Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
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.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
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.

Slender-body theory for steady sheared plumes in very viscous fluid

2008 ◽  
Vol 612 ◽  
pp. 21-44 ◽  
Author(s):  
ROBERT J. WHITTAKER ◽  
JOHN R. LISTER
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Experimental Studies ◽  
Slender Body ◽  
Slender Body Theory ◽  
Dimensionless Parameters ◽  
Dynamical Regimes ◽  
Body Theory ◽  
Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

Sway, Roll, and Yaw Motion Coefficients Based on a Forward-Speed Slender-Body Theory—Part 1

1981 ◽  
Vol 25 (01) ◽  
pp. 8-15
Author(s):  
Armin Walter Troesch
Keyword(s):  
Cross Coupling ◽  
Added Mass ◽  
Numerical Results ◽  
Slender Body ◽  
Forward Speed ◽  
Coupling Coefficients ◽  
Slender Body Theory ◽  
Damping Coefficients ◽  
The Cross ◽  
Body Theory

The added-mass and damping coefficients for sway, roll, and yaw are formulated for a ship with forward speed. The theory is similar to that given by Ogilvie and Tuck (1969) for the heave and pitch coefficients of a slender ship. Numerical results are presented for the cross-coupling coefficients.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

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.

Application of Slender-Body Theory

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.

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

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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