Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T17:49:27.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Pressure-impulse theory for liquid impact problems

Published online by Cambridge University Press:  26 April 2006

Mark J. Cooker  and
D. H. Peregrine
Mark J. Cooker
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK Present address: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK.
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical model is presented for the high pressures and sudden velocity changes which may occur in the impact between a region of incompressible liquid and either a solid surface or a second liquid region. The theory rests upon the well-known idea of pressure impulse, for the sudden initiation of fluid motion in incompressible fluids. We consider the impulsive pressure field which occurs when a moving fluid region collides with a fixed target, such as when an ocean wave strikes a sea wall. The boundary conditions are given for modelling liquid-solid and liquid-liquid impact problems. For a given fluid domain, and a given velocity field just before impact, the theory gives information on the peak pressure distribution, and the velocity after impact. Solutions for problems in simple domains are presented, which give insight into the peak pressures exerted by a wave breaking against a sea wall, and a wave impacting in a confined space. An example of liquid-liquid impact is also examined. Results of particular interest include a relative insensitivity to the shape of the incident wave, and an increased pressure impulse when impact occurs in a confined space. The theory predicts that energy is lost from the bulk fluid motion and we suggest that this energy can be transferred to a thin jet of liquid which is projected away from the impact region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 193 - 214
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bagnold, R. A. 1939 Interim report on wave pressure research. J. Inst. Civil Engrs 12, 201–226.Google Scholar
Batchelor, G. K. 1973 An Introduction to Fluid Dynamics. Cambridge University Press.
Blackmore, P. A. & Hewson, P. J. 1984 Experiments on full-scale wave impact pressures. Coastal Engng 8, 331–346.Google Scholar
Chan, E. S. 1994 Mechanics of deep water plunging-wave impacts on vertical structures. Coastal Engng 22, 115–133.Google Scholar
Chan, E. S. & Melville, W. K. 1988 Deep water plunging wave pressures on a vertical plane wall. Proc. R. Soc. Lond. A 417, 95–131.Google Scholar
Cointe, R. 1989 Two-dimensional water-solid impact. Trans. ASME: J. Offshore Mech. Arctic Engng 111, 109–114.Google Scholar
Cointe, R. & Armand, J.-L. 1987 Hydrodynamic impact analysis of a cylinder. Trans. ASME: J. Offshore Mech. Arctic Engng 109, 237–243.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1990a Violent water motion at breaking wave impact. Proc. 22nd Intl Conf. Coastal Engng, ASCE, Delft, pp. 164–176. (Also School of Mathematics, University of Bristol Rep. AM-90-15.)Google Scholar
Cooker, M. J. & Peregrine, D. H. 1990b A model for breaking wave impact pressures. Proc. 22nd Intl Conf. Coastal Engng, ASCE, Delft, pp. 1473–1486.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1992 Wave impact pressure and its effect upon bodies lying on the sea bed. Coastal Engng 18, 205–229.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1995 Computations of water wave impact and flip-through. In preparation.
Cumberbatch, E. 1960 The impact of a water wedge on a wall. J. Fluid Mech. 7, 353–374.Google Scholar
Denny, D. F. 1951 Further experiments on wave pressures. J. Inst. Civil Engrs 35, 330–345.Google Scholar
Füuhrböuter, A. 1986 Model and prototype tests for wave impact and run-up on a uniform 1:4 slope. Coastal Engng 10, 49–84.Google Scholar
Goda, Y. 1985 Random Seas and the Design of Maritime Structures. University of Tokyo.
Hattori, M., Arami, A. & Yui, T. 1994 Wave impact pressure on vertical walls under breaking waves. Coastal Engng 22, 79–114.Google Scholar
Howison, S. D., Ockendon, J. R. & Wilson, S. K. 1991 A note on incompressible water entry problems at small dead-rise angles. J. Fluid Mech. 222, 215–230.Google Scholar
Hwang, J.-B. G. & Hammitt, F. G. 1977 High-speed impact between curved liquid surface and rigid flat surface. Trans. ASME: J. Fluids Engng 99, 396–404.Google Scholar
Johnstone, E. A. & Mackie, A. G. 1973 The use of Lagrangian coordinates in the water entry and related problems. Proc. Camb. Phil. Soc. 74, 529–538.Google Scholar
Jolley, J. G. W. 1961 Summation of Series. Dover.
King, A. & Needham, D. J. 1994 The initial development of a jet caused by fluid, body and free surface interaction. J. Fluid Mech. 268, 89–101.Google Scholar
Kirkgöuz, M. S. 1982 Shock pressure of breaking waves on vertical walls. J. Waterways, Port Ocean Engng Div. ASCE 108, 81–95.Google Scholar
Kirkuoz, M. S. 1991 Impact pressure of breaking waves on vertical and sloping walls. Ocean Engng 18, 45–59.Google Scholar
Korobkin, A. 1992 Blunt body impact on a compressible liquid surface. J. Fluid Mech. 244, 437–453.Google Scholar
Korobkin, A. 1994a Blunt-body penetration into a slightly compressible liquid. 20th Symposium on Naval Hydrodynamics.
Korobkin, A. 1994b Some integral characteristics in the jet impact problem. J. Fluid Mech. (submitted).Google Scholar
Korobkin, A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Ann. Rev. Fluid Mech. 20, 159–185.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lesser, M. B. 1981 Analytic solutions of liquid drop impact problems. Proc. R. Soc. Lond. A 377, 289–308.Google Scholar
Lesser, M. B. & Field, J. E. 1983 The impact of compressible liquids. Ann. Rev. Fluid Mech. 15, 97–122.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th Edn, Examples xvii, prob. 44, p. 544. Macmillan.
Nagai, S. 1960 Shock pressures exerted by breaking waves on breakwaters. J. Waterways, Harbors Div. ASCE 86, 1–38.Google Scholar
Okamura, M. 1993 The impulsive pressure due to wave impact on an inclined plane wall. Fluid Dyns Res. 12, 215–228.Google Scholar
Partenscky, H. W. & Tounsi, K. 1989 Theoretical analysis of shock pressures caused by waves breaking at vertical structures. Proc. XXIII Congr. IAHR, Ottawa (ed. J. Ploeg), vol. C-113-118.
Peregrine, D. H. 1981 The fascination of fluid mechanics. J. Fluid Mech. 106, 59–80.Google Scholar
Peregrine, D. H. 1994 Pressure on breakwaters: a forward look. Intl Workshop on Wave Barriers in Deep Waters, Port and Harbour Research Institute, Japan (ed. T. Takayama), pp. 553–573.
Richert, G. 1968 Experimental investigation of shock pressures against breakwaters. Proc. 11th Conf. Coastal Engng, ASCE, pp. 954–973.Google Scholar
Roberts, A. 1987 Transient free surface flows generated by a moving vertical plate. Q. J. Mech. Appl. Maths 40, 128–158.Google Scholar
Rouville, A. De, Besson, P. & Petry, P. 1938 Etat actuel des études internationales sur les efforts dus aux lames. Ann. Ponts Chaussées 108, 5–113.Google Scholar
Savic, P. & Boult, G. T. 1957 The fluid flow associated with the impact of liquid drops with solid surfaces. Heat Transfer and Fluid Mechanics Inst., Cal. Tech., pp. 43–84.Google Scholar
Sedov, L. I. 1965 Two-Dimensional Problems in Hydrodynamics and Aerodynamics (transl. from Russian by C. Chu, H. Cohen, B. Seckler). Wiley Interscience.
Stevenson, T. 1886 Design and Construction of Harbours, 3rd edn. Black.
Topliss, M. E. 1994 Water wave impact on structures. Ph.D. dissertation, University of Bristol.
Wagner, H. 1932 Uber Stoss- und Gleitvorgange an der Oberfache. Z. Angew. Math. Mech. 12, 193–215. (English transl: Phenomena associated with impacts and sliding on liquid surfaces. NACA Translation 1366.)Google Scholar
Weggel, J. R. & Maxwell, W. H. C. 1970 Numerical model for wave pressure distributions. J. Waterways Harbours, Coastal Engng Div. ASCE 96, 623–642.Google Scholar
Wijngaarden, L. Van 1980 Sound and shock waves in bubble liquids. Cavitation and Inhomogeneities in Underwater Acoustics (ed. W. Lauterborn), pp. 127–140. Springer.
Witte, H.-H. 1988 Druckschlagbelastung durch Wellen in deterministischer under stochastischer Betrachtung. Mitteilungen, Leichtweiss Inst. für Wasserbau, Tech. University Braunschweig, vol. 102, pp. 1–227.
Worthington, A. M. 1908 A Study of Splashes. Longmans Green & Co. (see also 1963 reprint, Macmillan).
Zhang, S., Duncan, J. H. & Chahine, G. L. 1993 The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech. 257, 147–181.Google Scholar