American J. of Engineering and Applied Sciences 2 (2): 399-406, 2009 ISSN 1941-7020 2009 Science Publicaions Backscaered Acousic Energy by Monobubbles Experimenal Approach and Saisical Sudy of he Aenuaion 1 Ali Khelil and 2 Claude Mane 1 Deparmen of Physics, Menouri Universiy, Ain-El-Bey Road, 25000 Consanine, Algeria 2 Oceanological Cener of Marseilles, Campus of Luminy, Case 901, F13288 Marseilles, Cedex 9, France Absrac: Problem saemen: As he number of air bubbles in he sea is very high, hey are so many acousic diffusers who make illegible he recordings he purpose of which is o quanify he alive bodies. The signals backscaered by air bubbles consiue a parasie in offshore recordings and mus be eliminaed. I is planned o finalize echniques allowing he localizaion and he idenificaion of a signal backscaered by an air bubble. Once his ype of signal was localized and idenified on an offshore recording, i is easy o eliminae i. From hen, we could have recordings where he only diffusers would be alive bodies like he zooplankon. Approach: We began a work of characerizaion of signals of bubbles o discriminae beween hem and hose backscaered by alive diffusers. We realized in laboraory a bench es hen we finalized an original mehod of producion of air bubbles wih known size in a liquid medium. Five ypes of monobubbles were generaed in a waer column by a echnique using a perisalic pump. This echnique allowed obaining a coninuous waer flow carrying same-sized air bubble. The bubbles radii were calculaed from he measure of rise limi speed. The acousic responses of hese bubbles (o a frequen wide bandwidh ulrasonic wave) were sudied by saisical mehods in order o deermine he variaion of he energy backscaered by a calibraed bubble according o is deph. Resuls: Besides he producion echnique of calibraed bulles ha was finalized, we esablished ha he variaion of backscaered energy according o deph can be explained by simple exponenial models which permied o esimae he consan of absorpion. Conclusion: The coming sep will be o correc he signal of he effec of he absorpion of energy by he middle, hen o elaborae a proocol of localizaion of he signals of bubbles on recordings where muliple diffusers appear. The resuls had o be refined and adaped for in-siu applicaions. Key words: Acousics, air bubbles, absorpion, model, variance analysis INTRODUCTION Air bubbles, or more generally gas bubbles, exis in he sea ; mos of hem are siuaed jus below he free surface. Generally, small-sized ones (a few dozens microns) are invisible and hey eliminae by dissoluion [1]. The bigger ones disappear by rising up o he surface (floaabiliy) [2]. Their origin may be mechanical [3,4], biological [5] or oher [1]. The knowledge of he characerisics of gas bubbles in naural medium has become imporan abou various subjecs as oceanamosphere exchanges [3], low amosphere visibiliy, clouds developmen, surface chemisry, verical ransporaion, underwaer acousics and is miliary applicaions [6] and carbon cycle research. The sudy proposed in his aricle consiues he firs par of a research subjec developed by he eam "Acousic of Paricles in he Sea" of he "Oceanological Cener of Marseilles". As he number of air bubbles, especially hose close o he sea surface, is very high [2,7,8], hey are so many acousic diffusers who make illegible he recordings he purpose of which is o quanify he alive bodies. In his area of research, i is planned o finalize echniques allowing he localizaion and he idenificaion of a signal backscaered by an air bubble. Once his ype of signal was localized and idenified on an offshore recording, i is easy o eliminae i. From hen, we could have recordings where he only diffusers would be alive bodies like he zooplankon [5]. Because of he difficulies of offshore experimen, he choice was o begin in laboraory; hus o consruc a pilo sudy and make a diphasic environmen: Waerair bubbles. Corresponding Auhor: Ali Khelil, Dparmen of Physics, Menouri Universiy, Ain El Bey Road, 25000 Consanine, Algeria 399
For his research, air bubbles have been sudied from he surface of a waer column, ouside heir resonance domain [9,10]. However, he acousic energy backscaered by bubbles ouside resonance depends on heir immersion deph. A sudy abou he variaion of his energy according o deph allows o correc he signal from deph effec and o deermine he rue response of a bubble. A saisical sudy of he absorpion of acousic energy backscaered by calibraed Monobubbles has been sared and proposed [10,11]. In a firs par, we describe an original mehod of air bubbles producion in a waer column. Then, we evoke echniques used o record acousic answers (backscaered energy) of hese bubbles o an ulrasound wave. A las, by variance and covariance analyses [12,13], a model is proposed in order o explain energy variaion backscaered by bubbles according o heir deph. MATERIALS AND METHODS Descripion of he experimenal raining: In experimenal acousic sudies on gas bubbles in liquid medium, wo ways are possible o quanify he bubble effec on he acousic wave propagaion. The firs one uses wo ransducers, an emier and a receiver, which limis he invesigaion range o he inerval beween his wo ransducers [14]. The second way uses one ransducer as a verical sounder wih only one ransducer which works alernaively as an emier, hen a receiver [5].This las mehod has been adoped for his research because i allows o sudy also marine organisms concenraions in he deepes layers of he sea. The experimenal raining (Fig. 1) is made up of a cylindrical Plexiglas ube (waer column), a perisalic pump o draw up air and waer, a signal generaor, a broad band ransducer of 500 khz cenral frequency and a Nicole (490) numerical oscilloscope which allows o acquire signals a high speed. Bubbles producion: Waer and air are pumped simulaneously ino calibraed pipes, which provides a consan waer flow carrying air bubbles. This flow flows down owards he boom of he waer column, where hen a bubbles sring rise is obained. So, he generaed bubbles are considered o be of he same size when arriving in he waer column. To modify he bubble size, i is necessary o change he calibraed pipe ha draws up he air, each differen pipe providing differen size bubbles ype. The pump flow being slow, he number of liberaed bubbles is also very low. Bubbles rise, one by one, along an almos recilinear rajecory in he waer column. 400 Fig. 1: Diagram of he raining sysem Table 1: Some saisics on pah duraions of five ypes of monobubbles, measured a 1m disance Type 1 Type 2 Type 3 Type 4 Type5 Air condui ypeφ c (mm) 0.005 0.0075 0.010 0.020 0.030 Average moy (s) 11.64 11.12 10.26 8.77 7.12 Median m (s) 11.67 11.06 10.28 8.66 6.97 Variance σ (s) 0.97 0.12 0.07 0.56 0.32 Sandard deviaion s (s) 0.98 0.35 0.26 0.75 0.57 Deviaion from average moy (s) 0.70 0.26 0.20 0.56 0.47 Deviaion from median m (s) 0.38 0.22 0.16 0.48 0.44 Averages moy and medians m decrease linearly wih diameer of air pipe φ c. The variances σ are very differen from one o anoher. The sandard deviaion s presens no orderly relaionship wih bubble sizes Rise speed measure and average radii: The obained bubbles mus be small o be quie spherical (if i is no he case, he air pipe mus be changed, decreasing air pipe diameer φ c ). As well, he movemen mus be recilinear and unvarying (avoiding he case where bubbles could overake ohers). The disance covered by he bubbles beween wo seleced marks is imed. The lower mark mus be slighly disan from he bubble exi poin in order ha he movemen should be quie uniform (o avoid he influence of a possible iniial speed). Around hiry bubbles are imed on he chosen way (1 m) and as he bubbles are same-sized, he average rise speed is calculaed using he average ime [11,15]. This experimen is repeaed several imes o be insured ha a chosen air-pipe always give same-sized bubbles. The way ime of he bubbles and he saisical calculus are presened in Table 1. These resuls show ha: The values of variances σ are very differen from one o anoher and do no have any connecion wih he ype of he pipe. This means ha he measures are oally disinc, ha is o say ha he background noise characerisics are differen from one measure o anoher The values of average moy and he median m being pracically equal in a same serie of five ypes of measures, here is no aberran value and he errors disribuion is symmerical
Table 2: Average radii of he five ypes of produced bubbles, deduced from rise limi speed Type 1 Type 2 Type 3 Type 4 Type 5 Air condui ypeφ c(mm) 0.005 0.0075 0.010 0.020 0.030 R b (µm) 303.00 347.00 382.00 481.00 551.00 Average duraion of pah (s) 11.64 11.12 10.26 8.77 7.12 Average speed (cm sec 1 ) 8.50 9.00 9.70 11.40 14.00 Bubble radius (µm) 327.00 342.00 364.00 412.00 484.00 R b: The radius calculaed by Tae s law, a he orifice from where bubbles spring ou Average radii of bubbles are esimaed according o Tae s law (o be sure ha sizes of generaed bubbles say in he range 70-500 µm) and using resuls of Comole [16] and Peebles [17] sudies on he moion of an air bubble in a liquid. The resuls are assembled in Table 2. Acousic response: The ransducer is immersed a 20 cm deep (disance free waer surface-vibraing base of he ransducer). This deph is kep consan by waer bringing. The seing parameers of he generaor and he oscilloscope have been chosen idenical for all he recordings, in order o ge he bes relaion signal/noise. The ransducer is placed in such a way ha is axis merges wih he axis of he waer column. So he sronges signal is recorded as bubble response, since he reflecion coefficiens of he bubbles surface are maximized [18,19]. The oscilloscope allows a coninuous vision of he response of he bubbles and he background noise. Bu as bubbles are a very good acousic reflecor, he informaion coming from he bubbles can be easily discerned from he background noise [20,21]. As bubbles rise one afer anoher, he recording works only when he disance beween wo following bubbles is big enough so ha he reflecing volume can conain only one bubble. Thus each peak on he recording is compared o only one bubble response. Wih only one recording, here are several peaks, herefore several bubbles echoes. The ime beween he saring signal and one peak allows o calculae he disance z beween he bubble and he ransducer. Figure 2 and 3 show respecively a complee recording and a bubble echo example. Saisical analysis: Before developing analysis, le us give a brief reminder on acousic wave aenuaion in a liquid medium. Every poin in he acousic field receives alernaively kineic energy of moving paricles and poenial energy coming from pressure differences. The acousic wave inensiy decreases wih he ransducer-bubble disance because of he wave divergence and he aenuaion ha i ges by absorpion condiions: 401 Fig. 2: A recording example where we see a firs arch of very grea power represening he exciaion signal, hen, ohers weaker in power, represening acousic responses of bubbles Fig. 3: An example of acousic response of air bubble in he propagaion medium. The divergence in an ideal medium can be defined [20] as: I I = r 0 r 2 where, I 0 and I r are he radiaed acousic inensiies, respecively o he source and o he disance r from he source. In a real medium, he wave is aenuaed because of he fricions beween paricles and his effec, aken separaely, resuls in an exponenial decrease of he acousic inensiy wih he disance o he source. I is expressed by exp(-β r) wih a rae β depending on he acousic characerisics of he medium and on he sound wavelengh. Gahering boh effecs, his expression is defined [22,23] as: I0 I r = exp β r 2 r ( ) By analogy wih wha has jus been reminded, here is he descripion of he variaions of he energy backscaered by a bubble in our experimenal
E = α exp ( β z) (1) where, E represens he energy backscaered by a bubble siuaed a a disance z from he vibraing ransducer base α and β are wo real coefficiens. The aim is o sudy he behavior of he wo coefficiens α and β in relaion o our very special experimenal condiions: Waer column (1 m), deph of he nearby field (calculaed as 13 cm), very high work frequencies (500±200 khz). I will be paricularly useful wih hese special experimenal condiions, o calculae coefficien β represening he aenuaion by absorpion. Various calculus and analyses will be made wih help of SAS programs and in paricular is GLM procedure [24]. Preliminary analysis: The daa: To sudy he energy backscaered by bubbles, daa are aken from seveneen recordings (Table 3). They are filered in order o eliminae background noise. The filer is a pass-band (450 khz wide) and has been chosen according o he pass-band of he ransducer. The resul of his filering is saisfacory as he signals corresponding o he bubbles are no a all damaged. The inegraion of all he signals conained in each recording is performed afer recificaion of he negaive par (calculus of he norm L1). The energizing conribuions are calculaed and each one will represen a chosen bubble. They are gahered according o bubbles size and form he daa o analyze in funcion o deph. Correlaions wih size and deph: Basic saisics on energy conribuions of Monobubbles such as average, correlaion (Pearson s) beween energy and deph, are calculaed in Table 4. The average energy backscaered by a bubble increases according o is size, apar from ype 4 bubbles (R = 410 µm). The number of bubbles and heir relaively high dephs would explain his singulariy (Table 4). The correlaion coefficiens explain he link beween he variables: So, for he firs bubble group (R = 325 µm) his coefficien (-0.84) expresses ha he energy variaions are up o 84% due o deph. The negaive sign gives he direcion of he variaion and in his las case, i indicaes ha he more he deph increases, he more he energy backscaered by a bubble decreases: The smaller he bubble is, he more he energy variaions ha i sends back are conrolled by is deph. Table 3: Daa represened by recordings and echoes numbers Bubble ype 1 2 3 4 5 Bubble radius (µm) 325 345 365 410 485 Recordings number 3 4 4 4 2 Number of observed echoes (bubbles) 10 21 41 47 29 Noe: For each ype of bubbles, a definie number of recordings was used. The number of bubble echoes appearing in each recording is differen from one o anoher Table 4: Saisics on energies backscaered by bubbles of disinc sizes Bubble radius (µm) 325.00 345.00 365.00 410.00 485.00 Bubbles number 10.00 21.00 40.00 47.00 29.00 Average energy/ 0.69 0.71 0.89 0.57 0.89 bubble 10 7 (Vs) Correlaion beween -0.84-0.66-0.63-0.57-0.52 energy and deph Noe: The average value increases wih he bubble size excep in he fourh case. The correlaion coefficiens decrease (in absolue value) wih bubble size The values of correlaion coefficiens energydeph and energy-bubbles size are respecively-0.55 and-0.03 in he case where all daa are gahered wihou size disincion. The fac ha he global correlaion beween energy and size is very weak shows ha size has no go a direc relaion wih energy. The resuls gahered in Table 4 show ha size influences he shape (and/or inensiy) of he relaion beween energy and deph. Regressions on daa according o size: For each size of bubble, a regression according o an exponenial model energy-deph is performed. In pracice he regression is calculaed beween log(energy) and log(deph). This elemenary ransformaion allows o say in he domain of linear analysis. Applied o daa, regression allows an adjusmen by exponenial curves whose general expression is as relaion (1). The resuls summarized on Fig. 4 show ha apparenly he coefficiens α and β vary according o he bubbles size. Then he following quesions may be asked: Is his variaion significan? Has deph an effec on α or β? In oher words, has he model 1 a local or global validiy? Sudy of energy-deph curves: Variance and covariance analysis: The coefficiens α and β will be conneced o boh facors conrolling energy variaions: Size and deph. In order o es he effec of hese facors, analysis of variance is usually employed. For his a hird variable will be inroduced, subsiuing for deph (non qualiaive variable), ha will be called layer and which has he real significaion of a liquid layer. This new variable have four modaliies: 402
Layer A 7 cm z 15.6 cm Layer B 15.6 cm < z < 31.3 cm Layer C 31.3 cm z < 45.3 cm Layer D z 45.3 cm The number of layers is chosen in such a way ha he number of bubbles appearing in each of hem has he same magniude. In addiion, he fac ha layer A is parly siuaed in he near field ransducer is aimed o see if i will behave differenly from he ohers. Firs, he inerpreaion of he energy variaions in funcion o boh facors (size and layer) is realized by an analysis of variance according o he following no linear model [25] : E,c Emoy + E + Ec + E c + ε (2) This equaion means ha he energy E,c associaed o bubbles of size, insonified in layer C, expresses like he sum of an average erm E moy, plus a erm linked o size E, plus a erm linked o layer E c, plus a erm linked o he ineracion size-layer E *c and plus a erm represening he error ε. The resuls of his analysis show ha: erms E and E c are significan he ineracion size-layer erm is no significan: E *c = 0 Which reduces he model equaion o: E,c Emoy + E + Ec + ε (3) In conclusion, for each bubble size, he dependence beween he energy (log E) and he layer is a sep funcion. Can dependence express iself by means of a linear model? To answer his quesion, deph z is re-inroduced as a new acive variable and, hrough a covariance analysis, a mixed model [26] is esed, as follows: E,c Emoy + E + E c + β z + ε (4) βz represens here a linear effec of deph, if need be compleed by non-linear erm E c. The resuls of his las analysis show ha: Effec layer becomes non significan E c 0 Effec size remains significan β is significanly differen from zero The disappearance of effec layer shows ha he linear model is saisfacory enough o realize he par of deph. Finally, he model is reduced o: E,z Emoy + E + β z + ε (5) %, E,z becomes: If E = Emoy + E E E % + β z + ε,z Fig. 4: Adjusmen of energy-deph curves for each ype of bubbles 403 As E,z represens in fac log(e), he ransiion o exponenial gives: (,z ) = (% + β + ε) exp E exp E z If he erm error is very small (ε 0) and if exp E % = α, we obain: ( ) ( ) ( ) E, z = α exp β z (6) The heoreical model proposed a he beginning (1) is back again wih: A coefficien α which depends on bubbles size (or on experimenal condiions) A coefficien β which is consan
Fig. 5: Adjusmen of energy-deph curve for all gahered bubble As a deducion effec size represened by coefficien α is very significan and he flucuaions of coefficien β are negligible. Esimaion of absorpion coefficien: Coefficien β being consan in he five sudied cases, he daa se (wihou size disincion) is submied o a general regression, afer correcion by coefficiens α. In each daa group, E is divided by α, hen daa are gahered ogeher. An adjusmen a he sense of he leas squares gives he resuls shown on Fig. 5. The numerical values calculaed for α and β when E is expressed in 10 8 Vs and z in cm, are: α = 0.98 and β =-0.0233 The homogeneiy of he correced daa is confirmed by he fac ha α is close o uni (α 1). If E 0 is he source energy, i is for all bubbles wihou size disincion: E exp( 0.0233z) E = (7) 0 In conclusion, he energy backscaered by a bubble varies wih deph according o he model (1) where coefficien α depends on he bubble size and β is consan and linked only o he experimenal medium. RESULTS The firs resul of he saring sudy is he realizaion of he bench es. Indeed, he resemblance of he bench wih he real middle, especially he echniques of producion of calibraed bubbles in a 404 liquid middle, is so much surmouned wih difficulies. The fac ha hese bubbles appear in he column of waer, one by one (where from he naming of Monobubbles), allowed he recording of a signal resuling from a unique diffuser. Because of he differences very marked he acousic impedances beween air and waer, he air bubbles are known o be excellen diffusers of he acousic signals. Neverheless, he acousicians always sudied hem in he resonance frequency domain o obain he bes possible acousic answer. By cusom, i became a curren and usual principle when we deal as air bubbles. Our sudy, driven ouside resonance domain of air bubbles, denied his principle because he acousic answers of he obained bubbles are easily localizable on he recordings. We can even advise o sound he aquaic middles where here are many air bubbles ouside resonance o avoid sauraing he recordings. In he par dedicaed o he signal processing of bubbles, we showed ha: The non linear model o explain he variaions of he backscaered energy by an air bubble was useless; hese variaions are very described by a linear model The effec "bubble size" was conneced o coefficien α appearing in he expression of he reserved linear model he absorpion is, iself, represened by a coefficien β expressing he proporionaliy wih he deph The absorpion coefficien β was esimaed in our experimenal condiions DISCUSSION The realized bench es is funcional, even if we feigned he real condiions offshore, especially in he absence of curren and oher diffusers ha bubbles in he environmen. However, i is pracicable and easily adapable. Concerning producion of calibraed bubbles, i remains o sudy he possibiliy of generaing differen sizes bubbles, presen a he same ime in he waer column. In ha case, he finalized saisical model could allow discriminaing beween he acousic signals by he size of bubbles having backscaered hem. In his sudy, he air bubbles radii were calculaed from he ascen limi speed of bubbles. Bu, when we know ha bubbles appear in he waer column by series like rosaries, we can wonder abou he updraf of he rosary and is influence on he speed of bubbles. This
flow can hus modify bubbles speeds and consequenly induce differences beween he calculaed radii and he real radii of bubbles. For us, we hink ha his flow is very weak and ha is influence on he speed of bubbles is limied as in our case all happens on a small disance of hardly 1 m. The finalized saisical model will, on he oher hand, allow o deermine on a recording he deph of he bubble having backscaered his signal. I consiues a considerable advance in his research subjec. CONCLUSION A he end, we succeeded o build a pilo sudy which simulaes approximaely he offshore experimenal condiions: Acousic sounding of a waer column from he surface and wih a single ransducer acing simulaneously as ransmier and as recepor. On he oher par, we made an original echnique for he producion of calibraed air bubbles in a liquid environmen and we have recorded a signal backscaered by a unique bubble (Monobubbles) of known size. The firs saisical reamens allowed deermining he aenuaion of his signal in he environmen waerair bubbles. The coming sep will be o correc he signal of he effec of he absorpion of energy by he middle, hen o elaborae a proocol of localizaion of he signals of bubbles on recordings where muliple diffusers appear by heir acousic answers. REFERENCES 1. Chapelon, J.Y., P.M. Shankar and V.L. Newhouse, 1985. Ulrasonic measuremen of bubble cloud size profiles. J. Acous. Soc. Am., 78: 196-201. hp://sciaion.aip.org/geabs/servle/geabsservle?prog=normal&id=jasman00007800000100019 6000001&idype=cvips&gifs=Yes 2. Avellan, F. and A. Resh, 1982. A scaering ligh probe for he measuremen of oceanic air bubble sizes. J. Muliphase Flow, 8: 649-663. DOI: 10.1016/0301-9322(83)90114-3 3. Kozhevorikova, I. and L. Bjorno, 1993. Bubble clouds in he sea. Advanced Course on Acousical Oceanography, Iraklion, Greece. hp://www.hcmr.gr/english_sie/insiues/oceanog raphy/index.hml 4. Baldy, S., 1987. The mechanisms of generaion and scaering of bubbles resuling from he breaking of waves: Observaions, analyses and models. Thesis Universiy. Aix-Marseille II, France. 405 5. Guerin-Ancey, O. and P.M. David, 1993. Use of a mulibeam-mulifrequency sounder o sudy he disribuion of small zooplankon. Deep-Sea Res., 40: 119-128. DOI: 10.1016/0967-0637(93) 90 056-9 6. Medwin, H., 1977. Couning bubbles acousically: A review. Ulrasonics, 15: 7-13. 7. Medwin, H., 1970. In siu acousic measuremens of bubble populaions in coasal ocean waers. J. Geophys. Res., 75: 599-611. hp://www.agu.org/journals/abs/1970/jc075i003 p00599.shml 8. Wu, J., 1981 Bubble populaion and specra in near ocean summary: Review of field and measuremens. J. Geophys. Res., 86: 457-463. hp://www.agu.org/journals/abs/1981/jc086ic01 p00457. shml 9. Farmer, D.M. and D.D. Lemon, 1984. The influence of bubbles on ambien noise in he ocean a ligh wind speeds. J. Phys. Oceanograp., 14: 1762-1778. DOI: 10.1175/1520-85(1984)014<1762:TIOBOA>2.0.CO;2 10. Khelil, A., 1995. Acousics of air bubbles in a waer column. Idenificaion and Discriminaion. Thesis, Univ. Aix-Marseille2, France. hp://ca.inis.fr/?amodele=affichen&cpsid=1742 14 INIST-CNRS, Coe INIST : T 105832 11. Khelil, A., C. Mané and P. David, 1997. Saisical mehods for localisaion and discriminaion of acousical signals backscaered by air bubbles. Trai. Sign., 14: 151-159. hp://hdl.handle.ne/2042/1993 12. Azais, J.M. and J.M. Barde, 2006. The linear model by he example. Dunod Paris. hp://www.dunod.com/pages/ouvrages/ficheouvra ge.asp?id=9782100495597 13. Draper, N.R. and H. Smih, 1998. Applied Regression Analysis. New York, Wiley, ISBN: 978-0-471-17082-2, pp: 706. 14. Ye, Z. and A. Alvarez, 1998. Acousic localizaion in bubbly liquid media. Phys. Rev. Le., 80: 3503-3506. DOI: 10.1103/PhysRevLe.80.3503 15. Desch, R.M., 1991. Small air bubbles in reagen grade waer and sea waer. Rise velociies of 20 o 1000 µm diameer bubbles. J. Geophys. Res., 96: 8901-8906. hp://www.agu.org/journals/abs/1991/91jc00484.shml 16. Comole, R., 1979. On he movemen of a gaz bubble in a liquid. La Houille Blanche, 1: 31-42. hp://www.shflhb.org/index.php?opion=issues&view=all&iemi d=39&lang=fr#
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