On the confinement parameter in HRAM bubble Rayleigh-Plesset modelling

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. Similarities in bubble behaviour between HRAM and underwater explosion situations were observed in recent high-speed tank penetration/water entry experiments. The present work concerns the application of a confined version of the Rayleigh-Plesset equation - which is 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. This equation is applied to two cases of impact, one in a small closed tank and one in a larger pool. The initialisation of the model is based on experimental data and a conservation principle of the initial energy (of the projectile). To apply this equation a relationship between the pressure applied on the structure and the structure deformation is needed. However it can only be obtained explicitly for spherical containers. The authors discuss on the parameters needed in this equation and compare their calibrated values to theoretical ones calculated with analytical plates formulae.