Analysis of bubbles dynamics created by Hydrodynamic Ram in confined geometries using the Rayleigh–Plesset equation

• Confinement effects from container added in the Rayleigh–Plesset equation.
• This equation is applied to predict the radii of two bubbles created by HRAM events.
• Towards confirmation of similarities: underwater explosions vs HRAM cavitation.
• Use of this equation to study the influence of the bubble pressure on its dynamics.

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 Rayleigh–Plesset equation – classically used for bubble dynamics analysis (including underwater explosion) – to simulate a bubble created by an HRAM event induced by projectile penetration at ballistic 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 Rayleigh–Plesset 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 Rayleigh–Plesset 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).