Slamming Coefficient Research Articles

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.

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.

An efficient three-dimensional multiphase fluid structure interaction model on GPU for water impact of a moving body with complex geometries

This paper presents an efficient three-dimensional (3D) multiphase fluid structure interaction (FSI) model to simulate water impact of complex moving bodies in ocean engineering. This numerical model adopts an improved ghost cell method (GCM) to enforce the boundary conditions on the moving boundaries and the gradient augmented level set (GALS) method to capture the nonlinear free surfaces. An improved iso-surface representation method is highlighted to track arbitrary moving bodies such as sharp or concave shapes. Also, a GPU-CUDA parallel framework is incorporated to greatly accelerate the computational performance. The accuracy and capability of the present model is validated by simulating 3D water entry of arbitrary free-falling bodies (a sphere, a wedge, a wedge with side plates, and a catamaran). Excellent acceleration performance of the present GPU model is demonstrated. The present results including the slamming coefficient, the acceleration, and the local pressure agree satisfactorily with the experimental data. The complex flow evolutions are well captured such as long cavity wall, the pinch-off of the cavity, and the air entrapment. Also, the air entrapment and 3D effects are confirmed to be nonnegligible for the water impact of complex bodies with enclosed sections, which can be well predicted by the present model.

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.

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.

Quantification of spatial free-surface air entrapment during rigid body impacts into a quiescent fluid

This work quantifies the spatial distribution of air entrapped below rigid wedge, curved and flat specimens impacting water in free-fall. We have achieved unintrusive quantification by processing high-speed camera images using MATLAB® binarization and filtering techniques. Results have been quantified as a percentage area of the impacting specimen. For experiments with 300mm wide specimens, little to no air entrapment occurs for deadrise angles ≥2∘ and curved surfaces with radii ≤2.5m. The entire specimen is covered by an air layer for deadrise angles ≤0.5∘ or radii ≥10m. Importantly air entrapment was transitional/variable for deadrise angles between 0.5∘ and 2° or radii between 2.5 and 10m. Loading during the impacts has been used to compute experimental slamming coefficients. The cushioning is apparent in the wedge and curved slamming coefficients for β≤0.5∘ and R≥10m respectively, correlating to complete air layer entrapment. The wedge deadrise angle of 1° and curved radius of 5m experience elevated slamming coefficients, correlating to transitional spatial air entrapment. Finally, a flat plate slamming coefficient reduction occurs as width increases, suggesting an increase in air cushioning.

URANS PREDICTION OF THE SLAMMING COEFFICIENTS FOR PERFORATED PLATES DURING WATER ENTRY

The slamming coefficients for perforated plates of various perforation ratios and layout configurations were predicted using Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver STAR-CCM+. The numerical model was validated by comparing with experimental measurements of slamming coefficient for a circular cylinder. The slamming coefficients and free surface profiles of perforated plates were then predicted at full-scale. It was found the air compressibility plays an important role by studying flat plate water entry phenomena. For perforated plates with small gap length/width ratios, the ability of the trapped air to evacuate through the space between the bottom of the plate and free surface is similar. For perforated plates with different gap number at a fixed perforation ratio, the slamming coefficient is increased with the increase in gap length/width ratio. However, a further increase in length/width ratio may impose a negative impact on the escape of trapped air due to the increase of gap number.

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.

Fluid Structure Interaction of 2D Objects through a Coupled KBC-Free Surface Model

In this study, the capabilities of a coupled KBC-free surface model to deal with fluid solid interactions with the slamming of rigid obstacles in a calm water tank were analyzed. The results were firstly validated with experimental and numerical data available in literature and, thereafter, some additional analyses was carried out to understand the main parameters’ influence on slamming coefficient. The effect of grid resolution and Reynolds number were firstly considered to choose the proper grid and to present the weak impact of such a non-dimensional number on process evolution. Hence, the influence of Froude number on fluid-dynamics quantities was pointed out considering vertical impacts of both cylindrical, as in the references, and ellipsoidal obstacles. Different formulations of slamming coefficient were used and compared. Results are pretty encouraging and they confirm the effectiveness of lattice Boltzmann model to deal with such a problem. This leaves the door open to additional improvements addressed to the study of free buoyant bodies immersed in a fluid domain.

Slam-Induced Loads on a Three-Dimensional Bow With Various Pitch Angles

Abstract A 3D water entry of a typical bow model of river-to-sea ship is studied experimentally. A large number of systematic experiments have been performed for the bow model with different pitch angles. Considering various pitch angles and impact velocities in the model tests, the slamming pressure distributions on the bottom of the bow are presented and discussed. The measured slamming pressures on the bow are identified in terms of the maximum slamming coefficient. The effects of the pitch angle and impact velocity on slamming pressure are discussed as well, based on the experimental measurements. It is shown that the slamming load on the bottom of the model increases as the pitch angle decreases in most cases. With a higher impact velocity, the coefficient of the maximum slamming pressure is smaller for most of the tested cases.

Numerical investigation of solitary wave interaction with a row of vertical slotted piles on a sloping beach

To improve our current understanding of tsunami-like solitary waves interacting with a row of vertical slotted piles on a sloping beach, a 3D numerical wave tank based on the CFD tool OpenFOAM® was developed in this study. The Navier-Stokes equations were employed to solve the two-phase incompressible flow, combining with an improved VOF method to track the free surface and a LES model to resolve the turbulence. The numerical model was firstly validated by our laboratory measurements of wave, flow and dynamic pressure around both a row of piles and a single pile on a slope subjected to solitary waves. Subsequently, a series of numerical experiments were conducted to analyze the breaking wave force in view of varying incident wave heights, offshore water depths, spaces between adjacent piles and beach slopes. Finally, a slamming coefficient was discussed to account for the breaking wave force impacting on the piles.

Parameter estimation of a breaking wave slamming load model using Monte Carlo simulation

For offshore wind turbines (OWTs) located in relatively shallow water, the design is influenced by the occurrence of breaking waves. The strongly nonlinear properties associated with the wave breaking process result in challenges in modelling their impact loads on the structures. The total impact loads are normally calculated as the sum of a slowly varying quasi-static load and an impulsive slamming load. The quasi-static load is normally calculated using Morison’s equation and the slamming load is approximated by the Goda model or the Wienke-Oumeraci model. Given the dynamic properties of OWTs, structural resonances might be excited by the impulsive slamming load. Therefore, there is a clear need to evaluate the response effect excited by the slamming load. In this paper, the response of a vertical pile subjected to a severe breaking wave case is investigated by a combination of data from a large-scale experiment and numerical simulations. The slowly varying quasi-static load obtained in a non-breaking wave packet is modelled using Morison’s equation with the wave kinematics obtained from a fully nonlinear potential flow solver OceanWave3D. The governing parameters used in a slamming load model are estimated using the Monte Carlo method and verified by comparing the experimental data with the numerical simulation results. It is found that the slamming coefficient and the curling factor are close to the values found by the Wienke-Oumeraci model, however the impact duration is significantly larger than the values found by the Goda model and the Wienke-Oumeraci model, which is important for the assessment of the dynamic responses of OWTs.

Impact Pressure Distribution on a Monopile Structure Excited by Irregular Breaking Wave

Abstract The problem of impact pressure distribution on a monopole structure excited by irregular breaking waves is investigated. The analysis is performed by applying a numerical model that combines potential flow model with a Navier-Stokes/VOF solution. The temporal pressure distribution is analysed for two breaking wave cases characterized by the significant difference in the steepness of the wave front. The peak impact pressures are observed in the region below the overturning wave jet where the pressure increases rapidly resulting in a peak value of the slamming coefficient equal to Cs=2π. The vertical load distribution provided by the derived model is more realistic than a rectangular shape distribution applied in engineering practice. This is because the vertical load distribution strongly depends on breaking wave shape and it is difficult to uniquely approximate such a load distribution by a rectangle.

URANS Prediction of the Slamming Coefficients for Perforated Plates During Water Entry

The slamming coefficients for perforated plates of various perforation ratios and layout configurations were predicted using Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver STAR-CCM+. The numerical model was validated by comparing with experimental measurements of slamming coefficient for a circular cylinder. The slamming coefficients and free surface profiles of perforated plates were then predicted at full-scale. It was found the air compressibility plays an important role by studying flat plate water entry phenomena. For perforated plates with small gap length/width ratios, the ability of the trapped air to evacuate through the space between the bottom of the plate and free surface is similar. For perforated plates with different gap number at a fixed perforation ratio, the slamming coefficient is increased with the increase in gap length/width ratio. However, a further increase in length/width ratio may impose a negative impact on the escape of trapped air due to the increase of gap number.

Global slamming forces on jacket structures for offshore wind applications

This study investigates the global slamming forces due to plunging breaking waves on a jacket structure, based on the statistical analysis of the experimental data from the WaveSlam project. Hammer tests and wave tests were conducted in the project, and the data are used to reconstruct the time series of the global slamming force by employing a method based on linear regression. The used wave test data were acquired under one wave condition. A total of 3910 force time series are reconstructed and analyzed statistically to reveal the characteristics of the slamming force. For each force time series, six parameters are introduced to describe it, including the peak force, duration, impulse and rising time, etc. The variability and correlation of these parameters are investigated. The distribution of these parameters is modeled with various probability distributions. The results show the high variability of the slamming force and the importance of statistical analyses. Based on these statistical analyses, the slamming coefficient is estimated from the peak force. For a curling factor of 0.4, the mean slamming coefficient is about 1.29. When considering one standard deviation around the mean, the slamming coefficient varies from 0.70 to 6.78 for a curling factor ranging from 0.1 to 0.5. A representative time series of wave slamming force is obtained by averaging the individual force time series. Accordingly, a 3-parameter triangular force model and a 5-parameter exponential force model are proposed to describe the development of the slamming force in time.

Wave impact load on jacket structure in intermediate water depth

The aim of this study is to estimate impact forces on a jacket using the improvised methodology and to propose a slamming coefficient for the jacket structures. Four types of structures have been discussed in this study, single cylinder (SC), legs with connecting braces in wave direction, legs with connecting braces transverse to wave direction and jacket structure. The SC case was analyzed using the improvised methodology and the obtained slamming coefficient was validated with the existing literature. Based on this initial validation, the methodology was extended for other models. Four loading cases were identified based on the location of the wave breaking. The impact load estimated was compared with theoretical formulas given by Goda et al. (1966), Wienke and Oumeraci (2005) for all models. The slamming coefficient (Cs) was found for wave characteristics having spectral bandwidth ratios of 1 and 0.75. For both the wave characteristics, the Cs was found to be higher for the loading case, when the wave breaks in front of the structure. The Cs varies between 2.2 and 4.6 depending upon the wave characteristics, with maximum obtained for 0.75. The method used in this paper can be used for estimating impact loads on complex structures.

Breaking solitary waves and breaking wave forces on a vertically mounted slender cylinder over an impermeable sloping seabed

In the present study, breaking solitary waves over a sloping seabed and breaking wave forces on a vertically mounted cylinder are simulated with the three-dimensional CFD model REEF3D. The numerical model uses the Reynolds-Averaged Navier–Stokes (RANS) equations together with the level set method (LSM) for the free surface and the $$k-\omega $$ for the turbulence. The numerical model is validated for simulating breaking solitary waves and breaking wave forces against the experimentally measured free surface profiles and vertical and horizontal velocities by Mo et al. (Ocean Eng 74:48–60, 2013) and the experimentally measured free surface elevation and breaking wave force by Chakrabarti et al. (Appl Ocean Res 19:113–140, 1997). The main purpose of the paper is to examine the effects of the breaking characteristics, the geometric properties, the relative cylinder positions and the incident wave heights on the breaking wave force characteristics. A total of 21 simulations are performed to investigate the characteristics and the geometric properties of solitary waves breaking over a slope and the associated breaking wave forces on a cylinder. First, the characteristics and geometric properties of breaking solitary waves are investigated with two-dimensional simulations. Further, the study explores the effect of the relative distance between the breaking point and the cylinder on breaking wave forces. Finally, the study examines breaking solitary wave forces for different incident waves. This also includes the analysis of breaking wave force characteristics such as the impact duration and rise time, the peak force, the average slamming coefficient and the force impulse. The results of the numerical simulations show that the relative distance between the cylinder and the breaking point plays an important role in obtaining the maximum force. In addition, the numerical model is capable of representing the most important physical flow features related to the breaking solitary waves and the interaction with the vertical slender cylinder.

WAVE SLAMMING IMPACT ON OFFSHORE WIND TURBINE FOUNDATIONS

This study proposes a new parameter, the wave front steepness parameter, to better describe the wave slamming coefficient. Four cases of wave breaking were employed to study the relationship between wave front steepness and wave slamming coefficients. Based on model results with OpenFOAM, an empirical formula was derived to relate the slamming coefficient to the wave front steepness.

Hydrodynamic Analysis of Wave Impact Forces on a Horizontal Circular Cylinder

Information about the forces acting on cylindrical structures subjected to wave impact is of significant importance in ocean engineering and naval architecture. The purpose of this paper is to analyse the wave impact forces acting on a fixed, slender, horizontal circular cylinder in the vicinity of the free surface, taking account of the intermittent submergence and wave slamming. Predictions of the wave slamming force generally involve the use of a slamming coefficient. A new mathematical model is presented for the slamming coefficient as a function of the Froude number, wave amplitude, cylinder diameter, depth of cylinder immersion, instantaneous height of the surface wave above the mean water level and the added mass per unit length of the cylinder. A computer programme is developed in order to estimate wave slamming on a horizontal circular cylinder. The computational results are plotted in terms of non-dimensional parameters and interpreted with a view to explain the salient features of wave slamming...

A Level Set Immersed Boundary Method for Water Entry and Exit

The interaction between free surface flow and structure is investigated using a new level set immersed boundary method. The incorporation of an improved immersed boundary method with a free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving body/bodies of almost arbitrary shape to be modelled. A new algorithm is proposed to locate exact forcing points near solid boundaries, which provides an accurate numerical solution. The discretized linear system of the Poisson pressure equation is solved using the Generalized Minimum Residual (GMRES) method with incomplete LU preconditioning. Uniform flow past a cylinder at Reynolds number Re=100 is modelled using the present model and results agree well with the experiment and numerical data in the literature. Water exit and entry of a cylinder at the prescribed velocity is also investigated. The predicted slamming coefficient is in good agreement with experimental data and previous numerical simulations using a ComFlow model. The vertical slamming force and pressure distribution for the free falling wedge is also studied by the presentmodel and comparisons with available theoretical solutions and experimental data are made. AMS subject classifications: 6D05, 76T10, 65B99, 65E05