Dynamics and acoustics of a spherical bubble rising under gravity in an inviscid liquid

AbstractThe rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.

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Drag of a Spherical Bubble Rising in Power Law Fluids at Intermediate Reynolds Numbers

Industrial & Engineering Chemistry Research ◽

10.1021/ie0610086 ◽

2007 ◽

Vol 46 (3) ◽

pp. 939-946 ◽

Cited By ~ 17

Author(s):

Sunil D. Dhole ◽

Rajendra P. Chhabra ◽

Vinayak Eswaran

Keyword(s):

Power Law ◽

Reynolds Numbers ◽

Spherical Bubble ◽

Power Law Fluids ◽

Bubble Rising

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Finite element calculations of flow past a spherical bubble rising on the axis of a cylindrical tube

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/bf00942750 ◽

1994 ◽

Vol 45 (5) ◽

pp. 733-745 ◽

Cited By ~ 4

Author(s):

G. P. Hartholt ◽

A. C. Hoffmann ◽

L. P. B. M. Janssen ◽

H. W. Hoogstraten ◽

J. H. Moes

Keyword(s):

Finite Element ◽

Cylindrical Tube ◽

Spherical Bubble ◽

Flow Past ◽

Finite Element Calculations ◽

Bubble Rising

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Dynamics of a spherical bubble rising in gravity, subject to traveling pressure disturbance

Communications in Applied and Industrial Mathematics ◽

10.2478/caim-2018-0020 ◽

2018 ◽

Vol 9 (1) ◽

pp. 149-158

Author(s):

Giorgio Riccardi ◽

Enrico De Bernardis

Keyword(s):

Gravitational Field ◽

Wave Front ◽

Crucial Role ◽

Equations Of Motion ◽

Center Of Mass ◽

Bubble Radius ◽

Spherical Bubble ◽

Pressure Step ◽

Bubble Rising ◽

Traveling Speed

Abstract The motion of a spherical bubble rising in a gravitational field in presence of a traveling pressure step wave is investigated. Equations of motion for the bubble radius and center of mass are deduced and several sample cases are analysed by means of their numerical integration. The crucial role played by the traveling speed of the wave front and by the intensity of the pressure step are discussed. A first comparison with the axisymmetric dynamics is discussed.

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Simulation of Rising Bubble With Conservative Level Set Method

Volume 2: Fora, Parts A and B ◽

10.1115/fedsm2007-37556 ◽

2007 ◽

Author(s):

Luka Sˇtrubelj ◽

Iztok Tiselj

Keyword(s):

Level Set Method ◽

Level Set ◽

Test Case ◽

Final Shape ◽

Spherical Bubble ◽

Rising Bubble ◽

Bubble Rising ◽

Bubble Rising Velocity ◽

Viscous Stresses ◽

Conservative Level Set

Conservative level set method, introduced by E. Olsson and G. Kreis in 2005 is discussed. The test case with rising bubble consists of spherical bubble of smaller density in stagnant liquid of higher density. Due to the buoyancy spherical bubble is rising up and changing its shape. After certain time the bubble reaches final velocity and final shape. An in-house code was used to perform the simulations. The final shape of the bubble was investigated and also build-up of the bubble rising velocity, starting from the rest exhibiting an overshoot before reaching its final asymptotic value. This test allows testing of numerical model which has to accurately take into account buoyancy, viscous stresses and surface tension effects.

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