Sloshing model tests or wave impact tests in flumes show large variability of local impact pressure measurements. One of the reasons of such variability is the generation of free surface instabilities by the shearing gas flow at the free surface just before the impacts (Kelvin-Helmholtz and possibly Rayleigh-Plateau when fragmentation occurs). Our long-term objective is to study the influence of surface tension (or Weber number) and viscosity (or Reynolds number) on the development of gas-liquid interface instabilities until fragmentation for breaking wave impacts and to relate the statistical distributions describing these instabilities to those of the pressure measurements.
To better understand the first steps of development of free surface instabilities around the crest of breaking waves, a bi-fluid high-fidelity front-tracking software based on the Navier-Stokes equations has been developed. Named CADYF, this software simulates separated two-phase incompressible viscous flows with surface tension. The numerical method uses adaptivity in space (adaptive remeshing) and time (hp-adaptivity) to yield accurate predictions while keeping computational cost low.
As first application, the simple experiment carried out by Thorpe (1969), enabling the generation of Kelvin-Helmholtz instability in a rectangular tube completely filled with two liquids of different densities, is simulated. Numerical results are compared to experimental results and to simulations from Strubelj and Tiselj (2011). A parametric study is performed varying the surface tension and the viscosities of the fluids at constant ratio of viscosity. The evolutions of the main parameters describing the Kelvin-Helmholtz instability are provided in dimensionless form giving some clues about the scaling process.
The context of the present study is the sloshing assessment of Liquefied Natural Gas (LNG) tanks on floating structures based on sloshing model tests. The model tank, most of the time at scale 1:40, is put on the platform of a six-degree-of-freedom motion generator. The liquid inside the model tank is water, the ullage gas is a mixture of Sulfur Hexafluoride (SF6) and Nitrogen tuned in order to keep the gas-to-liquid density ratio the same as in the reality with LNG and Natural Gas (NG). The excitations are down-scaled from ship motions calculated at scale 1 with a boundary element method (BEM) according to Froude-scaling. Numerous pressure sensors, arranged in rectangular arrays, are placed in the locations submitted to liquid impacts. All conditions (sea-states, loading cases and speeds of the floater, incidences of the wave with regard to the floater, filling levels) that the floating structure is expected to encounter during its life are studied. Long-term distributions of pressure peaks are built for different sizes of the loaded area, mixing all conditions with an estimated probability of occurrence. Because of the high variability of the local pressure measurements, the conditions, especially those which are contributing the most, are needed to be tested many times in order to build a converged long-term pressure peak distribution. This leads to sloshing model tests running night and days during many weeks (at least seven in GTT) to perform a reliable sloshing assessment.
