An integral model based on slender body theory, with applications to curved rigid fibers

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

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Slender-body theory for slow viscous flow

Journal of Fluid Mechanics ◽

10.1017/s0022112076000475 ◽

1976 ◽

Vol 75 (4) ◽

pp. 705-714 ◽

Cited By ~ 177

Author(s):

Joseph B. Keller ◽

Sol I. Rubinow

Keyword(s):

Integral Equation ◽

Incompressible Fluid ◽

Viscous Incompressible Fluid ◽

Unit Length ◽

The Body ◽

Slender Body ◽

Slow Flow ◽

Slender Body Theory ◽

Slow Viscous Flow ◽

Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

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Rods falling near a vertical wall

Journal of Fluid Mechanics ◽

10.1017/s0022112077001190 ◽

1977 ◽

Vol 83 (2) ◽

pp. 273-287 ◽

Cited By ~ 51

Author(s):

W. B. Russel ◽

E. J. Hinch ◽

L. G. Leal ◽

G. Tieffenbruck

Keyword(s):

Integral Equation ◽

Viscous Fluid ◽

Numerical Solution ◽

Vertical Wall ◽

Numerical Results ◽

Slender Body ◽

Asymptotic Results ◽

Slender Body Theory ◽

Friction Coefficients ◽

Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

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Application of Slender-Body Theory

Journal of Ship Research ◽

10.5957/jsr.1957.1.4.40 ◽

1957 ◽

Vol 1 (04) ◽

pp. 40-49

Author(s):

Paul Kaplan

Keyword(s):

Slender Body ◽

Vertical Force ◽

Regular Waves ◽

Slender Body Theory ◽

Surface Theory ◽

Surface Ship ◽

Submerged Body ◽

Dynamic Forces ◽

Body Theory

The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow concepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Has-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also included.

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A Wave Resistance Formulation for Slender Bodies at Moderate to High Speeds

Journal of Ship Research ◽

10.5957/jsr.2012.56.4.207 ◽

2012 ◽

Vol 56 (04) ◽

pp. 207-214

Author(s):

Brandon M. Taravella ◽

William S. Vorus

Keyword(s):

General Solution ◽

High Speed ◽

Near Field ◽

Wave Resistance ◽

Slender Body ◽

Slender Body Theory ◽

Rates Of Change ◽

Order Of Magnitude ◽

Flow Variables ◽

Body Theory

T. Francis Ogilvie (1972) developed a Green's function method for calculating the wave profile of slender ships with fine bows. He recognized that near a slender ship's bow, rates of change of flow variables axially should be greater than those typically assumed in slender body theory. Ogilvie's result is still a slender body theory in that the rates of change in the near field are different transversely (a half-order different) than axially; however, the difference in order of magnitude between them is less than in the usual slender body theory. Typical of slender body theory, this formulation results in a downstream stepping solution (along the ship's length) in which downstream effects are not reflected upstream. Ogilvie, however, developed a solution only for wedge-shaped bodies. Taravella, Vorus, and Givan (2010) developed a general solution to Ogilvie's formulation for arbitrary slender ships. In this article, the general solution has been expanded for use on moderate to high-speed ships. The wake trench has been accounted for. The results for wave resistance have been calculated and are compared with previously published model test data.

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Side Forces on a Ship’s Hull

Journal of Ship Research ◽

10.5957/jsr.1988.32.3.203 ◽

1988 ◽

Vol 32 (03) ◽

pp. 203-207

Author(s):

W. S. Hunter ◽

P. N. Joubert

Keyword(s):

Froude Number ◽

Asymptotic Expansions ◽

Experimental Results ◽

Slender Body ◽

Flat Plates ◽

Slender Body Theory ◽

Towing Tank ◽

Side Force ◽

Low Froude Number ◽

Body Theory

Side forces on a ship traveling at small yaw angles are predicted using slender-body theory. The approach uses the method of matched asymptotic expansions, with a cascade of flat plates as a model for the submarine portion of the ship's hull. Resulting predictions of side force coefficients are then compared with experimentally measured values derived from towing tank tests of a typical (tanker) hull. Correlation between theoretical and experimental results was very good for yaw angles less than 8 deg at low Froude number (Fn = 0.134).

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Time-Domain Hydroelasticity Theory of Ships Responding to Waves

Journal of Ship Research ◽

10.5957/jsr.1997.41.4.286 ◽

1997 ◽

Vol 41 (04) ◽

pp. 286-300

Author(s):

Jinzhu Xia ◽

Zhaohui Wang

Keyword(s):

Time Domain ◽

Separation Of Variables ◽

Mathematical Formulation ◽

Rigid Motion ◽

Surface Flow ◽

Slender Body ◽

Irregular Waves ◽

Restoring Force ◽

Slender Body Theory ◽

Body Theory

A time-domain linear theory of fluid-structure interaction between floating structures and the incident waves is presented. The structure is assumed to be elastic and represented by general separation of variables, whereas the fluid is described as an initial boundary value problem of potential free surface flow. The general interface boundary condition is used in the mathematical formulation of the fluid motion around the flexible structure. The general time-domain theory is simplified to a slender-body theory for the analysis of wave-induced global responses of monohull ships. The structure is represented by a nonuniform beam, while the generalized hydrodynamic coefficients can be obtained from two-dimensional potential flow theory. The linear slender body theory is generalized to treat the nonlinear loading effects of rigid motion and structural response of ships traveling in rough seas. The nonlinear hydrostatic restoring force and hydrodynamic momentum action are considered. A numerical solution is presented for the slender body theory. Numerical examples are given for two ship cases with different geometry features, a warship hull and the S175 containership with two different bow flare forms. The predicted results include linear and nonlinear rigid motions and structural responses of ships advancing in regular and irregular waves. The results clearly demonstrate the importance and the magnitude of nonlinear effects in ship motions and internal forces. Numerical calculations are compared with experimental results of rigid and elastic material ship model tests. Good agreement is obtained.

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