Recent experimental (Lafeber et al., 2012b) and numerical (Bredmose et al. (2008), Guilcher et al. (2012)) studies showed that the behaviour of gas pockets entrapped by a breaking wave when impacting a wall is well described by the piston model first modelized with a single Ordinary Differential Equation (ODE) by Bagnold under the assumption of a perfect gas and isentropic conditions (Bagnold, 1939).
In Bagnold's original work, the solid piston was only animated by an initial velocity. A dimensionless form of the piston dynamics was proposed. Therefore, the problem depended only on two dimensionless numbers: the isentropic constant of the gas [y]g and Bagnold number [S]B.
As for a sloshing impact inside the tank of LNG vessels, an inertial acceleration is always involved during the impacts and as several authors observed some evidence of the influence of liquid compressibility during wave impact tests (Brosset et al., 2011) or simulations of such tests (Bredmose et al., 2009), a 1D model of the liquid piston problem including a constant inertial acceleration is proposed based on isentropic compressible Euler equations, as an extension of the previous 0D model.
A dimensionless form of the equations is proposed relying on six dimensionless numbers, including the initial Bagnold number, Froude number and the dimensionless compressibility index of the liquid. From this model can be derived a 0D model of the solid piston problem assuming that the liquid is incompressible and the density is constant into the gas. It simplifies to the initial Bagnold model when considering no acceleration.
Two different computing programs have been developed separately by ENS-Cachan/Eurobios and by HydrOcean based on the general 1D model, giving equivalent results. A parametric study is performed with the first one looking at the influence of each dimensionless number on the maximum pressure at wall. Three different regimes are observed, each of them governed by a restricted list of dimensionless numbers. A phenomenological study is performed with the second program looking in depth to the physics involved in the three different regimes.
