Numerical Simulation of Hydrodynamic Wave Loading by a Compressible Two-phase Model

The numerical simulation of hydrodynamic wave loading on different types of offshore structures is important to predict forces on and water motion around these structures. This paper presents a numerical study of the effects of two-phase flow on an offshore structure subject to breaking waves. The numerical model, an improved Volume Of Fluid (iVOF) method, has been developed initially as a one-phase model to study the sloshing of liquid fuel in satellites. In the one-phase approach, the method solves the incompressible Navier-Stokes equations with a free-surface condition on the free boundary. The discretisation of the equations is done on a staggered grid, using an explicit first order Forward Euler Method. The model has been extended recently to take two-phase flow effects into account. In the incompressible two-phase model the VOF-function is used to determine the aggregated density value inside a grid cell. Rapid changes in density in grid cells, up to a factor 1000, impose a challenge with respect to numerical stability. However, by using a newly-developed gravity-consistent discretisation, spurious velocities at the free surface are prevented. Thus far, the second phase has been treated as incompressible. Taking compressibility into account makes it possible to simulate in particular the behaviour of the air phase more realistic. As the condition of incompressibility no longer holds for gaseous grid cells, an equation of state is required as the third main equation. The calculation of pressure and density values now occurs simultaneously due to this equation of state, while the expansion and compression of air pockets are considered as an adiabatic process. The numerical model has been validated on several test cases. In this paper special attention is paid to both the validation on a simple test case (falling drop) and the validation of wave loading on a fixed offshore structure.