Inertia effects on the motion of long slender bodies

1989 ◽  
Vol 209 ◽  
pp. 435-462 ◽  
Author(s):  
R. E. Khayat ◽  
R. G. Cox
Keyword(s):  
Reynolds Number ◽  
Asymptotic Expansion ◽  
Body Length ◽  
Unit Length ◽  
The Body ◽  
Total Force ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Slender Bodies ◽  
Valid Solution

A solid long slender body with curved centreline is held at rest in a fluid undergoing a uniform flow. Assuming that the Reynolds number Re based on body length is fixed, the force per unit length on the body is obtained as an asymptotic expansion in terms of the ratio κ of the cross-sectional radius to body length. In the limit of large Re, this result is no longer valid and an asymptotic expansion in κRe is necessary. A uniformly valid solution is obtained from these two expansions. The total force and torque acting on a body with a straight centreline are explicitly determined. The limiting cases of small and large Re are studied in detail.

An improved slender-body theory for Stokes flow

1980 ◽  
Vol 99 (2) ◽  
pp. 411-431 ◽  
Author(s):  
Robert E. Johnson
Keyword(s):  
Boundary Condition ◽  
Cross Sections ◽  
Unit Length ◽  
The Body ◽  
Entire Body ◽  
Slender Body Theory ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Centre Line ◽  
Slender Bodies

The present study examines the flow past slender bodies possessing finite centre-line curvature in a viscous, incompressible fluid without any appreciable inertia effects. We consider slender bodies having arbitrary centre-line configurations, circular transverse cross-sections, and longitudinal cross-sections which are approximately elliptic close to the body ends (i.e. prolate-spheroidal body ends). The no-slip boundary condition on the body surface is satisfied, using a convenient stepwise procedure, to higher orders in the slenderness parameter (ε) than has previously been possible. In fact, the boundary condition is satisfied up to an error term of O(ε2) by distributing appropriate stokeslets, potential doublets, rotlets, sources, stresslets and quadrupoles on the body centre-line. The methods used here produce an integral equation valid along the entire body length, including the ends, whose solution determines the stokeslet strength or equivalently the force per unit length up to a term of O(ε2). The O(ε2) correction to the stokeslet strength is also found. The theory is used to examine the motion of a partial torus and a helix of finite length. For helical bodies comparisons are made between the present theory and the resistive-force theory using the force coefficients of Gray & Hancock and Lighthill. For the motion considered the Gray & Hancock force coefficients generally underestimate the force per unit length, whereas Lighthill's coefficients provide good agreement except in the vicinity of the body ends.

An analytical solution for two slender bodies of revolution translating in very close proximity

2007 ◽  
Vol 582 ◽  
pp. 223-251 ◽  
Author(s):  
Q. X. WANG
Keyword(s):  
Body Length ◽  
Present Model ◽  
The Body ◽  
Attraction Force ◽  
Bodies Of Revolution ◽  
Plane Flow ◽  
Lateral Forces ◽  
Close Proximity ◽  
Slender Bodies ◽  
Two Bodies

The irrotational flow past two slender bodies of revolution at angles of yaw, translating in parallel paths in very close proximity, is analysed by extending the classical slender body theory. The flow far away from the two bodies is shown to be a direct problem, which is represented in terms of two line sources along their longitudinal axes, at the strengths of the variation rates of their cross-section areas. The inner flow near the two bodies is reduced to the plane flow problem of the expanding (contracting) and lateral translations of two parallel circular cylinders with different radii, which is then solved analytically using conformal mapping. Consequently, an analytical flow solution has been obtained for two arbitrary slender bodies of revolution at angles of yaw translating in close proximity. The lateral forces and yaw moments acting on the two bodies are obtained in terms of integrals along the body lengths. A comparison is made among the present model for two slender bodies in close proximity, Tuck & Newman's (1974) model for two slender bodies far apart, and VSAERO (AMI)–commercial software based on potential flow theory and the boundary element method (BEM). The attraction force of the present model agrees well with the BEM result, when the clearance, h0, is within 20% of the body length, whereas the attraction force of Tuck & Newman is much smaller than the BEM result when h0 is within 30% of the body length, but approaches the latter when h0 is about half the body length. Numerical simulations are performed for the three typical manoeuvres of two bodies: (i) a body passing a stationary body, (ii) two bodies in a meeting manoeuvre (translating in opposite directions), and (iii) two bodies in a passing manoeuvre (translating in the same direction). The analysis reveals the orders of the lateral forces and yaw moments, as well as their variation trends in terms of the manoeuvre type, velocities, sizes, angles of yaw of the two bodies, and their proximity, etc. These irrotational dynamic features are expected to provide a basic understanding of this problem and will be beneficial to further numerical and experimental studies involving additional physical effects.

scholarly journals The Effects of Hypergravity on Xenopus Embryo Growth and Cardiac Hypertrophy

2012 ◽  
Vol 11 (1 and 2) ◽  
Author(s):  
Bryce Duchman ◽  
Darrell Wiens
Keyword(s):  
Xenopus Laevis ◽  
Body Length ◽  
Cardiac Tissue ◽  
Cross Sectional Area ◽  
The Body ◽  
Sectional Area ◽  
Cross Sectional ◽  
Organism Growth ◽  
Ventricle Size ◽  
Average Body

All life on earth has developed and evolved in a unity gravity (1G) environment. Any deviation below or above 1G could affect animal development, a period when much change occurs and sensitivity is high. We imposed simulated hypergravity through centrifugation and analyzed the effects on the overall body length and cardiac growth of Xenopus laevis embryos. We predicted that increased contractile force would be required from the heart to adequately circulate blood, dispersing nutrients, and that this would inhibit organism growth and possibly induce a state of hypertrophy. Embryos reaching gastrulation stage were exposed to a 7G or 1G (control) field via centrifugation for 96 hours. We then recorded behavior, mortality and took body length measurements. We found no significant differences in behavior or mortality, however, body length was significantly reduced by an average of 6.8% in the 7G group. We then fixed, embedded, sectioned and stained embryos in order to investigate the dimensions of cardiac tissue and of the cardiac region of the body using image analysis software. We found the 7G group had a significantly reduced average body cross-sectional area (-18%) and yet a significantly larger ventricular cross-sectional area (+36%) when compared to the 1G group. The average ratio of ventricle cross-sectional area to average body cross-sectional area was significantly higher in the 7G group when compared to the 1G. From these data, we conclude that hypergravity has a significant inhibitory impact on the Xenopus laevis embryo growth and causes a significant increase in ventricle size.

The wakes of cylindrical bluff bodies at low Reynolds number

1978 ◽  
Vol 288 (1354) ◽  
pp. 351-382 ◽  
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
The Body ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Near Wake ◽  
Cross Sectional ◽  
Molecular Diffusivity ◽  
Splitter Plates ◽  
Low Reynolds

Experiments on the near wake of a cylinder will be discribed in an attempt to present a coherent picture of the events encountered as the Reynolds number increases from small values up to values of a few thousand. Much work on this subject has already been done, but there are gaps in our description of these flows as well as more fundamental deficiencies in our understanding of them. The subject has been reviewed several times and most recently by Berger & Wille (1972) whose paper covers much of the ground that will be discussed again here. The present work may be regarded as built upon this latest review. I remember with gratitude many helpful discussions with the late Rudolph Wille who contributed so much to this subject. The investigation has concentrated on circular cylinders, but the wakes of bluff cylinders of different cross sectional shapes have also been observed. Bluff cylinders in general are considered in §§4 and 5, together with the effect of splitter plates on circular cylinders in §9. The experiments concern, almost exclusively, flow visualization of the wakes by means of dye washed from the bodies. The patterns of dye observed are, therefore, filament line representations of the flow leaving the separation lines on the body. It must be stressed that the dye does not make visible the vorticity bearing fluid because at low Reynolds number, vorticity diffuses considerably more rapidly than does dye. The ratio of the molecular diffusivity of momentum to that of mass of dye is of the order of 100.

An asymptotic theory of wind-tunnel-wall interference on subsonic slender bodies

1987 ◽  
Vol 177 ◽  
pp. 19-35 ◽  
Author(s):  
N. D. Malmuth
Keyword(s):  
Wind Tunnel ◽  
Body Length ◽  
Asymptotic Theory ◽  
Wall Layer ◽  
The Body ◽  
Length Ratio ◽  
Asymptotic Model ◽  
Tunnel Wall ◽  
Numerical Studies ◽  
Slender Bodies

An asymptotic theory of solid cylindrical wind-tunnel-wall interference about subsonic slender bodies has been developed. The basic approximation used is one of large wall-radius to body-length ratio. Matched asymptotic expansions show that in contrast to the analogous two-dimensional problem of a confined airfoil, three regions exist. Besides the incompressible crossflow and nearly axisymmetric zones, a wall layer exists where reflection in the wall of the line source representing the body becomes of dominant importance. From the theory, the interference pressures are shown to be approximately constant for closed bodies. Also demonstrated is that D'Alembert's paradox holds for interference drag of such shapes. Numerical studies comparing the exact theory to the asymptotic model which provides drastic simplifications, show that the latter can be used with reasonable accuracy to describe flows, even where the characteristic tunnel-radius to body-length ratio is as low as 1.5.

Supersonic Flow Past Slender Bodies With Discontinuous Profile Slope

1955 ◽  
Vol 6 (2) ◽  
pp. 114-124 ◽  
Author(s):  
L. E. Fraenkel ◽  
H. Portnoy
Keyword(s):  
Internal Flow ◽  
Leading Edge ◽  
Rate Of Change ◽  
The Body ◽  
Cross Sectional ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Slender Bodies ◽  
External Forces ◽  
Sectional Shape

SummaryWard’s slender-body theory is extended to derive first approximations to the external forces on slender bodies of general cross section with discontinuous profile slope. Two classes of body are considered: bodies whose profile (typified by the local radius) is continuous between the nose and base, and certain bodies whose profile is discontinuous, such as bodies with annular or side air intakes and wing-bodies on which the wing has an unswept leading edge. (Where air intakes are concerned, it is assumed that they are sharp-edged and that there is no “ spillage ” of the internal flow).The following conclusions apply to the former class of bodies. The variation of drag with Mach number is found to depend only on the discontinuities in the longitudinal rate of change of the cross-sectional area, and is thus independent of cross-sectional shape. The drag itself is unchanged if the direction of the flow is reversed. The expressions for lift and moment assume the same forms as for smooth pointed bodies, the lift depending only on conditions at the base of the body.The general theory is applied to winged bodies of revolution with an unswept wing leading edge: the results bear a marked resemblance to those obtained by Ward. The results for wings alone are seen to be applicable, with one modification, to subsonic as well as to supersonic speeds.

The motion of long slender bodies in a viscous fluid. Part 2. Shear flow

1971 ◽  
Vol 45 (4) ◽  
pp. 625-657 ◽  
Author(s):  
R. G. Cox
Keyword(s):  
Shear Flow ◽  
Viscous Fluid ◽  
Fluid Velocity ◽  
Axial Rotation ◽  
Axisymmetric Body ◽  
The Body ◽  
Total Force ◽  
Axis Ratio ◽  
Linear Flow ◽  
Slender Bodies

A long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis. Formulae for the total force and torque on the body are found as an expansion in terms of a small parameter κ defined as the radius-to-length ratio of the body. These general results are used to determine the resistance to axial rotation of the body and also the equivalent axis ratio of the body for motion in a shear flow.

scholarly journals Effects of Streamlining a Bluff Body in the Laminar Vortex Shedding Regime

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Ritvik Dobriyal ◽  
Maneesh Mishra ◽  
Markus Bölander ◽  
Martin Skote
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Shape Factor ◽  
Bluff Body ◽  
The Body ◽  
Cross Sectional ◽  
Shape Factors ◽  
Rear Part ◽  
Lift And Drag

Abstract Two-dimensional flow over bluff bodies is studied in the unsteady laminar flow regime using numerical simulations. In previous investigations, lift and drag forces have been studied over different cross-sectional shapes like circles, squares, and ellipses. We aim to extend the previous research by studying the variation of hydrodynamic forces as the shape of the body changes from a circular cylinder to a more streamlined or a bluffer body. The different body shapes are created by modifying the downstream circular arc of a circular cylinder into an ellipse, hence elongating or compressing the rear part of the body. The precise geometry of the body is quantified by defining a shape factor. Two distinct ranges of shape factors with fundamentally different behavior of lift and drag are identified. The geometry constituting the limit is where the rear part ellipse has a semi-minor axis of half the radius of the original circle, independent of the Reynolds number. On the other hand, the vortex shedding frequency decreases linearly over the whole range of shape factors. Furthermore, the variation of the forces and frequency with Reynolds number, and how the relations vary with the shape factor are reported.

scholarly journals Form, function, and divergence of a generic fin shape in small cetaceans

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255464
Author(s):  
Vadim Pavlov ◽  
Cecile Vincent ◽  
Bjarni Mikkelsen ◽  
Justine Lebeau ◽  
Vincent Ridoux ◽  
...  
Keyword(s):  
Body Length ◽  
Cross Sections ◽  
The Body ◽  
Hydrodynamic Characteristics ◽  
Wing Design ◽  
Cross Sectional ◽  
Aquatic Life ◽  
Dorsal Fin ◽  
Primary Function ◽  
Fin Shape

Tail flukes as well as the dorsal fin are the apomorphic traits of cetaceans which appeared during the evolutionary process of adaptation to the aquatic life. Both appendages present a wing-like shape associated with lift generation and low drag. We hypothesized that the evolution of fins as lifting structures led to a generic wing design, where the dimensionless parameters of the fin cross-sections are invariant with respect to the body length and taxonomy of small cetaceans (Hypothesis I). We also hypothesized that constraints on variability of a generic fin shape are associated with the primary function of the fin as a fixed or flapping hydrofoil (Hypothesis II). To verify these hypotheses, we examined how the variation in the fin’s morphological traits is linked to the primary function, species and body length. Hydrodynamic characteristics of the fin cross-sections were examined with the CFD software and compared with similar engineered airfoils. Generic wing design of both fins was found in a wing-like planform and a streamlined cross-sectional geometry optimized for lift generation. Divergence in a generic fin shape both on the planform and cross-sectional level was found to be related with the fin specialization in fixed or flapping hydrofoil function. Cross-sections of the dorsal fin were found to be optimized for the narrow range of small angles of attack. Cross-sections of tail flukes were found to be more stable for higher angles of attack and had gradual stall characteristics. The obtained results provide an insight into the divergent evolutionary pathways of a generic wing-like shape of the fins of cetaceans under specific demands of thrust production, swimming stability and turning control.

Note on the Numerical Evaluation of the Wave Drag of Smooth Slender Bodies Using Optimum Area Distributions for Minimum Wave Drag

1956 ◽  
Vol 60 (541) ◽  
pp. 61-63 ◽  
Author(s):  
E. Eminton ◽  
W. T. Lord
Keyword(s):  
Numerical Evaluation ◽  
Practical Method ◽  
Wave Drag ◽  
The Body ◽  
Cross Sectional ◽  
Area Distribution ◽  
Slender Bodies ◽  
Kinetic Pressure ◽  
Image Position ◽  
Sectional Shape

The linearised theory value of the wave drag D at zero lift of a smooth slender body of arbitrary cross-sectional shape was shown by Ward to be given bywhere S (x), 0 ⩽ x ⩽ 1, is the cross-sectional area distribution of the body and q is the kinetic pressure. The development of this result has aroused interest in two problems: the derivation of the optimum area distribution for minimum wave drag under certain specified conditions and the numerical evaluation of the wave drag of a specified area distribution. These apparently distinct problems have hitherto been treated separately, but it is shown here how an attempt to solve the first problem has led to a practical method of solving the second.

Sign in / Sign up

Export Citation Format

Share Document