Hydroelastic behaviour of a conical shell impacting on a quiescent-free surface of an incompressible liquid

Abstract

Hydroelastic effects are simulated by coupling a hydrodynamic Wagner model to a linear model of elasticity for thin shells. Applications are done for a cone falling on a flat-free surface of an incompressible liquid. Both hydrodynamic and structural models are linearized on the basis of a flat disk approximation. This is justified when the deadrise angle is small. In the hydrodynamic Wagner model, the main task is to evaluate the time-varying expansion of the wetted surface. The coupling with the linear model of elasticity is achieved via a modal-based method. This means that the hydrodynamic variables must project onto the family of eigenfunctions; this is the second main difficulty of the present problem. The coupled problem is solved mainly analytically. Special attention is paid to the energy conservation law. In particular, it is shown that kinetic energy evacuated in the jet plays as significant a role in the distribution of energy as the kinetic energy transmitted to the fluid or the kinetic and potential energies of the elastic shell. The importance of elasticity is discussed by comparing the rigid and elastic behaviours for free drop tests. A parametric study shows the influence of each parameter: thickness, deadrise angle and drop height. Comparisons with available experimental pressure data show a reasonable agreement. On the basis of this work, lines of future research are outlined.