Oscillatory motion and wake instability of freely rising axisymmetric bodies

2007 ◽  
Vol 573 ◽  
pp. 479-502 ◽  
Author(s):  
PEDRO C. FERNANDES ◽  
FRÉDÉRIC RISSO ◽  
PATRICIA ERN ◽  
JACQUES MAGNAUDET
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Axial Velocity ◽  
Body Shape ◽  
Rigid Bodies ◽  
The Body ◽  
Body Motion ◽  
Wake Instability ◽  
Moving Bodies

This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. Beyond a critical Reynolds number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds numbers, Recf1 and Recf2, decrease. Introducing a Reynolds number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds $\hbox{\it Re}^*_{cf1}$ and $\hbox{\it Re}^*_{cf2}$ that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ < 6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Rec to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, $\sqrt{((\rho_f-\rho_b)/\rho_f)\,gh}$, while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, $\sqrt{((\rho_f-\rho_b)/\rho_f)\,gd}$, respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the modified Reynolds number, Re*; they no longer depend on the body shape.

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Men, appearance, and cosmetic surgery: The role of confidence, self-esteem, and comfort with the body

2008 ◽  
Vol 34 (1) ◽  
pp. 105-134 ◽  
Author(s):  
Rosemary Ricciardelli ◽  
Kimberley Ann Clow
Keyword(s):  
Cosmetic Surgery ◽  
Body Shape ◽  
Online Survey ◽  
Identity Theory ◽  
Self Esteem ◽  
The Body ◽  
Sociology Of The Body ◽  
Lower Confidence

Recent research has suggested that perceptions of the body are important to men’s sense of confidence and that men see the body as a vehicle for personal improvement. To build on this research, an online survey investigated Canadian men’s perspectives on their appearance and their attitudes toward cosmetic surgery. Low self-esteem, lack of confidence, and comfort with one’s body uniquely predicted different aspects of men’s experiences, including attitudes about body shape, perceptions of others, pressures to lose weight, and perspectives regarding cosmetic surgery. For example, participants who were more comfortable with their bodies and higher in self-esteem were happier with their current body shape and features, whereas participants who were less comfortable with their bodies and lower in confidence put more pressure on themselves to lose weight. In addition, lower confidence significantly predicted willingness to undergo cosmetic surgery. Men’s perspectives on cosmetic surgery were thematically analyzed. These findings are situated within identity theory and sociology of the body.

ENVELOPING SURFACES AND ADMISSIBLE VELOCITIES OF HEAVY RIGID BODIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2525-2553 ◽  
Author(s):  
IGOR N. GASHENENKO ◽  
PETER H. RICHTER
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
First Integrals ◽  
The Body ◽  
Heegaard Splitting ◽  
Body Motion ◽  
Invariant Sets ◽  
Poisson Problem ◽  
Integral Manifolds ◽  
Angular Velocities

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

scholarly journals The steady oblique path of buoyancy-driven disks and spheres

2012 ◽  
Vol 707 ◽  
pp. 24-36 ◽  
Author(s):  
David Fabre ◽  
Joël Tchoufag ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Density Ratio ◽  
Steady Motion ◽  
The Body ◽  
Body Motion ◽  
Angle Of Incidence ◽  
Weakly Nonlinear ◽  
Numerical Studies ◽  
Flow Past

AbstractWe consider the steady motion of disks of various thicknesses in a weakly viscous flow, in the case where the angle of incidence $\ensuremath{\alpha} $ (defined as that between the disk axis and its velocity) is small. We derive the structure of the steady flow past the body and the associated hydrodynamic force and torque through a weakly nonlinear expansion of the flow with respect to $\ensuremath{\alpha} $. When buoyancy drives the body motion, we obtain a solution corresponding to an oblique path with a non-zero incidence by requiring the torque to vanish and the hydrodynamic and net buoyancy forces to balance each other. This oblique solution is shown to arise through a bifurcation at a critical Reynolds number ${\mathit{Re}}^{\mathit{SO}} $ which does not depend upon the body-to-fluid density ratio and is distinct from the critical Reynolds number ${\mathit{Re}}^{\mathit{SS}} $ corresponding to the steady bifurcation of the flow past the body held fixed with $\ensuremath{\alpha} = 0$. We then apply the same approach to the related problem of a sphere that weakly rotates about an axis perpendicular to its path and show that an oblique path sets in at a critical Reynolds number ${\mathit{Re}}^{\mathit{SO}} $ slightly lower than ${\mathit{Re}}^{\mathit{SS}} $, in agreement with available numerical studies.

Low Reynolds numbers flow past an ellipsoid of revolution of large aspect ratio

1965 ◽  
Vol 23 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Yun-Yuan Shi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Major Axis ◽  
Reynolds Numbers ◽  
The Body ◽  
Large Aspect Ratio ◽  
Low Reynolds Numbers ◽  
Ellipsoid Of Revolution ◽  
Limiting Case

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.

Dynamics of axisymmetric bodies rising along a zigzag path

2008 ◽  
Vol 606 ◽  
pp. 209-223 ◽  
Author(s):  
PEDRO C. FERNANDES ◽  
PATRICIA ERN ◽  
FRÉDÉRIC RISSO ◽  
JACQUES MAGNAUDET
Keyword(s):  
Aspect Ratio ◽  
Transverse Direction ◽  
Transverse Velocity ◽  
Density Ratio ◽  
Transverse Component ◽  
The Body ◽  
Force Balance ◽  
Body Motion ◽  
Major Influence ◽  
Inertia Force

The forces and torques governing the planar zigzag motion of thick, slightly buoyant disks rising freely in a liquid at rest are determined by applying the generalized Kirchhoff equations to experimental measurements of the body motion performed for a single body-to-fluid density ratio ρs/ρf ≈ 1. The evolution of the amplitude and phase of the various contributions is discussed as a function of the two control parameters, i.e. the body aspect ratio (the diameter-to-thickness ratio χ = d/h ranges from 2 to 10) and the Reynolds number (100 < Re < 330), Re being based on the rise velocity and diameter of the body. The body oscillatory behaviour is found to be governed by the force balance along the transverse direction and the torque balance. In the transverse direction, the wake-induced force is mainly balanced by two forces that depend on the body inclination, i.e. the inertia force generated by the body rotation and the transverse component of the buoyancy force. The torque balance is dominated by the wake-induced torque and the restoring added-mass torque generated by the transverse velocity component. The results show a major influence of the aspect ratio on the relative magnitude and phase of the various contributions to the hydrodynamic loads. The vortical transverse force scales as fo = (ρf − ρs)ghπd2 whereas the vortical torque involves two contributions, one scaling as fod and the other as f1d with f1 = χfo. Using this normalization, the amplitudes and phases of the vortical loads are made independent of the aspect ratio, the amplitudes evolving as (Re/Rec1 − 1)1/2, where Rec1 is the threshold of the first instability of the wake behind the corresponding body held fixed in a uniform stream.

Wake instability of a fixed spheroidal bubble

2007 ◽  
Vol 572 ◽  
pp. 311-337 ◽  
Author(s):  
JACQUES MAGNAUDET ◽  
GUILLAUME MOUGIN
Keyword(s):  
Reynolds Number ◽  
Body Surface ◽  
Bubble Surface ◽  
The Body ◽  
Rigid Sphere ◽  
Instability Mechanism ◽  
Aspect Ratios ◽  
Wake Instability ◽  
Vorticity Flux ◽  
Axis Length

Direct numerical simulations of the flow past a fixed oblate spheroidal bubble are carried out to determine the range of parameters within which the flow may be unstable, and to gain some insight into the instability mechanism. The bubble aspect ratio χ (i.e. the ratio of the major axis length over the minor axis length) is varied from 2.0 to 2.5 while the Reynolds number (based on the upstream velocity and equivalent bubble diameter) is varied in the range 102 ≤ Re ≤ 3 × 103. As vorticity generation at the bubble surface is at the root of the instability, theoretical estimates for the maximum of the surface vorticity and the surface vorticity flux are first derived. It is shown that, for large aspect ratios and high Reynolds numbers, the former evolves as χ8/3 while the latter is proportional to χ7/2Re−1/2. Then it is found numerically that the flow first becomes unstable for χ = χc ≈ 2.21. As the surface vorticity becomes independent of Re for large enough Reynolds number, the flow is unstable only within a finite range of Re, this range being an increasing function of χ − χc. An empirical criterion based on the maximum of the vorticity generated at the body surface is built to determine whether the flow is stable or not. It is shown that this criterion also predicts the correct threshold for the wake instability past a rigid sphere, suggesting that the nature of the body surface does not really matter in the instability mechanism. Also the first two bifurcations of the flow are similar in nature to those found in flows past rigid axisymmetric bluff bodies, such as a sphere or a disk. Wake dynamics become more complex at higher Reynolds number, until the Re−1/2-dependency of the surface vorticity flux makes the flow recover its steadiness and eventually its axisymmetry. A qualitative analysis of the azimuthal vorticity field in the base flow at the rear of the bubble is finally carried out to make some progress in the understanding of the primary instability. It is suggested that the instability originates in a thin region of the flow where the vorticity gradients have to turn almost at right angle to satisfy two different constraints, one at the bubble surface, the other within the standing eddy.

scholarly journals Evaluating Lumbar Shape Deformation With Fabric Strain Sensors

2020 ◽  
pp. 001872082096530
Author(s):  
Linh Q. Vu ◽  
Han Kim ◽  
Lawrence J. H. Schulze ◽  
Sudhakar L. Rajulu
Keyword(s):  
Injury Risk ◽  
Body Shape ◽  
Human Motion ◽  
The Body ◽  
Strain Sensors ◽  
Body Motion ◽  
Space Suit ◽  
Extravehicular Activity ◽  
Shape Prediction ◽  
Space Suits

Objective To better study human motion inside the space suit and suit-related contact, a multifactor statistical model was developed to predict torso body shape changes and lumbar motion during suited movement by using fabric strain sensors that are placed on the body. Background Physical interactions within pressurized space suits can pose an injury risk for astronauts during extravehicular activity (EVA). In particular, poor suit fit can result in an injury due to reduced performance capabilities and excessive body contact within the suit during movement. A wearable solution is needed to measure body motion inside the space suit. Methods An array of flexible strain sensors was attached to the body of 12 male study participants. The participants performed specific static lumbar postures while 3D body scans and sensor measurements were collected. A model was created to predict the body shape as a function of sensor signal and the accuracy was evaluated using holdout cross-validation. Results Predictions from the torso shape model had an average root mean square error (RMSE) of 2.02 cm. Subtle soft tissue deformations such as skin folding and bulges were accurately replicated in the shape prediction. Differences in posture type did not affect the prediction error. Conclusion This method provides a useful tool for suited testing and the information gained will drive the development of injury countermeasures and improve suit fit assessments. Application In addition to space suit design applications, this technique can provide a lightweight and wearable system to perform ergonomic evaluations in field assessments.

Evidence of a heritable component to body shape in the northern redbelly dace (Phoxinus eos)

1997 ◽  
Vol 75 (8) ◽  
pp. 1247-1253 ◽  
Author(s):  
C. Anna Toline ◽  
Allan J. Baker
Keyword(s):  
Body Shape ◽  
Natural Populations ◽  
The Body ◽  
Foraging Ability ◽  
Environmental Induction ◽  
Foraging Tactics ◽  
Selection For ◽  
Shape Changes ◽  
Common Laboratory

Hypotheses about the role of selection on body-shape evolution assume a heritable component to this phenotypic character. To examine the influence of environmental induction on body shape, offspring form two morphologically differentiated populations of northern redbelly dace (Phoxinus eos) were reared in a common laboratory environment. Additionally, shape changes were monitored over 3 consecutive years in six populations. Offspring reared in a common environment retained the body shape of individuals from their natal pond, and shape changes among fish in different ponds were maintained in natural populations over years. These results strongly suggest a heritable component to body shape in P. eos. These results complement earlier work examining foraging tactics as a potential selection pressure on body shape and support the conclusion that body-shape differences among fish in different ponds are being maintained by selection for foraging ability.

7. Shape and Motion Integration in People Perception Depends on the Action of the Performer

2018 ◽  
Author(s):  
Claire Honda
Keyword(s):  
Visual Information ◽  
Body Shape ◽  
Object Perception ◽  
Human Action ◽  
The Body ◽  
Motion Information ◽  
Centre Of Mass ◽  
Indirect Object ◽  
Throw Distance

Perception of human action depends on both the body shape and motion of a performer. We can indirectly perceive the properties of an object being acted upon even when visual information is limited and the object itself is not visible; we accomplish this using internal models of a body’s dynamics and an action’s kinematics (Runeson & Frykholm, 1981). We are also sensitive to correlations between a performer’s shape and motion, known as internal consistency (Runeson & Frykholm, 1983). To investigate how decorrelating shape and motion affects indirect object perception, we ran an experiment where participants watched realistic avatars of performers manipulating invisible objects. Unbeknownst to participants, half of the stimuli were internally inconsistent: the shape of one performer was combined with the motion of a performer with a dissimilar body shape. Participants saw sled pushes, beanbag throws, and box lifts, and estimated the sled weight, throw distance, or box weight. For sled pushes, there was a shape-motion interaction such that heavy bodies were perceived as pushing heavier weights when animated with motion from light performers, and light bodies were perceived as pushing lighter weights when animated with motion from heavy performers. In contrast, participants estimated beanbag throw distance primarily from performer motion. Interpretation of the box lift data is more complex. In conclusion, the way in which our visual system combines shape and motion information depends on the role of body shape and centre of mass on the outcome of an action.

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