Numerical Study of Density Ratio Influence on Global Wave Shapes Before Impact

Abstract

The influence of the gas-to-liquid density ratio (DR) on the global wave shape before impact is studied through numerical simulations of the propagation of two different waves in a rectangular wave canal. Two different codes are used: the first one, named FSID, is a highly non-linear 2D bi-fluid potential code initially developed in the frame of SLOSHEL JIP (Kaminski et al. (2011)) to simulate incompressible inviscid free-surface flows without surface tension thanks to a desingularized technique and series of conformal mappings; the second one, named CADYF, is a bi-fluid high-fidelity front-tracking software developed by Ecole Polytechnique Montreal to simulate separated two-phase incompressible viscous flows with surface tension. The first studied wave leads to a flip-through impact while the second one leads to a large gas-pocket impact. Each condition is studied with water and three different gases with increasing densities corresponding to DR = 0.001, 0.003 and 0.005. The global wave shapes are compared a few tenths of second before the impact, before free surface instabilities triggered by the shearing gas flow have developed and also before any gas compressibility matters. Both codes give precisely the same global wave shapes. Whatever the condition studied, it is shown that DR has an influence on these global wave shapes. The trends observed from the simulations are the same as those described in Karimi et al. (2016) obtained from sloshing model tests with Single Impact Waves (SIW) in a 2D tank with a low filling level. A small part of the mechanical energy of the liquid is progressively given to the gas. The larger the DR, the larger this transfer of energy from the liquid to the gas. This explains an increasing delay of the wave front for increasing DRs.