Confined Rayleigh–Plesset equation for Hydrodynamic Ram analysis in thin-walled containers under ballistic impacts

• Confinement parameter added in Rayleight–Plesset equation for container effect on bubble.
• Equation applied to HRAM bubble dynamics with calibrated confinement parameter.
• Calibrated vs analytical values computed for spherical and orthorhombic containers.
• Towards predictions of container effect on bubble dynamics.

To reduce the vulnerability of both civilian and military aircraft, it is essential to take the Hydrodynamic Ram (HRAM) pressure into account when designing their fuel tanks. In particular HRAM is especially dangerous for thin walled lightweight structures that cannot be armoured due to weight penalty reasons. 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 a case of impact in a small closed tank. 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 the parameters needed in this equation and compare their calibrated values to theoretical ones calculated with analytical plates formulae.