Acoustic measurements of bubbles in the wake of ship model in tank

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1 Acoustic mesurements of bubbles in the wke of ship model in tnk A. Sutin,b, A. Benilov, H.-S. Roh nd Y.I. Nh c Stevens Institute of Technology, Cstle Point on Hudson, Hoboken, NJ 07030, USA b Artnn Lbortories, 1753 Linvle-Hrbourton, Lmbertville, NJ 08350, USA c Agency of Defense Development, P.O.Box, ChinHe, Kyung Nm, Republic of Kore 4873

2 The interest in bubble genertion by moving ships is due to the fct tht the lrge bubble wke res, which cn rech severl kilometers, cn be used for ship detection. The lbortory towing tnk experiments with selfpropelled model ship models enbled the collection of lrge dt set in controlled conditions, which cn be used for development nd vlidtion of the theory of bubbles nd turbulent ship wkes. Bubble concentrtions in vrious sptil points ws mesured by using the ttenution of the ultrsonic sweep signl in the frequency bnd from 100 to 800 khz between two coustic sensors plced t distnce 20cm. The ttenution of sound produced by bubbles ws observed for severl minutes fter model of ship pssed the point of mesurement. The ttenution ws reclculted to the bubble size distribution for bubbles from 4 to 32 microns using the theory of resonnce bubble ttenution. The dependencies of bubble concentrtion of model ship speed nd type of propeller were investigted. A theory describing the dynmics of wke turbulence bsed on the sher-free turbulent wke ws developed. The mesured reduction of bubble concentrtion s function of time ws in good greement with the developed theory. 1 Introduction Moving ships cn generte bubbles by propeller cvittion, by the breking of ship generted wves, nd by ir entrpment in the turbulent boundry lyer under the ship hull. Interest in bubbles produced by moving ships is often connected with the bubble influence on sound propgtion ner the ship. The bubble lyer cn ffect the prmeters of sound propgtion through the lyer [1-6] nd ship noise rdition [7]. The interest in bubble genertion by moving ships is lso connected with the opportunity of ship detection, since bubble wkes cn rech lengths of severl kilometres. The first detiled tests of bubble mesurements in wkes of ships nd submrines were conducted during WWII [1] using mesurements of sonr signl scttering nd ttenution. These methods re still re widely used for bubble mesurements. High frequency multibem sonrs were used for mesurements of sptil bubble distributions in wkes of ships [8,9]. The experiments demonstrted tht the length of the bubble lyer cn rech 1500m nd its depth could be up to 10m. Even if it ws known tht bubble genertion in the wke of ship is connected with turbulence generted by the ship, there is no developed theory for prediction of bubble concentrtion. Such theory could be used for estimtion of bubble concentrtion for vrious ships, propellers nd speeds. It could predict possible distnces of bubble detection. Also, temporl vrition of bubble density cn be used for ship clssifiction nd its speed estimtions. The first step in the development of this theory is to connect known theory of ship turbulent wke genertion with results of experimentl reserch. It ws shown [10] tht sher-free turbulent model is good pproch to describe the turbulent wke behind self-propelled body, or shipwke. Lter [11,12] this pproch ws extended to llow the wke turbulence prmeteriztion by chrcteristics of the wke source. There re limited field dt vilble, nd more cn be collected in controllble conditions in lbortory tnk.. The bubble mesurements using ship model in towing tnk cn be used for theory vlidtion nd for the determintion of the theoreticl model prmeters. For mesurements of bubble density in the towing tnk we pplied method bsed on the ttenution of coustic wves in wide frequency bnd ( kHz), which llows detection of bubbles with rdii 4-32 μm. This frequency rnge is wider thn ws used in previous experiments t se [13]. 2 Experimentl setup A self-propelled ship model ws used in experiments conducted t Stevens towing tnk hving length of 100m, width of 6 m nd depth of 3m.. The ship model hs length 1.60 m, mximum width 0.3 m, nd height bout 0.2 m. The model ws moved in the tnk using specil control system to set the propeller rottion so s to keep the propulsion rection on supporting strut ner zero. Different sizes nd shpes of propellers were tested. In this pper we present results for two of them: propeller #2 hs dimeter of 0.09 m, nd blde width of 0.04 m; propeller #3 hs dimeter of m nd blde width 0.025m ( see Fig.1). Fig.1 Two tested propellers (left pnel propeller #2, right pnel #3) Fig.2. Picture of wke bubbles generted by the ship model mde by n underwter cmer. For mesurements of the bubble size distribution nd the bubble density vrition in time we used the mesurements of sound ttenution t short distnce (0.2m) between 4874

3 trnsmitter nd receivers tht were plced prllel to the ship pth. The bubble-produced excess ttenution ws mesured over wide frequency bnd using n coustic rdition with liner frequency sweep (Fig. 3()). A similr technique ws described in [13] with top frequency of 100kHz. In our experiments, the signl ws received by the second sensor nd sent to n electronic processing unit. To increse the signl-to-noise rtio nd to cncel the influence of reflections, we cross-correlted the rdited nd received signls. This gives the much shorter pulse shown in Fig. 3c. Fig. 3. Time trcks of signls used for bubble density mesurements: () emitted signl; (b) recorded signl; (c) cross-correltion of emitted nd recorded signls. The cross-correltion ws used for mesurements of ttenution. This cross correltion ws filtered using bnd pss filters. In this pper, we present results of mesurements in 7 frequency bnds from 100 to 800 khz hving width of 100kHz. The ttenution of sound ws mesured by comprison of the bnd pss filtered cross-correltion of received signls in cler wter A 0 (f) with mplitude of the sme signl mesured in wter with bubbles A b (f). Attenution of the wve ws expressed in db: In the bubble wke, bubbles of vrious sizes re present. They re descried by the bubble size distribution function N(), so N()d is number of bubble in volume unit hving rdii from to +d. Different units hve been used in different ppers for bubble density descriptions. In the first detiled tests conducted by the US Nvy [1] bubble density ws presented in cm -4. In modern literture [2] bubble density is expressed in m -3 μm -1 nd n() is reported s the number of bubbles per m 3 per micron rdius increment. b c (1) For reclcultion of the sound ttenution to the bubble density we cn pply the widely used expression for sound ttenution of signl with frequency f in bubble lyer [1,2,9]. (2) In this eqution, c 0 is the speed of sound in bubble-free se wter, f is the frequency of the pplied sound field, is the bubble rdius,, f is the resonnce frequency of bubble with rdius, nd δ is the dmping prmeter, α is ttenution coefficient in nepers per meter. Eqution (2) is Fredholm integrl eqution of the first kind. An ttempt to invert this eqution to find the bubbledensity distribution, n(), from mesurements of ttenution over rnge of frequencies leds to complex system of integrl equtions, mking direct clcultions of n() imprcticl. The simplifying ssumptions presented in [1,14] gives n pproximte solution of Eq.(2) under the following ssumptions: ) The dmping bubble prmeter δ is constnt, b) only those bubbles t resonnce with the pplied sound wve. contribute significntly to ttenution, c) the bubble distribution chnges slowly bout the resonnce rdius, nd d) surfce tension is negligible. In terms of this resonnce bubble pproximtion, the bubble density is connected with the ttenution produced by resonnce bubbles by the reltionship [14]: n( ) 4.62 *10 L 12 f 3 I = (3 For bubbles ner the surfce, the resonnce frequency of bubble is connected with the bubble rdius by reltionship 3250 f = (4) where frequency is presented in khz nd bubble rdius in μm. The temporl vrition of coustic signl ttenution connected with bubble presence ws mesured t 10 points, positions of which re shown in Fig m m m Ship model z 0.1 m 0.2 m 0.35 m 0.5 m 0.6 m Fig.4. Schem of coustic sensor plcement. y 4875

4 3 Results of mesurements 3.1 Time vrition of bubble concentrtion The conducted experiments demonstrted tht fter the ship pssing, the ttenution of n coustic signl first increses nd thn rpidly decreses to reltively smll level. The first strong ttenution is probbly produced by reltively lrge bubbles tht rpidly rise to the surfce. Reltively lower longer time ttenution is probbly produced by smll bubbles. The sme ctegoriztion of the bubbles in wkes to lrge nd smll bubbles ws used to explin the field experiments described in [4]. The concentrtion of smll bubbles decys much more slowly thn the concentrtion of lrge bubbles. This is probbly due to the slow spreding nd dissolving of smll bubbles. The exmple of such ttenution vrition is shown in Figs. 5, 6 for two tests with the sme experimentl conditions. Fig.6. Time dependence of coustic wve ttenution (Fig.5) presented in log/log scle. Solid line shows theoreticl dependence α~t -2/3. From the presented results is seen tht there is the lrge vrition of the coustic ttenution for sme experimentl conditions. 3.2 Lrge bubble sptil distribution for vrious propellers nd speed For estimtion of lrge bubble sptil distributions, the mximum ttenution, which occurred short time fter ship pssing, ws presented for vrious sptil points for vrious propellers nd model speeds. Figures 7 shows the sptil distribution of mximl sound ttenution for propeller #3 nd speed model of 2.74m/s. b Attenution, db Dept h 5.08cm Dept 17.8cm Dept h 35cm Distnce from xis, m Fig.7. Dependence of mximl ttenution on distnce from xis for vrious depths for model speed 2.74 m/s, propeller #3, bnd of filtering kHz. Fig.5. Mesured vrition of sound ttenution in the frequency bnd kHz for two similr tests t depth 5.08 cm nd distnce 20cm from ship pth xis. Propeller #2, model speed 2.74m/s. Fig 5 shows the long time record where the bubbles re detected for time up to 70 sec. Fig 5b shows the initil prt of the record where lrge bubbles re detected with lifetimes of up to 15 sec. It is seen tht lrge bubbles were generted is reltively shllow subsurfce lyer nd lrge bubbles do not penetrte to the depth of 17.8 nd 35 cm Fig.8 presents dependence of mesured ttenution produced by lrge bubbles on distnce from xis. The mesurements were conducted t depth of 5.08 cm for vrious model speed nd propellers. Fig. 6. presents the time dependence of coustic ttenution mesured in these two tests in log-log scle showing tht the time dependence of ttenution produced by smll bubbles cn be interpolte by the theoreticl dependence: α~ t -2/3 ( see theoreticl prt below) 4876

5 Attenution, db Dsitnce from xis, m Prop#2, Speed 1.52 m/s Prop#2, Speed 2.13 m/s Prop#2, Speed 2.74 m/s Prop#3, Speed 1.52 m/s Prop#3, Speed 2.13 m/s Prop#3, Speed 2.74 m/s Fig.8. Mximl sound ttenution produced by lrge bubble t vrious distnces from the xis t depth 5.08 cm for vrious propellers nd speeds. Bnd of filtering kHz This does not include possible contribution of reltively lrge bubbles, which ws not investigted. Mesurements t depth 17.8 nd 35 cm did not show the presence of lrge bubbles, but smll bubbles cn penetrte to this depth due to turbulence spreding. Fig. 10 presents the time dependence of ttenution for the depth 17.8 cm under the ship pth for propeller #3 nd speed 2.13 m/s. It cn be seen tht there is similr level of ttenution for ll presented frequencies. 3.3 Smll bubble size distribution nd gs volume content Filtering in severl frequency bnds llows the estimtion of bubble size distributions. Fig. 9 shows the time dependence of ttenution mesured for the model with propeller #2 moving with speed 2.74m/s, for the point t distnce 20 cm from the xis nd depth 5.08 cm. It is seen tht for time up to 60 s the ttenution of ll bubbles is roughly the sme. This mens tht ccording the formuls (3) nd (4) bubble size distribution is proportionl to -3. Fig. 10. Acoustic ttenution temporl vrition in three frequency bnds kHz, kHz, kHz. model with propeller #3 moved with speed 2.13m/s for the mesured point under the model pth t depth 17.8 cm. It is worth mentioning tht the smll bubbles penetrte to this depth for time bout 40 s nd their estimted void frction is even higher thn in the previous cse nd reches Turbulent model nd comprison with experiment Fig. 9. Acoustic ttenution temporl vrition in three frequency bnds kHz, kHz, kHz mesured t the point t distnce 20 cm from the xis nd depth 5.08 cm. Model with propeller #2 ws moved with speed 2.74m/s Eq. (3) cn be used for estimtion of bubble density. For exmple, bubble density for time bout 40 s fter ship pssing is bout m -3 μm -1 for bubbles with rdii round 13 μm. This density is bit higher thn mbient bubble density in the ocen, which ws mesured by Medwin in Sn Diego ([2], fig.8.4.5c). In the presence of reltively strong wind, the bubble density cn by much higher ([2], fig.8.4.5]. The rough estimtion of totl gs volume (void frction) cn be mde bsed on the ssumption tht the mximl size of bubbles is bout 30 μm (resonnce bubble frequency 110kHz) nd ttenution is bout 0.5dB/m for higher frequency. In this cse the estimtion of void frction of smll bubbles gives the vlue We hve employed the turbulent-wke theory [10,11] for the dt interprettion. This model cn not be pplied to describe behviour of lrger bubbles. Therefore, we will pply it for estimtion of temporl vrition of smll bubble concentrtions. Becuse the micro-bubbles with rdii less thn 30 μm hve rising speed less thn 0.2 cm/s [8] the rte of bubble degrdtion is low enough so tht the microbubbles in the wke turbulent field cn be ssumed s pssive dmixture of the wke wter body. Hence we hve coupled the wke theory with the bubble turbulent diffusion in the wke s pssive dmixture. In this cse the totl bubble men concentrtion in wke cross-section obeys the bubble mss-conservtion lw. Tht mens tht the men bubble concentrtion decys with inverse proportionlity to the re of wke cross-section. According to the wke theory the wke rdius increses in time proportionl to t n, where the power coefficient n is in the rnge 0 < n < 0.5 [10,11]. Then the cross-section re of turbulent wkes increses in proportionlity to t 2n, nd the men bubble concentrtion decys s t -2n. As is seen from Fig. 6, the bubble concentrtion decy in time for ll collected dt cn be pproximted by function tht is proportionl to t -2/3, therefore the coefficient n=0.33. This result grees with the theoreticl prediction on limittions for the coefficient n nd known numericl vlues of n for surfce ships which re bout n = Hence, this 4877

6 result is qulittively consistent with theoreticl conclusion nd quntittively with known estimtes of this coefficient. 5 Conclusion The coustic system, bsed on sound ttenution in wide frequency bnd ( kHz) ws used for mesurements of bubble concentrtion in the wke of self-propelled ship model in the Stevens towing tnk. It ws found tht the ship model cn generte two kinds of bubbles: one kind consists of lrge bubbles tht rise rpidly to the surfce nd with lifetime tht does not exceed 15 seconds. The second kind, the smller bubbles cn be detected much longer nd their size distribution is in rnge from 4 to 32 microns. This ws estimted from the sound ttenution dt using bubble resonnce theory. In mny cses bubble size distribution ws proposition to -3. Bubbles with rdii round microns were observed for up to five minutes As observed in experiments the temporl vritions of bubble concentrtion cn be pproximted s t -2/3. This power lw is qulittively consistent with theoreticl conclusion nd quntittively with known estimtes of the model prmeters. The ttenution technique used in this work is scientific tool for mesurements of bubble concentrtions in wide rnge of bubble sizes. From the perspective of best sensitivity of bubble detection, nonliner coustic methods look preferble, s they tht cn detect even single bubbles with rdii round few microns [15,16]. Appliction of these methods cn extend the bubble wke detection time. Acknowledgments The work ws supported by Agency of Defense Development, Chinhe, Republic of Kore. References [1] Physics of Sound in the Se, 1989, Peninsul, Los Altos. Originlly issued s Summry technicl report of Division 6, NDRC, volume 8, Wshington, D.C., [2] H.Medwin. C.S.Cly. Fundmentls of cousticl ocenogrphy. Acdemic Press, [3] Stnic S., Kennedy E., Brown B., Medley D., Goodmn R., Cruthers J. Brodbnd coustic trnsmission mesurements in surfce ship wkes. IEEE Ocens p [4] Vgle, S., nd Burch, H., Acoustic mesurements of the sound speed profile in the bubbly wke formed by smll motor bot, J. Acoust. Soc. Am, 117(1), (2005) [5] Stnic S., Kennedy E., Brown B., Medley D., Goodmn R., Cruthers J. Brodbnd coustic trnsmission mesurements in surfce ship wkes. IEEE Ocens p [6] Vgle, S., nd Burch, H., Acoustic mesurements of the sound speed profile in the bubbly wke formed by smll motor bot, J. Acoust. Soc. Am, 117(1), (2005) [7] Brdley, D.L., Culver, R.L., Di, X., Bjørnø, L.Acoustic qulities of ship wkes. Act Acustic united with Acustic, 88 (5), (2002) [8] Trevorrow, M.V., Vgle, S., Frmer, D.M. Acousticl mesurements of microbubbles within ship wkes, J. Acoust. Soc. Am, 95 (4), (1994) [9] Trevorrow, M.V., Vsiliev, B., Vgle, S. Wke coustic mesurements round mneuvering ship. Cndin Acoustics - Acoustique Cndienne, 34 (3), (2006) [10] Nudscher E., Flow in the Wke of Self-Propelled Bodies nd Relted Sources of Turbulence. J. Fluid Mech., 22, ( 1), , (1965) [11] Benilov A.Y., Ship - Wke Turbulence, In: Numericl Methods in Lminr & Turbulent Flow, vol. 10, Edited by: C. Tylor nd J.Cross, Pineridge Press, Swnse, U.K., pp (1997). [12] Benilov A.Yu, G.Bng, A.Sfry, I.Tkchenko, Ship Wke Detectbility in the Ocen Turbulent Environment, 23 rd Symposium on Nvl Hydrodynmics, Vl De Reuil, Frnce, 3, , (2000). [13] E. J. Terrill nd W. K Melville. A Brodbnd coustic technique for mesuring bubble size distributions: lbortory nd shllow wter mesurements, Journl of Atmospheric nd Ocenic Technology, 17, 2, (2000) [14] Cruthers J. W., Elmore P. A., Novrini J. C. nd. Goodmn R. R,, An itertive pproch for pproximting bubble distributions from ttenution mesurements, J. Acoust. Soc. Am. 106 (1), (1999) [15] Sutin A. Nonliner coustic phenomen in subsurfce bubble lyers nd its usge for bubble mesurements. Breking wves: IUTAM Symposium. Sydney, Austrli, M.L. Bnner, R.H.J. Crimshw (eds). Springer-Verlg, Berlin Heidelberg (1992) [16] Sutin A.M., Yoon S.W., Kim E J, Didenkulov I.N. Nonliner coustic method for bubble density mesurements in wter. J. Acoust. Soc. Am., 1998, 103 (5), pp

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