In the event of impacts of high speed/high energy projectiles in liquid filled tanks, the container may suffer large hydrodynamic loads that could possibly rupture the entire structure. This impact scenario is referred as Hydrodynamic Ram (HRAM) in the literature. To design an aircraft fuel tank that resists such HRAM events is a particularly difficult task due to structural optimisation constraints that already exist in aeronautics (weight, range, etc). HRAM events are generally characterized by four stages: the shock stage (Figure 1, t=0 ms), the drag stage (Figure 1, t=0.2 ms), the cavity growth and collapse stages (Figure 1, t=2.5 – 4.5 ms). The ballistic projectile first penetrates the container and creates a shock wave that propagates in the liquid. Then a cavity bubble is created in the wake of the projectile. The growth and collapse of this bubble induce large hydrodynamics loads on the container structure that are hardly measurable during complex and expensive experiments.
Figure 1 – Ballistic impact test of a 7.62 mm projectile at 790 m/s on a dummy tank.
A solution would be to use full-3D non linear numerical simulations (projectile, fluid and container) to determine the loads and/or subsequent structural damage. However such numerical simulations of the container response and failure under HRAM conditions still prove to be very challenging. The most advanced numerical simulation used for the simulation of the HRAM phenomenon are well illustrated by the work of Varas et al. [1], where the authors discus the capacity of a commercial explicit finite element code (Ls-Dyna) to simulate this phenomenon. They succeed in simulating the first stages of the phenomenon for the impact of a non deformable projectile, but they did not simulate the end of the growth stage and the following decay of the cavity created in the wake of the projectile.
Another option relies on the use of analytical models in order to estimate the hydrodynamic loads occurring during HRAM events. The present work describes such an alternative method which is here used to determine the “key parameters" that are necessary to perform physically justified full-3D numerical simulations. Hence, recent experimental results where the evolution of the bubble created in the wake of a tumbling projectile was observed (which seems to be comparable to the ones observed in other fields, e.g. underwater explosion) led to propose to use Rayleigh-Plesset like equations [2] to determine the influence of different physical phenomena (cavitation, compressibility, etc) on ballistic bubbles dynamics (and subsequent hydrodynamic loads).
This equation was applied to predict the bubble dynamics for two tests of ballistic impacts in water filled tank performed at the ONERA [3]. These first results permits to confirm that the dynamics of a cavitation bubble created by ballistic impact could be coarsely reproduced using the Rayleigh-Plesset equation. Then the classic Rayleigh-Plesset equation has been modified in particular to apply it to a finite domain of liquid and with a structural confinement (Figure 2). This formulation was used to proceed to sensibility analysis on the effect of the container stiffness, dimensions, or to the influence of the initial presence of air (in addition to the water vapour) on the dynamic of the cavity [4].
Figure 2 – Comparison of the bubble dynamics obtained experimentally (blue) and numerically using the Rayleigh-Plesset equation (red), large ones in a hydrodynamic pool and small ones in a container.
The proposed analytical model stays however limited because the geometries of the bubble and container are idealised (spherical bubble in a monolithic mono-material spherical container). So the Rayleigh-Plesset equation in its actual form needs to be calibrated to improve the correlation with experimental results available. Other analyses have been performed to determine the extent to which this calibration could be replaced by the use of analytical formulae to predict the structural response. The obtained results (see Figure 3) are promising [5].
Figure 3 – Comparison of the bubble dynamics obtained experimentally (blue) and numerically using the Rayleigh-Plesset equation using calibration (black) and analytical formulae (red) to predict the structure response.
In order to fully validate the proposed model on a spherical geometry, optical cavitations tests have being performed in a small spherical container. During these tests a laser beam is focussed in the container and creates a cavitation bubble. Tests in the container have being compared to tests performed in an “infinite” domain of liquid. The bubble dynamics is clearly affected by the confinements (see Figure 4), the same modifications of the bubble dynamics than during HRAM event is observed.
Figure 4 – Experimental bubble radius time histories for bubbles created by optic cavitation in a 120x190x380 mm3 aquarium and in a 13.1 mm internal diameter spherical container.
The exploitation of these results seems very promising and should give more insight on the interaction between the fluid and the structure.
Acknowledgement
This study has been carried out as part of the PhD thesis of the main author. The authors would like to thank the French Ministry of Defence and DGA (French Armament Procurement Directorate), for their financial support.
References
[1] D. Varas, R. Zaera, and J. López-Puente. Numerical modelling of the hydrodynamic ram phenomenon. International Journal of Impact Engineering, 36:363–374, 2009.
[2] C. Brennen, Cavitation and bubble dynamics, Oxford University Press, Oxford, United Kingdom, 1995.
[3] E. Deletombe, J. Fabis, J. Dupas, and J.M. Mortier. Experimental analysis of 7.62 mm hydrodynamic ram in containers. Journal of Fluids and Structures, 37:1–21, 2013.
[4] T. Fourest, J.M. Laurens, E. Deletombe, J. Dupas, and M. Arrigoni. Analysis of bubbles dynamics created by hydrodynamic ram in confined geometries using the rayleigh-plesset equation. International Journal of Impact Engineering, 76 :66-74, 2014.
[5] T. Fourest, J.M. Laurens, E. Deletombe, J. Dupas, and M. Arrigoni. Confined Rayleigh-Plesset equation for Hydrodynamic Ram analysis in thin-walled containers under ballistic impacts. Thin Walled Structures
