ABSTRACT

A numerical study is proposed to highlight the sensitivity of the structural response with respect to the fluid pressures derived by a fluid dynamics analysis. The fluid characteristics are computed by using two Computational Fluid Dynamics (CFD) methods, namely a Unsteady Reynolds Averaged Navier Stokes (URANSE) method and a Smoothed Particle Hydrodynamics (SPH) solver. Based on the CFD results, the structure response is calculated by means of a Finite Element Method (FEM). Different level of accuracy are explored in the CFD computations, i.e. varying the mesh and particle resolutions for the URANSE and the SPH, respectively. The study is performed on a selected test case, namely a reinforced wedge-like section falling into the water. Results are discussed in the light both of the comparison between the two CFD methods and in terms of global and local structural properties.

INTRODUCTION

The study of slamming induced loads and vibrations on ship structures has been approached since a long time by using both numerical and experimental techniques. Considering the intrinsic multidisciplinary nature of this problem, involving both hydrodynamics and structural responses, achieving an accurate numerical solution requires fully coupled Fluid-Structure Interaction (FSI) simulations possibly accounting for side effects such as air entrapment within the water-body interface. Even if this is recently considered a viable approach for research purposes, such a kind of simulations are still particularly demanding in terms of computational effort and still not completely available for a design practice or to characterize a stochastic response of the structure. In this context, to uncouple the hydrodynamic and the structural solutions represent a rational approach to characterize the most relevant phenomena involved in the slamming process.

Numerical solution of violent impact problems has been developed since a long time. One of the first theoretic formulations has been proposed by Von Karman (1929) and Wagner (1932) for small wedge angles. An implicit numerical solution called similar solution has been later provided by Dobrovol'skaya (1969). A marked step forward to the solution of such a complex hydrodynamic problem that is strongly related to the structural integrity of the ships has been made with the development of medium and high fidelity numerical models. In particular non-linear Boundary Element Methods (BEMs) have been formulated in order to account for the effects of the water jet detached from the wedge surface (see for instance Zhao & Faltinsen, 1993 and Sun & Faltinsen, 2006). Considering higher fidelity techniques that rely on the solution of Navier Stokes (NS) equations, two different approaches have been largely used in the recent years, namely Reynolds Averaged Navier Stokes (RANS) and Smoothed Particles Hydrodynamics (SPH) methods, respectively. The first is a meshbased technique typically exploiting the capabilities of a Volume of Fluid (VoF) approach to capture the water-air interface kinematics. The latter is instead a Lagrangian mesh-less method that resolve the interactions among a set of fluid particles, hence allowing e.g. strongly non-linear free surface fragmentation. Even if RANSE based methods can rely on a overall longer development story, SPH techniques starts to be considered at a satisfactory level of accuracy for both research and engineering applications (see for instance Shadloo et al., 2016). Due to their complexity those two higher fidelity techniques have always been developed to become general purpose methods. However, there are still some open questions on the effects of the model set-up on the accuracy and stability of the provided solutions and, ultimately, on the chance to generalize the obtained findings. In this perspective there are many researches carried out by using the two mentioned methods (Muzaferija & Peric, 1999, Oger et al., 2006, Veen & Gurlay, 2008, Viviani et al., 2009, Marcer et al., 2010, Brizzolara et al., 2011 and Farsi & Ghadimi, 2015). Preliminary results of systematic analysis of the influence of model parameters on the solution of falling wedges have been recently provided by Farsi & Ghadimi (2014), Sasson et al. (2016) and Bonfiglio et al. (2017).

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