On the Planar Translation of Two Bodies in a Uniform Flow

1992 ◽  
Vol 36 (01) ◽  
pp. 38-54
Author(s):  
Zhi Guo ◽  
Allen T. Chwang
Keyword(s):  
Mass Formula ◽  
Numerical Solutions ◽  
Added Mass ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Transverse Motion ◽  
Lagrange Equations ◽  
Direction Parallel ◽  
Added Masses ◽  
Two Bodies

The general planar translation of two bodies of revolution through an inviscid and incompressible fluid is considered. The moving trajectories and the hydrodynamic interactions are computed based on the generalized Lagrange equations of motion, including the effects of solid constraints, external forces in the plane of motion, and a uniform stream in any direction parallel to the plane of motion. In a relative coordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centers of two bodies. Analytical solutions of added masses in series form are obtained for the motion of two spheres. A new iterative formula based on the analysis of velocity potentials around each body is developed for added masses and their derivatives with respect to the separation distance due to the transverse motion. The method of successive images and Taylor's added-mass formula are applied to determine the added masses and their derivatives due to the centroidal motion. These results are compared with the numerical solution of added masses computed by the boundary-integral method and the generalized Taylor added-mass formula. The integral equations, in terms of surface-source distributions on both surfaces, are modified for obtaining accurate numerical solutions. Numerical results are given for several practical engineering problems.

Theory and experiment on the low-Reynolds-number expansion and contraction of a bubble pinned at a submerged tube tip

1998 ◽  
Vol 356 ◽  
pp. 93-124 ◽  
Author(s):  
HARRIS WONG ◽  
DAVID RUMSCHITZKI ◽  
CHARLES MALDARELLI
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Numerical Solutions ◽  
Full Range ◽  
Boundary Integral ◽  
Gas Pressure ◽  
Boundary Integral Method ◽  
Liquid Density ◽  
Gravitational Acceleration ◽  
Dynamic Surface

The expansion and contraction of a bubble pinned at a submerged tube tip and driven by constant gas flow rate Q are studied both theoretically and experimentally for Reynolds number Re[Lt ]1. Bubble shape, gas pressure, surface velocities, and extrapolated detached bubble volume are determined by a boundary integral method for various Bond (Bo=ρga2/σ) and capillary (Ca=μQ/σa2) numbers, where a is the capillary radius, ρ and μ are the liquid density and viscosity, σ is the surface tension, and g is the gravitational acceleration.Bubble expansion from a flat interface to near detachment is simulated for a full range of Ca (0.01–100) and Bo (0.01–0.5). The maximum gas pressure is found to vary almost linearly with Ca for 0.01[les ]Ca[les ]100. This correlation allows the maximum bubble pressure method for measuring dynamic surface tension to be extended to viscous liquids. Simulated detached bubble volumes approach static values for Ca[Lt ]1, and asymptote as Q3/4 for Ca[Gt ]1, in agreement with analytic predictions. In the limit Ca→0, two singular time domains are identified near the beginning and the end of bubble growth during which viscous and capillary forces become comparable.Expansion and contraction experiments were conducted using a viscous silicone oil. Digitized video images of deforming bubbles compare well with numerical solutions. It is observed that a bubble contracting at high Ca snaps off.

Generation and Propagation of Long-Crested Finite-Depth Surface Waves: Comparison Between the Corresponding Results From Numerical Models and a Wave Tank

2008 ◽  
Author(s):  
M. Hasanat Zaman ◽  
Wade Parsons ◽  
Okey Nwogu ◽  
Wooyoung Choi ◽  
R. Emile Baddour ◽  
...  
Keyword(s):  
Surface Waves ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Finite Depth ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Elevation ◽  
Ocean Engineering ◽  
Measured Time ◽  
Wave Maker

The evolution of long-crested surface waves subject to side-band perturbations is investigated with two different numerical models: a direct solver for the Euler equations using a non-orthogonal boundary-fitted curvilinear coordinate system and an FFT-accelerated boundary integral method. The numerical solutions are then validated with laboratory experiments performed in the NRC-IOT Ocean Engineering Basin with a segmented wave-maker operating in piston mode. The numerical models are forced by a point measurement of the free surface elevation at a wave probe close to the wave-maker and the numerical solutions are compared with the measured time-series of the surface elevation at a few wave probe locations downstream.

Hydrodynamic Interaction and Drift Forces on a Rectangular Barge and Modified Wigley Hull Arranged Side-by-Side

2008 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Hydrodynamic Interaction ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Floating Platform ◽  
Close Proximity ◽  
Wigley Hull ◽  
Exciting Forces ◽  
Two Bodies ◽  
Drift Forces

The paper studies the hydrodynamic interactions between two bodies in close proximity oscillating on the free surface due to incident harmonic waves, inspired in the problem of offloading from a LNG floating platform to a tanker. It deals with a modified Wigley hull and a rectangular barge arranged side by side. The numerical results include hydrodynamic coefficients, exciting forces, absolute motions, and drift forces, and they are compared with published experimental data followed by further analysis of the effects of free surface elevation between the two bodies. The calculations are carried out with the WAMIT® code, which is based on a panel method, or boundary integral method.

Interaction Between Two Bodies Translating in an Inviscid Fluid

1991 ◽  
Vol 35 (01) ◽  
pp. 1-8
Author(s):  
L. Landweber ◽  
A. T. Chwang ◽  
Z. Guo
Keyword(s):  
Translational Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Inviscid Fluid ◽  
Added Masses ◽  
Two Bodies ◽  
Good Agreement

The equations of motion of two bodies in translational motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

Transient cavities near boundaries. Part 1. Rigid boundary

1986 ◽  
Vol 170 ◽  
pp. 479-497 ◽  
Author(s):  
J. R. Blake ◽  
B. B. Taib ◽  
G. Doherty
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relative Magnitude ◽  
Boundary Integral ◽  
Stagnation Point Flow ◽  
Boundary Integral Method ◽  
Physical Parameters ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Parameter Ranges

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.

scholarly journals Smoothly attaching bow flows with constant vorticity

2001 ◽  
Vol 42 (3) ◽  
pp. 354-371
Author(s):  
S. W. McCue ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Surface Flow ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Front Face ◽  
Infinite Body ◽  
Constant Vorticity

AbstractThe free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

Oblique Impact of Two Cylinders in a Uniform Flow

1991 ◽  
Vol 35 (03) ◽  
pp. 219-229
Author(s):  
Zhi Guo ◽  
Allen T. Chwang
Keyword(s):  
Kinetic Energy ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Separation Distance ◽  
Uniform Flow ◽  
Polar Coordinate System ◽  
Lagrange Equations ◽  
Surface Source ◽  
Moving Cylinder ◽  
Added Masses

The oblique motion of a circular cylinder through an inviscid and incompressible fluid, conveyed by a uniform flow at infinity, in the vicinity of another cylinder fixed in space is considered. In a relative polar coordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centers of the cylinder pair. The Lagrange equations of motion are then integrated for the trajectories of the moving cylinder. In order to evaluate the added masses and their derivatives with respect to the separation distance between the cylinders in terms of the hydrodynamic singularities, the method of successive images, initiated by Hicks [1],2 and the Taylor added-mass formula are applied, and analytic solutions in closed form are obtained thereafter. The dynamic behavior of a drifting body in close proximity of a fixed one is investigated by considering the limiting values of the fluid kinetic energy and the interaction forces on each body. The reliability of the numerical approximation of added masses and their derivatives is also discussed in the present study. The integral equations, in terms of surface source distributions and their derivatives on both circles, are carefully modified for obtaining accurate numerical solutions.

Geometric Modeling for Fully Nonlinear Ship-Wave Interactions

1997 ◽  
Vol 41 (01) ◽  
pp. 17-25
Author(s):  
M.S. Celebi ◽  
R.F. Beck
Keyword(s):  
Body Surface ◽  
Geometric Modeling ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Lagrange Equations ◽  
Time Step ◽  
Fully Nonlinear ◽  
Node Placement

Using the desingularized boundary integral method to solve transient nonlinear water-wave problems requires the solution of a mixed boundary value problem at each time step. The problem is solved at nodes (or collocation points) distributed on an ever-changing body surface. In this paper, a dynamic node allocation technique is developed to distribute efficiently nodes on the body surface. A B-spline surface representation is employed to generate an arbitrary ship hull form in parametric space. A variational adaptive curve grid generation method is then applied on the hull station curves to generate effective node placement. The numerical algorithm uses a conservative form of the parametric variational Euler-Lagrange equations to perform adaptive gridding on each station. Numerical examples of node placement on typical hull cross sections and for fully nonlinear wave resistance computations are presented.

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