Water Entry Of Wedge Research Articles

Fluid–structure interaction analysis of curved wedges entering into water

The water entry of wedges with curvature differs significantly from that of linear wedges, which have been fully investigated and formulated. The safety and integrity of structures prompt an urgent investigation into the mechanism by which the curvature affects slamming loads and structural responses during water entry. This study examines the slamming force characteristics, pressure distributions, fluid jet evolutions, and structural response behaviors of two-dimensional curved wedge sections, considering five different curvatures and two panel thicknesses. A two-way coupling fluid–structure interaction (FSI) solver has been proposed within an open-source framework. The FSI solver was validated against published literature to ensure its high-fidelity. The small deadrise angle results in a more complicated time-domain characteristics for the slamming pressure, with a gradual transition from a single peak to a double peak. The half-peak pressure duration time were defined, and the quantitative results reveal that the hydroelastic effect of the linear wedge is significantly higher than the curved wedges. When considering the geometric curvature, the elastic wedges do not consistently reduce the peak slamming pressure and lengthen the pulse time. Additionally, large deformations generated by the panel vibrations alter the evolutionary pattern of the fluid jet. In contrast to the linear wedge, the structural responses of the curved wedges show distinctive two-stage behaviors.

A general solution for the water entry of an arbitrary curved wedge

ABSTRACT The present study proposes a general solution for the water entry of an arbitrary curved wedge with a constant speed. The solution is based on the assumption that the impact flow is an incompressible potential flow with negligible effects of gravity and surface tension. The slamming and transition stages of the water entry of the curved wedge are addressed theoretically. For the slamming stage, pressure and hydrodynamic force models are derived from a quasi self-similar assumption based on the wetted length and a similarity solution of the water entry of linear wedges. The solution can be applied to the water entry of linear and curved wedges, where the curvature effects are absorbed into the wetted length and the derivative of the wetted length with respect to the penetration depth. For the transition stage, where a fixed separation point of flow detachment is located at the knuckle of the wedge, a hydrodynamic force model is proposed by extending the transition stage model of the water entry of linear wedges to that of curved wedges. The present solution can quickly predict the pressure distributions and hydrodynamic forces for the water entry of curved wedges. The predictions are in good agreement with the experimental and numerical results for the slamming and transition stages.

A hybrid FEM-IBM-level set algorithm for water entry of deformable body

Water entry of deformable bodies has been investigated extensively despite the major challenges in precise simulations of the whole physical process. Inspired by the basic idea of immersed boundary method (IBM), a hybrid FEM-IBM-level set algorithm is proposed where structural compliance is considered. The flow is described by Navier-Stokes equations with an added body force while the drastically moving object of arbitrary geometry is represented by several Lagrangian points on solid boundary. The direct forcing IBM is enhanced and coupled with finite element method (FEM) to facilitate simulation of severe fluid-structure interactions. Consequently, the added body force is calculated implicitly based on the exact velocity boundary condition with divergence-free condition ensured simultaneously. The improved conservative level set technique is adopted for accurate depiction of instantaneously distorted water surface, and the strongly coupled system is resolved iteratively through a partitioned scheme. Examples including sedimentation of a disk, water entry of deformable wedge and cylindrical shell are performed for validation. Specifically, hydroelastic impact of a three-dimensional conical shell is investigated, and the influence factors of entry dynamics are discussed. The results demonstrate the reliability and great potential of present algorithm for practical applications in ocean engineering, naval architecture and military engineering, etc.

Study on the free surface evolution and slamming pressure of curved-wedge water entry using a Riemann-smoothed particle hydrodynamics method

The present study aims to provide a deep understanding of curved wedge water entry. It involves a numerical simulation investigation into the kinematic and dynamic properties of water entry for two curved wedges with deadrise angles of 25° and 35°. The meshless Riemann-smoothed particle hydrodynamics (SPH) model embedded with an acoustic damper is developed to simulate these violent water entries. The validation of the Riemann-SPH accuracy is confirmed through comparison with experimental data, and subsequently, we make a systematical simulation study on curved wedge water entry, including a comparative study of free surface evolution and pressure distribution at different curvatures and drop heights. Furthermore, the kinematics analysis of velocity and displacement of curved wedges and time domain characteristics of slamming pressure loads on both sides of the wedge are investigated. It is revealed that the pressure distribution is symmetrical, with high-pressure regions forming near the bottom of the wedge and gradually propagating outward. The free surface profiles are symmetrical, with deeper depressions formed by sharper wedges. The entry depth and velocity are correlated with the initial theoretical entry velocity, and the rate of speed decline varies with the curvature of the wedge. The slamming pressure loads exhibit distinct time-domain patterns, with lower pressure loads by sharper wedges.

Experimental and Numerical Prediction of Slamming Impact Loads Considering Fluid–Structure Interactions

Slamming impacts on water are common occurrences, and the whipping induced by slamming can significantly increase the structural load. This paper carries out an experimental study of the water entry of rigid wedges with various deadrise angles. The drop height and deadrise angle are parametrically varied to investigate the effect of the entry velocity and wedge shape on the impact dynamics. A two-way coupled approach combing CFD method software STAR-CCM+12.02.011-R8 and the FEM method software Abaqus 6.14 is presented to analyze the effect of structural flexibility on the slamming phenomenon for a wedge and a ship model. The numerical method is validated through the comparison between the numerical simulation and experimental data. The slamming pressure, free surface elevation, and dynamic structural response, including stress and strain, in particular, are presented and discussed. The results show that the smaller the inclined angle at the bottom of the wedge-shaped body, the faster the entry speed into the water, resulting in greater impact pressure and greater structural deformation. Meanwhile, studies have shown that the bottom of the bow is an area of concern for wave impact problems, providing a basis for the assessment of ship safety design.

Study on the effect of cavity oscillation on wedge water entry with a multiphase smoothed particle hydrodynamics model

Previous Smoothed Particle Hydrodynamics (SPH) study on water entry issues has primarily been conducted for the load analysis of impact phase rather than the cavity oscillation effect because the calculation and simulation of this complex physical process are more complicated and time consuming. In order to increase computational efficiency and accuracy, the multiphase δ+-SPH model is combined with Adaptive Particle Refinement technology to investigate the whole process of the wedge's water entry. The hydrodynamic phenomena in the stages before cavity closure for the four cases with different Froude numbers (Fn) are compared and analyzed. After the cavity is pinched off, the wedge exhibits kinematic oscillation. Our test shows that the adoption of sound speed has a significant influence on the oscillation period and peak value of closed cavities in weakly compressible SPH calculations. Then, a suitable sound speed adoption is selected to simulate the oscillatory phenomenon accurately. Comparing the pressure profile with the surface pressure and acceleration of the wedge at the same time, it can be concluded that the oscillation of the hydrodynamic load on the wedge is caused by the pressure oscillation in the closed cavity. Especially for the case of low Fn, the pressure peak on the wedge's surface in the oscillation stage is even greater than the pressure load in the impact stage. The peak pressure of closed cavity is positively correlated with Fn and negatively correlated with Euler number (Eu). Finally, by analyzing the influence of wedge width and impact velocity, it is found that the oscillation period of the closed cavity is related to the morphology of the cavity. The larger the aspect ratio of the closed cavity, the longer the oscillation period.

Study of the water entry and exit problems by coupling the APR and PST within SPH

In this manuscript, the adaptive particle refinement (APR) and particle shifting technique (PST) are coupled and applied to investigate the entire process of water entry and exit. The PST implementation for various types of particles is quantitatively discussed in detail in the coupled APR-PST approach. A comprehensive analysis of different APR-PST coupled schemes is conducted with crucial variables compared and analyzed for the first time. The stability, accuracy and robustness of the developed numerical model are verified by three benchmark tests: 2D wedge water entry, 2D cylinder water exit and 2D cylinder water entry and exit. The obtained results show that the current model can ensure the overall computational precision in the situation of local refinement, which indicates it is a viable way to solve the problems of water entry and exit.

On the three-dimensional effects of the water entry of wedges

Three-dimensional (3D) effects on the total and spanwise slamming coefficients and the pressure reductions acting on the wedge surface during water entry are modeled in a unified manner. First, the water entry of wedges with a constant speed is numerically studied using the finite volume method (FVM) combined with the volume of fluid (VOF) method. The wedge is assumed to enter water with high speeds such that the compressibility, viscosity, gravity and surface tension effects of the fluid can be neglected. The numerical method is validated against an experimental measurement of a freefall water entry of a wedge with a deadrise angle of 30°. Then, the water entry of 3D wedges with deadrise angles of 30, 35, 40 and 45° and beam-span ratios between the width and length varying from 0 to 1 are simulated. The total and spanwise slamming coefficients and the reduction of the pressure distribution are analyzed. The total slamming coefficient is derived with a 3D effect coefficient using a dimensional analysis in the slamming stage and its expression for the transition stage is proposed based on a two-dimensional (2D) transition stage model of the water entry. The spanwise slamming coefficients on the different spanwise sections are modeled with the pressure coefficient distribution of a supercavitating flow around a 2D flat plate. The reductions of the pressure acting on the wedge surface are found to be approximately constant along the wetted length for all spanwise sections, which can be derived using the expressions of the total and spanwise slamming coefficients. Finally, using the proposed model, the predictions of the abovementioned variables are in good agreement with the numerical simulation results in the slamming and transition stages during the water entry of the wedges with different deadrise angles and beam-span ratios.

Application of IITM-RANS3D to free-fall water entry of prismatic and non-prismatic finite wedges

Application of IITM-RANS3D to free-fall water entry of prismatic and non-prismatic finite wedges

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).

Numerical Assessment of Symmetric Wedge Water-entry Impact Using OpenFOAM

The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, initially flat, with a deadrise angle of 30° is considered. This numerical study assesses turbulence, gravity, viscosity, and surface tension during the early stage of penetration. The OpenFOAM software package has been used to simulate the water entry of the wedge at a constant speed of 3 m/s. The governing equations have been numerically built in the solver called overInterDyMFoam. The method has also been used to model the turbulence effect. The effects of turbulent and laminar flow assumptions and for the laminar flow, viscosity, gravity, and surface tension influence on pressure distributions along the wedge's walls have been investigated. It is illustrated that turbulence, viscosity, and surface tension have negligible effects on the pressure distribution in the primary water entry process. However, the pressure distribution is found to be significantly influenced by gravity.

Formulations of hydrodynamic force in the transition stage of the water entry of linear wedges with constant and varying speeds

The slamming and transition stages are the most important for the water entry of wedges, in which the wedges experience the main hydrodynamic forces. The slamming stage is fully investigated by analytical methods, while there are few formulations for the transition stage where the spray root exceeds the top of wedge. Motivated by that, this paper numerically studies the transition stage of the water entry of linear wedges with constant and varying speeds, with assumptions that the fluid is incompressible, inviscid and with negligible effects of gravity and surface tension, and the flow is irrotational. For the constant speed impact, the similitude of the declining forces between different deadrise angles in the transition stage is found by scaling the differences between the maximum values in the slamming stage and the results of steady supercavitating flow. The hydrodynamic force is formulated based on the similitude of the declining forces in the transition stage together with the linear increasing forces in the slamming stage. For the varying speed impact, the hydrodynamic force component caused by the acceleration effect in the transition stage is formulated by an added mass coefficient with an average increase of 27.13% compared with that of slamming stage. Finally, a general expression of the hydrodynamic forces in both the slamming and transition stages is thus proposed and has good predictions in the range of deadrise angles from 5° to 70° for both the constant and varying speed impacts.

Acceleration effects in slamming and transition stages for the water entry of curved wedges with a varying speed

Water entry of wedges with curvature, including slamming and transition stages, differs from the linear wedge cases that were fully investigated and formulated. The transition stage is a successive stage of the slamming stage, where the spray root has exceeded the top of the wedge. In this paper, the slamming and transition stages of a two-dimensional (2D) normal water entry of curved wedges with a varying speed are numerically studied by a hybrid boundary-finite element method (HBF), which solves the fully nonlinear, 2D incompressible potential flow without considering the effects of gravity and the surface tension of water. For the slamming stage, an approximate solution based on the similitude of flow characteristics between the constant and varying speed impacts is proposed, and the expressions of the pressure coefficient and the hydrodynamic force formulated by the acceleration effects are derived. The approximate solution provides fast predictions of pressure distribution and the hydrodynamic force acting on the wedge surface for the varying speed impact. For the transition stage, the acceleration effect is addressed by extending the correction of the added mass coefficient from the linear wedge cases to curved wedge cases. The formula of hydrodynamic force for water entry in varying speeds is given by the slamming coefficient of constant-speed impact and the correction of the added mass coefficient. The predictions by the new formula are in good agreement with the HBF results and experimental results for varying speed impact cases of various curved wedges.

Numerical study of wave effect on water entry of a three-dimensional symmetric wedge

Marine and aerospace structures are frequently subject to impact loads on wave surface. The primary aim of this paper is to obtain a fundamental understanding of wave effect on wedge entry problem. A three-dimensional (3D) full-scale symmetric wedge with three degrees of freedom (3DOF) is numerically modeled in the incompressible air–water two phase flows. The numerical implementation and regular wave surface are realized in Reynolds-averaged Navier–Stokes equations (RANS) framework (STAR-CCM+ 2020.1) by combining with volume of fluid (VOF) and velocity-inlet wavemaking methods. The accuracy of the present numerical model is validated by the experimental tests. Various case studies are then carried out to investigate the difference between calm water and wave crest entries, and to analyze the mechanisms of the wave position and wave height effects through several physical results, including acceleration, velocity, pressure, displacement, rotation and free surface. Results indicate that the process of water entry can be divided into early, vertical-down and bounce-up stages. Further, the wave effect on the water entry problem can be explained as that the incident wave particle velocities and the surface slope result in the variations of effective impacting velocity and entry type of the wedge, and thus remarkably influence the hydrodynamic loads and rotating motion of the wedge. The parametric study reveals that the wave height has no significant effect on the vertical force but positively affects the horizontal impact force and rotating motion of the wedge.

Formulations of Hydrodynamic Force in the Transition Stage of the Water Entry of Linear Wedges with Constant and Varying Speeds

There is an increasing need to develop a two-dimensional (2D) water entry model including the slamming and transition stages for the 2.5-dimensional (2.5D) method being used on the take-off and water landing of seaplanes, and for the strip theory or 2D+t theory being used on the hull slamming. Motivated by that, this paper numerically studies the transition stage of the water entry of a linear wedge with constant and varying speeds, with assumptions that the fluid is incompressible, inviscid and with negligible effects of gravity and surface tension, and the flow is irrotational. For the constant speed impact, the similitude of the declining forces of different deadrise angles in the transition stage are found by scaling the difference between the maximum values in the slamming stage and the results of steady supercavitating flow. The formulation of the hydrodynamic force is conducted based on the similitude of the declining forces in the transition stage together with the linear increasing results in the slamming stage. For the varying speed impact, the hydrodynamic force caused by the acceleration effect in the transition stage is formulated by an added mass coefficient with an averaged increase of 27.13% compared with that of slamming stage. Finally, a general expression of the hydrodynamic forces in both the slamming and transition stages is thus proposed and has good predictions in the ranges of deadrise angles from 5 deg to 70 deg for both the constant and varying speed impacts.

On the energy conversion characteristics of a top-mounted pitching absorber by using smoothed particle hydrodynamics

The top-mounted pitching point absorber is one of the most promising wave energy converters in that it can be easily attached to an existing offshore structure. However, it is difficult to predict accurately its energy conversion performance because of the strongly nonlinear hydrodynamic behaviour. Herein, smoothed particle hydrodynamics (SPH) is used to solve this wave-structure interaction problem. The SPH method is first validated against free surface deformation measurements obtained from a wedge water entry experiment. SPH simulations of regular wave interaction with fixed and freely pitching devices agree well with measured data, providing confidence in the prediction of power conversion performance. Absorbed power and capture width ratio exhibit uni-modal behaviour with wave period. The wave period of peak power within this distribution increases with PTO damping. According to the observed scaling behaviour with device scale, an optimally damped larger scale device is effective at absorbing energy from incident waves of longer wavelength. In finite deep water, the larger device achieves higher efficiency compared with the smaller ones, and its peak efficiency at 2πh/λ=1.1 provides reference for siting.

Vertical Wedge Drop Experiments as a Model for Slamming

_ A deeper comprehension of hydrodynamic slamming can be achieved by revisiting the wedge water entry problem using flexible structures. In this work, two wedge models that are identical, with the exception of different bottom thicknesses, are vertically dropped into calm water. Pressure, full-field out-of-plane deflection, strain, vertical acceleration, and vertical position are measured. Full-field deflections and strains are measured using stereoscopic-digital image correlation (S-DIC) and strain gauges. A nondimensional number, R, quantifying the relative stiffness of the structure with respect to the fluid load is revisited. An experimental parametric study on the effect of R on the nondimensional hydrodynamic pressure and the maximum strain is presented. It was found there is a sharp change in the trend of pressure and strain when R passes through a critical value. It was also discovered that the structural deformation causes a delay in the peak pressure arrival time and a reduction in the peak pressure magnitude during the wedge water entry. Introduction When high-speed planing craft operating in waves becomes airborne and reenters the water surface, a substantial impact or “slam” between the vessel bottom and the water surface will occur (Faltinsen 2005; Lloyd 1989). The bottom slamming events occur frequently and may injure the passengers, compromise the equipment onboard, or even damage the structure. Slamming is a major cause of speed reduction in small craft where slamming loads are important. Current design criteria are primarily based on empirical measurements with little regard for the fluid–structure interaction (FSI) physics of the slamming phenomenon. This study offers a first step toward better understanding of FSI in slamming for optimal structural design in the future. Since the cross sections of most surface effect ships may be approximated by a V-shaped wedge, the slamming characteristics of these sections may be examined by dropping a wedge model into water (Faltinsen 2005; Lloyd 1989). Studying the wedge water entry problem is also helpful in shedding light on the wet deck slamming of catamaran, sloshing under the chamfered roof of a partially filled tank (Faltinsen 2000), seaplane landing (Wagner 1932), water landing of spacecraft and solid rocket boosters, water landing/ditching of aircraft (Abrate 2013), and animal diving behavior (Chang et al. 2016).

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.

Experimental investigation of water entry of bodies with constant deadrise angles under hydrophobic effects

The effects of hydrophobicity on free surface elevation and impact loads are experimentally investigated during the water entry of wedges and cones with various deadrise angles, with particular attention given to the early stages of the impact. As opposed to spheres and cylinders, there is no Froude number dependency and hydrophobicity is not associated only with cavity formation, since a cavity is created at any velocity and at any contact angle in case of wedges and cones. It is observed that the formation of the jet flow, pileups and cavities during the water entry of the objects with constant deadrise angles are modified under the hydrophobic effects. There is no flow separation and the jet root travels faster along the solid surface and larger pileups with larger wetting factors change the chine wetting time resulting in smaller magnitudes when hydrophobicity is present. The slamming coefficient values under hydrophobic effects are measured about 10–25% smaller than the ones obtained with hydrophilic surfaces. Hydrophobic effects are stronger at smaller deadrise angles. It is also shown that the wetted length depends not only on the geometry but also the solid surface characteristics, and the amount of added mass is not proportional to the wetted area and may be decreased with increased wetted width depending on the contact angle.

Cavity Formation during Asymmetric Water Entry of Rigid Bodies

This work numerically evaluates the role of advancing velocity on the water entry of rigid wedges, highlighting its influence on the development of underpressure at the fluid–structure interface, which can eventually lead to fluid detachment or cavity formation, depending on the geometry. A coupled FEM–SPH numerical model is implemented within LS-DYNA, and three types of asymmetric impacts are treated: (I) symmetric wedges with horizontal velocity component, (II) asymmetric wedges with a pure vertical velocity component, and (III) asymmetric wedges with a horizontal velocity component. Particular attention is given to the evolution of the pressure at the fluid–structure interface and the onset of fluid detachment at the wedge tip and their effect on the rigid body dynamics. Results concerning the tilting moment generated during the water entry are presented, varying entry depth, asymmetry, and entry velocity. The presented results are important for the evaluation of the stability of the body during asymmetric slamming events.