Slamming Loads on a Wedge Elastically Suspended on a Marine Structure

2015 ◽  
Author(s):  
Hui Sun ◽  
Jens B. Helmers
Keyword(s):  
Free Surface ◽  
Impact Force ◽  
Water Entry ◽  
The Body ◽  
Water Impact ◽  
Surface Conditions ◽  
Marine Structure ◽  
Nonlinear Free Surface ◽  
Stiffness And Damping ◽  
Water Exit

Slamming loads on a two-dimensional wedge elastically suspended on a marine structure are analyzed by using either a combined Wagner and von Karman method (W-vK) or a boundary element method (BEM). Fully nonlinear free surface conditions are satisfied in the BEM. Hydroelasticity effects are considered in both methods. A sinusoidal free surface motion relative to the marine structure is specified for the slamming event. Both the water entry phase and the water exit phase are simulated. The numerical results by the two different methods are compared. The W-vK method can generally predict the same trend of the variation of the body motions and the water forces, although the predicted maximum forces are larger than those by the BEM. The influence of the stiffness and damping of the elastic connection on the water impact force are discussed.

ANALYTICAL SOLUTION OF WEDGE WATER ENTRY BY USING SCHWARTZ–CHRISTOFFEL CONFORMAL MAPPING

2011 ◽  
Vol 02 (03) ◽  
pp. 337-354 ◽  
Author(s):  
PARVIZ GHADIMI ◽  
AMIR SAADATKHAH ◽  
ABBAS DASHTIMANESH
Keyword(s):  
Conformal Mapping ◽  
Impact Force ◽  
Offshore Structures ◽  
Water Entry ◽  
The Body ◽  
Water Impact ◽  
Local Pressure ◽  
Maximum Impact Force ◽  
The Impact ◽  
First Time

Water impact is one of the most critical phenomena from the viewpoint of the structural design of ships and offshore structures. The impact force can impose a large load with high local pressure on the body surface. On the other hand, determination of the maximum impact force during impact and acting point itself is very important in the design of floats. In this paper, the water entry of a two-dimensional wedge section is considered. This study is carried out in the framework of a potential-flow assumption. In particular, water impact on a dropping wedge with a constant velocity is pursued analytically by using the Schwartz–Christoffel conformal mapping. In order to determine a position of the wedge where the instantaneous effective force is largest during the impact, a particular equation is introduced here for the first time. The pressure distribution and maximum impact force are also calculated. The obtained results are compared against other numerical and experimental works and favorable agreement is displayed.

Nonlinear Computation of Water Impact of Axisymmetric Bodies

2011 ◽  
Vol 55 (01) ◽  
pp. 29-44
Author(s):  
Hongmei Yan ◽  
Yuming Liu
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Impact Force ◽  
Surface Profile ◽  
The Body ◽  
Gravity Effect ◽  
Water Impact ◽  
Free Surface Profile ◽  
Axisymmetric Bodies ◽  
The Impact

A fully nonlinear numerical simulation based on a boundary element method was used to investigate water impact of axisymmetric bodies that strike vertically the horizontal free surface from the air. The main objective was to understand the gravity effect on flow/wave kinematics and dynamics and to quantify the range of validity of existing theories and computations that are based on the infinite Froude number assumption. Two body geometries were considered: inverted cone and sphere. For the inverted cone, we obtained detailed dependencies of free-surface profile and impact pressure and load on the body on the generalized Froude number (Fr(V/gt)1/2, where V is the impact velocity, g is the gravitational acceleration, and t is time) and deadrise angle a. Based on these, we developed an approximate formula for evaluating the contribution of the gravity effect to the total impact force on the body in terms of a similarity parameter Fr/a1/2. For the sphere, we developed and applied a pressure-based criterion to follow the evolution of flow separation on the body and to obtain an appropriate description of the free-surface profile near the body and accurate evaluation of the impact pressure and load on the body during the entire impact process. The numerical result of impact force on the body agreed well with existing experimental measurements. We confirmed that the gravity effect is unimportant in initial impact of the sphere. Significantly, we found that in a later stage of impact, flow separation remains at an almost fixed position at an angle u 62.5 deg to the bottom of the sphere for a wide range of Froude numbers, Fr V/(gR)1/2 1, where R is the radius of the sphere.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

scholarly journals Cavity dynamics in water entry at low Froude numbers

2009 ◽  
Vol 641 ◽  
pp. 441-461 ◽  
Author(s):  
HONGMEI YAN ◽  
YUMING LIU ◽  
JAKUB KOMINIARCZUK ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Asymptotic Theory ◽  
Numerical Study ◽  
Three Dimensional ◽  
Maximum Size ◽  
Water Entry ◽  
Boundary Integral ◽  
The Body ◽  
Gravitational Acceleration ◽  
Slender Body Theory

The dynamics of the air cavity created by vertical water entry of a three-dimensional body is investigated theoretically, computationally and experimentally. The study is focused in the range of relatively low Froude numbers, Fr ≡ V(gD)−1/2 ≤ O(10) (where V is the dropping velocity of the body, D its characteristic dimension and g the gravitational acceleration), when the inertia and gravity effects are comparable. To understand the physical processes involved in the evolution of cavity, we conduct laboratory experiments of water entry of freely dropping spheres. A matched asymptotic theory for the description of the cavity dynamics is developed based on the slender-body theory in the context of potential flow. Direct comparisons with experimental data show that the asymptotic theory properly captures the key physical effects involved in the development of the cavity, and in particular gives a reasonable prediction of the maximum size of the cavity and the time of cavity closure. Due to the inherent assumption in the asymptotic theory, it is incapable of accurately predicting the flow details near the free surface and the body, where nonlinear free surface and body boundary effects are important. To complement the asymptotic theory, a fully nonlinear numerical study using an axisymmetric boundary integral equation is performed. The numerically obtained dependencies of the cavity height and closure time on Froude number and body geometry are in excellent agreement with available experiments.

Numerical Simulation of Water-Entry and Sedimentation of an Elliptic Cylinder Using Smoothed-Particle Hydrodynamics Method

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Roozbeh Saghatchi ◽  
Jafar Ghazanfarian ◽  
Mofid Gorji-Bandpy
Keyword(s):  
Free Surface ◽  
Smoothed Particle Hydrodynamics ◽  
Elliptic Cylinder ◽  
Water Entry ◽  
The Body ◽  
Numerical Code ◽  
Sph Method ◽  
Navier Stokes Equation ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

This paper studies the two-dimensional water-entry and sedimentation of an elliptic cylinder using the subparticle scale (SPS) turbulence model of a Lagrangian particle-based smoothed-particle hydrodynamics (SPH) method. The motion of the body is driven by the hydrodynamic forces and the gravity. The present study shows the ability of the SPH method for the simulation of free-surface-involving and multiphase flow problems. The full Navier–Stokes equation, along with the continuity equation, have been solved as the governing equations of the problem. The accuracy of the numerical code is verified using the case of the water-entry and exit of a circular cylinder. The numerical simulations of the water-entry and sedimentation of the vertical and horizontal elliptic cylinder with the diameter ratio of 0.75 are performed at the Froude numbers of 0, 2, 5, and 8, and the specific gravities of 0.5, 0.75, 1, 1.5, 1.75, 2, and 2.5. The effect of the governing parameters and vortex shedding behind the elliptic cylinder on the trajectory curves, velocity components within the flow field, rotation angle, the velocity of ellipse, and the deformation of free-surface have been investigated in detail.

A multimodal method for liquid sloshing in a two-dimensional circular tank

2010 ◽  
Vol 665 ◽  
pp. 457-479 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Form ◽  
The Body ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Natural Modes ◽  
Body Boundary ◽  
Multimodal Method

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

A Nonlinear Numerical Wave Tank and its Applications

2013 ◽  
Author(s):  
Hui Sun ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Horizontal Cylinder ◽  
The Body ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
Reflected Waves ◽  
Numerical Wave ◽  
Nonlinear Free Surface ◽  
Numerical Beach

A two-dimensional fully nonlinear numerical wave tank is developed by using a boundary element method (BEM). The water depth can be shallow or deep. The waves are generated by simulating a piston wave maker or by specifying the input velocity at the upstream boundary. Fully nonlinear free surface conditions are satisfied in the numerical simulations. In the downstream region, a numerical beach is employed to dissipate the wave energy to avoid waves reflecting from the vertical downstream boundary. When there is a body piercing the free surface, another numerical beach is applied upstream the body to damp out only the reflected waves from the body. Two different applications are presented in this paper. The first one is to compute the pressure and velocity at any point inside the wave field. The other application is to calculate the forces on a horizontal cylinder fixed on the free surface. This second application is related to the investigation of the hydrodynamic forces on the pontoon of a fish farm. Nonlinearities are significant since the wave amplitudes can be large relative to the wavelength and the dimension of the cylinder.

Free-Surface Effects for Yawed Surface-Piercing Plates

1976 ◽  
Vol 20 (03) ◽  
pp. 125-136
Author(s):  
R. B. Chapman
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Angle Of Attack ◽  
Present Formulation ◽  
Surface Conditions ◽  
Side Force ◽  
Experimental Values ◽  
Two Parameters ◽  
Nonlinear Free Surface ◽  
Good Agreement

The problem of a yawed surface-piercing flat plate is solved by applying the slender-body approximation and solving the resulting equations by a finite-difference method. The solution is shown to depend on two parameters & the product of the length Froude number and the square root of the aspect ratio of the plate, and the ratio of the angle of attack to the aspect ratio. Numerical methods are developed with linear, second-order, and nonlinear free-surface conditions. Calculated side force and yawing moment coefficients show good agreement with experimental values near the limit of zero angle of attack. At finite angles of attack, the experimental data exhibit nonlinearities not contained in the present formulation.

Multiphase Flow Simulation of Water-Entry and -Exit of Axisymmetric Bodies

2013 ◽  
Author(s):  
Van-Tu Nguyen ◽  
Cong-Tu Ha ◽  
Warn-Gyu Park
Keyword(s):  
Multiphase Flow ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Water Entry ◽  
Navier Stokes ◽  
Water Impact ◽  
Navier Stokes Equations ◽  
Vertical Accelerations ◽  
Underwater Projectile ◽  
Water Exit

A fully-compressible, multiphase, homogeneous mixture model, based on unsteady Reynolds-averaged Navier-Stokes equations is presented in this study. Dual-time preconditioning method was employed to improve the computational efficiency of the solution. The multiphase flow solver has been applied to computations of: (1) cavitating flows over underwater projectiles; (2) transonic flow past an underwater projectile; (3) water impact of a circular cylinder entering the water; (4) water-entry of a hemisphere with one degree of freedom; and (5) supercavitating flows over an axisymmetric projectile during water-entry and water-exit. The surface pressure coefficients, water impact forces, vertical accelerations, and impact velocities are compared with available experiments and other published results. Good agreements with those results are obtained. Aspects of water-entry and water-exit flow physics of a projectile with and without gaseous exhaust plume including cavity shape, phase topography and drag coefficients are presented.

scholarly journals Water entry of a wedge with rolled-up vortex sheet

2017 ◽  
Vol 835 ◽  
pp. 512-539 ◽  
Author(s):  
Yuriy A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Body Surface ◽  
Vortex Shedding ◽  
Vortex Sheet ◽  
Water Entry ◽  
The Body ◽  
Surface Shape ◽  
Force Coefficients ◽  
Local Singularity

The problem of asymmetric water entry of a wedge with the vortex sheet shed from its apex is considered within the framework of the ideal and incompressible fluid. The effects due to gravity and surface tension are ignored and the flow therefore can be treated as self-similar, as there is no length scale. The solution for the problem is sought through two mutually dependent parts using two different analytic approaches. The first one is due to water entry, which is obtained through the integral hodograph method for the complex velocity potential, in which the streamline on the body surface remains on the body surface after passing the apex, leading to a non-physical local singularity. The second one is due to a vortex sheet shed from the apex, and the shape of the sheet and the strength distribution of the vortex are obtained through the solution of the Birkhoff–Rott equation. The total circulation of the vortex sheet is obtained by imposing the Kutta condition at the apex, which removes the local singularity. These two solutions are nonlinearly coupled on the unknown free surface and the unknown vortex sheet. This poses a major challenge, which distinguishes the present formulation of the problem from the previous ones on water entry without a vortex sheet and ones on vortex shedding from a wedge apex without a moving free surface. Detailed results in terms of pressure distribution, vortex sheet, velocity and force coefficients are presented for wedges of different inner angles and heel angles, as well as the water-entry direction. It is shown that the vortex shedding from the tip of the wedge has a profound local effect, but only weakly affects the free-surface shape, overall pressure distribution and force coefficients.

Sign in / Sign up

Export Citation Format

Share Document