Slamming Force 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.

Coupling a time-domain code with a RANS solver for slamming analysis

ABSTRACT A time domain hydroelastic code (TD) based on strip theory is two-way coupled with a Reynolds Averaged Navier−Stokes (RANS) solver to capture the bottom slamming effects on ships. The study is conducted on an Ultra Large Container Ship (ULCS). The methodology considers the hull’s flexibility and analyses longitudinal bending in head seas. Ship motions are calculated using a body non-linear time-domain method based on strip theory. The equations of motion are solved, and time integration is performed using the fourth-order Runge–Kutta method. When a slamming event is identified, the TD code activates a RANS solver to determine the bottom slamming force. The simulations are conducted under extreme sea conditions, and the hull experiences springing and whipping responses. The numerical results of vertical bending moments are compared with experimental data. The bottom and bow flare slamming are identified from the simulations.

Experimental study on wave-induced loads and nonlinear effects for pier-pile group foundations of sea-crossing bridges: Wave slamming and suction effect

Strong nonlinear effects, such as wave slamming, suction effects, and wave overtopping, may be induced during wave-bridge interaction. However, an accurate understanding of these nonlinear effects is still insufficient. This study comprehensively investigates the wave slamming and suction effects on pier-pile group foundations of sea-crossing bridges in a 1:50 scale laboratory experiment. Random and regular waves with different strengths are generated based on wave conditions at the bridge site. Five water depths with a 2 cm spacing are designed to simulate varying pile cap clearances. Various pile arrangements are also set up to explore the influence of piles. Results show that wave slamming is low-aeration and is triggered mainly on the cap bottom wall, whereas the wave action on the vertical wall of the pile cap is quasi-static. The suction effect is generally recorded in the quasi-static phase of pressures and depends on the water exit process and the wave crest height. Moreover, the pressure oscillation after the impact phase results from the flow separation and rotation at structure corners. The wave slamming enhances with the increasing wave frequency when the impact area is constant, otherwise, it depends on the impact area. On the cap bottom wall, the wave slamming on inter-pile areas is enhanced, but the suction effect is less affected by pile arrangements. The increase in pile cap clearances reduces vertical forces but has less effect on horizontal forces. Additionally, a sustained increase in the wave crest height may reduce the slamming force. An empirical method for predicting wave forces is finally proposed based on the water entry theory and experimental findings. This work enhances the physical understanding of nonlinear effects during wave-bridge interaction and aims to support the design of substructures for sea-crossing bridges.

Wave front perturbation effect on the variability of monopile wave impact loads

The slamming wave force and pressure variabilities for monopile wave impacts are studied as functions of wave breaking shape and transverse perturbations on the breaking wave front. The impacting wave topology is characterized as slosh, flip-through, $\varOmega$ , overturning and fully broken. Fifty test repetitions are conducted for each type of wave impact to assess the variability of force impulse, force and pressure. The results for the unperturbed cases show that the slamming force is highest among the nominal slosh, flip-through and $\varOmega$ tests, and that the slamming force variability is highest for the first two. We demonstrate that the slamming force and pressure variabilities decrease notably after selecting and regrouping the tests by similar crest heights and temporal slopes measured at an upstream wave gauge. The group representing $\varOmega$ wave impacts shows the largest mean slamming force and peak pressure, and their variability is the highest among all groups. Further, the effect of lateral perturbations on the pressure, force and impulse variabilities is investigated. Due to the perturbations, the slamming pressure variability for the wave impacts in which the wave front hits the monopile surface increases significantly. The variability of the slamming force is also increased for the perturbed impacts; however, it is smaller than the slamming pressure variability. The force impulse variability shows a low sensitivity to perturbations, and its magnitude is smaller than that of the force variability. Finally, the slamming pressure using fifteen pressure sensors for five selected events is studied. For these tests, oscillations at frequencies associated with structural or bubble oscillations are seen. Further, the air entertainment is documented through video recordings.

Numerical study of slamming and whipping loads in moderate and large regular waves for different forward speeds

This paper describes the development of a time-domain hydroelastic numerical model for investigating the slamming and whipping loads imposed on a ship traveling at different forward speeds. The numerical model integrates a beam model, the 3-D Rankine panel model, and the 2-D modified Logvinovich model. The tilt angle of the 2-D profile in the slamming model is determined by the direction of relative velocity, which takes the forward sailing speed into account. The computational results are validated against a segmented model test of a large cruise ship. The convergence of the model with different numbers of elastic modes and slamming profiles is studied to ensure that the numerical results are stable. The main contributor to the whipping response is found to be the vibration of the first-order elastic mode. The slamming force is sensitive to the longitudinal interval of the slamming profiles, especially in the stern. The characteristics of the slamming pressure under bow flare and the whipping response at midship are also investigated. The numerical and experimental whipping responses are found to be in good agreement, and the local slamming pressure based on the slamming profile is more accurate when considering the effect of the ship's forward speed.

Slamming forces during water entry of a simple harmonic oscillator

When a blunt body impacts an air–water interface, large hydrodynamic forces often arise, a phenomenon many of us have unfortunately experienced in a failed dive or ‘belly flop’. Beyond assessing risk to biological divers, an understanding and methods for remediation of such slamming forces are critical to the design of numerous engineered naval and aerospace structures. Herein we systematically investigate the role of impactor elasticity on the resultant structural loads in perhaps the simplest possible scenario: the water entry of a simple harmonic oscillator. Contrary to conventional intuition, we find that ‘softening’ the impactor does not always reduce the peak impact force, but may also increase the force as compared with a fully rigid counterpart. Through our combined experimental and theoretical investigation, we demonstrate that the transition from force reduction to force amplification is delineated by a critical ‘hydroelastic’ factor that relates the hydrodynamic and elastic time scales of the problem.

Research on the sloshing characteristics of the ship tank with baffles under rolling motion based on smoothed particle hydrodynamics method

The problem of liquid sloshing is widespread in the field of naval architecture and ocean engineering. During the sloshing process, the liquid will produce a large slamming force on the bulkhead. At the same time, the coupled sloshing of the liquid in tank and the hull will also affect the floating state and stability of the hull, and even induce safety accidents. The tank sloshing simultaneous with baffles and under rolling excitation is particularly focused in this paper, which is rarely concerned preciously. Based on the theory of fluid dynamics, the program of tank sloshing under large-amplitude rolling conditions by the smoothed particle hydrodynamics method is compiled, and the accuracy of the numerical model is validated through existing experimental results. Furthermore, the slamming pressure and the wetted height of the tank wall are studied for the cases of different excitation amplitudes and excitation frequencies. Then, the dynamic response characteristics of the sloshing tank with vertical and horizontal baffles are studied, and the effects of different baffle lengths are analyzed. The result shows that under rolling excitation the vertical baffle longer than the water depth can mitigate sloshing to some extent, but the vertical baffle whose length is less than the water depth and the horizontal baffles cannot play a role in mitigating the sloshing.

Laboratory studies of the impact of non-breaking waves on a horizontal emerged deck

The horizontal elements of maritime structures are susceptible to both wave impact and resulting vibrations. These vibrations can lead to a partial or complete failure of structures and require detailed investigations. To address this issue, laboratory experiments were conducted in a wave flume. The aim of this study was to investigate the problem of standing wave impact underneath a horizontal deck. The main focus was on the effect of the wave-induced vertical forces on the global response of the structure. The physical model of the deck was installed above a still water level in front of a vertical barrier. The model was supported by a system of strings and springs. The mechanical system had one degree of freedom corresponding to a small rotational displacement around rear deck edge. Among other physical parameters, the impact pressure generated under the structure due to wave impact was measured. The high sampling frequency of the data acquisition system allowed to capture momentary slamming pressure. The systems of accelerometers and displacement gauges were installed to measure induced vibrations. Thorough analysis of the influence of wave parameters and the deck clearance on the structure response was performed based on the measurements. The rapid slamming force increase, recorded at the moment of impact is not revealed in the dynamic response of the plate.

Vertical force prediction of planing craft in calm water based on variable section slamming model

This paper proposes a prediction method based on a variable section slamming model for the precise calculation of the vertical force of planing craft. Using the idea of 2D+t theory, the three-dimension planing craft hydrodynamic problem is transformed into a two-dimensional slamming problem. For better hydrodynamic performance in practical engineering, the transverse geometrical section of monohull planing craft is usually designed to be variable in the longitudinal direction. In the 2D+t point of view, this problem is numerically treated as a water impact problem of a section with constantly deforming shape. However, previous conventional slamming models cannot directly take the section variation effect into account. To address this deficiency, this paper develops a new Modified Logvinovich Model (MLM). By revising the body surface boundary condition, the newly proposed model can be applied to calculate the slamming force of two-dimensional variable transverse section. The vertical force distribution and the attitude of planing craft are determined by 2D+t theory and the computational fluid dynamics (CFD) method. The results of 2D+t theory considering the variable transverse section are in good agreement with the CFD results.

Experimental Study of Flow Kinematics and Impacting Pressures on a Suspended Horizontal Plate by Extreme Waves

The flow kinematics and impacting pressures on a suspended horizontal plate under extreme waves were investigated experimentally. Three different stages of extreme waves, unbreaking, incipient breaking, and broken, were separately generated using a dispersive focusing method. The flow field kinematics around the plate during the slamming process was measured using a combination of particle image velocimetry and bubble image velocimetry techniques. We found that for aerated areas, there are significant differences in flow patterns under different conditions. The velocity distribution in aeration areas is more discrete. The slamming peak on the upper surface is influenced greatly by the aeration effect, resulting in the maximum slamming peak of the unbreaking case being 3.8 kPa, which is 0.41 times larger than that of the incipient-breaking case and 1.12 times larger than that of the broken case. However, for the area below the plate, the slamming force and flow evolution under different types of breaking exhibit similarity.

Cylinder water entry on a perturbed water surface

The perturbations existing on a breaking wavefront can be a potential explanation for the slamming pressure variability in wave impacts. Here, we investigate the effect of these perturbations by forced vertical slamming of a two-dimensional circular cylinder with constant downward velocity on standing waves. Through experimental modelling and numerical simulation, the slamming force is measured for several standing wave amplitudes and wavelengths. The standing wave phase is tuned such that the impact occurs symmetrically at the instant of maximum crest or trough. Our observations show that slamming coefficients vary with the standing wave amplitude when the wavelength is kept constant and vice versa. The trough impact slamming coefficient can be more than two times the flat impact, and up to four times the crest impact. The experimental results are reproduced by numerical simulations and they agree reasonably well in general. Two analytical approaches based on the von Kármán (NACA, vol. 321, 1929, pp. 1–8) and Wagner (Z. Angew. Math. Mech., vol. 12, 1932, pp. 913–215) methods, which consider the effect of water surface curvature, are introduced. The slamming coefficient calculated from these methods can provide a bound in which the slamming coefficient can be found for each standing wave amplitude and wavelength. Further insight is achieved by numerical simulations of impact on the shorter wavelength to diameter ratio of$0.05<\lambda /D<0.4$. As the wavelength to diameter ratio becomes smaller, the cylinder impacts the water surface at several locations. As a result, multiple peaks occur, and the trapped air at different locations between the cylinder and the water surface yields oscillations with different frequencies on the slamming coefficient time history.

Experimental investigation of breaking regular waves slamming on offshore wind jacket structure

A series of experiments were carried out to investigate the breaking regular wave slamming on an offshore wind jacket structure in a wave flume. The breaking wave characteristics, global slamming forces and local pressure distributions are analyzed. The effects of relative location between jacket structure and breaker location, bottom slope, water depth, incident wave period and wave height on the slamming force and pressure distribution of the jacket structure are investigated. The results show that the maximum value of normalized peak pressure and location will be significantly affected by the bottom slope and water depth. Modified empirical formulas are proposed to calculate the slamming force and slamming duration for the offshore wind jacket structure.

3D motion model for the freefall lifeboat during its launching from a moving ship

Studying a lifeboat’s launch motion mechanism is essential for safe marine evacuation. Motion modeling and simulation offer an effective approach for analyzing the motion characteristics of lifeboat launches under different environmental conditions. However, existing models of the complete launch process for a freefall lifeboat (FFLB) do not capture the latitudinal motion of both the FFLB and its parent body, resulting in models with reduced accuracy and general applicability. To address this issue, we propose a 3D motion model for FFLB launch from a moving ship using Kane’s method. The launch process is divided into the sliding phase and the water entry phase. To account for the impact of ship motion on the lifeboat during the sliding phase, we utilize the mathematical model of Manoeuvring Modelling Group (MMG) to simulate the ship’s motion in waves. Contact forces between the FFLB and the skid are calculated using the node-to-segment method based on elasticity and friction theory. During the water entry phase, hydrodynamic forces are calculated using the strip method, and the slamming force is captured by employing the asymmetric water entry of a finite wedge. Flow separation from the lifeboat’s body is calculated by introducing a fictitious body surface. Our experiments verify the accuracy of the model, with acceleration curves matching well, and a 20% maximum relative error of acceleration extremes during the water entry phase. The simulation results indicate that ship latitudinal motion leads to a similar motion of the FFLB. The ship’s longitudinal motion affects the maximum acceleration of the FFLB and may cause it to setback after water entry. Additionally, the occupants experience less impact when the FFLB enters the water near the wave crest.

Progress in the Research of Wave Slamming Forces on Vertical Cylinders

Progress in the Research of Wave Slamming Forces on Vertical Cylinders

Calculation of slamming wave loads on monopiles using fully nonlinear kinematics and a pressure impulse model

The design methods for highly nonlinear wave loads on monopile structures has over the past years been extended with methods based on pre-computed fully nonlinear wave kinematics. Yet, the slamming events of the strong sea states cannot currently be predicted with these methods. We here present a simple recipe for the application of a recent pressure impulse based slamming load model in combination with fully nonlinear wave kinematics and validate the results against lab measurements of uni- and multi-directional storm sea states. The experimental slamming loads are extracted from lab measurements equivalent to 954 full scale hours. Six methods for the extraction of the slamming force are developed and analysed in detail, with a final selection of two for the further analysis. The experimental analysis shows that the frequency of slamming is larger in uni-directional sea states relative to sea states with directional spreading, and with slightly smaller force impulses. The calculated slamming frequencies from the measurements are used in the application of the numerical slamming model. It is shown that the application is straightforward and robust and involves an intuitive selection of the model inputs from the incident wave kinematics. A generally good agreement between the model and measurement distributions of the force impulse is observed. The difference between 3D and 2D slamming impulses, though, is found to be larger in the numerical model. This is traced to the numerical particle velocities in the wave crests. The pressure impulse model is next extended by assuming a predefined generic slamming force time variation and through calibration of the peak slamming force, a generally good agreement between the model and ensemble-averaged measured slamming force time series is obtained, given the uncertainty in the slamming load extraction. It is also observed that the commonly used non-dimensional slamming force peak of 2π is unrealistically large in the irregular slamming waves because of the 3D effects of small curling factors.

A numerical method to compute flexible vertical responses of containerships in regular waves

In this paper, a series of simulations of hydroelastic problems of containerships are conducted by a nonlinear 3D panel method which is based on the generalized Taylor Expansion Boundary Element Method (TEBEM). In the structure part, the Transfer Matrix Method is selected to perform a modal analysis which provides key parameters of hydroelastic calculation. In the hydrodynamic part, the nonlinearities arising from the variations of instantaneous wetted surface area are considered in the solutions of hydrostatic restoring forces as well as 1st order incident wave forces. Meanwhile, an extended Modified Logvinovich Model (MLM) is presented to predict the slamming forces due to the large-amplitude incident waves. The numerical predictions of the hydroelastic responses of a 6750-TEU containership and S175 in regular waves are presented. The effects of wave steepness and sailing speed as well as the variation characteristics of load components against with wave direction are studied. The numerical and experimental results are in acceptable agreement which proves the accuracy of the proposed method.

Efficient Calculation of Hydrodynamic Loads on Offshore Wind Substructures Including Slamming Forces

Abstract Estimation of the hydrodynamic loads based on strip theory using the Morrison equation provides an inexpensive method for load estimation for the offshore industry. The advantage of this approach is that it requires only the undisturbed wave kinematics along with inertia and viscous force coefficients. Over the recent years, the development in numerical wave tank simulations makes it possible to simulate nonlinear 3-h sea states, with computational times in the order of real time. This presents the possibility to calculate loads using wave spectrum input in numerical simulations with reasonable computational time and effort. In the current paper, the open-source fully nonlinear potential flow model REEF3D::FNPF is employed for calculating the nonlinear wave kinematics. Here, the Laplace equation for the velocity potential is solved on a σ-coordinate mesh with the nonlinear free surface boundary conditions to close the system. A technique to calculate the total acceleration on the σ-coordinate grid is introduced which makes it possible to apply strip theory in a moving grid framework. With the combination of strip theory and 3-h wave simulations, a unique possibility to estimate the hydrodynamic loads in real time for all discrete positions in space within the domain of the numerical wave tank is presented in this paper. The numerical results for inline forces on an offshore wind mono-pile substructure are compared with measurements, and the new approach shows good agreement.

Dynamic characteristics analysis of three-bucket jacket foundation lowering through the splash zone

The offshore wind turbine three-bucket jacket foundation (TBJF) bears some complex force at the stage of lowering though splash zone, and two nonlinear phenomena appear in the bucket foundation: The air cushion structure is formed in the bucket and generates a slamming force on the roof. This paper point at two nonlinear phenomena, the model tests research on the lowering and installation of the TBJF are carried out. The effects of waves and control conditions on air cushion response, the variation law of sling tension and the dynamic characteristics of foundation are investigated. Moreover, the calculation formula of air pressure during foundation lowering process on comprehensively considering various factors to be deduced. In contrast to the experiment tests, the contraction coefficient is revised. In addition, different theoretical analysis models of slamming load on roof during lowering process are established. The influence mechanism of the foundation structure, perforation ratio and lowering speed on the response of air cushion structure and slamming load are revealed. Meanwhile, the attitude control mode during the lowering process of the TBJF is defined. This study provides a theoretical basis for the optimization of foundation installation construction technology and cost control.

Dynamic performance of simply supported girder bridges subjected to successive earthquake-tsunami events

Coastal bridges are susceptible to severe damage when subjected to successive earthquake-tsunami events. Previous studies mainly consider the tsunami loadings as hydrodynamic forces, whereas other hydrodynamic forces such as uplift and slamming forces, are not fully investigated. Moreover, there are limited studies on the dynamic performance of simply supported girder bridges under the earthquake-tsunami sequences. To this end, this paper aims to conduct an in-depth investigation on dynamic performance of simply supported bridges subjected to sequential earthquake and tsunami hazards by means of a high-fidelity wave force simulation approach. More specifically, a typical, already constructed simply supported girder bridge is taken as the example bridge, and the numerical model of this bridge is built using the analytical platform OpenSees. The applied time series of tsunami wave force with five wave heights are generated based on a refined computational fluid dynamics (CFD) model, and are separately combined with the time histories of 21 pairs of far-field earthquake records to generate the sequential earthquake and tsunami loadings. Subsequently, nonlinear time history analyses (NTHAs) are carried out to obtain the structural dynamic responses, and the effects of preceding earthquakes and wave heights on the performance are investigated. Results indicate that the bearings are susceptible to the damage in the longitudinal direction of the bridge under the sequential earthquake and tsunami loadings, while the piers sustain more damage in the transverse direction. The preceding earthquakes have a significant effect on the bridge performance, and the effect becomes more pronounced with the increase of the ground motion intensity. The contribution of the tsunami loadings to the bridge response increases as the wave height rises. In particular, the transverse pier drift is dominated by the tsunami loadings when the wave height is higher than 7 m. The outcome of this study could aid the design and management of coastal bridge subjected to successive earthquake-tsunami events.

Experimental study of stern slamming and global response of a large cruise ship in regular waves

This paper presents an experimental investigation of stern slamming and global responses using a segmented model test. A model of large cruise ship with a long and flat stern is selected for the test, with a scale ratio of 1:60. Experimental random uncertainty is analyzed by considering the model responses in a series of regular waves. It is found that different types of response have different levels of dispersion. A calculation model that can reproduce ship–wave relative motions during stern slamming is established based on the experimental data. The influences of the instantaneous impact velocity and longitudinal deadrise angle on the distribution of local slamming pressure are analyzed. Finally, the effect of stern slamming on global responses is discussed. This investigation shows that the longitudinal deadrise angles are usually small in following waves, and this results in a large slamming force loaded on the stern in a short time. In addition, a whipping response of the hull girder will be excited.