A Generalized Wagner Method for Three-Dimensional Slamming

2005 ◽  
Vol 49 (04) ◽  
pp. 279-287
Author(s):  
O. M. Faltinsen ◽  
M. Chezhian
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Surface Condition ◽  
Three Dimensional ◽  
Water Entry ◽  
The Body ◽  
Experimental Results ◽  
Vertical Force ◽  
Free Surface Condition ◽  
Drop Tests

Impact between the water and ship, that is, slamming, can cause important global and local effects. A numerical method has been applied to predict water entry loads on three-dimensional bodies. The problem is solved as an initial value problem using the boundary element method. The Green second identity is used to represent the velocity potential as a distribution of Rankine sources and dipoles over the body surface and free surface. The problem is stepped up in time using the information from the boundary conditions. The kinematic free-surface condition is used to determine the intersection between the body surface and free surface at each time step. The exact body boundary condition is used, whereas the dynamic free-surface condition, φ = 0, is approximated on to a horizontal line and not on the exact free-surface profile. The approach presented by Zhao et al (1996) for two-dimensional water entry problems was extended to arbitrary three-dimensional bodies in this presented work. An idealized shape, which consists of cylindrical mid-body and hemispherical ends, was studied. The wetted body surface is calculated with great detail and is considered to be more important than the free-surface elevation away from the body. Drop tests have been carried out to verify and validate the numerical simulation. The effect of the angle between the free surface and the body surface has also been studied. The agreement between theory and experiments is good, and the effect of three-dimensionality is documented. The presented computational method is found to be robust for engineering use and computationally less demanding. The experimental results for vertical force have a strong oscillatory nature, and this has been analyzed using a simplified hydroelastic model. The hydroelastic model gives reasonable representation of the dynamic oscillations found in the vertical force. Reasons for the observed deviations between the numerical and the experimental results are documented. Recommendations for conducting drop tests with minimal dynamic effects are also presented.

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 Study of Forward-Speed Ship Motion and Added Resistance

2017 ◽  
Author(s):  
D. C. Hong ◽  
T. B. Ha ◽  
K. H. Song
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Results ◽  
Surface Boundary ◽  
Forward Speed ◽  
Added Resistance ◽  
Following Seas

The added resistance of a ship was calculated using Maruo’s formula [1] involving the three-dimensional Kochin function obtained using the source and normal doublet distribution over the wetted surface of the ship. The density of the doublet distribution was obtained as the solution of the three-dimensional frequency-domain forward-speed Green integral equation containing the exact line integral along the waterline. Numerical results of the Wigley ship models II and III in head seas, obtained by making use of the inner-collocation 9-node second-order boundary element method have been compared with the experimental results reported by Journée [2]. The forward-speed hydrodynamic coefficients of the Wigley models have shown no irregular-frequencylike behavior. The steady disturbance potential due to the constant forward speed of the ship has also been calculated using the Green integral equation associated with the steady forward-speed free-surface Green function since the so-called mj-terms [3] appearing in the body boundary conditions contain the first and second derivatives of the steady potential over the wetted surface of the ship. However, the free-surface boundary condition was kept linear in the present study. The added resistances of the Wigley II and III models in head seas obtained using Maruo’s formula showing acceptable comparison with experimental results, have been presented. The added resistances in following seas obtained using Maruo’s formula have also been presented.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

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.

scholarly journals Water entry of an expanding body with and without splash

2019 ◽  
Vol 862 ◽  
pp. 924-950 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Water Entry ◽  
The Body ◽  
Surface Shape ◽  
Cylinder Surface ◽  
Hodograph Method ◽  
Expansion Speed ◽  
Attached Flow ◽  
Self Similar

A self-similar flow generated by water entry of an expanding two-dimensional smooth and curved body is studied based on the incompressible velocity potential theory, with gravity and surface tension effects being ignored. At each expansion speed, mathematical solutions for detached flow with a splash jet and attached flow with jet leaning on the body surface are obtained, both of which have been found possible in experiment, corresponding to hydrophobic and hydrophilic bodies, respectively. The problem is solved using the integral hodograph method, which converts the governing Laplace equations into two integral equations along the half real and imaginary axes of a parameter plane. For the detached flow, the conditions for continuity and finite spatial derivative of the velocity at the point of flow departing form the body surface are imposed. It is found that the Brillouin–Villat criterion for flow detachment of steady flow is also met in this self-similar flow, which requires the curvatures of the free surface and the body surface to be the same at the detachment point. Solutions for the detached flow have been obtained in the whole range of the expansion speeds, from zero to infinity, relative to the water entry speed. For the attached flow there is a minimal expansion speed below which no solution cannot be obtained. Detailed results in terms of pressure distribution, free surface shape and streamlines and tip angle of the jet are presented. It is revealed that when solutions for both detached and attached flows exist, the pressure distributions on the cylinder surface are almost the same up to the point near the jet root. Beyond that point, the pressure relative to the ambient one drops to zero at the detachment point in the former, while it drops below zero in the jet attached on the body and then returns to zero at the contact point in the latter.

Calculation of Propeller-Induced Vibratory Hull Forces, Force Distributions, and Pressures; Free-Surface Effects

1976 ◽  
Vol 20 (02) ◽  
pp. 107-117
Author(s):  
William S. Vorus
Keyword(s):  
Free Surface ◽  
Flat Plate ◽  
Surface Condition ◽  
Low Frequency ◽  
Surface Effects ◽  
Ship Hull ◽  
Vertical Force ◽  
Axial Distribution ◽  
Free Surface Condition

It is shown how a formula originally developed for calculating the total unsteady propeller-induced forces on a ship hull can be used for calculating the associated hull force distributions and pressures as well. Total vertical forces and the axial distribution of vertical force on a flat plate are calculated using the formula. Two different conditions on the water free-surface are investigated. These conditions correspond to approximations to the exact linearized free-surface condition in the extremes of high and low frequency. The calculations are also performed for circumferentially uniform and nonuniform propeller inflows.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

On the choice of CFD codes in the design process of planing sailing yachts

2009 ◽  
Author(s):  
Jérémie Raymond ◽  
Jean-Marie Finot ◽  
Jean-Michel Kobus ◽  
Gérard Delhommeau ◽  
Patrick Queutey ◽  
...  
Keyword(s):  
Free Surface ◽  
Design Process ◽  
Finite Differences ◽  
Potential Flow ◽  
Surface Condition ◽  
Cpu Time ◽  
Free Surface Condition ◽  
Finite Differences Method ◽  
Non Linear ◽  
Ranse Solver

The discussion is based on results gathered during the first two years of a 3 years research program for the benefits of Groupe Finot-Conq, Naval Architects. The introduction presents the objectives of the program: Setting up a practical method using numerical and experimental available tools to design fast planing sailing yachts. The aim of this paper is to compare advantages and disadvantages of four different kinds of CFD codes which are linear and non-linear potential flow approach, RANSE solver using finite differences method and RANSE solver using volume of fluid method. The Fluid Mechanics Laboratory of the Ecole Centrale de Nantes (France) has developed those three approaches so those homemade codes will be used for this study. The first one is REVA, a potential flow code with a linearised free surface condition. ICARE is a RANSE solver using finite differences method with a non linear free surface condition. It is extensively used for industrial projects as for sailing yachts projects (ACC for example). ISIS-CFD is a RANSE solver using finite volume method to build the spatial discretization of the transport equations with unstructured mesh. The latter is able to compute sprays for fast planing ships but is also the slower in terms of CPU time. In addition, we had the opportunity to test FS-FLOW which is a potential flow code with a non linear free surface condition distributed by FRIENDSHIP CONSULTING. Numerical results for the four codes are compared with the other codes' results as with tank tests data. Those tank tests were made using captive model test technique on two Open60' models. Reasons of the choice of the captive model technique are explained and experimental procedures are briefly described. Comparisons between codes are mainly based on the easiness of use, the cost in CPU time and the confidence we can have in the results as a function of the boat speed. Flow visualizations, pressure maps, free surface deformation are shown and compared. Analysis of local quantities integrated or by zone is also presented. Results are analyzed focusing on the ability of each code to represent flow dynamics for every speed with a special attention to high speeds. The practical question raised is to know which kind of answers each code can bring in terms of tendencies evaluation or sensitivity to hull geometry modifications. The main goal is to be able to judge if those codes are able to make reliable and consistent comparisons of different designs. Conclusion is that none of the codes is perfect and gather all the advantages. It is still difficult to propose a definitive methodology to estimate hydrodynamic performances at every speed and at every stage of the design process. Knowing each code limitations, it appears more coherent to use each of them at different stages of the design process: the quickest and less reliable to understand the main tendencies and the longest and more precise to validate the final options.

scholarly journals Microvilli on the External Surfaces of Gastropod Tentacles and Body-Walls

1963 ◽  
Vol s3-104 (68) ◽  
pp. 495-504
Author(s):  
NANCY J. LANE
Keyword(s):  
Free Surface ◽  
Surface Area ◽  
Body Surface ◽  
Body Wall ◽  
Free Cell ◽  
The Body ◽  
Outer Cell ◽  
Lamellar Bodies ◽  
Cell Surfaces ◽  
Histochemical Tests

In Helix aspersa the ‘cuticle’ on the free surface of the external epithelial cells of the optic tentacles has been shown to consist of a layer of microvilli. Microvilli are also present in the same species on the free cell borders of the body-wall, and in the slug Arion hortensis, on the outer cell surfaces of the external epithelium. In all three cases the microvilli are arranged in a hexagonal pattern. There are indications that branching may possibly occur. The microvilli have granular cores with cross- and longitudinal-striations and there are fibrillar connexions between their tips. On the tentacular and body surfaces of H. aspersa, the microvilli increase the surface area 15 and 12 times, respectively. On A. hortensis the increase in surface area is only 4 times. In H. aspersa, beneath the microvilli on the tips of the optic tentacles there is a layer, about 3 to 4 µ deep, composed of vertical, horizontal, and tangential fibres. Some of these fibres are attached to lamellar bodies, which may have a lipid content. Granules are also found among the fibres. Further, a greater depth of cuticle is found to be present on the tips of the inferior tentacles of H. aspersa than on their sides; this seems to indicate that a fibrillar layer, similar to that on the optic tentacles, may lie beneath the cuticle of microvilli on the tips of the inferior tentacles. A thicker cuticle is also found on the tips of the optic tentacles in other stylommatophoran pulmonates. It has not been found possible to ascertain whether the fibrillar layer is intracellular or extracellular, although the evidence points to the latter. Histochemical tests indicate that mucopolysaccharide is present on the surface of the cuticle. Electron micrographs show a granular precipitate caught on and between the fibrillae connecting the tips of the microvilli. It is suggested that the function of the microvilli is to hold the mucous secretions on the body-surface, which would give protection to the animals.

The Vertical Mean Force and Moment of Submerged Bodies Under Waves

1971 ◽  
Vol 15 (03) ◽  
pp. 231-245 ◽  
Author(s):  
C. M. Lee ◽  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Added Mass ◽  
Cross Sectional Area ◽  
The Body ◽  
Slender Body ◽  
Longitudinal Distribution ◽  
Vertical Force ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Mean

A neutrally buoyant slender body of arbitrary sectional form, submerged beneath a free surface, is free to respond to an incident plane progressive wave system. The fluid is assumed inviscid, incompressible, homogeneous and infinitely deep. The first-order oscillatory motion of the body and the second-order time-average vertical force and pitching moment acting on the body are obtained in terms of Kochin's function. By use of slender-body theory for a deeply submerged body, the final expressions for the mean force and the moment are shown to depend on the longitudinal distribution of sectional area and added mass and on the amplitude and the frequency of the ambient surface waves. The magnitude of the mean force for various simple geometric cylinders is compared with that of a circular cylinder of equal cross-sectional area. The mean force on a nonaxisymmetric body is often approximated by replacing the section with circular profiles of equivalent cross-sectional area. A better scheme of approximation is presented, based on a simple way of estimating the two-dimensional added mass. It is expected that the effect of the cross-sectional geometry on mean vertical force and moment will be more significant when the body is very close to the free surface.

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