Experimental Investigation of Water-Entry Phenomenon

Journal of Beijing Instiute of Technology, 2010, Vol. 19, No. 2Experimental Investigation of Water-Entry PhenomenonWEI Zhuo-hui(魏卓慧)，WANG Shu-shan(王树山)，MA Feng(马峰),LU Quan-zhou(吕全洲)，ZHONG Xiao(仲霄)(State Key Laboratory of Explosion Science and Technology , Beijing Institute of Technology, Beijing 100081, China)Abstract: In order to investigate the cavity shape and velocity attenuation of steel epheres afer high-speed waterentry, the high-speed water entry of different water entry angles were perforned. The eavity shapes were recor-ded using high-speed photo recorder, and the velocities after water entry were measured. The diameters of equivalent disk of steel spheres after water entry were obtained from the processing of cavity images. Based onthe steady and uncompressing flow assumption, a theoretical model for velocity attenuation of steel spheres withcavity was proposed and caleulated resuls were in good agreement with the experinental results. The secondcavity breaking off phenomenon , which has not been reported before, was discovered. The established theoreti-cal model provides a reference for other relative researches.Key words: water entry; cavity; velocity atenuationCLC number: 0353. 4Document code: AArticle ID: 1004-0579(2010)02-0127-05W ater-entry ballstics affect on the projectile's un-the low-speed( < 60 m/s) water-entry and high. speedderwater movement directly, it is a common but com-horizontal water-entry.plex engineering and technical problem for underwaterThe water-entries of steel spheres of different entryweapon ( torpedo, depth charge, high-speed projec-angles have been carried out. Influence of water-entrytile), wound ballistics, spacecraft recovery and so on.parameters on cavity is analyzed. The second cavityWhen a steel sphere enters into water from air itbreaking off phenomenon, which has not been studiedfollows several steps: shock-wave, flow-forming, open-yet, is discussed. After fiting the cavity shape, the di-cavity, closed-cavity ，collapsing-cavity, fully wetted.ameters of equivalent disk of steel spheres after waterThe cavity varies with the water entry parameters andentry are calculated. Based on the steady and uncom-condition. The investigation for water-entry phenome-pressing flow assumption, a theoretical model for veloc-non has a history of more than 70 years. Early inty attenuation of steel spheres with cavity is proposed，1940s, David CGilbarg" discussed the efct of atmos-calculated results are in good agreement with the exper-pheric pressure on water-entry phenomenon. At theimental results.same time, Albert May'2) studied the drag cofficients1 Experimental Equipmentsof steel spheres entering water vertically. In 1970Abelson') studied the cavity pressure after water. en-The experimental equipments are shown in Fig. 1.try. In 2000 M. Leel4J calculated the cavity dynamicsSteel spheres(8 mm, 2.1 g) are fired from a pipeof high-speed water entry. Gu Jiannong') studied thelauncher. The steel sphere enters into a 100 cm xpenetration law for a rotating pellet entering water.70cmx 100 cm water tank made from 10mm thickChen Xianful°o] described the cavity after horizontal wa-glass, and the water depth in the tank is 80 cm. Theter-entry. The above researches are mainly focused on experimental images are recorded by high-speed videoRecelved 2009-03-16中国煤化工Sponsored by State Key Laboratory of Explosion Science and Technology FoundatiBiographies WEI Zhuo-hui( 1983 - ), doctoral student, weizhuohui36@ bit. eduMYHC N M H Gor, detorl dvieer.一127一Joumal of Beijing Insiule of Technology, 2010, Vol. 19, No.2camera with the frequency of 1 500s-' and 2 000 s-' .atmospheric pressure represented by Bernoulli's equa-In order to get clear images , the light is fixed above thetion, the effect of the decreased pressure and the watertank. The velocities of vertical entry and oblique entrysurface tension cause the surface closure. The timeare about 100 m/s.when surface closure happens is 1.8 ms. The steelsphere moves downwards with the closed cavity， thelightd steel spherecavity becomes longer and lomger. But the hydrostatichigh-ped digitalpressure inereases with depth; the steel sphere slowsvide rcurerdown and gives less transverse velocity to the waterater tankwith the depth increasing; and the pressure reduceswithin the cavity. In Fig. 2 it can be seen that the cavi-romputerty becomes longer and thinner, narrows at a point, at .Fig.1 Experimental equipmentslast the deep closure happens at 6.4 ms. After deep2 Experimental Results and Analysisclosure the steel sphere continues to move downwards ,the effect of the hydrostatic pressure and the water flow2.1 Water-Entry Phenomenonnear the cavity make the cavity break off, the time ofThe water-entry phenomenon is recorded. Thecavity breaking off is 7.8 m8.effect of water entry conditions towards cavity is ana-2. 1.2 Second Cavity Breaking offlyzed. The second cavity breaking off is discussed ，At 6. 47ms the first cavity breaking off happens.which has not been studied before.From experiment it can be seen that at 9. 13 ms the2.1.1 Evolvement of Cavitysecond cavity breaking off happens. After the frstThe cavities after water entry at different times arebreaking off, the steel sphere's velocity is so big , aboutshown in Fig. 2. First, the steel sphere impacts the wa-20 m/s, that the water gets enough transverse velocityter, which cause the water around the entry point getsto conquer the hydrostatic pressure and the water sur-transverse velocity. As the steel sphere travels down-face tension, and thus a small cavity appeared. Thuwards, a cavity generates which is open to the atmos-the second and third breaking off happen until the steelphere. When the steel sphere travels further down-sphere is fully wetted. When the cavity collapses, awards, the cavity becomes longer'l. The width of thecloud of small bubbles forms at the rear of the cavity ，cavity is decided by the energy that the water get, thusin the experiments the bubble pulse can be seen.is dependent on the diameter and velocity of the2.1.3 Deep Closuresphere. The pressure in the cavity is smaller than theTab. 1 are the deep closures for different water en-中国煤化工(向)0.47 ms(b)2.47 ms(e)4.47 ms .(d) 6.47 ms) 13.13 msFig.2 Water enty cavie of dMYHCNMHG一128--WEI Zhuo-hui(魏卓慧) et al. / Experimental Invesigatin of Water Eniry Phenomenontry parameters. The velocity is measured using a high-the later deep closure happens. The deep closure isspeed video camera, the error of velocity is土1 m/s.dependent on surface closure. With surface closureIn Tab.1 it can be seen that at the same water entrythe further passage of air into the cavity ceases, so thatveloeity, the smaller the entry angle, the later deepthe normal continued expansion of the cavity is inhibi-closure happens. When the deep closure happens theted by the resulting under pressure in the cavity. Thevelocities of the sphere are almost the same; at theresult is earlier deep closure.same water entry angle, the larger the entry velocity ,Tab.1 Deep closure of different water entry conditionswater entrywater entry velocity/time of surfacetime of deepenlry depth at veloeity at deep closure/angle/ (°)(m.s"')closure/ msclosure/ mdeep closure/ mm(m.s-')89109.82.06.533022.0113.16.934628.235105.46.433628. 30110.52. 58.529922. 891.72.511. 0270110. 013. 021.92.1.4 Cavity Breaking offIn Fig. 3 the cavity breaking off at dfferent waterentry parameters is shown. The water entry parametersare: (a) water entry angle 0 =60°, water entry veloci-ty o=110.5m/s; (b) θ=85°, 0=105.4 m/s; (c)θ=86°, r=113. 1 m/s. From the experimental resultsit can be seen that when the cavity breaks off, the en-try depths of the steel spheres are almost the same ,35.5 cm. It can be concluded that at the same waterentry velocity, the time of cavity breaking off is essen-tially dependent on the hydrostatic pressure, with theentry depth increases the hydrostatic pressure resear-(0)0-60*(2)0-850(2)0-86°ches critical number, the cavity breaks off. From ex-Fig.3 Carity breaking ofperimental results it can be seen that the cavity-runningsteel sphere's trajectory is straight until the cavitybreaking off happens. This is because the breaking offis not symmetrical which cause the force imbalance.2.2 Shape Fitting of Open CavityThe cavity-running drag of steel sphere is mainly apressure drag, which is directly dependent on the posi-tion of cavity separation. In the experimental images，the position of cavity separation is unclear. The cavityimage processing program was compiled, and the cavity中国煤化工shapes were obtained, shown in Fig. 4. Based on theYHCNMHGrg.4 Upen eavity aer waler entryapproximation of ideal cavity, the positions of cavity一129一Journal of Beijing Institue of Technology, 2010, Vol. 19, No.2separation were calculated.assumption that at every time step the steel sphere isThe water entry open cavity can be considered un-resting and the water velocity is equal to the actual ve-der three simplifying assumptions: constant speed ，locity of steel sphere，the Bernolli's equation is satis-cavity pressure equal to the ambient pressure, and thefied10].absence of gravity. An approximation to the universalP. +1pv. =p+2p'.(2)form of the ideal cavity equation'9) was found experi-mentally to beThe flow around the steel sphere can be seen inFig.6. P. is the water pressure far from the cavity.0. 583和= (毒)(1)Regardless of hydrostatic pressure, the water pressurewhere Cg is the drag cofficient, it can be known thatP。is equal to the atmosphere pressure. v. is the ve-C。=0. 3 from experience, d is the diameter of equiva-locity of incoming flow，which is equal to the velocitylent disk. After cavity closed, the cavity nearby steelof steel sphere at every time step. A is the position ofsphere is caused by the energy that the around waterthe cavity separation, d is the diameter of equivalentget. The cavity shape of this part can be substituted bydisk. B is the point which is contact with water in ver-Eq. (1). First ftting the cavity shape, then the diam-tical plane. The velocity of point B 0, =v. sin 0k, ap-eter of equivalent disk at the cavity separation positionproximately，where k is the correction coefficientcan be calculated by comparing the ftting shape with(k>1). Here h = 1.5. Based on the Bernoulli'sEq. (1). The diameters of equivalent disk of differentequation, the pressure at point Bwater entry angles are shown in Fig.5. It can be seenP。=P. +-po2. --p(v。sin k)'.that the diameters of equivalent disk became biggerwith time, which is smaller than the diameter of steelIntegrating on the whole welting part, the pressure dragsphere. It can be concluded that the cavity separatescan be obtainedfrom steel sphere at the front of the sphere equator.F。=”2πx(P. +pr。-p(r. sin k,)”-The larger the velocity , the detachment point is closerto the top point.Po)dx= f。2ux(P. +2po2. -6.5甘85Swater entry部(0。制)“-P。)dx. . (3).0+ 58 water entry士47°water entryWith the assumption ofP. =Po, Eq. (3) be-sscomes0FR.=。2u*(令。 一起(.制))d=4.5-凯。(1-8)(4)4.0t-之3456)u/mFig.5 Diameters of equivalent diskP__B3 Velocity After Water EntryThe mass of the steel sphere and the entry depthare small, the effect of gravity and hydrostatie pressure中国煤化Ipherewill be negligible. In order to get cavity-running drag,at every time step of cavity-running, the flow can beYHCN M H G, uhe deleraionsubstituted by steady and uncompressing one. On thefrom the impact velocity can be described by Newton'sWEI Zhuo-hui( 魏卓慧) et al. / Experimental Investigation of Water- Entry Phenomenonsecond law.section 3, the velocities of three water entry parameterscan be calculated. Fig. 7 shows both the experimentalF=之整2(1-号5)=m凯 (5)”aresults and the theoretical results , indicating that theirUsing the diameters of equivalent disk obtained incoincidence is good.20r)0-10甘pxprimental resuts+ + experimental teults一exprnmentad reultls甘theoreical reultes一90十theoretiral rsutu80-+ treretial resultrs70-t 60-040-205十735830十25只06十→+号(间)859(1)1588() 470fig.7 Velocitie after water entry[3] Abelson H 1. Pressure measurements in the water enty4 Conclusionscavity[J].J Fluid Mech, 1970, 44: 129.From the water-entry experiments, the open-cavi-[4] Lee M, Longoria R G, Wilson D E. Cavity dynamics inhih-epeed water entry[J]. Phys Fluids, 1997, 9 (3):ty, deep closure, water jet and collapsing cavity were540 - 550.obtained. Effect of water-entry parameters on the cavity[5] Cu Jiannong. Experimental sudy on the penetration lawwas analyzed. The second cavity breaking off phenom-fora rotating pellet entering water[J]. Explosion andenon was discovered.Shock Waves, 2005, 27(4) :341 -349. ( in Chinese)A theoretical model for velocity attenuation of steel[6] Chen Xianfu. Experimental studies on the cavitation phe-spheres with cavity was set up, calculated results arenomenon a a pellet entering water[ J]. Explosion andin good agreement with the experimental one. TheShock Waves, 1985, 5(4):70 -73. (in Chinese)model provides a reference for other relative resear-[7] May Albert. W ater entry and the cavity -running behaviorches.of misils, ADAO20429[R]. [S.1.]: AD, 1975.[8] Waugh J G, Stubetad G w. Hylrobllistics modelingReferences:[M]. Beijing: National Defense Industry Pres, 1979:55 -67. (in Chinese)[1] Gilbarg David, Andersons R A. Influence of atmosphericpressure on the phenomenon accompanying the entry of[9] Xu Xuanzhi. Torpedo mechanics[ M]. Beijing: NationalDefense Industry Press, 1992 :284 - 390. ( in Chinese)spheres into water [ J]. Joumal of Applied Physics,[10] May Albert. Vertical entry of misiles into water[J].1948，19(2): 127 - 139.Joumal of Applied Physics, 1952, 23( 12): 1362 -[2] May Albert, Woodbull Jean C. Drag cofficients of steel1372. .spheres entering water vertically[J]. Jourmal of Applied(Edited by Wang Yuxia)Physics, 1948, 19(12): 1109-1121.中国煤化工MYHCNMHG-131一