Air entrapment by a falling water mass

Oğuz, Hasan N.; Prosperetti, Andréa; Kolaini, Ali R.

doi:10.1017/s0022112095002850

Cited by 61 publications

(37 citation statements)

References 9 publications

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“…The regime for low Froude numbers obeys a scaling behavior z c =R 0 Fr with an exponent 1 0:1. This is in contrast to earlier experiments [13], which showed a single continuous scaling behavior with 1 3 , for which a theoretical explanation in terms of inertia and gravity could be given [11,13,14]. At the end of the low Froude regime, the data abruptly depart to an intermediate regime without any experimentally clearly discernible structure.…”

contrasting

confidence: 98%

“…The final regime scales with 2 0:43. Considering that the theory from [11,13,14] assumes a purely radial flow pattern and an initially perfectly cylindrical cavity shape, the prediction of 1 3 is reasonably close to our observed exponent. Our simulations even make the identification of an intermediate regime possible, which due to its small range in Froude numbers cannot be clearly observed in experiments.…”

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 83%

“…manifesting itself in clearly distinct regimes of the closure depth as a function of the submerging velocity. We have thus illustrated the lower limit to the continuous inertial-gravitational scaling regime observed in [11][12][13][14]. Since capillary waves are an unavoidable consequence of disturbances on a water surface, we expect that the effects elaborated in this Letter will be of relevance to a wide range of related phenomena.…”

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 57%

“…For the last regime capillary waves are irrelevant and the scaling behavior of the closure depth can be derived independent of surface tension [11,13,14]. We have performed simulations with a tenfold increase and decrease of as compared to the natural value of 72:8 mN=m for water as well as for a hypothetical liquid without any surface tension ( 0).…”

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…When the colliding walls meet, a violent jet shoots up into the air. Regardless of the nonuniversality of the pinch-off [7], the location at which it takes place has been reported (experimentally and theoretically) to scale in a continuous fashion with the object velocity for such different systems as spheres on prefluidized sand [11], solid disks [12], spheres and cylinders [13] on water, and even water columns on water [14]. Our experimental and numerical evidence shows the lower limit where this universal scaling is broken through the interference of a second phenomenon unrelated to hydrostatic pressure.…”

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confidence: 99%

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Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

et al. 2008

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A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude 1=3 power law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary wave effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the nonuniversality of the void collapse. DOI: 10.1103/PhysRevLett.100.084502 PACS numbers: 47.55.Dÿ, 47.11.Hj, 47.35.Pq Many phenomena in fluid dynamics are known to be self-similar [1] and universal, allowing physicists to describe their final outcome without precise knowledge of the initial conditions. Prime examples for such universality are the breakup of an elongated fluid filament inside another viscous fluid [2] and the pinch-off of a liquid droplet in air [3][4][5]. For the inverse problem [6 -10], i.e., when an air bubble pinches off inside a liquid, the dynamics retains a memory of its creation until the very end, indicating nonuniversality. As an example for such a breakup, we examine the air-filled cavity created when a solid object is rapidly submerged through a water surface. The walls of the cavity subsequently collapse due to hydrostatic pressure from the liquid bulk. When the colliding walls meet, a violent jet shoots up into the air. Regardless of the nonuniversality of the pinch-off [7], the location at which it takes place has been reported (experimentally and theoretically) to scale in a continuous fashion with the object velocity for such different systems as spheres on prefluidized sand [11], solid disks [12], spheres and cylinders [13] on water, and even water columns on water [14]. Our experimental and numerical evidence shows the lower limit where this universal scaling is broken through the interference of a second phenomenon unrelated to hydrostatic pressure. Surface waves created as the object passes the water surface significantly alter the pinch-off location in a noncontinuous manner. Similar effects for the breakdown of a universal behavior due to wave interaction have been observed in, e.g., magnetohydrodynamics [15] and turbulence [16].In our experiment we drag a cylinder with radius R 0 20 mm and length l 147 mm through the surface of a large water tank using a linear motor connected to the cylinder bottom by a rod. We prescribe a constant cylinder velocity V between 0.5 and 2:5 m=s. With the kinematic viscosity the global Reynolds number Re R 0 V= is of the order of 10 4 , while the local Reynolds number Re R _ R= defined with the cavity radius R for the point of minimum radius lies between 10 2 and 10 5 , demonstrating that inertia dominates viscous effects. Further, wi...

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contrasting

confidence: 98%

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 83%

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 57%

Section: Prl 100 084502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

mentioning

confidence: 99%

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Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

et al. 2008

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A mixed finite element solver for liquid–liquid impacts

Bertolazzi

Manzini

2004

Commun. Numer. Meth. Engng.

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SUMMARYThe impact of a liquid column on a liquid surface initially at rest is numerically modelled to describe air entrapment and bubble formation processes. The global quantities of interest are evaluated in the framework of the potential theory. The numerical method couples a potential ow solver based on a Mixed Finite Element Method with an Ordinary Di erential Equation solver discretized by the CrankNicholson scheme. The capability of the method in solving liquid-liquid impacts is illustrated in two numerical experiments taken from literature and a good agreement with the literature data is obtained.

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The entrainment of air by water jet impinging on a free surface

Soh

Khoo

Yuen³

2005

Exp Fluids

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High-speed cine and video photographs were used to capture the flow patterns of a column of water jet impinging into a pool of water. The impact results in air entrainment into water in a form of a void and there are no mixing between the water in the jet and the surrounding water. Conservation of fluid momentum shows that the rate of increase of the height of the air void depends on the drag coefficient of the jet front. By neglecting the frictional losses, the application of energy conservation yields an expression that relates the maximum height of the air void with the properties of the water jet.3

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Air entrapment by a falling water mass

Cited by 61 publications

References 9 publications

Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

A mixed finite element solver for liquid–liquid impacts

The entrainment of air by water jet impinging on a free surface

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