scholarly journals A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary

1984 ◽  
Vol 26 (1) ◽  
pp. 31-44 ◽  
Author(s):  
P. Cerone ◽  
J. R. Blake
Keyword(s):  
Free Surface ◽  
Stagnation Point ◽  
Cavitation Bubble ◽  
Maximum Pressure ◽  
Rigid Boundary ◽  
Initial Distance ◽  
Bubble Pressure ◽  
Collapse Phase

AbstractInstantaneous streamlines, particle pathlines and pressure contours for a cavitation bubble in the vicinity of a free surface and near a rigid boundary are obtained. During the collapse phase of a bubble near a free surface, the streamlines show the existence of a stagnation point between the bubble and the free surface which occurs at a different location from the point of maximum pressure. This phenomenon exists when the initial distance of the bubble is sufficiently close to the free surface for the bubble and free surface to move in opposite directions during collapse of the bubble. Pressure calculations during the collapse of a cavitation bubble near a rigid boundary show that the maximum pressure is substantially larger than the equivalent Rayleigh bubble of the same volume.

scholarly journals A note on the impulse due to a vapour bubble near a boundary

1982 ◽  
Vol 23 (4) ◽  
pp. 383-393 ◽  
Author(s):  
J. R. Blake ◽  
P. Cerone
Keyword(s):  
Free Surface ◽  
Point Source ◽  
Cavitation Bubble ◽  
High Speed ◽  
Liquid Jet ◽  
Vapour Bubble ◽  
Rigid Boundary ◽  
Two Fluids ◽  
Collapse Phase

AbstractAn expression for the impluse due to a vapour (cavitation) bubble is obtained in terms of an integral over a nearby boundary. Examples for a point source near a free surface, rigid boundary, inertial boundary and a fluid of different density are considered. It appears that the sign of the impluse determines the direction a cavitation bubble will migrate and the direction of the high speed liquid jet during the collapse phase. The theory may explain recent observations on buoyant bubbles near an interface between two fluids of different densities.

Investigation of a cavitation bubble between a rigid boundary and a free surface

2007 ◽  
Vol 102 (9) ◽  
pp. 094904 ◽  
Author(s):  
Peter Gregorčič ◽  
Rok Petkovšek ◽  
Janez Možina
Keyword(s):  
Free Surface ◽  
Cavitation Bubble ◽  
Rigid Boundary

scholarly journals Numerical Simulation for Cavitation Bubble Near Free Surface and Rigid Boundary

2015 ◽  
Vol 56 (4) ◽  
pp. 534-538 ◽  
Author(s):  
Kanae Oguchi ◽  
Manabu Enoki ◽  
Naoya Hirata
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Cavitation Bubble ◽  
Rigid Boundary

scholarly journals A model for the free-surface flow due to a submerged source in water of infinite depth

1998 ◽  
Vol 39 (4) ◽  
pp. 528-538 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Nonuniform Distribution ◽  
Infinite Depth ◽  
Collocation Points ◽  
Series Truncation Method

AbstractWe consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.

Investigation of cavitation bubble collapse near rigid boundary by lattice Boltzmann method

2016 ◽  
Vol 28 (3) ◽  
pp. 442-450 ◽  
Author(s):  
Ming-lei Shan ◽  
Chang-ping Zhu ◽  
Xi Zhou ◽  
Cheng Yin ◽  
Qing-bang Han
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Cavitation Bubble ◽  
Bubble Collapse ◽  
Rigid Boundary ◽  
Boltzmann Method

scholarly journals A note on withdrawal through a point sink in fluid of finite depth

1996 ◽  
Vol 37 (3) ◽  
pp. 406-416 ◽  
Author(s):  
Lawrence K. Forbes ◽  
Graeme C. Hocking ◽  
Graeme A. Chandler
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Flow Through

AbstractWithdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.

scholarly journals Cavitation and bubble dynamics: the Kelvin impulse and its applications

2015 ◽  
Vol 5 (5) ◽  
pp. 20150017 ◽  
Author(s):  
John R. Blake ◽  
David M. Leppinen ◽  
Qianxi Wang
Keyword(s):  
Cavitation Bubble ◽  
High Speed ◽  
Bubble Dynamics ◽  
Clinical Medicine ◽  
Bubble Collapse ◽  
Rigid Boundary ◽  
Design Problems ◽  
Practical Applications ◽  
Wide Range ◽  
Naval Engineering

Cavitation and bubble dynamics have a wide range of practical applications in a range of disciplines, including hydraulic, mechanical and naval engineering, oil exploration, clinical medicine and sonochemistry. However, this paper focuses on how a fundamental concept, the Kelvin impulse, can provide practical insights into engineering and industrial design problems. The pathway is provided through physical insight, idealized experiments and enhancing the accuracy and interpretation of the computation. In 1966, Benjamin and Ellis made a number of important statements relating to the use of the Kelvin impulse in cavitation and bubble dynamics, one of these being ‘One should always reason in terms of the Kelvin impulse, not in terms of the fluid momentum…’. We revisit part of this paper, developing the Kelvin impulse from first principles, using it, not only as a check on advanced computations (for which it was first used!), but also to provide greater physical insights into cavitation bubble dynamics near boundaries (rigid, potential free surface, two-fluid interface, flexible surface and axisymmetric stagnation point flow) and to provide predictions on different types of bubble collapse behaviour, later compared against experiments. The paper concludes with two recent studies involving (i) the direction of the jet formation in a cavitation bubble close to a rigid boundary in the presence of high-intensity ultrasound propagated parallel to the surface and (ii) the study of a ‘paradigm bubble model’ for the collapse of a translating spherical bubble, sometimes leading to a constant velocity high-speed jet, known as the Longuet-Higgins jet.

scholarly journals A note on the flow induced by a line sink beneath a free surface

1991 ◽  
Vol 32 (3) ◽  
pp. 251-260 ◽  
Author(s):  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Ideal Fluid ◽  
Critical Value ◽  
Homogeneous Fluid ◽  
Substitution Method ◽  
A Value ◽  
Line Sink ◽  
Low Froude Number

AbstractThe problem of withdrawing water through a line sink from a region containing an homogeneous fluid beneath a free surface is considered. Assuming steady, irrotational flow of an ideal fluid, solutions with low Froude number containing a stagnation point on the free surface above the sink are sought using a series substitution method. The solutions are shown to exist for a value of the Froude number up to a critical value of about 1.4. No solutions of this type are found for Froude numbers greater than this value.

An example where lubrication theory comes short: hydraulic jumps in a flow down an inclined plate

2014 ◽  
Vol 764 ◽  
pp. 277-295 ◽  
Author(s):  
E. S. Benilov ◽  
V. N. Lapin
Keyword(s):  
Free Surface ◽  
Stagnation Point ◽  
Hydraulic Jump ◽  
Stable Solution ◽  
Local Scale ◽  
Lubrication Theory ◽  
Hydraulic Jumps ◽  
Two Dimensional ◽  
Inclined Plate ◽  
Steady Solutions

AbstractWe examine two-dimensional flows of a viscous liquid on an inclined plate. If the upstream depth $h_{-}$ of the liquid is larger than its downstream depth $h_{+}$, a smooth hydraulic jump (bore) forms and starts propagating down the slope. If the inclination angle of the plate is small, the bore can be described by the so-called lubrication theory. In this work we demonstrate that bores with $h_{+}/h_{-}<(\sqrt{3}-1)/2$ either are unstable or do not exist as steady solutions of the governing equation (physically, these two possibilities are difficult to distinguish). The instability/evolution occurs near a stagnation point and, generally, causes overturning – sometimes on the scale of the whole bore, sometimes on a shorter, local scale. The overturning occurs because the flow advects disturbances towards the stagnation point and, thus, ‘compresses’ them, increasing the slope of the free surface. Interestingly, this effect is not captured by the lubrication theory, which formally yields a well-behaved stable solution for all values of $h_{+}/h_{-}$.

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