Most offshore structures are made of vertical cylinders and may be exposed to breaking waves, which are known to generate impulsive forces that are challenging to estimate. In particular, engineering formulas are often based on an oversimplified representation of the breaking wave, leading to a poor estimate of the load time history. In this study, the wave shape and the fluid kinematics are obtained from a fully nonlinear potential flow solver to reduce the uncertainty on the wave characterisation. The slamming force is then estimated using a semi-analytical water impact model based on Wagner theory and the data from the fully nonlinear simulations. The modelled forces are compared with experimental data on a segmented cylinder impacted by breaking waves of various strengths. The influence of the distance between the cylinder and the breaking point is studied. The model is shown to reproduce accurately the force measurements on the two upper sections impacted by strong plunging breaking waves. The model is compared to other formulations and is shown to improve the estimation of the load time history. For waves of low and mid-breaking strength, the model highly overestimates the force acting on the upper section impacted by the wave crest. The presence of the cylinder in the wave field leads to run-up and diffraction effects that disturb the wave profile. Therefore, accounting for the unperturbed wave kinematics is a conservative approach to evaluate the force acting on the upper section, whereas the evolution of load in time on the lower section is accurately reproduced for all waves.

This article presents experimental measurements of breaking wave impact loads on a vertical cylinder. The focus is on the influence of some of the breaking wave properties on the measured force. These properties are the distance to breaking, $\delta$ , defined as the distance between the breaking location and the front face of the cylinder, and the breaking strength, characterised here by the $\varGamma$ parameter proposed by Derakhti et al. (J. Fluid Mech., 2018, vol. 848, p. R2). The wave characteristics are obtained through numerical simulations of the breaking waves using a fully nonlinear potential flow solver. Seven breaking waves with different breaking strengths have been considered. For each wave, the distance to breaking has been systematically varied and the resulting impact force time-history was measured. It is found that except for the two less intense breaking cases, corresponding to values of $\varGamma$ lower than one, there is a value of $\delta$ for which the magnitude of the impact force is maximum. Small variations of the distance to breaking $\delta$ strongly influence the impact force time-history and its maximum. A linear relationship is observed between the maximum force and the breaking strength $\varGamma$ . For the wave cases with values of $\varGamma$ higher than one, the maximum impact force is observed when the distance to breaking $\delta$ is close to 5 % of the wavelength.

The possibility of predicting the occurrence of wave breaking and the intensity of the breaking events using linear wave models is investigated. For this purpose, a new linear breaking onset criterion is proposed, based on the definition of a linear-equivalent wave, which has the same energy and impulse as the associated nonlinear wave. The strength of breaking is characterized by the T parameter introduced by Derakhtiet al. (2018) and we derive an empirical law to estimate the breaking strength from the linear-equivalent wave model. The predictive ability of this criterion is assessed through comparisons with results of fully nonlinear potential flow simulations, for focused wave packets of various characteristics. For the considered configurations, the proposed approach is able to predict the onset and strength of breaking with good accuracy.

A new experimental method is proposed to improve the force measurements during water impact experiments (e.g. water entry or wave impact tests) carried out with “pseudo-rigid” mock-ups. Despite the efforts of making the mock-up as stiff as possible, the impulsive nature of water impact loads may induce a transient response of the mock-up with a broad frequency content and a perturbation of the force measurements. Using the principles of momentum conservation, it can be shown that the load cell signal is the sum of the hydrodynamic forcing term and of an additional inertial term directly related to the vibrations of the structure. In the present paper, we suggest to estimate the inertial term using several accelerometers which record the response of the structure at different locations. Assuming that the structure response can be approximated by a set of natural modes, we show that it is possible to estimate the inertial term by a linear combination of the acceleration signals. The coefficients of the linear combination may be identified a priori by performing hammer tests, but in certain cases they can also be identified a posteriori using a segment of the signal time series. The performance of the method is demonstrated by considering two experimental test cases of increasing complexity. The first test case is a hydrofoil of constant section impacting water at constant speed which exhibits two-dimensional beam-like vibrations. The second test case is a segmented model of a vertical cylinder impacted by a breaking wave whose segments exhibit three-dimensional vibrations. The proposed method is efficient, conceptually simple and very simple to implement from a signal processing point of view, which makes it promising not only for water impact problems but also for other unstationary fluid–structure interaction problems.

This paper introduces a new stereo-video-based free-surface reconstruction system developed for wave-tank experiments. The originality of the proposed approach relies on the use of short water waves and an adapted lighting system to create a fine texture suitable for the cross-correlation of the stereo image pairs. The feasibility of the approach is demonstrated experimentally in a wave flume. The accuracy of the stereo-video free-surface reconstruction method is assessed through comparisons with measurements performed with a servo-controlled wave gauge. The reconstruction of the free surface at rest and during different regular (periodic) long-crested wave experiments are considered for this purpose. The results demonstrate that, with a suitable free-surface roughness, the accuracy of the stereo-system can be similar to the accuracy of the wave gauge. The accuracy, the simplicity and the flexibility of the approach, which does not necessitate any seeding or dying of the water, nor the use of a laser light source, make it a promising measurement technique for water-wave experiments.

The present study aims to assess the possibility of describing suction using coupled Eulerian–Lagrangian approach. The water entry and subsequent exit of conical and hemispherical bodies is investigated numerically using the Finite Element simulation software Radioss. The numerical method relies on an explicit numerical scheme. An Eulerian and a Lagrangian formulation are considered for the fluid and the structure, respectively. The fluid–structure interaction is based on an immersed contact interface. Particular attention is given to the evolution of the hydrodynamic (positive and negative) force and wetted surface. The numerical results are compared to experimental results from the literature for different impact conditions (maximum velocity and penetration depth). The influence of several parameters of the numerical model is analysed to assess its robustness and improve the numerical results. The numerical model especially shows a satisfying ability to predict suction forces.

Measuring accurately the shape of the free surface in medium-scale hydrodynamic testing facilities is challenging with conventional wave gauges. To overcome this problem, it is necessary to go towards higher resolution measurement systems. For this purpose, we investigate the ability of stereo-video acquisition systems to reconstruct free surface waves in laboratory conditions. This technique has been proven to give satisfactory results in open sea conditions, although it is dependent on the environmental conditions (weather, solar incidence angle). At sea, the stereo-video reconstruction algorithm makes profit of the short waves generated by the wind in order to correlate the points from the left and right images. The main challenge of adapting this technique to laboratory conditions, i.e. in absence of sun and wind, is to overcome the absence of texture on the free surface. This paper presents recent work aiming at developing a stereo-vision measurement system for laboratory conditions. Our efforts have been devoted to finding an adapted lighting system and generating a texture suitable for the reconstruction algorithm. Different lighting configurations have been tested in order to understand its impact on the reconstructions. For the texture generation, we have investigated different means of generating short surface waves (water droplets, air blowing, circulation current, underwater acoustic emissions) in different experimental facilities. Our conclusions show that it is possible to reconstruct the shape of surface gravity waves in the presence of short surface waves and that the effects of lighting and texture on the quality of the reconstruction are strongly coupled.

This work is part of the DIMPACT project that addresses breaking-wave-induced loads on floating wind turbines. In this context, the hydrodynamic impact of a strong plunging breaking wave on a cylinder is studied using semi-analytical models, with a focus on the loads sensitivity to the cylinder tilt and wave-cylinder relative motion. Two semi-analytical models are applied in a strip theory approach under the Froude-Krylov assumption. A numerical wave is generated using a Fully Nonlinear Potential Flow (FNPF) solver, whose free surface geometry and kinematics feed the semi-analytical models. Semi-analytical slamming loads are compared with force measurements collected in a wave flume for different pitch angles and surge speeds. The temporal variation of the force as well as the maximum force acting on the cylinder are well estimated by the semi-analytical models. A new engineering formula is finally developed, accounting for the inclination and surge motion of the cylinder. The impact loads computed with this formula also show good agreement with the experimental tests.

This paper presents new results regarding numerical simulations of breaking wave impacts on a surface-piercing cylinder. The computational fluid dynamics solver, code_saturne, using the volume of fluid approach, is presented and used for offshore hydrodynamics. Phase-focused waves are generated to recreate singular breaking events under relatively controlled conditions. The numerical results compare favourably with a recent experimental campaign for the same conditions, although there is better agreement over the force impulse than the maximum force. The fluid shape and kinematics are described during the breaking process and the load produced by a plunging breaker on a rigid cylinder is investigated.

During the emergency landing of an aircraft on water, the structure may experience critical forces and could eventually fail.The appropriate design of the structure should minimize the risk of occupant injuries.The recent progress in computation capabilities led to the increased use of numerical simulations in the certification process of aircraft.A specific challenge concerns the modelisation of suction forces that develop near the aircraft tail, where the first contact with water occurs.This phenomenon is due to the high horizontal velocity of the structure at impact and the longitudinal curvature of the fuselage.It can affect the overall aircraft kinematics during ditching.In this work, as an effort to improve aircraft ditching simulations and to assess the capabilities of numerical models to describe suction forces, the simple test case of the wedge water entry and subsequent exit is considered.Numerical simulations with the Eulerian formulation for the fluid and the Lagrangian formulation for the structure are used.The method used for the fluid-structure interaction is based on an immersed contact interface with penalty forces.The present work focuses on impact and suction forces modelling.Results show a satisfying capacity of the numerical approach to model negative hydrodynamic force (suction).

The effect of gravity during the water entry of two-dimensional and axisymmetric bodies is investigated analytically and numerically. An extension to the Wagner model of water impact is proposed in order to take into account the effect of gravity. For this purpose, the free-surface condition is modified. The pressure is computed using the modified Logvinovich model of Korobkin ( Eur. J. Appl. Maths , vol. 6, 2004, pp. 821–838). The model has been implemented and validated through comparisons with fully nonlinear potential flow simulations of different two-dimensional and axisymmetric water entry problems. Our investigation shows that it is equally important to account for gravity when computing the pressure distribution and to account for gravity when computing the size of the wetted surface in order to obtain accurate force results with the Wagner model. Simulations of wedges and cones with different values of deadrise angle ( $\beta$ ) entering water at constant speed ( $V$ ) demonstrate the accuracy of the semi-analytical model and show that the effect of gravity in such water impacts is governed by the effective Froude number defined as $Fr^*=V/(\sqrt {gh}\sqrt {\tan \beta })$ , with $g$ the acceleration due to gravity and $h$ the penetration depth. The accuracy of the semi-analytical model for decelerated water entries is also demonstrated by investigating the water entry of a wedge and a cone with a $15^\circ$ deadrise angle with deceleration until full stop. The semi-analytical model is able to accurately predict the effect of gravity during both two-dimensional and axisymmetric water entry problems with deceleration.

A stochastic approach is implemented to address the problem of a marine structure exposed to water wave impacts. The focus is on (i) the average frequency of wave impacts, and (ii) the related probability distribution of impact kinematic variables. The wave field is assumed to be Gaussian. The seakeeping motions of the considered body are taken into account in the analysis. The coupling of the stochastic model with a water entry model is demonstrated through the case study of a foil exposed to wave impacts.

The present paper is dedicated to the development of a numerical model for the water impact of two-dimensional (2D) and axisymmetric bodies with imposed motion. The work is a first step towards the implementation of a 2D+t procedure to be used for the analysis of aircraft ditching. The problem is investigated under the assumptions of an inviscid and incompressible fluid, which is modeled by a potential flow model with fully non-linear boundary conditions at the free-surface. The unsteady boundary value problem with a free-surface is numerically solved through a boundary element method, coupled to a simplified finite element method to describe the thinnest part of the jet. The study is aimed at describing the entry and exit phases. Specific numerical solutions are developed to tackle the exit phase and to improve the stability of the model. Results are presented in terms of free-surface shape, pressure distribution and hydrodynamic load acting on the impacting body. The model is used to study the water entry and exit of a 2D wedge and an axisymmetric cone, for which numerical or experimental results are available in the literature. The numerical investigation shows that the proposed model accurately simulate both the entry and exit phases. For the exit phase, it is shown that the proposed model, being fully non-linear, provides a much better prediction of the loads and the wetted area compared to simplified (analytical) approaches. The effects of the gravity, usually missing in the approaches available in the literature, are also investigated, showing they are rather important, especially, in the exit phase.

This paper presents an experimental investigation of the evolution of the wetted surface and of the hydrodynamic force during the water exit of a body initially floating at the water surface, and during combined water entry and exit. The evolution of the surface of contact between the body and the water is measured using transparent mock-ups and an LED edge-lighting system. This technique makes it possible to follow the evolution of the wetted surface during both the entry and exit phases with a high-speed video camera placed above the mock-up. The feasibility of the technique is shown for different axisymmetric bodies: a circular disc, a cone and a sphere. The evolution of the hydrodynamic force and of the radius of the wetted surface measured during the experiments are compared with theoretical results obtained with a combined Wagner-modified von Karman approach (Tassin et al. J. Fluids Struct., vol. 40, 2013, pp. 317-336), the linearized water exit model of Korobkin et al. (J. Fluids Struct., vol. 69, 2017a, pp. 16-33) and the small-time self-similar solution of Korobkin et al. (J. Engng Maths, vol. 102, 2017b, pp. 117-130).

The aircraft ditching, despite being a rare event, has to be considered in the design phase to guarantee safety and to respect certification. As a way to avoid the expensive full scale experimental tests, computational approaches able to provide a reasonably accurate description of hydrodynamics and fluid-structure interaction taking place during the aircraft ditching are of primary interest. Besides high fidelity, fully coupled, fluid and structural solvers, fast and efficient solvers, albeit approximate, are strongly needed by aircraft manufacturers for the design and certification stage when many different configurations have to be analyzed. Simplified methods based on Modified Logvinovich Model [1] or Generalized Wagner [2] have been found to be very efficient and able to provide accurate predictions of the sectional forces. In this paper, a fully nonlinear model is developed with the aim of providing a more accurate prediction of the pressure distribution and of the fluid-structure coupling. The model is based on the mixed Eulerian-Lagrangian BEM formulation. As a preliminary step towards the development of a 2D+t procedure, in this paper the model is tested in the vertical water entry and exit of a wedge and a cone and validated against other numerical or experimental data.

The vertical water entry of asymmetric two-dimensional bodies with flow separation is considered. As long as there is no flow separation, linearised Wagner's theory combined with the modified Logvinovich model has been shown to provide computationally fast and reliable estimates of slamming loads during water entry. Tassin et al. [11] introduced the fictitious body continuation (FBC) concept as a way to extend the use of Wagner's model to separated flow configurations, but they only considered symmetric bodies. In the present study, we investigate the ability of the FBC concept to provide accurate estimates of slamming loads for asymmetric bodies. In this case, flow separation may not occur simultaneously on both sides of the body. During an intermediate phase, slamming loads are governed by a competition between the local drop in pressure due to partial flow separation and the ongoing expansion of the wetted area. As a first benchmark for the model, we consider the water entry of an inclined flat plate and compare the FBC estimates with the results of a nonlinear model. Then, we consider the case of a foil and compare the FBC results with computational fluid dynamics predictions. In both cases, we find that the FBC model is able to provide reliable estimates of the slamming loads.

We investigate experimentally the time evolution of the wetted surface during the lifting of a body initially floating at the water surface. This phenomenon is referred to as the water exit problem. The water exit experiments were conducted with transparent (PMMA) mock-ups of two different shapes: a circular disc and a square flat plate. Two different lighting systems were used to diffuse light in the mock-up material: a central high-power LED light normal to the surface and an edge-lighting system featuring an array of LED lights. These setups make it possible to illuminate the contact line, which delimits the surface of contact between the mock-up and the water. The characteristic size of the mock-ups is about 20 cm and the acceleration of the mock-up oscillates between 0 and 25 m/ s^2 . We show that the central light setup gives satisfactory results for the circular disc and that the edge lighting technique makes it possible to follow a contact line with a time-evolving complex shape (strong changes of convexity) up to 1000 fps. The observations presented in the paper support the possibility of extending this promising technique to more general three-dimensional bodies with arbitrary motion (e.g., including pitch motion).

Two-dimensional water entry with separation is investigated through different analytical models. This study focuses on the transient force acting on the body when the jet root detaches from the body surface and a cavity starts to develop behind the body. Logvinovich (1972) suggested a separation model in order to estimate the transient force acting on a finite wedge entering water. This model is revisited, developed further and assessed through comparison with more recent works on flow separation. The concept of Fictitious Body Continuation combined with the Modified Logvinovich Model is also investigated to estimate the transient drag during the initial stage of cavity formation. This model accounts for the variation in speed of the body during the separation stage. Several case studies are presented in order to show the relevance of this model. These include separation from chines and separation from smooth bodies.