scholarly journals Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack

2018 ◽  
Vol 845 ◽  
pp. 682-712 ◽  
Author(s):  
Zhi Fu Li ◽  
Guo Xiong Wu ◽  
Chun Yan Ji
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Ice Sheet ◽  
Integral Form ◽  
Multipole Expansion ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
The Green Function

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

2021 ◽  
Vol 928 ◽  
Author(s):  
Y.F. Yang ◽  
G.X. Wu ◽  
K. Ren
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Ice Sheet ◽  
The Body ◽  
Thin Elastic Plate ◽  
Uniform Current ◽  
The Green Function

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed.

Time-Domain Second-Order Wave Radiation in Two Dimensions

1993 ◽  
Vol 37 (01) ◽  
pp. 25-33 ◽  
Author(s):  
Michael Isaacson ◽  
Joseph Y. T. Ng
Keyword(s):  
Circular Cylinder ◽  
Time Domain ◽  
Body Position ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Second Order ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
Time Step

This paper presents a time-domain second-order method to study the nonlinear wave radiation problem in two dimensions. A time-stepping scheme is adopted to obtain the resulting flow development which satisfies the nonlinear free-surface boundary conditions and the radiation condition to second order, and the numerical procedure utilizes a boundary integral equation method based on Green's theorem to calculate the field solution at each time step. The body surface boundary condition is expanded about the mean body position to second order by a Taylor series. The method is applied to the cases of a semi-submerged circular cylinder and a rectangular cylinder undergoing sinusoidal sway, heave and roll motions. For the case of the circular cylinder, comparisons of the computed hydrodynamic forces at first and second order are made with previous theoretical and experimental results and a favorable agreement is indicated. The importance of second-order effects in the calculation of the hydrodynamic force is discussed.

Hydrodynamic forces on a submerged circular cylinder undergoing large-amplitude motion

1993 ◽  
Vol 254 ◽  
pp. 41-58 ◽  
Author(s):  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Large Amplitude ◽  
Surface Condition ◽  
Multipole Expansion ◽  
The Body ◽  
Surface Boundary ◽  
Instantaneous Position ◽  
Large Amplitude Oscillation ◽  
Surface Boundary Condition

The hydrodynamic problem of a circular cylinder submerged below a free surface and undergoing large-amplitude oscillation is investigated based on the velocity potential theory. The body-surface boundary condition is satisfied on its instantaneous position while the free-surface condition is linearized. The solution is obtained by writing the potential in terms of the multipole expansion. Various interesting results associated with the circular cylinder are obtained.

Studies on Natural Convection Induced Flow and Thermal Behavior Inside Electronic Equipment Cabinet Model

2001 ◽  
Author(s):  
Masaru Ishizuka ◽  
Guoyi Peng ◽  
Shinji Hayama
Keyword(s):  
Natural Convection ◽  
Thermal Behavior ◽  
Body Surface ◽  
Stokes Equations ◽  
The Body ◽  
Electronic Equipment ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Induced Flow

Abstract In the present work, an important basic flow phenomena, the natural convection induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the temperature equation are solved on the basis of finite difference method. Generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. Differential terms with respect to time are approximated by forward differences, diffusions terms are approximated by the implicit Euler form, convection terms in the Navier-Stokes equations are approximated by the third order upwind difference scheme. The heat flux at the body surface of heater is specified. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behavior inside electronic equipment cabinet model which is very difficult, if not impossible, to gather by experiment.

A Numerical Solution of Two-Dimensional Deep Water Wave-Body Problems

1984 ◽  
Vol 28 (01) ◽  
pp. 48-54 ◽  
Author(s):  
A. Nestegard ◽  
P. D. Sclavounos
Keyword(s):  
Deep Water ◽  
Numerical Technique ◽  
Logarithmic Singularity ◽  
Harmonic Wave ◽  
Outer Region ◽  
Multipole Expansion ◽  
Two Dimensions ◽  
The Body ◽  
Forced Oscillations ◽  
The Green Function

A numerical technique is presented for the solution of deep water linear and time-harmonic wave-body-interaction problems in two dimensions. A mathematical boundary of circular shape surrounding the body is introduced in the fluid domain, thus defining two flow regions. A multipole expansion valid in the outer region is then matched to an integral representation of the solution in the inner region which is obtained by applying Green's theorem and by using the fundamental logarithmic singularity as the Green function. The method applies both to surface-piercing and submerged bodies. Numerical results are presented for the forced oscillations of three surface-piercing ship-like sections of regular shape. No irregular frequencies are encountered. Comparisons with existing numerical methods are made to test the accuracy and emphasize the computational efficiency of the present approach.

The hydrodynamic forces on a submerged sphere moving in a circular path

1990 ◽  
Vol 428 (1874) ◽  
pp. 215-227 ◽  
Keyword(s):  
Green Function ◽  
Body Surface ◽  
Velocity Potential ◽  
Surface Condition ◽  
Hydrodynamic Forces ◽  
Constant Angular Velocity ◽  
The Body ◽  
Circular Path ◽  
Legendre Functions ◽  
Submerged Sphere

Analytical solutions for various hydrodynamic problems are briefly reviewed. The case of a submerged sphere moving in a circular path at constant angular velocity is then analysed based on the linearized velocity potential theory. The potential is expressed by means of a Green function and a distribution of sources over the body surface, written in terms of Legendre functions. The coefficients in the series of the Legendre functions are obtained by imposing the body surface condition. Figures are provided showing the hydrodynamic forces on the sphere.

Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction

1986 ◽  
Vol 30 (02) ◽  
pp. 69-84 ◽  
Author(s):  
J. G. Telste ◽  
F. Noblesse
Keyword(s):  
Green Function ◽  
Power Series ◽  
Water Wave ◽  
Numerical Evaluation ◽  
Recurrence Relations ◽  
Numerical Approximation ◽  
Computing Time ◽  
Absolute Error ◽  
Wave Radiation ◽  
The Green Function

This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series obtained previously in Noblesse [1].2 These series express the Green function and its gradient as sums of power series and terms involving functions of only one variable. The power series can be evaluated quickly by using recurrence relations; and the functions of one variable, by using rational approximations. The method permits the Green function and its gradient to be evaluated with an absolute error smaller than 10–6 very efficiently (with computing time less than 6 × 10–5 sec on a CDC CYBER 176 computer). A listing of the FORTRAN subroutine is included in the paper.

Numerical Solution of Wave Diffraction Problem in the Time Domain With the Panel-Free Method

2004 ◽  
Vol 126 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. Qiu ◽  
J. M. Chuang ◽  
C. C. Hsiung
Keyword(s):  
Body Surface ◽  
Time Domain ◽  
Diffraction Problem ◽  
The Body ◽  
Floating Body ◽  
B Splines ◽  
Rankine Source ◽  
Diffracted Waves ◽  
The Green Function ◽  
The Time Domain

A panel-free method (PFM) was developed earlier to solve the radiation problem of a floating body in the time domain. In the further development of this method, the diffraction problem has been solved. After removing the singularity in the Rankine source of the Green function and representing the body surface mathematically by Non-Uniform Rational B-Splines (NURBS) surfaces, integral equations were globally discretized over the body surface by Gaussian quadratures. Computed response functions and forces due to diffracted waves for a hemisphere at zero speed were compared with published results.

Zero Speed Rankine-Kelvin Hybrid Method With a Cylinder Control Surface

2015 ◽  
Author(s):  
Hui Li ◽  
Hao Lizhu ◽  
Huilong Ren ◽  
Xiaobo Chen
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Hybrid Method ◽  
Exterior Domain ◽  
Control Surface ◽  
Surface Boundary ◽  
Rankine Source ◽  
Free Surface Boundary Condition ◽  
Interior Domain ◽  
The Green Function

The solution of hydrodynamic problem with forward speed still has some well-known problems such as high oscillation and slow convergence of the wave term when using a moving and oscillating source as the Green function. Recently, Ten and Chen (2010) has come up with a new method to benefit the merits of both the Rankine source and moving and oscillating source by taking a hemisphere as the control surface which separates the fluid region into two domains, but some troubles have been induced in the process of solution. Therefore, in this paper, a cylindrical surface instead of a hemisphere is selected to be the control surface to make the solution easy, and in this method, the control surface isn’t divided into panels. In the interior domain near the ship, the Rankin Green function is used to simplify the calculation. In the exterior domain some distance from the ship, there is no panels representing the free surface by using the Green function which satisfy the free surface boundary condition. The whole fluid region matches by the condition that the velocity potentials and their normal derivatives in the interior domain and exterior domain are equal on the control surface separately. In this paper, we have validated the Rankine-Kelvin hybrid method is applicable by adopting it to solve the zero speed problem in this work.

Determination of the sonic line in hypersonic flow past a blunt body

1965 ◽  
Vol 21 (3) ◽  
pp. 495-501 ◽  
Author(s):  
M. I. G. Bloor
Keyword(s):  
Circular Cylinder ◽  
Hypersonic Flow ◽  
Body Surface ◽  
Blunt Body ◽  
The Body ◽  
Newtonian Theory ◽  
Plane Symmetric ◽  
Sonic Line ◽  
Subsonic Region

The Newtonian theory of inviscid hypersonic flow is extended to obtain a solution uniformly valid in the subsonic region, and that is used to determine the position and shape of the sonic line. The main modification to the theory has to be made near the body surface and an expansion, essentially in terms of the stream function, is employed.For simplicity the solution is limited to the cases of axially- and plane-symmetric flows. As an illustration of the theory the flows past a sphere and a circular cylinder are treated in some detail. Comparison with the numerical results of Garabedian and Lieberstein gives favourable agreement.

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