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.

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.

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.

Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

2006 ◽  
Author(s):  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Circular Cylinder ◽  
Vortex Core ◽  
Computational Study ◽  
Three Dimensional ◽  
The Body ◽  
Transient Growth ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies

1964 ◽  
Vol 8 (04) ◽  
pp. 22-44 ◽  
Author(s):  
John L. Hess ◽  
A. M. O. Smith
Keyword(s):  
Body Surface ◽  
Potential Flow ◽  
Fluid Velocity ◽  
Normal Component ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
The Body ◽  
Algebraic Equations ◽  
Source Density ◽  
Linear Algebraic Equations

A general method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, nonlifting, three-dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. When this set of equations has been solved, the flow velocity both on and off the body surface is calculated. After the basic ideas and equations have been derived end discussed, the accuracy of the method is exhibited by means of comparisons with analytic solutions, and its usefulness is shown by comparing calculated pressure distributions with experimental data. Some of the design problems to which the method has been applied are also presented, to indicate the variety of flow situations that can be calculated by this approach.

On the Numerical Radiation Condition in the Steady-State Ship Wave Problem

1987 ◽  
Vol 31 (01) ◽  
pp. 14-22
Author(s):  
Peter Schjeldahl Jensen
Keyword(s):  
Green Function ◽  
Three Dimensional ◽  
Radiation Condition ◽  
Function Technique ◽  
Wave Problem ◽  
Ship Wave ◽  
Rankine Source ◽  
Wigley Hull ◽  
The Green Function ◽  
The Waves

The waves created by a thin ship sailing in calm water are examined. The velocity potential of the ship in the zero Froude number case is known and the additional potential due to the waves is calculated by the Green function technique. The simple Green function corresponding to the Rankine source potential is used here. Two major problems exist with this method. In the Neumann-Poisson boundary-value problem- probably the first iteration toward a full nonlinear solution to the ship wave problem _it is necessary to impose a radiation condition in order to get uniqueness. This problem is related to the second one, which arises due to the existence of eigensolutions. The two-dimensional situation is here analyzed first, thereby easing the three-dimensional analysis. A numerical scheme is constructed and results for the twodimensional waves generated by a submerged vortex and for the three-dimensional waves due to the Wigley hull are presented.

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.

Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature

2007 ◽  
Vol 592 ◽  
pp. 89-115 ◽  
Author(s):  
A. MILIOU ◽  
A. DE VECCHI ◽  
S. J. SHERWIN ◽  
J. M. R. GRAHAM
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
Axial Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
The Body ◽  
Vertical Extension ◽  
Flow Past

Three-dimensional spectral/hp computations have been performed to study the fundamental mechanisms of vortex shedding in the wake of curved circular cylinders at Reynolds numbers of 100 and 500. The basic shape of the body is a circular cylinder whose centreline sweeps through a quarter section of a ring and the inflow direction lies on the plane of curvature of the quarter ring: the free stream is then parallel to the geometry considered and the part of the ring that is exposed to it will be referred to as the ‘leading edge’. Different configurations were investigated with respect to the leading-edge orientation. In the case of a convex-shaped geometry, the stagnation face is the outer surface of the ring: this case exhibited fully three-dimensional wake dynamics, with the vortex shedding in the upper part of the body driving the lower end at one dominant shedding frequency for the whole cylinder span. The vortex-shedding mechanism was therefore not governed by the variation of local normal Reynolds numbers dictated by the curved shape of the leading edge. A second set of simulations were conducted with the free stream directed towards the inside of the ring, in the so-called concave-shaped geometry. No vortex shedding was detected in this configuration: it is suggested that the strong axial flow due to the body's curvature and the subsequent production of streamwise vorticity plays a key role in suppressing the wake dynamics expected in the case of flow past a straight cylinder. The stabilizing mechanism stemming from the concave curved geometry was still found to govern the wake behaviour even when a vertical extension was added to the top of the concave ring, thereby displacing the numerical symmetry boundary condition at this point away from the top of the deformed cylinder. In this case, however, the axial flow from the deformed cylinder was drawn into the wake of vertical extension, weakening the shedding process expected from a straight cylinder at these Reynolds numbers. These considerations highlight the importance of investigating flow past curved cylinders using a full three-dimensional approach, which can properly take into account the role of axial velocity components without the limiting assumptions of a sectional analysis, as is commonly used in industrial practice. Finally, towing-tank flow visualizations were also conducted and found to be in qualitative agreement with the computational findings.

scholarly journals Studies in wave resistance: influence of the form of the water-plane section of the ship

1923 ◽  
Vol 103 (723) ◽  
pp. 571-585 ◽  
Keyword(s):  
Three Dimensional ◽  
Median Plane ◽  
Wave Resistance ◽  
The Body ◽  
Horizontal Section ◽  
Ship Waves ◽  
Sources And Sinks ◽  
Interesting Paper ◽  
Uniform Current ◽  
Stream Lines

1. The problem which is investigated in some details in the following paper is the wave resistance of a vertical post in a uniform stream. The horizontal section of the post is of ship-shape form and the lines are varied in a certain manner while keeping the area of the section constant. A direct study of ship waves as a three-dimensional problem for a ship of finite dimensions has not yet been attacked by the method of an equivalent distribution of pressure on the surface of the water. Some advance has also been made in the case of submerged bodies; I have shown previously how to calculate the wave resistance of a body whose form is derive by combining the stream-lines of a uniform current with certain distributions of sources and sinks, under the limitation that the dimensions of the body are small compared with its depth. On the other hand Michell in an extremely interesting paper, gave a general expression for wave resistance; but it suffers from a serious limitation, in that the surface of the ship must be everywhere inclined at only a small angle to its vertical median plane.

scholarly journals Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160255 ◽  
Author(s):  
Oscar P. Bruno ◽  
Stephen P. Shipman ◽  
Catalin Turc ◽  
Stephanos Venakides
Keyword(s):  
Green Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Green Functions ◽  
Lattice Sums ◽  
Periodic Arrays ◽  
The Green Function ◽  
Three Dimensional Space

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.

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