fraction of the total time that bubbles are present within the critical radius. Since, with the present system, a finite time is required to detect a bubble pulse, the average void fraction φ is given by

__ _a ^r ι ._, (10) total

which makes the assumption that if the time taken to collect all the pulses (t_totai) is equal to the minimum possible (nt_st0re), the average void fraction is the maximum possible. The result is shown in Figure 13, depicting spatial distribution of acoustically estimated void fraction (percent).

The distribution of estimated void fraction, despite being based on a number of assumptions, gives a result generally consistent with both visual observations and data from an electrical void-fraction probe. The highest void fraction is in the region near the impeller tips. Considering both Figures 12 and 13, it may be concluded that the tank is performing reasonably well: the region of high void fraction generally contains small bubbles.

The technique described above is of particular application in simpler bubbly flows where spatial distributions of the bubble-size and void fractions are determined at their formation points, for example for a sparging plate or diffuser.

It is to be understood that various alterations, additions and/or modifications may be made to the parts previously described without departing from the ambit of the present invention.

Claims

1. A method of investigating a characteristic of a bubble in a fluid in which said bubble is introduced or produced, including the steps of : (a) obtaining an acoustic signal from said fluid, representing an acoustic signature of said bubble;

(d) obtaining the characteristic of said bubble from said time parameter.

2. A method according to claim 1 wherein said time parameter is associated with no more than the first five signal periods subsequent to said time reference.

3. A method according to claim 1 wherein said time parameter is associated with the first signal period or part thereof subsequent to said time reference.

4. A method according to any one of the preceding claims wherein the characteristic is determined at two or more locations in said fluid to provide an estimation of distribution of the obtained characteristic.

5. A method according to any one of the preceding claims wherein a plurality of bubbles is introduced, including the step of controlling introduction of said bubbles in response to the obtained characteristics.

A method according to claim 4 wherein a plurality of bubbles is introduced, including the step of controlling introduction of said bubbles in response to said estimation of distribution of the obtained characteristics.

7. A method according to any one of the preceding claims wherein said acoustic signature is produced in response to an interrogation signal.

8. A method according to any one of the preceding claims wherein the characteristic includes size of the or each bubble in said fluid.

9. A method according to any one of claim 1 to claim 7 wherein the characteristic includes void fraction of the or each bubble in said fluid.

10. A method according to any one of the preceding claims, including the further steps of :

(a) measuring a first and a second signal period associated with said acoustic signal subsequent to said reference; (b) comparing the magnitude of the first and second periods; and

(c) if the magnitude of said first period is greater than the magnitude of the said second period, disregarding the characteristic obtained from said time parameter.

11. A method according to any one of the preceding claims wherein said analysing includes a Fourier transform.

12. A method according to any one of the preceding claims wherein said at least one signal period is determined by separation between successive valleys in said acoustic signal.

13. A method according to any one of claims 1 to 11 wherein said at least one signal period is determined by a zero crossing of said acoustic signal.

14. An apparatus for investigating a characteristic of a bubble in a fluid in which said bubble is introduced or produced, said apparatus including : (a) means for obtaining an acoustic signal from said fluid representing an acoustic signature of said bubble; (b) means for identifying a time reference representing a beginning of said acoustic signature;

(c) means for analysing a time parameter of at least one signal period associated with said acoustic signature subsequent to said time reference; and

(d) means for obtaining the characteristic of said bubble from said time parameter.

15. An apparatus according to claim 14 wherein said time parameter is associated with no more than the first five signal periods subsequent to said time reference.

16. An apparatus according to claim 14 wherein said time parameter is associated with the first signal period or part thereof subsequent to said time reference.

17. An apparatus according to any one of claims 14, 15 or 16 wherein the characteristic is determined at two or more locations in said fluid to provide an estimation of distribution of the obtained characteristic.

18. An apparatus according to any one of claims 14 to 17 wherein a plurality of bubbles is introduced, including a means for controlling introduction of said bubbles in response to the obtained characteristics.

19. An apparatus according to claim 17 wherein a plurality of bubbles is introduced, including a means for controlling introduction of said bubbles in response to said estimation of distribution of the obtained characteristics.

20. An apparatus according to any one of claims 14 to 19 wherein said acoustic signature is produced in response to an interrogation signal.

21. An apparatus according to any one of claims 14 to 20 wherein the characteristic includes size of the or each bubble in said fluid.

22. An apparatus according to any one of claims 14 to 20 wherein the characteristic includes void fraction of the or each bubble in said fluid.

23. An apparatus according to any one of claims 14 to 22 further including an error correction means.

24. An apparatus according to claim 23 wherein the error correction means includes : (a) means for measuring a first and a second signal period associated with said acoustic signal subsequent to said reference; (b) means for comparing the magnitude of the first and second periods; and (c) means for disregarding the characteπstic obtained from said time parameter when the magnitude of said first period is greater than the magnitude of said second period.

25. An apparatus according to any one of claims 14 to 24 wherein said means for analysing includes a Fourier transform.

26. An apparatus according to any one of the claims 14 to 25 wherein said at least one signal period is determined by separation between successive valleys in said acoustic signal.

27. An apparatus according to any one of the claims 14 to 25 wherein said at least one signal period is determined by a zero crossing of said acoustic signal.

28. A method of investigating a characteristic of a bubble in a fluid, substantially as herein before described with reference to the accompanying drawings.

9. An apparatus for investigating a characteristic of a bubble in a fluid, substantially as herein before described with reference to the accompanying drawings.