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Trapping of air in impact between a body and shallow water

Published online by Cambridge University Press:  25 September 2008

A. A. KOROBKIN ,
A. S. ELLIS  and
F. T. SMITH
A. A. KOROBKIN
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia
A. S. ELLIS
Affiliation:
Dept. of Mathematics, UCL, Gower Street, London WC1E 6BT, UK.
F. T. SMITH
Affiliation:
Dept. of Mathematics, UCL, Gower Street, London WC1E 6BT, UK.
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Abstract

Near-impact behaviour is investigated for a solid body approaching another solid body with two immiscible incompressible viscous fluids occupying the gap in between. The fluids have viscosity and density ratios which are extreme, the most notable combination being water and air, such that either or both of the bodies are covered by a thin film of water. Air–water interaction and the commonly observed phenomenon of air trapping are of concern in the presence of the two or three thin layers and one or two interfaces. The subcritical regime is of most practical significance here and it leads physically to the effect of inviscid water dynamics coupling with a viscous-dominated air response locally. This physical mechanism induces touchdown (or an approach to touchdown), which is found to occur in the sense that the scaled air-gap thickness shrinks towards zero within a finite scaled time according to analysis performed hand in hand with computation. A global influence on the local touchdown properties is also identified. Comparisons with computations prove favourable. Air trapping is produced between two touchdown positions, at each of which there is a pressure peak; an oblique approach would not affect the finding unless the approach itself is extremely shallow. The mechanism of air–water interaction leading to air trapping is suggested as a quite wide-ranging result.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 365 - 394
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Afandizadeh Zargari, E., Jimack, P. K. & Walkley, M. A. 2007 An investigation of the film thickness calculation for elastohydrodynamic lubrication problems.In Proc. 9th Conf. on Numerical Methods for Fluid Dynamics. ICFD, Reading.Google Scholar
Brocchini, M. & Peregrine, D. H. 1996 Integral flow properties of the swash zone and averaging. J. Fluid Mech. 317, 241–273.CrossRefGoogle Scholar
Couder, Y., Fort, E., Gautier, C. H. & Boudaoud, A. 2005 a From bouncing to floating drops: Non-coalescence of drops in a fluid bath. Phys. Rev. Lett. 94, 177801.CrossRefGoogle Scholar
Couder, Y., Protiere, S., Fort, E. & Boudaoud, A. 2005 b Dynamical phenomena: Walking and orbiting droplets. Nature 437, 208.CrossRefGoogle ScholarPubMed
Gent, R. W., Dart, N. P. & Cansdale, J. T. 2000 Aircraft icing. Phil. Trans. R. Soc. Lond. A 358, 2873–2911.CrossRefGoogle Scholar
Howison, S. D., Ockendon, J. R. & Oliver, J. M. 2002 Deep- and shallow-water slamming at small and zero deadrise angles. J. Engng Maths 42, 373–388.CrossRefGoogle Scholar
Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R. & Smith, F. T. 2005 Droplet impact on a thin fluid layer. J. Fluid Mech. 542, 1–25.CrossRefGoogle Scholar
Howison, S. D., Ockendon, J. R. & Wilson, S. K. 1991 Incompressible water entry problems at small deadrise angles. J. Fluid Mech. 222, 215–230.CrossRefGoogle Scholar
Josserand, C. & Zaleski, S. 2003 Droplet splashing on a thin liquid film. Phys. Fluids 15, 1650–1657.CrossRefGoogle Scholar
Korobkin, A. A. 1996 Water impact problems in ship hydrodynamics. In Advances in Marine Hydrodynamics (ed. Ohkusu, M.), pp. 323–371. Computational Mechanics Publications, Southampton.Google Scholar
Korobkin, A. A. 1997 Asymptotic theory of liquid–solid impact. Phil. Trans. R. Soc. Lond. A 355, 507–522.CrossRefGoogle Scholar
Korobkin, A. A. 1999 Shallow water impact problems. J. Engng Maths 35, 233–250.CrossRefGoogle Scholar
Korobkin, A. A. 2006 Two-dimensional problem of the impact of a vertical wall on a layer of a partially aerated liquid. J. Appl. Mech. Tech. Phys. 47, 643–653.CrossRefGoogle Scholar
Korobkin, A. A. & Khabakhpasheva, T. I. 1997 A shallow solid body approaching the interface of two media. J. Appl. Mech. Tech. Phys. 38, 857–867.CrossRefGoogle Scholar
Korobkin, A. A. & Khabakhpasheva, T. I. 2006 Impact on the boundary of a compressible two-layer fluid. Fluid Dyn. 41, 263–277.CrossRefGoogle Scholar
Liow, J. L. 2001 Splash formation by spherical drops. J. Fluid Mech. 427, 73–105.Google Scholar
Oliver, J. M. 2002 Water entry and related problems. PhD thesis, University of Oxford.Google Scholar
Pan, K. L. & Law, C. K. 2007 Dynamics of droplet-film collision. J. Fluid Mech. 587, 1–22.CrossRefGoogle Scholar
Protiere, S., Boudaoud, A. & Couder, A. 2006 Particle-wave association on a fluid interface. J. Fluid Mech. 554, 85–108.CrossRefGoogle Scholar
Purvis, R. & Smith, F. T. 2004 a Large droplet impact on water layers. AIAA Paper 2004–0414.CrossRefGoogle Scholar
Purvis, R. & Smith, F. T. 2004 b Air–water interactions near droplet impact. Eur. J. Appl. Maths 15, 853–871.CrossRefGoogle Scholar
Purvis, R. & Smith, F. T. 2005 a Droplet impact on water layers: Post-impact analysis and computations. Phil. Trans. R. Soc. Lond. A 363, 1209–1221.Google ScholarPubMed
Purvis, R. & Smith, F. T. 2005 b Air effects on droplet impact. AIAA Paper 2005-5184.Google Scholar
Quero, M., Hammond, D. W., Purvis, R. & Smith, F. T. 2006 Analysis of super-cooled water droplet impact on a thin water layer and ice growth. AIAA Paper 2006-466.CrossRefGoogle Scholar
Smith, F. T. 1982 On the high Reynolds number theory of laminar flows. IMA J. Appl. Maths 28, 207–281.CrossRefGoogle Scholar
Smith, F. T. 1988 Finite-time break-up can occur in any unsteady interactive boundary layer. Mathematika 35, 256–273.CrossRefGoogle Scholar
Smith, F. T., Li, L. & Wu, G.-X. 2003 Air cushioning with a lubrication/inviscid balance. J. Fluid Mech. 482, 291–318.CrossRefGoogle Scholar
Sobey, I. 2000 Introduction to Interactive Boundary Layer Theory. Oxford University Press.CrossRefGoogle Scholar
Tan, C. S. & Papadakis, M. 2005 Droplet breakup, splashing and re-impingement on an iced airfoil. In 4th AIAA Theoretical Fluid Mechanics Meeting.CrossRefGoogle Scholar
Thorodssen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. 2001 Damped waves generated by a moving pressure distribution. Eur. J. Appl. Maths 12, 357–366.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Miloh, T. 1996 The influence of a layer of mud on the train of waves generated by a moving pressure distribution. J. Engng Maths 30, 387–400.CrossRefGoogle Scholar
Wilson, S. K. 1991 A mathematical model for the initial stages of fluid impact in the presence of a cushioning fluid layer. J. Engng Maths 25, 265–285.CrossRefGoogle Scholar