A Two-Phase Incompressible-Compressible (Water-Air) Smoothed Particle Hydrodynamics (ICSPH) Method Applied to Focused Wave Slam on Decks

Lind, Steven J. (The University of Manchester) | Fang, Qinghe (The University of Manchester) | Stansby, Peter K. (The University of Manchester) | Rogers, Benedict D. (The University of Manchester) | Fourtakas, Georgios (The University of Manchester)



The accurate prediction of extreme wave forces and slam on offshore decks and platforms remains an important practical problem in offshore engineering. A particular challenge is the accurate prediction of local impact pressures. These pressures are particularly sensitive to local flow conditions and are characteristically high in magnitude and of very short duration. The two phase incompressible-compressible smoothed particle hydrodynamics (ICSPH) method (Lind et al., Applied Ocean Research, 49:57-71, 2015) has demonstrated capability in this area in offering favourable predictions to the extremely large and highly transient slam pressures observed during high-speed free-falling plate impacts on wave crests. In this paper, ICSPH is compared to new experimental data measuring impact pressures due to focused wave slam on a fixed horizontal deck. Complex flow behaviour is observed on the deck underside with wave breaking and air-trapping playing a role. For the studied wave profile, ICSPH pressure predictions are in good agreement with experimental measurements with near-independence in particle resolution demonstrated at key pressure transducers. Numerical studies undertaken with and without the presence of the air phase highlight its role in providing physical impact pressure predictions. Importantly, it is demonstrated that air does not necessarily reduce but can, in fact, increase impact pressures through modification of the local wave profile. With further model refinement and computational acceleration, ICSPH may soon be used to provide reliable quantitative predictions for the design of realistic 3-D offshore structures with air-trapping.


Extreme wave impact on offshore platforms and decks remains an important practical problem for the oil and gas industry. It is a problem of growing interest in offshore renewable energy following the deployment of offshore wind (and supporting structures) in ever more challenging environments. Extreme wave impacts or wave slam are characterised by very large but very short lived pressure peaks that are known to be very sensitive to initial conditions, local wave profiles and the presence of air at the impact site. Initial works on the prediction of pressures due to fluid-structure impact date back to Von Karman (1929), and ever since a range of theoretical, numerical and experimental studies have been undertaken in an effort to improve predictability and understanding of slam and similar impact phenomena. Examples include investigations into hydroelasticity (Kvåealsvold and Faltinsen, 1995), 3-D effects (Watanabe, 1986), the effect of trapped air (Verhagen, 1967), and air/water compressibility (Johnson, 1968). The reliable prediction of impact pressures in a practical context, where the wave field is highly non-linear or breaking, remains a considerable challenge, but progress is being made through the use of a relatively recent numerical method known as Smoothed Particle Hydrodynamics (SPH). SPH is a Lagrangian particle method that uses interpolation over particle positions to solve the governing equations of fluid mechanics. As the method is interpolative and Lagrangian, highly non-linear free surface flows, that may include breaking, can be modelled naturally and without special treatment. SPH has an advantage, therefore, over grid-based methods, which rely on costly and cumbersome re-meshing strategies and/or additional phase tracking functions when modelling free surfaces and interfaces (Scardovelli and Zaleski, 1999). The increasing popularity of SPH has seen its application to a range of free-surface and multiphase flow problems within offshore engineering and beyond (e.g. Gao et al. (2012), Khayyer and Gotoh (2016)). Recently, Lind et al. (2015) presented favourable experimental pressure comparisons for wave slam using a novel two-phase SPH method, known as incompressible-compressible SPH (ICSPH). ICSPH utilises a truly incompressible form of SPH for the water phase, where pressure is obtained from a pressure Poisson equation; this is an approach known to provide more accurate pressures (and so slam predictions) than its weakly compressible counterpart (Lee et al., 2008) (a recent review of ISPH methodologies can be found in Gotoh and Khayyer (2016)). A compressible SPH method (based on pressures from an ideal gas equation of state) is used to model the air phase surrounding the impact site, and so together the ICSPH method enables prediction of the highly non-linear two-phase dynamics typical in practical problems.