Hydroelastic Analysis of a Simple Oscillator Impacting the Free Surface

Abstract

The coupling between the hydrodynamic and elastic forces arising when a simple oscillator impacts the free surface is considered. The system is a two-mass oscillator, the lower mass being wedge-shaped, free falling on the free surface. Attention is devoted to a parametric investigation of the maximum of both hydrodynamic and elastic forces induced by the impact. The study is performed by a simplified theoretical model and by a numerical simulation of the fluid-structure interaction. The theoretical model suggested here provides an efficient tool for the computation of the hydrodynamic and elastic forces and of the corresponding maxima as a function of some parameters such as deadrise angle of the wedge, entry velocity, spring stiffness, and the masses. In particular, a closed-form expression for the critical value of the spring constant leading to the maximum elastic response is achieved as a function of the other parameters. Numerically, a panel method is adopted to solve the boundary integral formulation for the velocity potential. A suitable model is introduced to deal with the flow singularity at the intersection point between the free surface and the body contour. Time histories of the hydrodynamic and elastic forces are computed for different values of the spring stiffness and are compared with the corresponding results provided by the simplified theoretical model. The comparison shows that, despite the strong assumptions, the theoretical model allows a good estimate of the system critical condition.

Hydrodynamic shock of elastic structures impacting on the water: theory and experiments

“…More recently in Refs. [15,16] a similar system has been investigated providing a good understanding of the influence of the fluid and structural parameters involved in the phenomenon, leading to closed-form relationships for the maximum force (or acceleration) of the impacting body, as well as for the elastic reaction between the two masses. Such an analysis is made possible by the introduction of the shock spectrum approach to the vibration induced by the slamming phenomenon in combination with the use of the Wagner hydrodynamic model, producing simple prediction formulas.…”

The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results

“…Higher order gradient theories are needed when boundary layer phenomena must be described: when considering impact phenomena (e.g. [89,[178][179][180]) in general some ad hoc assumptions are imposed, especially when choosing boundary conditions. More detailed models for impact between solids or between solids and fluids, involving some space-time length scales, may cure some of the singularities which are present in many models presented in the literature: in particular, one could conceive to describe the phenomena of water spray formation or turbulence (see, respectively, [179] with references there cited or [181]) by means of suitable contact edge forces.…”

Comparaison de différentes approches pour la simulation numérique d’impacts hydrodynamiques

“…où F est l'effort hydrodynamique (par unité de longueur), V la vitesse d'entrée dans l'eau, l la masse volumique du fluide et l'angle du dièdre. En plus des résultats des 3 modèles numériques et de ceux du modèle de Zhao et Faltinsen, nous avons également inclus sur la figure 10 des résultats théoriques qui ont été obtenus à l'aide la méthode des similitudes par Zhao et Faltinsen (1993), ainsi que les résultats obtenus par Iafrati et al (2000). La méthode des similitudes repose sur l'hypothèse d'un fluide parfait incompressible.…”

“…Si bien que ces résultats sont considérés par beaucoup d'auteurs comme des résultats de référence dans le cas de l'impact de dièdres à vitesse constante. Iafrati et al (2000) ont utilisé quant à eux un modèle éléments de frontière basé sur la théorie du potentiel. Ce modèle est également totalement non linéaire ; dans ces simulations, la géométrie de la surface libre du fluide est mise à jour tout au long du calcul à partir de la connaissance du champ de vitesse et les conditions aux limites sont imposées sur cette surface.…”

“…figure 10 nous montre que les résultats obtenus avec Fluent et ABAQUS/Explicit, ainsi que ceux obtenus par Iafrati et al (2000), sont tous très proches des résultats de la méthode des similitudes. Les efforts prévus par impact++ et le modèle de Zhao et Faltinsen sont, quant à eux, plus élevés.…”