Short-wave instabilities on a vortex pair of unequal strength circulation ratio

So, Joine; Ryan, Kris; Sheard, Gregory J.

doi:10.1016/j.apm.2010.09.034

Cited by 6 publications

(6 citation statements)

References 29 publications

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“…The growth rates of the instability in vortex 2 are obtained by exchanging the subscripts 1 and 2 in all expressions. Donnadieu et al 2009, So et al 2011, each time showing the same good agreement. Equation 14 can then be used to explore the variation of the instability characteristics with the vortex pair parameters.…”

Section: Elliptic Instabilitysupporting

confidence: 53%

Dynamics and Instabilities of Vortex Pairs

Leweke

Dizès

Williamson

2016

Annu. Rev. Fluid Mech.

263

252

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This article reviews the characteristics and behavior of counter-rotating and corotating vortex pairs, which are seemingly simple flow configurations yet immensely rich in phenomena. Since the reviews in this journal by Widnall (1975) and Spalart (1998), who studied the fundamental structure and dynamics of vortices and airplane trailing vortices, respectively, there have been many analytical, computational, and experimental studies of vortex pair flows. We discuss two-dimensional dynamics, including the merging of same-sign vortices and the interaction with the mutually induced strain, as well as three-dimensional displacement and core instabilities resulting from this interaction. Flows subject to combined instabilities are also considered, in particular the impingement of opposite-sign vortices on a ground plane. We emphasize the physical mechanisms responsible for the flow phenomena and clearly present the key results that are useful to the reader for predicting the dynamics and instabilities of parallel vortices.

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Section: Elliptic Instabilitysupporting

confidence: 53%

Dynamics and Instabilities of Vortex Pairs

Leweke

Dizès

Williamson

2016

Annu. Rev. Fluid Mech.

263

252

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“…Examining the spanwise perturbation vorticity field of mode 5 (not shown) shows the characteristic lobe structure of Crow instability in the vortex pair as it moves away from the cylinder and the wall. By approximating the vorticity distributions within the pair at formation in terms of a sum of Gaussian distributions to extract the length scale for each vortex, together with the overall circulation ratio, a preferred wavelength of approximately λ 20d can be predicted from the work of So et al (2011). This is close to the observed preferred wavelength of mode 5 at Re = 160 of λ 18d.…”

Section: Stability Of the Fully Developed 2d Periodic Wakementioning

confidence: 55%

“…Such a system is subject to both the shortwavelength elliptic instability and the longer-wavelength Crow instability. The results of So et al (2011) can be used to obtain an estimate for the most unstable wavelength. A recent review of the Crow instability is given in Leweke et al (2016).…”

Section: Stability Of the Fully Developed 2d Periodic Wakementioning

confidence: 99%

“…At a point in time when this pair becomes unambiguously defined, i.e., between images 2 and 3 of figure 14, the ratio of circulations between the component vortices of the pair is approximately -2:1. So et al (2011) analysed the stability of unequal strength Lamb-Oseen vortices, which have a Gaussian vorticity distribution, examining how the growth rate and preferred wavelength varied with circulation ratio. Such a system is subject to both the shortwavelength elliptic instability and the longer-wavelength Crow instability.…”

Section: Stability Of the Fully Developed 2d Periodic Wakementioning

confidence: 99%

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Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

et al. 2017

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This paper presents the characteristics of the different stages in the evolution of the wake of a circular cylinder rolling without slipping along a wall at constant speed, acquired through numerical stability analysis and two-and three-dimensional numerical simulations. Reynolds numbers between 30 and 300 are considered. Of importance in this study is the transition to three-dimensionality from the underlying two-dimensional periodic flow and, in particular, the way that the associated transitions influence the fluid forces exerted on the cylinder, and the development and the structure of the wake. It is found that the steady two-dimensional flow becomes unstable to threedimensional perturbations at Re c,3D = 37, and that the transition to unsteady twodimensional flow -or periodic vortex shedding -occurs at Re c,2D = 88, thus validating and refining the results of Stewart et al. (2010). The main focus here is for Reynolds numbers beyond the transition to unsteady flow at Re c,2D = 88. From impulsive start up, the wake almost immediately undergoes transition to a periodic two-dimensional wake state, which, in turn, is three-dimensionally unstable. Thus, the previous threedimensional stability analysis based on the two-dimensional steady flow provides only an element of the full story. Floquet analysis based on the periodic two-dimensional flow was undertaken and new three-dimensional instability modes were revealed. The results suggest that an impulsively started cylinder rolling along a surface at constant velocity for Re 90 will result in the rapid development of a periodic two-dimensional wake that will be maintained for a considerable time prior to the wake undergoing threedimensional transition. Of interest, the mean lift and drag coefficients obtained from full three-dimensional simulations match predictions from two-dimensional simulations to within a few percent.

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“…The increase of the atomizer liquid velocity results in a shorter broken length of the liquid film. In addition, the liquid film becomes thinner and thinner until it is completely broken into many tiny droplets . The vortex formed by the gas–liquid cross flow moves upward, so the gas‐phase vortex entrainment droplets also increases.…”

Section: Resultsmentioning

confidence: 99%

Study on droplet entrainment in the composite scrubbing–cooling chamber

Wang

Yan

Guo

et al. 2017

Asia-Pacific J Chem Eng

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A cold model experimental device was established for studying droplet entrainment in the composite scrubbing-cooling chamber. The effect of the superficial gas velocity, the initial liquid flow velocity of the nozzle, and the radial position of nozzles on droplet entrainment was investigated. The experimental results show that the droplet entrainment increases with the increase of the superficial gas velocity and the flow rate of falling film, but its profile is quite mean in the radial direction in the chamber. The droplet entrainment decreases by about 40% when the number of nozzles increases from two to four. Increasing the nozzle number can make the droplet well distributed and reduce droplet entrainment. Based on the experiment data, an empirical correlation for droplet entrainment fraction is also obtained, as E ∝ Re 1.92 ·We 0.52 . The optimization study for the structure of the scrubbing-cooling chamber can provide some guidance for the industrial application.

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Short-wave instabilities on a vortex pair of unequal strength circulation ratio

Cited by 6 publications

References 29 publications

Dynamics and Instabilities of Vortex Pairs

Dynamics and Instabilities of Vortex Pairs

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

Study on droplet entrainment in the composite scrubbing–cooling chamber

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