Hydroelastic Slamming Research Articles

A two-way coupled fluid–structure interaction method for predicting the slamming loads and structural responses on a stiffened wedge

Ships navigating through rough seas are subjected to slamming loads from waves, which can lead to structural damage and maritime accidents. The wedge model is commonly employed to investigate slamming loads and structural responses. While a stiffened wedge closely resembles a real ship hull plate, incorporating it into fluid–structure interaction simulations presents challenges. This paper proposes a two-way coupled fluid–structure interaction method to examine slamming loads and structural responses of a free fall non-prismatic stiffened steel wedge. Hydrodynamic loads are determined through Reynolds-averaged Navier–Stokes computations using OpenFOAM, while structural responses are predicted using the finite element analysis (FEA) software Calculix. To achieve two-way coupling between computational fluid dynamics and FEA simulations, a coupling library for partitioned multi-physics simulations, preCICE, is introduced. The computed impact pressure and stress align well with available experimental data. Various free fall heights are investigated in the numerical simulations. The results indicate that elastic deformation mitigates impact pressure, while the presence of transverse ribs enhances the rigidity of the flexible plate. The duration of pressure and the peak slamming pressure exhibit an inverse correlation. Greater free fall heights result in shorter pressure duration times, and smaller free fall heights may reduce rise time. Three-dimensional effects cause pressure to decrease along the midpoint of the plate toward both sides. Additionally, structural stress in the central area exceeds that in the areas on both sides at the same height. In conclusion, the proposed two-way coupled model proves suitable for accurately and efficiently computing hydroelastic slamming on flexible wedges.

Water entry of an elastic conical shell

The axisymmetric problem of a conical shell impact onto an inviscid and incompressible liquid of infinite depth is studied. The shell is thin, and its deadrise angle is small. The problem is inertia dominated. Gravity, surface tension and viscous effects are not taken into account. The hydrodynamic loads acting on the shell and the shell displacements are determined at the same time. The model by Scolan (J. Sound Vib., vol. 277, issue 1–2, 2004, pp. 163–203) is used to find the flow and hydrodynamic pressure caused by the shell impact. This model is based on the Wagner theory of water impact, which was generalised to axisymmetric problems of hydroelastic slamming. Dry and wet modes of the conical shell, as well as the corresponding frequencies, are calculated. It is shown that a conical shell can be approximated by a circular plate only for a very small deadrise angle. Deflections and strains in the conical shell during the impact stage, when the wetted part of the shell increases at high rate, as well as the hydrodynamic loads, are determined and analysed.

Investigation of fluid added mass matrix during hydroelastic slamming of wedges

The investigation of the fluid added mass (FAM) matrix during the water entry of an elastic structure is crucial for understanding the mechanism of hydroelastic slamming, as it characterizes the fluid–structural interaction process. In this paper, we excavate a model for directly estimating the FAM matrix during hydroelastic slamming and employ this model to study the limitations and optimized values of the relaxation factor for a partitioned coupling solver. Our simulation of hydroelastic slamming couples the Wagner theory with the modal superposition method (MSM), and the FAM matrix is computed using a monolithic coupling scheme. We conduct a series of parametric studies to analyze how the modal number, hydroelasticity, deadrise angle, and structural boundary condition influence the eigenvalues of the FAM matrix. Based on these studies, we then propose an analytical model to directly express the eigenvalues of the FAM matrix, demonstrating their linear relationship with the wetted ratio. Furthermore, we apply this analytical model to analyze the relaxation factor in the partitioned coupling scheme, theoretically explaining its strong connection to the FAM effect. The limitations and optimized values of the relaxation factor are theoretically presented, and these results are verified through our numerical tests.

Experimental study of liquid slamming in elastic rectangular tanks under the flip-through impact

This paper considers the hydroelasticity effect in liquid slamming. A series of experiments were designed and performed in a nearly two-dimensional (2D) rectangular tanks with four elastic materials. The effect of the Young's modulus on the kinematic and dynamic characteristics of fluid-structure interaction (FSI) during flip-through impact is investigated. Furthermore, the peak values of slamming pressure, impact duration, pressure impulse and structural displacement in different cases are discussed. The hydrodynamic force of fluid acting on the sidewall is defined and compared for different cases. The results show that the Young's modulus of the sidewall plays an important role in hydroelasticity induced by liquid slamming. And a strong hydroelastic behavior could be observed when the impact occurs, especially in the case with a small Young's modulus. In addition, the artificial neural network (ANN) method is adopted to build the hydroelastic response prediction model. The relationship between Young's modulus and peak structural displacement is predicted with the model. This study could help verify and calibrate the theoretical and numerical models of the FSI problems in the sloshing tank and provide guidance on the study of hydroelastic slamming for the flexible cargo containment system.

FEM-SPH Numerical Simulation of Impact Loading on Floating Laminates

The study of dynamic events such as impact and hydroelastic slamming is of great importance in determining the structural integrity of naval or maritime structures, particularly those made of composite materials. This topic has been investigated by numerous researchers using analytical, experimental, and numerical approaches. In this study, we propose using a hybrid numerical model combining smoothed-particle hydrodynamics (SPH) and the finite element method (FEM) to investigate the impact of external objects on floating laminates. The results show a good agreement with the available experimental data regarding the impact dynamic and some limitations in the damage determination.

Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part II. Numerical simulations

An experimental study was carried out to examine the impact-induced loads and structural responses of a three-dimensional non-prismatic aluminium wedge. The findings of the experimental study were presented in the first part of this publication, entitled “Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part I. Experimental study.” This paper describes the second part of the study, which deals with numerical simulations of slamming loads acting on the wedge and its dynamic responses. Two different two-way coupling methods are assessed and compared to simulate the water entry problem. Initially, an explicit nonlinear finite element method with a Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver is employed to evaluate the elastic response of the structure following a free-fall water impact. Subsequently, the hydroelastic slamming problem is modelled using a two-way coupled technique with a k-ε turbulence model and implicit unsteady solver for both the fluid and structural domains (Star-CCM+/ABAQUS). The effect of viscosity on slamming loads and responses was examined, and numerical results are compared with experimental data. To investigate the effect of rigidity on structural response and bottom deflection, the wedge was designed with bottom plates of varying thickness. The computed results from the two numerical models and the experimental data are in good agreement. The study concluded that the bottom plates deformation affects hydrodynamic loads during slamming. It is also observed that impact-induced loads depend on the water impact velocity and the flexibility of the bottom plates. This suggests that the slamming pressure increases with an increase in impact velocity and decreases when the structures become more flexible. According to this study, both numerical models are suitable for accurate and efficient computations of hydroelastic slamming; however, the MMALE method results in larger numerical fluctuations.

Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part I. Experimental study

Hydroelastic slamming is a phenomenon that occurs when there is a fully coupled interaction between the water surface and a deformable structure, and it has a significant effect on the local and global loads of the structure during high impact velocities in rough seas. Estimating the simultaneous structural responses caused by hydrodynamic loads during high impact water entry is a challenging task. This article, which is Part I of a two-part companion paper, deals with the experimental studies of the impact-induced loads and structural responses of a three-dimensional non-prismatic aluminium wedge with stiffened panel during free-fall water entry. Two different plates were considered on the bottom of the wedge in order to study the influence of flexural rigidity on hydroelastic slamming. A description of the experimental conditions, including the geometry of the wedge, material properties, and the test plan is provided. The effects of water impact velocity, deadrise angle, mass of the wedge, and bending stiffness on the slamming pressures and structural responses are discussed in detail. It is shown that the maximum strain and deformation occur during the partially wetted phase of the slamming problem. The study concludes that the hydroelasticity effects on slamming responses generally increase at lower deadrise angles and higher impact velocities. The importance of FSI simulation is assessed using a hydroelasticity factor (RF), which is found to have a significant effect on the unstiffened bottom for all impact velocities studied. For a stiffened bottom panel, hydroelasticity is only significant at high impact velocities.

A Verification and Validation Study on a Loosely Two-Way Coupled Hydroelastic Model of Wedge Water Entry

_ The interaction between the structural response and hydrodynamic loading (hydroelasticity) must be considered for design and operation purposes of high-speed planing craft made of composites that are prone to frequent water impact (slamming). A computational approach was proposed to study the hydroelastic slamming of a flexible wedge. The computational approach is a loose two-way coupling between a Wagner-based hydrodynamic solution and a linear finite element plate model. Verification and validation (V&V) was performed on this coupled model. It was found that the model overpredicts rigid-body/spray root kinematics by <15% and hydrodynamic loading/ structural response by <26%. Introduction One of the primary constraints on the operational envelope of high-speed craft is slamming (water impact). Slamming occurs between the hull body and the water surface when a portion/whole of the craft exits the water and then reenters at high-enough velocity (Lloyd 1989; Faltinsen 2005). The frequent water impacts, which work like “water hammers,” along with their induced acceleration pose great jeopardy on hull structures as well as crew and instrument on-board (Yamamoto et al. 1985; Ensign et al. 2000; Hirdaris et al. 2014). With the growing use of lightweight materials, the interaction between the structural deformation and the hydrodynamic loading (hydroelasticity) becomes more prevalent. The current design criteria of high-speed craft are based on empirical procedures with no regard to hydroelasticity due to the lack of understanding of this complex phenomenon (DNV 2013; ABS 2016). Therefore, a better comprehension of hydroelastic slamming is the first step to designing more high-performance craft (Fu et al. 2014; Judge et al. 2020).

Investigations on the hydroelastic slamming of deformable wedges by using the smoothed particle element method

The nonlinearity and time-dependent nature of hydroelastic slamming along with violent fluid–structure interactions (FSIs) and evolution of free surfaces present great challenges to the numerical modeling. The inherent physical mechanisms of such a violent FSI involved with structural vibrations have not been well investigated so far. In this work, an adaptive element–particle coupling approach is extended to reveal the underlying mechanisms of hydroelastic slamming, which leverages the advantages of grid-based method in accurately modeling structural deformations and fluid flows with small deformations as well as particle method in effectively capturing moving interfaces. After well validating with experimental results, we focus on investigating the flow physics and hydrodynamic loads along with structural hydroelastic performances including wedge kinematics and dynamic responses. It is demonstrated that the plate deformation has minimal influence on the maximum hydrodynamic load in normal slamming, whereas it has significant effects in oblique slamming. Both rolling free surfaces and waves around the plate ends may affect the distribution of hydrodynamic loads on the elastic structure. For kinematics and dynamic responses of the structure under slamming loads, different configurations of deformation and stages of motion are identified. With increasing deadrise angle, the structural deformation becomes more pronounced and later gets smaller for a large structural flexibility. However, it may decrease in a direct manner with an increase in the deadrise angle when a smaller plate flexibility is adopted. Further, the important phenomenon of structural vibration is studied with typical influencing factors analyzed. A novel empirical formulation is proposed to predict vibrational characteristics of the wedge during hydroelastic slamming processes. This relation is unified and applicable for a broad of scenarios from normal to oblique slamming.

A semi-analytical method to simulate hydroelastic slamming of 2D structural sections by coupling Wagner theory with the finite element method

A semi-analytical method based on coupling Wagner theory with the finite element method is applied to numerically simulate hydroelastic slamming of arbitrary symmetric 2D structural sections subject to a constant impact velocity or to free fall motion. The averaged elastic velocity method is adopted to consider the influence of the elastic response on the distribution of the slamming load. A coupled dynamic equation is established to govern the fluid-structural interaction. The nonlinear pressure term improves accuracy. To validate the method, numerically predicted structural deformations and the associated strains during impact for several wedge-shaped sections and a cylindrical shell are compared with published results. The results show that the averaged elastic velocity method is efficient in estimating the structure dynamics. The effect of the nonlinear pressure term on hydroelastic structural dynamics is parametrically studied by considering wedge sections with different deadrise angles and with the elastic bottom plating under different end constraints. This nonlinear pressure term ensures reliably predicted hydroelastic structural responses, especially for wedges of larger deadrise angles and smaller hydroelastic properties. The proposed method provides an efficient tool to estimate structural strength under slamming during the initial design stage of the marine or aerospace structure.

Hydroelastic effects of slamming impact Loads During free-Fall water entry

ABSTRACT This paper examines the hydroelastic problems of a two-dimensional symmetric flexible wedge water entry through free-fall motion. Water entry is numerically investigated by coupled Finite Volume Method and Finite Element Method using a strong two-way coupling approach. The emphasis of this study is on numerical approach and the paper provides an accurate two-way FSI coupling method for the water entry of two-dimensional symmetric elastic wedge section in different conditions. The effect of freefall velocity is investigated by comparing the constant velocity and freefall impacts. It is shown that the bottom deflection is overestimated by using the constant velocity. In order to evaluate the accuracy of the numerical model, the numerical results are compared and validated against published experimental data and favourable agreement is reported. The vertical position, impact velocity, acceleration, pressure distribution, and deflection along the bottom plate of the elastic wedge are evaluated and compared to experimental data. For better understanding of the hydroelastic slamming, the results are presented for different deadrise angles and vertical velocities. The relation between the structural deflection and vertical velocity, deadrise angle, and pressure distribution is investigated. It is observed that the significance of hydroelasticity increases with decreasing deadrise angle and increasing impact velocity.

On the treatment of hydroelastic slamming by coupling boundary element method and modal superposition method

An efficient fluid and structure interaction (FSI) coupling strategy between boundary element method, i.e. BEM (fluid part), and modal superposition method (structure part) is proposed to study hydroelastic slamming of wedge sections. The coupling strategy possesses simplicity in coding construction by transmission of coordinates, velocity and pressure on the fluid-solid interface. Convergence property of grid size, time step and modal number are first investigated. After that, the accuracy of the model is verified by comparing the numerical results with published ones. Hydroelastic effect associated with plate thickness, deadrise angle, impact velocity and boundary condition is discussed by the comparison between quasi-static, decoupling and coupling solutions, where quasi-static and decoupling solutions are established by neglecting the influence of elastic response of structure on the water flow field. The results show that quasi-static solution underestimates structural maximum response under specified hydroelastic parameters, and a time-lag effect is found between results of decoupling and coupling solutions.

Kinematic and inertial hydroelastic effects caused by vertical slamming of a flexible V-shaped wedge

Due to the increasing use of composite materials in high-speed planing craft prone to frequent slamming, the interaction between the structural response and hydrodynamic loading, hydroelasticity, must be considered. In this work, a V-shaped wedge model with 20° deadrise angle was vertically dropped into the calm water to simulate a typical hydroelastic slamming. With varied impact velocity and flexural rigidity of the wedge bottom plate a wide range of hydroelasticity factors, 0.1≤R≤6.4, were examined. Measurements included rigid-body kinematic motions of the wedge model, spray root propagation, hydrodynamic loading, and structural response. It was found that the maximum deflection and strain occur in the chine-unwetted phase in this study. The kinematic effect of hydroelasticity changes the spray root propagation and hence the pressure, while the inertial effect increases the natural period of the plate.

An improved higher-order moving particle semi-implicit method for simulations of two-dimensional hydroelastic slamming

An improved higher-order moving particle semi-implicit (MPS) method has been developed to solve the problem of fluid–structure interactions for an elastic wedge entering calm water. The structural responses of the wedge with a reinforced tip were computed during the water entry. In the present method, the pressure gradient is corrected to guarantee the first-order consistency and to satisfy the conservation of momentum. Different particle spacings are used for the fluid and the structure. Convergence studies were carried out on particle spacings for the fluid and the structure and on a time step. A particle convergence index method was applied to evaluate numerical uncertainties in the improved MPS method. Validation studies were carried out on two elastic wedges with deadrise angles of 30° and 20° entering water at various velocities. Numerical solutions were compared with the results from the original higher-order MPS method and experimental data. The improved higher-order MPS methods led to better agreement with experimental data than the original one and significantly reduced the oscillations in numerical solutions.

A semi-analytical model of hydroelastic slamming

A semi-analytical model of hydroelastic slamming for two-dimensional symmetric flexible bodies is presented in this paper. The hydrodynamic loads are computed using the analytical Modified Logvinovich Model (MLM) with account for elastic deflections of the body surface. The elastic deflections are described by the modal approach. The rigid and elastic motions of the body are computed at the same time together with the wetted part of the body surface. The coupled problem of elastic impact is reduced to a system of nonlinear ordinary differential equations, which is integrated in time by the implicit Newmark method with iterations at each time step. Both free fall and constant water entry cases are considered. The developed model is validated for flexible wedge and cylindrical shell water entry problems. Good agreements with existing experimental and numerical results are achieved. It is shown that the MLM significantly improves predictions of the deflections and stresses cause by the impact compared with the Wagner model of water impact. The developed model is suitable for efficient and accurate computations of water elastic impacts.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

Hydroelastic slamming of flexible wedges: Modeling and experiments from water entry to exit

Fluid-structure interactions during hull slamming are of great interest for the design of aircraft and marine vessels. The main objective of this paper is to establish a semi-analytical model to investigate the entire hydroelastic slamming of a wedge, from the entry to the exit phase. The structural dynamics is described through Euler-Bernoulli beam theory and the hydrodynamic loading is estimated using potential flow theory. A Galerkin method is used to obtain a reduced order modal model in closed-form, and a Newmark-type integration scheme is utilized to find an approximate solution. To benchmark the proposed semi-analytical solution, we experimentally investigate fluid-structure interactions through particle image velocimetry (PIV). PIV is used to estimate the velocity field, and the pressure is reconstructed by solving the incompressible Navier-Stokes equations from PIV data. Experimental results confirm that the flow physics and free-surface elevation during water exit are different from water entry. While water entry is characterized by positive values of the pressure field, with respect to the atmospheric pressure, the pressure field during water exit may be less than atmospheric. Experimental observations indicate that the location where the maximum pressure in the fluid is attained moves from the pile-up region to the keel, as the wedge reverses its motion from the entry to the exit stage. Comparing experimental results with semi-analytical findings, we observe that the model is successful in predicting the free-surface elevation and the overall distribution of the hydrodynamic loading on the wedge. These integrated experimental and theoretical analyses of water exit problems are expected to aid in the design of lightweight structures, which experience repeated slamming events during their operation.

Towards development of a reliable fully-Lagrangian MPS-based FSI solver for simulation of 2D hydroelastic slamming

Towards development of a reliable fully-Lagrangian MPS-based FSI solver for simulation of 2D hydroelastic slamming

Analysis of hydroelastic slamming of flexible structures: modeling and experiments

With the growing interest in the integration of lightweight composite materials in marine vessels, the study of hydroelastic slamming becomes of paramount importance. Here, we propose an integrated theoretical and experimental approach to elucidate the physics of slamming during both the water entry and exit of flexible wedges. The deformation of the wedge is described through Euler-Bernoulli beam theory and the fluid flow is modelled using a combination of the classical Wagner and von Karman theories. Experiments are conducted on a wedge with 25° deadrise angle, whose motion is controlled using a pneumatic control system. The pressure field in the fluid is reconstructed from particle image velocimetry data by integrating incompressible Navier-Stokes equations. Experimental results confirm that the free surface elevation during water exit is significantly different than entry and the pressure is larger than the atmospheric pressure during water entry, while it may be less than atmospheric pressure during the exit stage.

An experimental investigation into whole body vibration generated during the hydroelastic slamming of a high speed craft

High-Speed planing Craft (HSC) expose their crew to high levels of vibration that regularly exceed the daily exposure limit set out by European directive 2002/44/EU; highest accelerations occur during a slam. Many Whole Body Vibration (WBV) reduction strategies are being researched (e.g. suspension seats), but Coats et al. (2003) and Coe et al. (2013) concluded that a combination of methods is required to reduce the level sufficiently to meet legislation.This paper describes an experimental investigation to determine whether hydroelasticity can affect the WBV of HSC using quasi-2D and full-scale drop tests. The quasi-2D tests revealed that hydroelasticity affected peak acceleration and Vibration Dosage Value (VDV), and that a wooden hull generated higher magnitude WBV than fabric hulls. The full-scale drop tests employed an inflatable lifeboat and the internal pressures of the sponson and keel controlled the hydroelasticity. The full-scale results showed that peak acceleration and VDV reduced while decreasing the internal pressures at the transom and crew locations; however, peak acceleration and VDV increased at the bow. Furthermore, the ability of fabric structures to reduce the mass of HSC is discussed. Incorporating hydroelasticity shows potential, alongside other reduction strategies, to alleviate human exposure to vibration of HSC.