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The water entry of a sphere in a jet

Published online by Cambridge University Press:  29 January 2019

Nathan B. Speirs ,
Jesse Belden ,
Zhao Pan Open the ORCID record for Zhao Pan [Opens in a new window] ,
Sean Holekamp ,
George Badlissi ,
Matthew Jones  and
Tadd T. Truscott Open the ORCID record for Tadd T. Truscott [Opens in a new window]
Nathan B. Speirs
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Jesse Belden
Affiliation:
Naval Undersea Warfare Center Division Newport, Newport, RI 02841, USA
Zhao Pan
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Sean Holekamp
Affiliation:
Naval Undersea Warfare Center Division Newport, Newport, RI 02841, USA
George Badlissi
Affiliation:
Department of Ocean Engineering, University of Rhode Island, Narragansett, RI 02882, USA
Matthew Jones
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Tadd T. Truscott*
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
*
†Email address for correspondence: [email protected]
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Abstract

The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise largely from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on a rigid sphere by placing the sphere inside a jet of water so that the jet strikes the quiescent water surface prior to entry of the sphere into the pool. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high-speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.

JFM classification

Flow Control: Drag reduction Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 956 - 968
Copyright
© 2019 Cambridge University Press 

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References

Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.10.1017/S0022112008004382Google Scholar
Baldwin, J. L.1971 Vertical water entry of cones. Tech. Rep. NOLTR 71-25. Naval Ordnance Lab White Oak MD.Google Scholar
Bodily, K. G., Carlson, S. J. & Truscott, T. T. 2014 The water entry of slender axisymmetric bodies. Phys. Fluids 26 (7), 072108.10.1063/1.4890832Google Scholar
Coleman, H. W. & Steele, W. G. 2009 Experimentation, Validation, and Uncertainty Analysis for Engineers. John Wiley and Sons.10.1002/9780470485682Google Scholar
Cook, S. S. 1928 Erosion by water-hammer. Proc. R. Soc. Lond. A 119 (783), 481–488.10.1098/rspa.1928.0107Google Scholar
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3 (3), 180–183.10.1038/nphys545Google Scholar
Faltinsen, O. M. & Zhao, R.1997 Water entry of ship sections and axisymmetric bodies. Tech. Rep. 827. High Speed Body Motion in Water.Google Scholar
Glasheen, J. W. & McMahon, T. A. 1996 Vertical water entry of disks at low Froude numbers. Phys. Fluids 8 (8), 2078–2083.10.1063/1.869010Google Scholar
Grady, R. J. 1979 Hydroballistics Design Handbook. Naval Sea Systems command Hydromechanics Committee.Google Scholar
Grumstrup, T., Keller, J. B. & Belmonte, A. 2007 Cavity ripples observed during the impact of solid objects into liquids. Phys. Rev. Lett. 99, 114502.10.1103/PhysRevLett.99.114502Google Scholar
Hicks, P. D., Ermanyuk, E. V., Gavrilov, N. V. & Purvis, R. 2012 Air trapping at impact of a rigid sphere onto a liquid. J. Fluid Mech. 695, 310–320.10.1017/jfm.2012.20Google Scholar
Hicks, P. D. & Purvis, R. 2013 Liquid–solid impacts with compressible gas cushioning. J. Fluid Mech. 735, 120–149.10.1017/jfm.2013.487Google Scholar
Korobkin, A. A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20 (1), 159–185.10.1146/annurev.fl.20.010188.001111Google Scholar
Mansoor, M. M., Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2014 Water entry without surface seal: extended cavity formation. J. Fluid Mech. 743, 295–326.10.1017/jfm.2014.35Google Scholar
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2011 Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680, 660–670.10.1017/jfm.2011.202Google Scholar
May, A.1975 Water entry and the cavity-running behavior of missiles. Tech. Rep. 72-2. Navsea Hydroballistics Advisory Committee Silver Spring MD.Google Scholar
May, A. & Woodhull, J. C. 1948 Drag coefficients of steel spheres entering water vertically. J. Appl. Phys. 19 (12), 1109–1121.10.1063/1.1715027Google Scholar
Miloh, T. 1991 On the initial-stage slamming of a rigid sphere in a vertical water entry. Appl. Ocean Res. 13 (1), 43–48.10.1016/S0141-1187(05)80039-2Google Scholar
Moghisi, M. & Squire, P. T. 1981 An experimental investigation of the initial force of impact on a sphere striking a liquid surface. J. Fluid Mech. 108, 133–146.10.1017/S0022112081002036Google Scholar
Oguz, H. N., Prosperetti, A. & Kolaini, A. R. 1995 Air entrapment by a falling water mass. J. Fluid Mech. 294, 181–207.10.1017/S0022112095002850Google Scholar
Shepard, T., Abraham, J., Schwalbach, D., Kane, S., Siglin, D. & Harrington, T. 2014 Velocity and density effect on impact force during water entry of sphere. J. Geophys. Remote Sens 3 (129), 2169–0049.Google Scholar
Shiffman, N. & Spencer, D. C.1945 The force of impact on a sphere striking a water surface. Tech. Rep. AMG-NYU-133. New York Univ NY Courant Inst of Mathematical Sciences.Google Scholar
Speirs, N. B., Mansoor, M. M., Belden, J., Hurd, R. C., Pan, Z. & Truscott, T. T. 2018a Fluted films. Phys. Rev. Fluids 3, 100504.10.1103/PhysRevFluids.3.100504Google Scholar
Speirs, N. B., Pan, Z., Belden, J. & Truscott, T. T. 2018b The water entry of multi-droplet streams and jets. J. Fluid Mech. 844, 1084–1111.10.1017/jfm.2018.204Google Scholar
Thompson, F. L.1928 Water-pressure distribution on seaplane float. Tech. Rep. 290. National Advisory Committee for Aeronautics.Google Scholar
Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139–148.10.1017/S0022112003007274Google Scholar
Truscott, T. T., Epps, B. P. & Techet, A. H. 2012 Unsteady forces on spheres during free-surface water entry. J. Fluid Mech. 704, 173–210.10.1017/jfm.2012.232Google Scholar
Tveitnes, T., Fairlie-Clarke, A. C. & Varyani, K. 2008 An experimental investigation into the constant velocity water entry of wedge-shaped sections. Ocean Engng 35 (14), 1463–1478.10.1016/j.oceaneng.2008.06.012Google Scholar
Von Karman, T.1929 The impact on seaplane floats during landing. Tech. Rep. 321. Natl. Advis. Comm. Aeronaut., Washington, DC.Google Scholar
Worthington, A. M. & Cole, R. S. 1900 Impact with a liquid surface studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 194, 175–199.10.1098/rsta.1900.0016Google Scholar
Zhao, M.-H., Chen, X.-P. & Wang, Q. 2014 Wetting failure of hydrophilic surfaces promoted by surface roughness. Sci. Rep. 4, 5376.10.1038/srep05376Google Scholar

Speirs et al. supplementary movie 1

Supplemental movie for Fig. 3a. A 50 mm diameter sphere impacts a quiescent pool surface with velocity U=4.39 m/s forming a subsurface air cavity, that experiences surface seal, deep seal and cavity shedding. Movie played back at 3% of real speed.

Download Speirs et al. supplementary movie 1(Video)
Video 2.3 MB

Speirs et al. supplementary movie 2

Supplemental movie for Fig. 3b A 50 mm diameter water jet impacts a pool surface forming a subsurface air cavity followed by a 50 mm diameter sphere that impacts the bottom of the jet cavity at velocity U=4.35 m/s without forming a cavity. Movie played back at 3% of real speed.

Download Speirs et al. supplementary movie 2(Video)
Video 3 MB

Speirs et al. supplementary movie 3

Supplemental movie for Fig. 5a A sphere impacts an initially quiescent pool at 4.23 m/s accelerating the liquid in front of it. The colouring of the images shows the vertical velocity of the fluid uy with positive defined in the upward direction as shown in the colour bar on the right. Movie played back at 0.04% of real speed.

Download Speirs et al. supplementary movie 3(Video)
Video 1 MB

Speirs et al. supplementary movie 4

Supplemental movie for Fig. 5b. A jet impacts a quiescent pool at 4.23 m/s, deforms and creates a large, local downward flow. The colouring of the images shows the vertical velocity of the fluid uy with positive defined in the upward direction as shown in the colour bar on the right. Movie played back at 0.4% of real speed.

Download Speirs et al. supplementary movie 4(Video)
Video 769.8 KB

Speirs et al. supplementary movie 5

Supplemental movie for Fig. 5c. A sphere at 4.45 m/s impacts the bottom of a cavity formed by a jet with the same impact conditions as in Movie 4. The colouring of the images shows the vertical velocity of the fluid uy with positive defined in the upward direction as shown in the colour bar on the right. Movie played back at 0.4% of real speed.

Download Speirs et al. supplementary movie 5(Video)
Video 504 KB