Free rising spheres do not obey newton's law for free settling

Karamanev, Dimitre; Николов, Л.

doi:10.1002/aic.690381116

Cited by 94 publications

(75 citation statements)

References 12 publications

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“…This assumption seemed so obvious that no one proceeded to check it experimentally. However, experimental results reported recently (Karamanev and Nikolov, 1992) showed that the trajectory of free rising solid particles in Newtonian fluids was completely different compared to that of free falling particles, especially in the Newton's law region. In addition, the terminal velocity of rising particles was much lower than that of falling ones.…”

Section: Newtonian Fluidsmentioning

confidence: 92%

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions

Margaritis

Bokkel

Karamanev

1999

Biotechnol. Bioeng.

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Section: Newtonian Fluidsmentioning

confidence: 92%

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions

Margaritis

Bokkel

Karamanev

1999

Biotechnol. Bioeng.

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“…For example, a slowly settling sedimenting sphere falls straight downwards [9] but above a certain sedimentation velocity, the sphere's motion becomes periodic and its trajectory a spiral or zigzag [10]. A deformable object, such as a droplet or bubble, can behave similarly even as its shape now changes [11,12].…”

mentioning

confidence: 99%

Dynamics of a Deformable Body in a Fast Flowing Soap Film

et al. 2006

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We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible body interacting in a two-dimensional flow. This coupled fluid-structure system shows bistability, with both stationary and oscillatory states. In its stationary state, the loop remains essentially motionless and its wake is a von Kármán vortex street. In its oscillatory state, the loop sheds two vortex dipoles, or more complicated vortical structures, within each oscillation period. We find that the oscillation frequency of the loop is linearly proportional to the flow velocity, and that the measured Strouhal numbers can be separated based on wake structure.PACS numbers: 47.32.ck, 47.54.De, The wake flow behind a rigid obstacle is a central object of study in fluid mechanics. When the oncoming flow velocity exceeds a threshold, vortices are shed behind the obstacle [1]. A typical wake is composed of successive eddies of alternating sign -the "von Kármán vortex street" -and is observed over a wide range of flow velocities and body shapes [2,3]. The frequency of vortex shedding (f ) is determined by the flow velocity (V ) and the object size (d), whose relation is captured by the near constancy of the Strouhal number,The dynamics of a rigid object which moves freely in the direction perpendicular to the flow is of interest in many industrial and biological applications [4,5,6]. Lateral motion of an object can be induced by interaction with the flow and is often called the vortex-induced vibration (VIV). At low flow velocities, the body starts to oscillate sideways with small amplitude (less than 0.4 times body diameter). Its associated wake structure is again a von Kármán vortex street. However, further increase of flow velocity causes the obstacle to oscillate in phase with the vortex shedding, and as a result, a series of dipoles are shed instead [7,8].Settling bodies or rising bubbles, where the balance of gravitational and drag forces set the velocity, also exhibit transitions as they interact with their wakes. For example, a slowly settling sedimenting sphere falls straight downwards [9] but above a certain sedimentation velocity, the sphere's motion becomes periodic and its trajectory a spiral or zigzag [10]. A deformable object, such as a droplet or bubble, can behave similarly even as its shape now changes [11,12].Finally, studies have shown the instability (and bistability) of slender deformable bodies to lateral oscillations in quasi-2D soap-film flows [13], and of heavy deformable sheets to lateral oscillations in fast 3D flows [14,15,16,17]. In these cases, the system corresponds to the flapping of a flag in a stiff breeze.Flowing soap film provides a practical template upon which to study the dynamics of a nearly 2D flow [18,19]. The experimental setup has been introduced earlier [13,18,19,20]. In this work, we introduce a deformable closed body into a fast flowing so...

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“…Simulations by Pan (1999) found that for Re > 135, a sphere falls with a spiral trajectory. This spiral motion has also been observed for the same Re in experiments on rising spheres (Karamanev & Nikolov 1992). For Re > 200, the wake develops a pair of bound counter-rotating vortex threads (Jenny, Dusek & Bouchet 2004), and for Re > 270, the vortex threads are shed in pairs behind the sphere as it descends (Clift et al 1978); simulations yield St = 0.176 for the shedding frequency (Jenny et al 2004).…”

Section: Related Workmentioning

confidence: 68%

“…If the sphere density is smaller than about one-third the fluid density, the sphere ascends in zigzagging or irregular spiral trajectory (Karamanev & Nikolov 1992). The irregular spiral motion is a consequence of the time-dependent forces that act on a sphere when the wake is unstable; the Strouhal number coincides with that of the unstable wake for fixed spheres (Karamanev 1994;Karamanev, Chavarie & Mayer 1996;Karamanev & Nikolov 1992). If the density of a sphere is comparable with or larger than the density of the fluid, the wake structure is similar to that of a fixed sphere (see the following subsection).…”

Section: Related Workmentioning

confidence: 99%

Sedimenting sphere in a variable-gap Hele-Shaw cell

2007

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We have measured the trajectory and visualized the wake of a single sphere falling in a fluid confined between two closely spaced glass plates (a Hele-Shaw cell). The position of a sedimenting sphere was measured to better than 0.001d, where d is the sphere diameter, for Reynolds numbers (based on the terminal velocity) between 20 and 330, for gaps between the plates ranging from 1.014d to 1.4d. For gaps in the range 1.01d-1.05d, the behaviour of the sedimenting sphere is found to be qualitatively similar to that of an unconfined cylinder in a uniform flow, but our sedimenting sphere begins to oscillate and shed von Kármán vortices for Re > 200, which is far greater than the Re = 49 for the onset of vortex shedding behind cylinders in an open flow. When the gap is increased to 1.10d-1.40d, the vortices behind the sphere are different -they are qualitatively similar to those behind a sphere sedimenting in the absence of confining walls. Our precision measurements of the velocity of a sedimenting sphere and the amplitude and frequency of the oscillations provide a benchmark for numerical simulations of the sedimentation of particles in fluids. IntroductionThe motion of blunt bodies in a fluid has been studied since the early days of the development of fluid mechanics. Even now sedimenting bodies yield surprising discoveries and challenges for theoretical analyses, but there have been few experiments using modern imaging techniques to examine a sedimenting body.We have examined the sedimentation of a single sphere in a fluid contained between vertical plates separated by a distance only slightly greater than the sphere diameter. We focus on the flow dependence on the separation between the plates. We make measurements for Reynolds numbers ranging from about 30 to 300, but we do not examine in detail the values of the Reynolds numbers corresponding to successive bifurcations. We measure the sphere position in a co-moving reference frame and obtain high-precision results for the sphere velocity and the properties of the wake. Our results for the sphere terminal velocity should long serve as a benchmark for algorithms designed for the difficult general problem of numerical simulation of the Navier-Stokes equation in a system with moving boundaries.Our observations reveal some qualitative features that are common to bodies sedimenting in the absence of sidewalls, and to flow past a fixed sphere or a fixed cylinder in unconfined geometries. Hence we review these situations in the following section.

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Free rising spheres do not obey newton's law for free settling

Cited by 94 publications

References 12 publications

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions

Dynamics of a Deformable Body in a Fast Flowing Soap Film

Sedimenting sphere in a variable-gap Hele-Shaw cell

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