Slamming Force Research Articles

Slamming force decomposition with gravity effect

In this paper, the original slamming force decomposition, where the total vertical slamming force is decomposed into speed and acceleration terms with coefficients depending on the penetration depth only, is further developed by including the gravity effect through an additional term that is only dependent on the penetration depth as well. The speed, acceleration and gravity related coefficients are extracted by Computational Fluid Dynamics (CFD) approach, where gravity can be readily included or excluded, using only small number of CFD computations for particular body motions. Then the components of the hydrodynamic force acting on the entering body can be evaluated using these coefficients and the force decomposition formula for any motion of the body avoiding direct CFD computations for each particular motion. CFD results show that the gravity significantly affects the slamming force for relatively small values of the entry speed. It is shown that the improved force decomposition provides an accurate approximation of the computed forces under various speed/acceleration combinations for arbitrary two-dimensional body shapes including vertical entry of symmetric/asymmetric bodies and oblique entry of symmetric bodies, except for penetrations with large deceleration when the body stops shortly after the flow separation.

Experimental investigation of breaking regular and irregular waves slamming on an offshore monopile wind turbine

A series of experiments were carried out to investigate the breaking regular and irregular wave forces on a monopile foundation in a wave flume with a model scale factor of 1:40. Breaking regular wave slamming characteristic was firstly analyzed and comparisons were made between typical plunging and spilling breakers. For the irregular wave conditions, the wave slamming processes were recorded to illustrate the concentration and dissipation of wave energy. The effects of bottom slope, water depth, significant wave height and peak period on the wave slamming force and pressure distribution on the monopile were investigated. The results show that the distribution of maximum wave slamming pressure is affected by the water depth and bottom slope. Multiple harmonic components of the wave slamming force are observed and the predominant harmonic forces are first- and second- order components. The significant wave height and turbulence kinetic energy dissipation have significant effects on the wave slamming forces. A Gaussian distribution formula is proposed to fit the exceedance probability distribution of wave slamming force. Modified empirical formulas are proposed to calculate the wave slamming coefficient for the breaking regular and irregular waves on the monopile.

Slamming dynamics of diving and its implications for diving-related injuries.

In nature, many animals dive into water at high speeds, e.g., humans dive from cliffs, birds plunge, and aquatic animals porpoise and breach. Diving provides opportunities for animals to find prey and escape from predators and is a source of great excitement for humans. However, diving from high platforms can cause severe injuries to a diver. In this study, we demonstrate how similarity in the morphology of diving fronts unifies the slamming force across diving animals and humans. By measuring a time-averaged impulse that increases linearly with the impact height, we are able to estimate the unsteady hydrodynamic forces that an average human body experiences during the slamming phase of a feet-first, hand-first, or head-first dive. We evaluate whether the unsteady forces put the diver at risk of muscle or bone injuries for a particular diving height. Therefore, this study sheds light on a hydrodynamics-based protocol for safe high diving and an evolutionary driver for animal morphology.

Experimental parametric study on hydroelastic behaviour of a 15000-TEU container ship based on segmented ship model

ABSTRACT Large-scale ships with high elasticity and low natural frequency, behave high dynamic response amplitude under impulsive wave loads (whipping) and short period waves (springing), which could result in serious ultimate loads and fatigue damage. The segmented model test is a more powerful approach for the ship hydroelastic analysis compared with ship seakeeping test. However, the effect of some test parameters on the hydroelastic responses is still not a clear statement. Therefore, the number of segments, propulsion mode and backbone form are chosen for the parametric study on ship hydroelastic behaviour. A three-dimensional (3-D) nonlinear time-domain hydroelastic method is developed, in which the nonlinearity of instantaneous wetted surface and slamming force are considered. Through the analysis of natural frequencies and vertical bending moments (VBM), the impact on hydroelastic behaviour is discussed. Results show that self-propelling models with variable cross-section backbones are more suitable and reliable in studying nonlinear hydroelastic behaviour.

Numerical investigation into water entry problems of a flat plate with air pockets

Computational Fluid Dynamics (CFD) investigations into water entry problems of a rigid flat plate with air pockets were systematically conducted. The Volume of Fluid (VOF) model was utilised to capture localised slamming phenomena that occur during, and post-impact events. The model's geometry was modified to include a pocket on the slamming impact surface to investigate the effect of air entrapment on the magnitude and distribution of slamming forces and pressures. A parametric study was conducted on the geometric parameters of the modelled pocket by altering its area, depth, and volume to examine the response of slamming force and pressure loading under several impact velocities. The numerical results of slamming forces and pressures were in good agreement with experimental drop test measurements (with relative error of -6% and 7% for the magnitude of slamming force and pressure, respectively). The numerical results proved that the peak pressure is proportional to the magnitude of impact velocity squared (pmax∝v2).

Three-Dimensional Effects on Slamming Loads on a Free-Falling Bow-Flare Cylinder Into Calm Water

Abstract Three-dimensional effects on slamming load predictions of a ship section are investigated numerically using the unsteady incompressible Reynolds-averaged Navier–Stokes (RANS) equations and volume of fluid (VOF) method, which are implemented in interDyMFoam solver in open-source library OpenFOAM. A convergence and uncertainty study is performed considering different resolutions and constant Courant (CFL) number following updated ITTC guidelines. The numerical solutions are validated through comparisons of slamming loads and motions between the computational fluid dynamics (CFD) simulations and the available experimental values. The slamming force and slamming pressures on a 2D ship section and the 3D model are compared and discussed. Three-dimensional effects on the sectional force and the pressures are quantified both in transverse and longitudinal directions of the body considering various entry velocities. Comparing with 2D simulations, the 3D models provide lower predictions on slamming loads. The results show that the three-dimensional effects on the maximum slamming force coefficient are about 25%, while the effects on pressures differ from locations and entry velocities, ranging from 11% to 29%.

NUMERICAL PREDICTION OF SLAMMING LOADS DURING WATER ENTRY OF BOW-FLARED SECTIONS

The two-dimensional water entry of bow-flared sections is studied by using a Multi-Material Arbitrary Lagrangian- Eulerian (MMALE) formulation and a penalty-coupling algorithm. A convergence study is carried out, considering the effects of mesh size, the dimension of fluids domain, and fluid leakage phenomenon through the structure. The predicted results on the wetted surface of a bow-flared section are compared with published experimental values in terms of vertical slamming force, pressure distributions at different time instances and the pressure histories at different points. Comparisons between the numerical results and measured values show satisfactory correlation. An approximation method is adopted to estimate the sectional slamming force showing good consistency for the peak forces.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method.
 Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Extraction of New Applicable Dimensionless Relations in the Wedge Impact Problem Using WCSPH Method

Impact problem associated with water entry of a wedge has important applications in various aspects of naval architecture and ocean engineering. In the present study, the 2DOF (2 Degrees of Freedom) wedge impact problem into the water with various wedge deadrise angles and impact velocities is investigated using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. Artificial viscosity and density correction are used to create stability and also to prevent the penetration of fluid particles into the solid boundary. Solving the impact problem is very time-consuming, therefore extracting new mathematical relations can be very useful to calculate some important and applicable parameters in a certain range of wedge angles and impact velocities. In the present research, some new dimensionless applicable relations using the Buckingham π theorem are extracted to investigate important parameters such as acceleration and slamming force in general cases of a wedge impact problem. Then, these mathematical relations are validated by the results obtained from the simulations.

Uncertainty due to discretization on the ALE algorithm for predicting water slamming loads

Numerical uncertainty due to discretization on the Arbitrary Lagrangian-Eulerian (ALE) Finite Element method is investigated in the study. The paper quantifies uncertainty using two ITTC recommended methods, and also applies a constant Courant-Friedrichs-Lewy (CFL) number based discretization approach, instead of performing the independent grid and time-based discretization recommended by ITTC. As a case study, water entry of a flat bottom rigid and flexible plate is simulated considering various entry velocities. The total slamming loads and structural responses on both the rigid and elastic bottom plates are predicted and validated against available experimental data. Results indicate that numerical errors due to discretization differ in the various parameters and from case to case. They do affect the analysis of slamming loads and associated structural responses, and the hydroelasticity analysis as well. The hydroelasticity effects on the slamming force generally increase as the entry velocity increases, however, the quantitative results differ much for models with different grids. For example, when the hydroelasticity effect is estimated using the finer model, the deviation of the total slamming force on the elastic plate relative to the one on the rigid body are 56%, 57%, and 63% respectively for the three constant entry velocities, whereas the estimations are −27%, −4% and 3% with the coarser model. The study concludes that the uncertainty due to discretization in ALE is not just case-specific, but also parameter specific. The uncertainty quantification procedures with a constant CFL number based refinement are recommended to investigate the uncertainty comparing to the individual grid and time step study, in particular for the ALE solution where the time step is adjusted automatically as the grid changes. Thus, consideration should be given to updating the ITTC guidelines to incorporate the constant CFL based discretization approach.

CFD modelling and grid uncertainty analysis of the free-falling water entry of 2D rigid bodies

The open source Computational Fluid Dynamics (CFD) library, OpenFOAM, is utilized to simulate the water impact of two-dimensional wedges and ship bow sections. For the free falling cases, the predicted results are validated against existing experimental data, and the parameter study is performed regarding the number of cells, time step, and width of the water domain applied in the numerical models. Grid uncertainty analysis for the CFD results is performed with a constant Courant–Friedrichs–Lewy number, to assess the consistency and accuracy of the CFD solver in solving the present problem. Three uncertainty estimation methods are compared on the peak slamming forces and pressures: Correction Factor (Cf), Factor of Safety (Fs), and Least-squares Fit (Lf) based approaches. All three of them can provide reliable uncertainty estimation for CFD simulations, as long as the right mesh configuration has been used. The variations of pressure distribution on wedge sections with various deadrise angles and initial entry velocities are analyzed. To examine the capability of the tool to predict the slamming loads for a section with roll motions two cases are simulated: one considering a free roll motion and another with constant roll angles. The predicted slamming loads are compared with the available experimental data and other numerical results.

Assessment of three-dimensional effects on slamming load predictions using OpenFoam

Three-dimensional effects on slamming loads predictions are investigated numerically using the unsteady incompressible Reynolds-Average Navier-Stokes (RANS) equations and volume of fluid (VOF) method, which are implemented in the open-source library OpenFoam. Three cases of free-falling water entry problems are considered. The numerical solutions are validated through the comparisons of slamming loads and motions between the CFD simulations and the available experimental values. The total slamming force and slamming pressures on the 3D wedge cylinder, ship section and slender circular cylinder are compared with the results on the 2D sections, respectively. The results show that the 3D predictions on the maximum slamming force coefficient are around 21%∼23% lower for the wedge with a deadrise angle of 30º and are around 16% lower for the slender circular cylinder, relative to the 2D calculations.

Operation of Ride Control Systems to Minimise Slamming of Wave-Piercing Catamarans

Wave slam produces dynamic loads on the centre bow of wave piercing catamarans that are related to the relative vertical motion of the bow to the encountered wave surface. Rapid slam forces arise when the arch sections between centre bow and main hulls fill with rising water. In this paper time domain solutions for high speed ship motion in waves, including the action of active motion controls, are used to compute the slam forces. Slamming occurs at specific immersions of the bow whilst the peak slam force is characterised by the maximum relative vertical velocity of the bow during bow entry. Vertical motions of bow and encountered wave are in antiphase at encounter frequencies where slamming is most severe. The range of encounter frequencies where slamming occurs increases with wave height. Wave slam loads reduce ship motions, the heave motion being most reduced. Deployment of a fixed, inactive T-foil can reduce slamming loads by up to 65 %. With active controls peak slamming loads on the bow can be reduced by up to 73% and 79% in 4 m and 3 m seas, local control feedback being marginally the most effective mode of control for reduction of slamming.

Experimental investigation of focused wave action on coastal bridges with box girder

The waves generated by hurricanes, together with storm surges, have led to severe damage and even failures in many coastal bridges in the Gulf of Mexico. Several studies have been conducted to investigate the effects of wave action on coastal bridges over the past 15 years. However, most of the existing research, both experimental and numerical, has used a regular or irregular wave as the incident wave; this cannot accurately and efficiently reproduce the features of hurricane waves. In this study, a periodical focused wave (PFW) was employed to experimentally investigate wave actions on coastal bridges. A coastal bridge model including a deck and box girder was set up in a wave flume to measure wave forces. PFWs with different peak frequencies and main crests were calibrated in the empty flume, and then were used to observe the wave action on the bridge model at different clearances. Using a smoothing method, the quasi-static and slamming parts were separated from the total wave forces. The experimental results show that the maximum horizontal and vertical wave forces both occur at approximately the time when the overhanging deck is fully submerged and wave water begins to overlap the bridge deck. The vertical quasi-static force is almost linear in relation to the main crest and clearance, but the horizontal and vertical slamming forces show a complicated tendency. The relationships between the dimensionless wave forces and relative maximum amplitude/wave steepness are studied, along with the relative relationships between the wave force components. The experimental results are also compared with those from two existing methods.

Experimental and Numerical Study of the Hydroelastic Response of a River-Sea-Going Container Ship

The hydroelastic behaviour of a river-sea-going ship hull is analysed experimentally and numerically. A segmented ship model connected by a steel backbone is tested in regular waves, and its high-frequency vibrations such as springing and whipping responses are identified. The hydroelastic response of the ship is numerically calculated using a hydroelastic time domain method based on strip theory, which is extended to include an improved model of the slamming load. The slamming forces in the bow section are determined using the Modified Longvinovich Model (MLM) instead of the Von Karman model. The vertical motions and wave-induced loads are calculated and compared with the experimental results. The response amplitude operators of the vertical loads and the high-order harmonics are analysed under different speeds, showing good agreement with the experiments. The slamming loads on the bow section of a river-to-sea ship are predicted utilizing the MLM model and compared with the Arbitrary Lagrangian Eulerian algorithm by LS-DYNA and with the measured results.

Computational Model for Simulation of Lifeboat Free-Fall during Its Launching from Ship in Rough Seas

In order to improve the accuracy of the freefall of lifeboat motion simulation in a ship life-saving simulation training system, a mathematical model using the strip theory and Kane’s method is established for the freefall of the lifeboat into the water from a ship. With the boat moving on a skid, the model of the ship’s maneuvering mathematical group (MMG) is used to model the motion of the ship in the waves. Based on the formula of elasticity and friction theory, the forces of the skid acting on the boat are calculated. When the boat enters the water, according to the analytical solution theory of slamming, the slamming force of water entry is solved. The simulation experiments are carried out by the established model. The results of the numerical simulation are compared with the calculation results of the hydrodynamics software Star CCM+ at water entry under initial condition A in the paper. The position and velocity of the center of gravity of the boat, the angle, and velocity and acceleration of pitch calculated by the two methods are in good agreement. There is a little difference between the values of translation acceleration calculated by the two methods, which is acceptable. This shows that our numerical algorithm has good accuracy. A qualitative analysis is performed to find the safe point of water entry under the condition of different wave heights and two situations of a ship encountering waves. Finally, the model is applied to the ship life-saving training system. The model can meet the system requirements and improve the accuracy of the simulation.

Wave Front Steepness and Influence on Horizontal Deck Impact Loads

In design storm sea states, wave-in-deck forces need to be analysed for fixed and floating offshore platforms. Due to the complex physics of wave impact phenomena, numerical analyses should be complemented by model test data. With a large statistical variability, such experiments usually involve running many 3-h storm realisations. Efforts are being done to establish efficient procedures and still obtain improved statistical accuracy, by means of an initial simplified screening based on parameters derived from the incident wave record only. Here, we investigate the vertical rise velocity of the incident wave elevation at a fixed point in space, which indirectly measures both the local slope and the near-surface orbital velocity. A derived simple deck slamming model is also suggested, to support the check of the physical basis of the approach. Correlation against data from a GBS wave-in-deck model test is used for checking this model. The results show that, although there is a significant random scatter in the measured impact forces, especially in the local slamming forces but also in the global forces, there is a correlation to the rise velocity. Comparisons to the simple load model also show promising results when seen on background of the complex physics and random scatter of the impact problem.

Experimental and numerical investigation of a jacket structure subject to steep and breaking regular waves

Jacket structures installed in shallow water less than 50 m for offshore wind turbines are frequently exposed to steep and even breaking waves, which may result in severe damage of the structure. However, the models for calculating wave loads were primarily developed for monopile structures, and may not be suitable for jacket structures. The aim of this paper is to improve the understanding of extreme wave loads on jacket structures exposed to steep and breaking waves, based on a combination of numerical modeling and large scale experiments. The experiments with a 1:8 scaled jacket structure exposed to controlled regular waves were conducted in the WaveSlam project. In this study, the measured wave surface elevations and water particle velocities from the experiments are reproduced using a fully nonlinear potential flow solver with a fairly good agreement. Furthermore, the validity of the Morison equation applied to jacket structures is investigated. A reasonably good agreement is achieved for the steep waves without occurrence of breaking. In terms of the breaking waves, the calculated hydrodynamic forcing is examined by subdividing it into a quasi-static and an impulsive slamming force component. The quasi-static force is well reproduced by the Morison equation given the fully nonlinear wave kinematics. Furthermore, eleven degrees of parameterization of the slamming force history are statistically analyzed for a better understanding of the slamming force characteristics. Significant variabilities are presented in these parameters, as a result of the inherent uncertainties in the wave breaking process. In the end, practical implications of the proposed slamming force description to load assessment of a realistic offshore wind jacket structure are discussed.

Numerical investigation of the effect of aeration and hydroelasticity on impact loading and structural response for elastic plates during water entry

This work presents a comprehensive numerical study of the impact of aeration and hydroelasticity on slamming loads and structural response of elastic plates during a water entry event. A numerical tool is developed with OpenFOAM and validated against experimental data from available benchmark tests. An extensive parameter investigation revealed that the structural flexibility of a plate exerts a noticeable effect on slamming loads for pure water entry cases, which almost completely disappears when the water is aerated. The effect of aeration on slamming loads is quite significant. With only 0.5 % air fraction, aeration can reduce substantially the peak slamming forces, but as the load duration increases at the same time the force impulse remains almost constant. The structural response, in terms of strain rates, reacts directly on the hydrodynamic loads for stiff plates, and exhibits resonating effects and less influence on aeration levels at higher flexibilities. This suggests that the structural performance in a slamming event must be carefully considered, and is only directly related to loads for very stiff structures. For this purpose, a new functional relation between peak impact forces/pressures and impact velocity in the presence of aeration is suggested within the present study.

Experimental study on the asymmetric impact loads and hydroelastic responses of a very large container ship

This paper presents an experimental investigation of asymmetric impact effects on hydroelastic responses. A 1:64 scaled segmented ship model with U-shape open cross-section backbone was newly designed to meet elastic similarity conditions of vertical, horizontal and torsional stiffness simultaneously. Different wave heading angles and wavelengths were adopted in regular wave test. In head wave condition, parametric rolling phenomena happened along with asymmetric slamming forces, the relationship between them was disclosed at first time. The impact forces on starboard and port sides showed alternating asymmetric periodic changes. In oblique wave condition, nonlinear springing and whipping responses were found. Since slamming phenomena occurred, high-frequency bending moments became an important part in total bending moments and whipping responses were found in small wavelength. The wavelength and head angle are varied to elucidate the relationship of springing/whipping loads and asymmetric impact. The distributions of peaks of horizontal and torsional loads show highly asymmetric property.