In this investigation the Reynolds-Averaged Navier-Stokes (RANS) equations are modified to account for variable density and viscosity of the two-fluids flow (i.e. water-air), assuming both fluids compressible. By introducing a preconditioner, the governing equations in terms of primitive variables are solved for both fluids in a unified manner. The non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to approximate convective flux vectors in the dual time formulation. The free surface waves inside the tank, due to sloshing, are implicitly captured by using a level set approach. The method is illustrated through applications to rectangular and chamfered tanks subject to sway or roll motions at different filling levels and excitation conditions (i.e. amplitude and frequency of oscillation). Comparisons are made between calculated and experimental pressures, where available.
The Liquefied Natural Gas (LNG) carrier is often dubbed as the pearl of the shipbuilding industry as the technology required is very demanding and complicated. Due to energy demands, increasing numbers of LNG carriers are required. The need for larger cargo capacity, coupled to the demand for more flexible operations, provide the stimulus for design changes in these vessels. There are, by and large, two types of LNG carrier tanks, namely Moss-type and membrane-type. Since LNG vessels with membrane type tanks are often the first choice for new very large vessels and as, unlike the Moss-type tanks, they experience large sloshing pressures on tank boundaries, the issue of sloshing induced pressure loads in membrane tanks has become more important than ever. The possibility of sloshing damage has already attracted much attention in the LNG industry today. In the case of shallow filling and severe sea-induced motions a hydraulic jump forming a vertical front may be generated, resulting in very large impacts on tank walls. On the other hand, in a nearly full tank, the excited progressive wave may cause high stresses acting on its roof (Mikelis et al, 1984).
