Transition to chaos in the wake of a rolling sphere

2012 ◽  
Vol 695 ◽  
pp. 135-148 ◽  
Author(s):  
A. Rao ◽  
P.-Y. Passaggia ◽  
H. Bolnot ◽  
M.C. Thompson ◽  
T. Leweke ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Free Stream ◽  
Low Frequency ◽  
Quantitative Information ◽  
Hairpin Vortices ◽  
Rotating Sphere ◽  
Transition To Chaos ◽  
Rolling Sphere ◽  
The One ◽  
Planar Symmetry

AbstractThe wake of a sphere rolling along a wall at low Reynolds number is investigated numerically and experimentally. Two successive transitions are identified in this flow, as the Reynolds number is increased. The first leads to the periodic shedding of planar symmetric hairpin vortices. The second and previously unknown transition involves a loss of planar symmetry and a low-frequency lateral oscillation of the wake, exhibiting a surprising 7:3 resonance with the hairpin vortex shedding. The two transitions are characterized by dye visualizations and quantitative information obtained from numerical simulations, such as force coefficients and wake frequencies (Strouhal numbers). Both transitions are found to be supercritical. Further increasing the Reynolds number, the flow becomes progressively more disorganized and chaotic. Overall, the transition sequence for the rolling sphere is closer to the one for a non-rotating sphere in a free stream than to that of a non-rotating sphere close to a wall.

Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow

2018 ◽  
Vol 857 ◽  
pp. 878-906 ◽  
Author(s):  
T. Nagata ◽  
T. Nonomura ◽  
S. Takahashi ◽  
Y. Mizuno ◽  
K. Fukuda
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Rotation Rate ◽  
Free Stream ◽  
Rotating Sphere ◽  
Free Stream Mach Number ◽  
Low Reynolds

In this study, direct numerical simulation of the flow around a rotating sphere at high Mach and low Reynolds numbers is conducted to investigate the effects of rotation rate and Mach number upon aerodynamic force coefficients and wake structures. The simulation is carried out by solving the three-dimensional compressible Navier–Stokes equations. A free-stream Reynolds number (based on the free-stream velocity, density and viscosity coefficient and the diameter of the sphere) is set to be between 100 and 300, the free-stream Mach number is set to be between 0.2 and 2.0, and the dimensionless rotation rate defined by the ratio of the free-stream and surface velocities above the equator is set between 0.0 and 1.0. Thus, we have clarified the following points: (1) as free-stream Mach number increased, the increment of the lift coefficient due to rotation was reduced; (2) under subsonic conditions, the drag coefficient increased with increase of the rotation rate, whereas under supersonic conditions, the increment of the drag coefficient was reduced with increasing Mach number; and (3) the mode of the wake structure becomes low-Reynolds-number-like as the Mach number is increased.

Reynolds Number Dependence of the Flow Structure Behind Two Side-by-Side Cylinders

2002 ◽  
Author(s):  
S. J. Xu ◽  
Y. Zhou ◽  
R. M. C. So
Keyword(s):  
Reynolds Number ◽  
Flow Structure ◽  
Free Stream ◽  
Present Finding ◽  
Dominant Frequency ◽  
Wind Tunnels ◽  
Stream Velocity ◽  
Single Vortex ◽  
The One ◽  
Reynolds Number Dependence

The wake structure of two side-by-side cylinders was experimentally investigated using flow visualization and hotwire techniques. The investigation was focused on the asymmetrical flow regime, i.e., T/d = 1.2 – 1.6, where T is the center-to-center cylinder spacing and d is the cylinder diameter. Experiments were conducted in both water and wind tunnels at a Reynolds number (Re) range of 150 – 14300. It has been found that, as Re increases, the flow structure behind the cylinders would change from one single vortex street to two streets with one narrow and one wide, for the same T/d. The one-street flow structure is dominated by one frequency ƒ0* = ƒ0d/U∞ ≈ 0.09, where ƒ0 is the dominant frequency and U∞ is the free-stream velocity. On the other hand, two frequencies, ƒ0* ≈ 0.3 and 0.09, characterized the two-street flow structure. These are associated with the narrow and wide street frequency, respectively. It is further observed that the critical Re, at which transition from single to two streets occurs, increases as T/d decreases. The present finding help clarify previous scattered reports for 1.2 < T/d < 1.5: detection of one dominant frequency by some but two by others.

Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity

1991 ◽  
Vol 233 ◽  
pp. 613-631 ◽  
Author(s):  
Renwei Mei ◽  
Christopher J. Lawrence ◽  
Ronald J. Adrian
Keyword(s):  
Reynolds Number ◽  
Free Stream ◽  
Low Frequency ◽  
Reynolds Numbers ◽  
Free Stream Velocity ◽  
Creeping Flow ◽  
Stream Velocity ◽  
Velocity Difference ◽  
Long Time ◽  
The Time Domain

Unsteady flow over a stationary sphere with small fluctuations in the free-stream velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady Stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the force has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & Mckee (1984) wherein for a particle introduced to a turbulent flow the initial velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effects of Reynolds number on the unsteady drag due to the fluctuating free-stream velocity are presented. The implications for particle motion in turbulence are discussed.

Further Studies of the Axisymmetric Disk Wake Using the “Slice POD”

2002 ◽  
Author(s):  
Peter B. V. Johansson ◽  
William K. George
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Free Stream ◽  
Stream Velocity ◽  
Azimuthal Mode ◽  
Wire Arrays ◽  
Mode 2 ◽  
High Reynolds ◽  
The One ◽  
Zero Frequency

This paper presents the findings of three experiments using multi-point hot-wire arrays in the high Reynolds number axisymmetric turbulent wake behind a disk. The purpose of the multiple experiments was to validate earlier and less extensive experiments. The ‘slice POD’ was applied to all sets to examine the effects of array coverage and the disk support system. The Reynolds number based on the free stream velocity and disk diameter was kept constant at 28,000. The investigated region spanned from 10 to 60 disk diameters downstream. These results confirm the earlier findings. In particular, the eigenvalues integrated over frequency show a azimuthal mode-1 dominance at x/D = 10 which evolves to a mode-2 dominance by x/D = 50. For all downstream positions, two distinct peaks were found in the first eigenspectrum: one for azimuthal mode-2 at near zero frequency, and another for azimuthal mode-1 at a Strouhal number (fd/U∞) of 0.126. Both peaks decrease in magnitude as the flow evolves downstream, but the peak at the Strouhal number 0.126 decrease more rapidly then the one at near-zero frequency, leaving the latter to eventually dominate.

Numerical and experimental studies of the rolling sphere wake

2010 ◽  
Vol 643 ◽  
pp. 137-162 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Experimental Studies ◽  
The Body ◽  
Streamwise Vortices ◽  
Hairpin Vortices ◽  
Number Range ◽  
Unsteady Wake ◽  
Rolling Sphere ◽  
Wake Modes ◽  
Reversed Rotation

A numerical and experimental investigation is reported for the flow around a rolling sphere when moving adjacent to a plane wall. The dimensionless rotation rate of the sphere is varied from forward to reversed rolling and the resulting wake modes are found to be strongly dependent on the value of this parameter. Results are reported for the Reynolds number range 100 < Re < 350, which has been shown to capture the unsteady transitions in the wake. Over this range of Reynolds number, both steady and unsteady wake modes are observed. As the sphere undergoes forward rolling, the wake displays similarities to the flow behind an isolated sphere in a free stream. As the Reynolds number of the flow increases, hairpin vortices form and are shed over the surface of the sphere. However, for cases with reversed rotation, the wake takes the form of two distinct streamwise vortices that form around the sides of the body. These streamwise structures in the wake undergo a transition to a new unsteady mode as the Reynolds number increases. During the evolution of this unsteady mode, the streamwise vortices form an out-of-phase spiral pair. Four primary wake modes are identified and a very good qualitative agreement is observed between the numerical and experimental results. The numerical simulations also reveal the existence of an additional unsteady mode that is found to be unstable to small perturbations in the flow.

Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes

2010 ◽  
Vol 664 ◽  
pp. 193-219 ◽  
Author(s):  
XIAOHUA WU
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Free Stream ◽  
Transitional Region ◽  
Hairpin Vortices ◽  
Turbulent Region ◽  
Total Shear Stress ◽  
Total Shear

Direct numerical simulation was performed on an incompressible, smooth flat-plate boundary layer at unit molecular Prandtl number and constant surface temperature under free-stream periodically passing turbulent planar wakes over the momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 1850. This inhomogeneous free-stream wake perturbation source with mean deficit differs markedly from the isotropic turbulent patch used in the previous studies of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5; Phys. Fluids, vol. 22, 2010, 085105). Preponderance of hairpin vortices is observed in both the transitional and turbulent regions of the boundary layer. In particular, the internal structure of merged turbulent spots is a hairpin forest; the internal structure of infant turbulent spots is a hairpin packet. Although more chaotic in the turbulent region, numerous hairpin vortices are readily detected in both the near-wall and outer regions of the boundary layer up to Reθ = 1850. This suggests that the hairpin vortices in the higher-Reynolds-number region are not simply the aged hairpin forests convected from the upstream transitional region. Temperature iso-surfaces in the companion thermal boundary layer are found to be a useful tracer in identifying boundary-layer hairpin vortex structures. Total shear stress overshoots wall shear stress in the transitional region and the excess relaxes gradually in the downstream turbulent region. This overshoot is shown to be associated with a localized streamwise acceleration of the streamwise velocity component. Breakdown of the wake-perturbed laminar boundary layer is closely related to the formation of hairpin packets out of quasi-streamwise vortices. Mean and second-order statistics are in good agreement with previous data on the standard turbulent boundary layer. Downstream of transition, normalized root-mean-square (r.m.s.) wall-shear-stress intensity shows almost no variation with Reθ, whereas normalized r.m.s. wall-pressure intensity increases slightly. Taken together with the previous results of Wu & Moin, the generality of the following three phenomena in quasi-standard boundary layers can be reasonably established, namely, preponderance of hairpin vortices in the transitional as well as in the turbulent regions up to Reθ = 1850, transitional total shear stress overshoot, and a laminar-layer breakdown process closely tied to the formation of hairpin packets.

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

2013 ◽  
Vol 732 ◽  
pp. 616-659 ◽  
Author(s):  
Ming Dong ◽  
Xuesong Wu
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Stream ◽  
Stokes Equations ◽  
Low Frequency ◽  
Streamwise Velocity ◽  
Bypass Transition ◽  
Leading Order ◽  
Local Boundary ◽  
Asymptotic Suction

AbstractSmall-amplitude perturbations are governed by the linearized Navier–Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr–Sommerfeld (O-S) and Squire equations. In this paper, we consider continuous spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blasius boundary layer, we highlight two particular properties of the CS: (i) the eigenfunction of a continuous mode simultaneously consists of two components with wall-normal wavenumbers $\pm {k}_{2} $, a phenomenon which we refer to as ‘entanglement of Fourier components’; and (ii) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when ${R}^{- 1} \ll \omega \ll 1$, where $R$ is the Reynolds number based on the local boundary-layer thickness. For the asymptotic suction boundary layer, which is an exactly parallel flow, both temporal and spatial CS may be defined mathematically. However, at a finite $R$ neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit $R\gg 1$, all three types of CS are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Low-frequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.

SEM image sharpness analysis

1996 ◽  
Vol 54 ◽  
pp. 142-143
Author(s):  
M. T. Postek ◽  
A. E. Vladar
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Quantitative Information ◽  
Primary Electron ◽  
Image Sharpness ◽  
Critical Dimensions ◽  
Sem Image ◽  
Frequency Changes ◽  
Electron Microscopes ◽  
Scanning Electron

Fully automated or semi-automated scanning electron microscopes (SEM) are now commonly used in semiconductor production and other forms of manufacturing. The industry requires that an automated instrument must be routinely capable of 5 nm resolution (or better) at 1.0 kV accelerating voltage for the measurement of nominal 0.25-0.35 micrometer semiconductor critical dimensions. Testing and proving that the instrument is performing at this level on a day-by-day basis is an industry need and concern which has been the object of a study at NIST and the fundamentals and results are discussed in this paper.In scanning electron microscopy, two of the most important instrument parameters are the size and shape of the primary electron beam and any image taken in a scanning electron microscope is the result of the sample and electron probe interaction. The low frequency changes in the video signal, collected from the sample, contains information about the larger features and the high frequency changes carry information of finer details. The sharper the image, the larger the number of high frequency components making up that image. Fast Fourier Transform (FFT) analysis of an SEM image can be employed to provide qualitiative and ultimately quantitative information regarding the SEM image quality.

scholarly journals Purcell’s Three-Link Swimmer: Assessment of Geometry and Gaits for Optimal Displacement and Efficiency

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1088
Author(s):  
Cristina Nuevo-Gallardo ◽  
José Emilio Traver ◽  
Inés Tejado ◽  
Blas M. Vinagre
Keyword(s):  
Reynolds Number ◽  
Multiobjective Optimization ◽  
The Other ◽  
Optimal Method ◽  
Optimal Velocity ◽  
Motion Primitives ◽  
Motion Primitive ◽  
Control Objective ◽  
Optimal Efficiency ◽  
The One

This paper studies the displacement and efficiency of a Purcell’s three-link microswimmer in low Reynolds number regime, capable of moving by the implementation of a motion primitive or gait. An optimization is accomplished attending to the geometry of the swimmer and the motion primitives, considering the shape of the gait and its amplitude. The objective is to find the geometry of the swimmer, amplitude and shape of the gaits which make optimal the displacement and efficiency, in both an individual way and combined (the last case will be referred to as multiobjective optimization). Three traditional gaits are compared with two primitives proposed by the authors and other three gaits recently defined in the literature. Results demonstrate that the highest displacement is obtained by the Tam and Hosoi optimal velocity gait, which also achieves the best efficiency in terms of energy consumption. The rectilinear and Tam and Hosoi optimal efficiency gaits are the second optimum primitives. Regarding the multiobjective optimization and considering the two criteria with the same weight, the optimum gaits turn out to be the rectilinear and Tam and Hosoi optimal efficiency gaits. Thus, the conclusions of this study can help designers to select, on the one hand, the best swimmer geometry for a desired motion primitive and, on the other, the optimal method of motion for trajectory tracking for such a kind of Purcell’s swimmers depending on the desired control objective.

scholarly journals Posturography with head movements in the assessment of balance in chronic unilateral vestibular lesions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Magdalena Janc ◽  
Mariola Sliwinska-Kowalska ◽  
Piotr Politanski ◽  
Marek Kaminski ◽  
Magdalena Jozefowicz-Korczynska ◽  
...  
Keyword(s):  
High Reliability ◽  
Low Frequency ◽  
Random Order ◽  
Head Movements ◽  
Canal Paresis ◽  
Eyes Closed ◽  
Static Posturography ◽  
Unstable Surface ◽  
Novel Method ◽  
The One

AbstractThe aim of our study was to validate the method of head-shake static posturography (HS-posturography) in healthy individuals and to establish the value of this novel method in the diagnostics of patients with unilateral vestibular lesion (UV). The study included 202 participants divided into two groups, one consisting of 133 patients with canal paresis CP > 19% and one of 69 healthy subjects. Participant was tested according to the standard protocol of static posturography (SP), and with head movements of 0.3 Hz (HS 40), 0.6 Hz (HS 70) in random order controlled by a metronome. HS-posturography revealed a similar repeatability and internal consistency as the standard posturography. In patients with UV, 4th condition revealed higher sensitivity (74%) and specificity (71%) in HS 40 than in the standard posturography (67%, 65% respectively) and HS 70 (54%, 70% respectively). Static posturography and HS- posturography revealed a high reliability of the testing method. The head movements added to static posturography improve the sensitivity and specificity of the method in group with vestibular impairment. The most important test for that purpose seems to be the one on unstable surface with the eyes closed, with low frequency of head movements.

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