Analysis of bubbles dynamics created by Hydrodynamic Ram in confined geometries using the RayleighePlesset equation Thomas Fourest a, b, * , Jean-Marc Laurens b , Eric Deletombe a , Jacques Dupas a , Michel Arrigoni b a ONERA e The French Aerospace Lab, F-59045 Lille, France b ENSTA Bretagne, EA 4325, Lab Brestois de M ecanique et des Syst emes, F-29806 Brest 9, France article info Article history: Received 29 January 2014 Accepted 27 May 2014 Available online 27 June 2014 Keywords: Liquid tank Hydrodynamic Ram Cavitation bubble RayleighePlesset equation Ballistic impact abstract The design of fuel tanks with respect to Hydrodynamic Ram (HRAM) pressure is a major need for Civil and Military aircraft in order to reduce their vulnerability. The present work concerns the application of the RayleighePlesset equation e classically used for bubble dynamics analysis (including underwater explosion) e to simulate a bubble created by an HRAM event induced by projectile penetration at bal- listic speed in a confined geometry filled with a liquid. Similarities in bubble behaviour between HRAM and underwater explosion situations were observed in recent high-speed tank penetration/water entry experiments. The RayleighePlesset equation is applied to two cases of impact, one in a small closed tank and one in a larger hydrodynamic pool. The initialisation of the model is based on experimental data and the conservation principle of the initial kinetic energy of the projectile. In order to study the confinement effect induced by the container on the bubble dynamics, the RayleighePlesset approach developed for an infinite domain of liquid is modified in order to take confinement effects into account. The domain is then considered as an equivalent spherical container in order to preserve the unidimensional character of the model. Finally the influence of the pressure of the gas bubble on its dynamics hence the need to model the gas in numerical simulations is discussed. This work is a first attempt to a global modelling of the bubbles created by tumbling projectiles, and their interactions with the container up to their collapse time (30 ms). © 2014 Elsevier Ltd. All rights reserved. 1. Introduction In case of the impact of high speed/high energy projectiles through liquid filled tanks, the container may suffer large hydro- dynamic loads that could possibly rupture the entire structure. This scenario is usually referred to as Hydrodynamic Ram (HRAM). The physical comprehension of the hydrodynamic effects that occur during an HRAM event is essential in the civilian domain as well as for the military aircraft design (vulnerability requirements). The physical comprehension of HRAM dynamics would in fact allow manufacturers to design better structures with respect to this particular threat. The HRAM event is generally characterized in four stages described by Ball [1]: the shock stage, the drag stage, and the cavity growth and collapse stages. These stages and their associated loads are illustrated in Fig. 1 . The first experimental observations were conducted by McMillen [2] and McMillen and Harvey [3] who studied the shock waves and drag stage produced by the penetration of small steel spheres at high speed (610 ms À1 to 1500 ms À1 ) into water using a shadowgraphy method. They were particularly interested in the liquid shock wave characteristics. They observed that the projectile was quickly slowed down by drag effects and that the shock wave velocity rapidly converged towards the speed of sound in the considered water. Using high speed cameras (1900 frames/sec), May [4] was the first author to observe the cavity motion, surface sealing and deep sealing (closure of the cavity occurring at the surface or under the surface of the liquid) phenomena induced by subsonic speed (8 ms À1 ) spheres entry into water. Shi et al. [5e9] made the same observations for supersonic speed in air (342 ms À1 ) water entry of bullets. More recently Deletombe et al. [10] presented experiments of the impact in water of non-academic projectiles (7.62 mm NATO * Corresponding author. ONERA e The French Aerospace Lab, F-59045, Lille, France. Tel.: þ33 320 496 900; fax: þ33 320 496 955. E-mail address: thomas_fourest@onera.fr (T. Fourest). Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng http://dx.doi.org/10.1016/j.ijimpeng.2014.05.008 0734-743X/© 2014 Elsevier Ltd. All rights reserved. International Journal of Impact Engineering 73 (2014) 66e74