Selected Basic Flows and Forces

Alexander L. Yarin; Ilia V. Roisman; Cameron Tropea

doi:10.1017/9781316556580.003

2 - Selected Basic Flows and Forces

Published online by Cambridge University Press: 13 July 2017

Alexander L. Yarin ,

Ilia V. Roisman and

Cameron Tropea

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Alexander L. Yarin: Affiliation:
University of Illinois, Chicago
Ilia V. Roisman: Affiliation:
Technische Universität, Darmstadt, Germany
Cameron Tropea: Affiliation:
Technische Universität, Darmstadt, Germany

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Summary

Penetration of solid bodies into liquids can be frequently treated in the framework of inviscid or potential flow hydrodynamics. In addition, collisions and penetration of solid bodies into solids in many cases, especially at the ordnance and ultra-ordnance velocities, can be effectively reduced to potential flows of ideal liquids possessing only inertia, since the stresses involved are significantly higher than the elastic and plastic stresses (see Section 1.1 in Chapter 1). Therefore, the present chapter is mostly devoted to several questions traditional to inviscid or potential flow hydrodynamics, which are either directly relevant in the context of collisions and penetration of solid bodies into liquids, or as simplified models useful for solid–solid collisions. Section 2.1 is devoted to the inviscid film flows on planar and curved surfaces. In the inertia-dominated regime characteristic of drop impact onto a thin liquid film on a wall, such flows give rise to kinematic discontinuities considered in Section 2.2 and associated with crown formation, which is considered in Section 6.7 in Chapter 6. The potential flow about an ovoid of Rankine discussed in Section 2.3 will be also employed in Chapter 13 in the case of projectile penetration into armor. The flow about an expanding and translating sphere outlined in Section 2.3 is also important in a purely hydrodynamic or rigid-projectile penetration context. Flows past axisymmetric bodies of revolution discussed in Section 2.4 are also important in the context of the projectile penetration. Transient motions of solid bodies in liquids inevitably involve deceleration associated with the added masses discussed in Section 2.5. A potential flow with separation about a blunt body (a plate moving normally to itself) is covered in Section 2.6 using the hodograph method of complex analysis to predict the shape drag. Friction drag associated with viscous effects is also discussed in Section 2.6. Finally, the dynamics of a rim bounding a free liquid film, for example a crown formed due to drop impact, is discussed in Section 2.7.

Type: Chapter
Information: Collision Phenomena in Liquids and Solids , pp. 44 - 84

DOI: https://doi.org/10.1017/9781316556580.003 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

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References

Ashgriz, N. and Poo, J. Y. (1990). Coalescence and separation in binary collision of liquid drops, J. Fluid Mech. 221: 183–204.Google Scholar

Bakshi, S., Roisman, I. V. and Tropea, C. (2007). Investigations on the impact of a drop onto a small spherical target, Phys. Fluids 19: 032102.Google Scholar

Bartolo, D., Josserand, C. and Bonn, D. (2005). Retraction dynamics of aqueous drops upon impact on non-wetting surfaces, J. Fluid Mech. 545: 329–338.Google Scholar

Batchelor, G. K. (2002). An Introduction to Fluid Dynamics, Cambridge University Press.

Birkhoff, G. and Zarantonello, E. (1957). Jets, Wakes, and Cavities, Academic Press, New York.

Brenn, G., Valkovska, D. and Danov, K. D. (2001). The formation of satellite droplets by unstable binary drop collisions, Phys. Fluids 13: 2463.Google Scholar

Brochard-Wyart, F. and de Gennes, P. G. (1997). Shocks in an inertial dewetting process, C. R. Acad. Sc. Paris 324-IIb: 257–260.Google Scholar

Brochard-Wyart, F., Di Meglio, J. and Quéré, D. (1987). Dewetting. growth of dry regions from a film covering a flat solid or a fiber, C. R. Acad. Sc. Paris 304-II-11: 553–558.Google Scholar

Bush, J. W. and Hasha, A. E. (2004). On the collision of laminar jets: fluid chains and fishbones, J. Fluid Mech. 511: 285–310.Google Scholar

Chien, S. F. (1994). Settling velocity of irregularly shaped particles, SPE Drill. Complet. 9: 281–289.Google Scholar

Clanet, C. and Villermaux, E. (2002). Life of a smooth liquid sheet, J. Fluid Mech. 462: 307–340.Google Scholar

Clark, C. and Dombrowski, N. (1972). On the formation of drops from the rims of fan spray sheets, J. Aerosol Sci. 3: 173–183.Google Scholar

Clift, R. and Gauvin, W. H. (1971). The motion of particles in turbulent gas streams, Brit. Chem. Eng. 16: 229.Google Scholar

Clift, R., Grace, J. and Weber, M. (1978). Bubbles, Drops, and Particles, Academic Press, New York.

Culick, F. (1960). Comments on a ruptured soap film, J. Appl. Phys. 31: 1128–1129.Google Scholar

Debrégeas, G., Martin, P. and Brochard-Wyart, F. (1995). Viscous bursting of suspended films, Phys. Rev. Lett. 75: 3886–3889.Google Scholar

Dioguardi, F. and Mele, D. (2015). A new shape dependent drag correlation formula for nonspherical rough particles. Experiments and results, Powder Technol. 277: 222–230.Google Scholar

Entov, V. M. and Yarin, A. L. (1984). The dynamics of thin liquid jets in air, J. Fluid Mech. 140: 91–111.Google Scholar

Entov, V. M., Rozhkov, A. N., Feizkhanov, U. F. and Yarin, A. L. (1986). Dynamics of liquid films. Plane films with free rims, J. Appl. Mech. Tech. Phys. 27: 41–47.Google Scholar

Feynman, R. P., Leighton, R. B. and Sands, M. (2006). The Feynman Lectures on Physics, Pearson/Addison-Wesley, San Francisco.

Ganser, G. H. (1993). A rational approach to drag prediction of spherical and nonspherical particles, Powder Technol. 77: 143–152.Google Scholar

Gurevich, M. I. (1966). The Theory of Jets in an Ideal Fluid, Pergamon Press, Oxford.

Haider, A. and Levenspiel, O. (1989). Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol. 58: 63–70.Google Scholar

Hölzer, A. and Sommerfeld, M. (2008). New simple correlation formula for the drag coefficient of non-spherical particles, Powder Technol. 184: 361–365.Google Scholar

Hsiang, L. P. and Faeth, G. M. (1992). Near-limit drop deformation and secondary breakup, Int. J. Multiph. Flow 18: 635–652.Google Scholar

Kirchhoff, G. (1897). Vorlesungen über Mechanik, Band 1 von Vorlesungen über mathematische Physik, edited by W., Wien, fourth edn, B. G. Teubner, Leipzig.

Kochin, N. E., Kibel, I. A. and Rose, N. V. (1964). Theoretical Hydrodynamics, Interscience Publishers, New York.

Krueger, B., Wirtz, S. and Scherer, V. (2015). Measurement of drag coefficients of non-spherical particles with a camera-based method, Powder Technol. 278: 157–170.Google Scholar

Lamb, H. (1959). Hydrodynamics, Cambridge University Press.

Landau, L. D. and Lifshitz, E. M. (1969). Mechanics, Pergamon Press, New York.

Landau, L. D. and Lifshitz, E. M. (1987). Fluid Mechanics, Pergamon Press, New York.

Loitsyanskii, L. G. (1966). Mechanics of Liquids and Gases, Pergamon Press, Oxford.

Loth, E. (2008). Drag of non-spherical solid particles of regular and irregular shape, Powder Technol. 182: 342–353.Google Scholar

Peregrine, D. H. (1981). The fascination of fluid mechanics, J. Fluid Mech. 106: 59–80.Google Scholar

Prandtl, L. and Tietjens, O. K. G. (1957). Applied Hydro- and Aeromechanics: Based on Lectures of L. Prandtl, Dover Publications, New York.

Roisman, I. V. (2004). Dynamics of inertia dominated binary drop collisions, Phys. Fluids 16: 3438–3449.Google Scholar

Roisman, I. V. (2010). On the instability of a free viscous rim, J. Fluid Mech. 661: 206–228.Google Scholar

Roisman, I. V., Rioboo, R. and Tropea, C. (2002). Normal impact of a liquid drop on a dry surface: model for spreading and receding, Proc. R. Soc. London Ser. A-Math. 458: 1411–1430.Google Scholar

Roisman, I. V. and Tropea, C. (2002). Impact of a drop onto a wetted wall: description of crown formation and propagation, J. Fluid Mech. 472: 373–397.Google Scholar

Roisman, I. V., Yarin, A. L. and Rubin, M. B. (1997). Oblique penetration of a rigid projectile into an elastic-plastic target, Int. J. Impact Eng. 19: 769–795.Google Scholar

Roth, C. B., Deh, B., Nickel, B. G. and Dutcher, J. R. (2005). Evidence of convective constraint release during hole growth in freely standing polystyrene films at low temperatures, Phys. Rev. E 72: 021802.Google Scholar

Rouse, H. (1964). Advanced Mechanics of Fluids, John Wiley & Sons, New York.

Rozhkov, A., Prunet-Foch, B. and Vignes-Adler, M. (2002). Impact of water drops on small targets, Phys. Fluids 14: 3485–3501.Google Scholar

Savva, N. and Bush, J. W. M. (2009). Viscous sheet retraction, J. Fluid Mech. 626: 211–240.Google Scholar

Schiller, L. and Naumann, A. (1933). Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung, Z. Ver. Dtsch. Ing. 77: 318–320.Google Scholar

Taylor, G. I. (1959). The dynamics of thin sheets of fluid II. Waves on fluid sheets, Proc. R. Soc. London Ser. A-Math. 253: 296–312.Google Scholar

Weinstock, R. (1974). Calculus of Variations, with Applications to Physics and Engineering, Dover Publications, New York.

Whitham, G. B. (1974). Linear and Nonlinear Waves, John Wiley & Sons, New York.

Yarin, A. L. (1993). Free Liquid Jets and Films: Hydrodynamics and Rheology, Longman & John Wiley & Sons, Harlow, New York.

Yarin, A. L. and Weiss, D. A. (1995). Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity, J. Fluid Mech. 283: 141–173.Google Scholar

Yarin, L. P. (2012). The Pi-Theorem: Applications to Fluid Mechanics and Heat and Mass Transfer, Springer, Heidelberg.

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