On the mechanism of air entrainment by liquid jets at a free surface

2000 ◽  
Vol 404 ◽  
pp. 151-177 ◽  
Author(s):  
YONGGANG ZHU ◽  
HASAN N. OĞUZ ◽  
ANDREA PROSPERETTI
Keyword(s):  
High Speed ◽  
Air Entrainment ◽  
Liquid Pool ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Liquid Jets ◽  
Unexpected Finding ◽  
Pool Surface ◽  
Sequence Of Events ◽  
High Reynolds

The process by which a liquid jet falling into a liquid pool entrains air is studied experimentally and theoretically. It is shown that, provided the nozzle from which the jet issues is properly contoured, an undisturbed jet does not entrap air even at relatively high Reynolds numbers. When surface disturbances are generated on the jet by a rapid increase of the liquid flow rate, on the other hand, large air cavities are formed. Their collapse under the action of gravity causes the entrapment of bubbles in the liquid. This sequence of events is recorded with a CCD and a high-speed camera. A boundary-integral method is used to simulate the process numerically with results in good agreement with the observations. An unexpected finding is that the role of the jet is not simply that of conveying the disturbance to the pool surface. Rather, both the observed energy budget and the simulations imply the presence of a mechanism by which part of the jet energy is used in creating the cavity. A hypothesis on the nature of this mechanism is presented.

scholarly journals Universal mechanism for air entrainment during liquid impact

2016 ◽  
Vol 789 ◽  
pp. 708-725 ◽  
Author(s):  
Maurice H. W. Hendrix ◽  
Wilco Bouwhuis ◽  
Devaraj van der Meer ◽  
Detlef Lohse ◽  
Jacco H. Snoeijer
Keyword(s):  
Experimental Data ◽  
Air Entrainment ◽  
Stokes Number ◽  
Liquid Pool ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Rigid Sphere ◽  
Entrained Air ◽  
The Impact ◽  
Universal Mechanism

When a millimetre-sized liquid drop approaches a deep liquid pool, both the interface of the drop and the pool deform before the drop touches the pool. The build-up of air pressure prior to coalescence is responsible for this deformation. Due to this deformation, air can be entrained at the bottom of the drop during the impact. We quantify the amount of entrained air numerically, using the boundary integral method for potential flow for the drop and the pool, coupled to viscous lubrication theory for the air film that has to be squeezed out during impact. We compare our results with various experimental data and find excellent agreement for the amount of air that is entrapped during impact onto a pool. Next, the impact of a rigid sphere onto a pool is numerically investigated and the air that is entrapped in this case also matches with available experimental data. In both cases of drop and sphere impact onto a pool the numerical air bubble volume $V_{b}$ is found to be in agreement with the theoretical scaling $V_{b}/V_{drop/sphere}\sim \mathit{St}^{-4/3}$, where $\mathit{St}$ is the Stokes number. This is the same scaling as has been found for drop impact onto a solid surface in previous research. This implies a universal mechanism for air entrainment for these different impact scenarios, which has been suggested in recent experimental work, but is now further elucidated with numerical results.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Kinematics of vortex ring generated by a drop upon impacting a liquid pool

2019 ◽  
Vol 875 ◽  
pp. 842-853 ◽  
Author(s):  
Abhishek Saha ◽  
Yanju Wei ◽  
Xiaoyu Tang ◽  
Chung K. Law
Keyword(s):  
Vortex Ring ◽  
High Speed ◽  
Morphological Evolution ◽  
Laser Induced Fluorescence ◽  
Liquid Pool ◽  
Viscous Effects ◽  
Penetration Process ◽  
Pool Surface ◽  
Three Stages ◽  
Unified Description

We herein report an experimental study on the morphological evolution of a vortex ring formed inside a liquid pool after it is impacted and penetrated by a coalescing drop of the same liquid. The dynamics of the penetrating vortex ring along with the deformation of the pool surface has been captured using simultaneous high-speed laser induced fluorescence and shadowgraph techniques. It is identified that the motion of such a vortex ring can be divided into three stages, during which inertial, capillary and viscous effects alternatingly play dominant roles to modulate the penetration process, resulting in linear, non-monotonic and decelerating motion in these three stages respectively. Furthermore, we also evaluate the relevant time and length scales of these three stages and subsequently propose a unified description of the downward motion of the penetrating vortex ring. Finally, we use the experimental data for a range of drop diameters and impact speeds to validate the proposed scaling.

scholarly journals Bubble dynamics in a compressible liquid in contact with a rigid boundary

2015 ◽  
Vol 5 (5) ◽  
pp. 20150048 ◽  
Author(s):  
Qianxi Wang ◽  
Wenke Liu ◽  
A. M. Zhang ◽  
Yi Sui
Keyword(s):  
Shock Waves ◽  
Thin Layer ◽  
High Speed ◽  
Bubble Radius ◽  
Time History ◽  
Bubble Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Imaging Method ◽  
Rigid Boundary

A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. The wall effects are modelled using the imaging method. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. Our computations correlate well with experiments for both the first and second cycles of oscillation. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s / R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage.

The role of ‘splashing’ in the collapse of a laser-generated cavity near a rigid boundary

1999 ◽  
Vol 380 ◽  
pp. 339-361 ◽  
Author(s):  
R. P. TONG ◽  
W. P. SCHIFFERS ◽  
S. J. SHAW ◽  
J. R. BLAKE ◽  
D. C. EMMONY
Keyword(s):  
High Speed ◽  
Vital Role ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Liquid Jet ◽  
Rigid Boundary ◽  
Jet Impact ◽  
Pressure Peak ◽  
Peak Pressures ◽  
The Impact

Vapour cavities in liquid flows have long been associated with cavitation damage to nearby solid surfaces and it is thought that the final stage of collapse, when a high- speed liquid jet threads the cavity, plays a vital role in this process. The present study investigates this aspect of the motion of laser-generated cavities in a quiescent liquid when the distance (or stand-off) of the point of inception from a rigid boundary is between 0.8 and 1.2 times the maximum radius of the cavity. Numerical simulations using a boundary integral method with an incompressible liquid impact model provide a framework for the interpretation of the experimental results. It is observed that, within the given interval of the stand-off parameter, the peak pressures measured on the boundary at the first collapse of a cavity attain a local minimum, while at the same time there is an increase in the duration of the pressure pulse. This contrasts with a monotonic increase in the peak pressures as the stand-off is reduced, when the cavity inception point is outside the stated interval. This phenomenon is shown to be due to a splash effect which follows the impact of the liquid jet. Three cases are chosen to typify the splash interaction with the free surface of the collapsing cavity: (i) surface reconnection around the liquid jet; (ii) splash impact at the base of the liquid jet; (iii) thin film splash. Hydrodynamic pressures generated following splash impact are found to be much greater than those produced by the jet impact. The combination of splash impact and the emission of shock waves, together with the subsequent re-expansion, drives the flow around the toroidal cavity producing a distinctive double pressure peak.

Gas bubbles bursting at a free surface

1993 ◽  
Vol 254 ◽  
pp. 437-466 ◽  
Author(s):  
J. M. Boulton-Stone ◽  
J. R. Blake
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
High Speed ◽  
Boundary Layer Separation ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Animal Cells ◽  
Jet Formation ◽  
Jet Breakup

When a small air bubble bursts from an equilibrium position at an air/water interface, a complex motion ensues resulting in the production of a high-speed liquid jet. This free-surface motion following the burst is modelled numerically using a boundary integral method. Jet formation and liquid entrainment rates from jet breakup into drops are calculated and compared with existing experimental evidence. In order to investigate viscous effects, a boundary layer is included in the calculations by employing a time-stepping technique which allows the boundary mesh to remain orthogonal to the surface. This allows an approximation of the vorticity development in the region of boundary-layer separation during jet formation. Calculated values of pressure and energy dissipation rates in the fluid indicate a violent motion, particularly for smaller bubbles. This has important implications for the biological industry where animal cells in bioreactors have been found to be killed by the presence of small bubbles.

Impact of a high-speed train of microdrops on a liquid pool

2016 ◽  
Vol 792 ◽  
pp. 850-868 ◽  
Author(s):  
Wilco Bouwhuis ◽  
Xin Huang ◽  
Chon U Chan ◽  
Philipp E. Frommhold ◽  
Claus-Dieter Ohl ◽  
...  
Keyword(s):  
Surface Tension ◽  
High Speed ◽  
Scaling Laws ◽  
Liquid Pool ◽  
Boundary Integral ◽  
High Speed Train ◽  
Cavity Depth ◽  
Simple Scaling ◽  
The Individual ◽  
The Impact

A train of high-speed microdrops impacting on a liquid pool can create a very deep and narrow cavity, reaching depths more than 1000 times the size of the individual drops. The impact of such a droplet train is studied numerically using boundary integral simulations. In these simulations, we solve the potential flow in the pool and in the impacting drops, taking into account the influence of liquid inertia, gravity and surface tension. We show that for microdrops the cavity shape and maximum depth primarily depend on the balance of inertia and surface tension and discuss how these are influenced by the spacing between the drops in the train. Finally, we derive simple scaling laws for the cavity depth and width.

scholarly journals Non-spherical bubble dynamics in a compressible liquid. Part 2. Acoustic standing wave

2011 ◽  
Vol 679 ◽  
pp. 559-581 ◽  
Author(s):  
Q. X. WANG ◽  
J. R. BLAKE
Keyword(s):  
Standing Wave ◽  
High Speed ◽  
Acoustic Pressure ◽  
Spherical Shape ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Outer Flow ◽  
Acoustic Standing Wave ◽  
Toroidal Bubble ◽  
Highly Nonlinear

This paper investigates the behaviour of a non-spherical cavitation bubble in an acoustic standing wave. The study has important applications to sonochemistry and in understanding features of therapeutic ultrasound in the megahertz range, extending our understanding of bubble behaviour in the highly nonlinear regime where jet and toroidal bubble formation may be important. The theory developed herein represents a further development of the material presented in Part 1 of this paper (Wang & Blake, J. Fluid Mech. vol. 659, 2010, pp. 191–224) to a standing wave, including repeated topological changes from a singly to a multiply connected bubble. The fluid mechanics is assumed to be compressible potential flow. Matched asymptotic expansions for an inner and outer flow are performed to second order in terms of a small parameter, the bubble-wall Mach number, leading to weakly compressible flow formulation of the problem. The method allows the development of a computational model for non-spherical bubbles by using a modified boundary-integral method. The computations show that the bubble remains approximately of a spherical shape when the acoustic pressure is small or is initiated at the node or antinode of the acoustic pressure field. When initiated between the node and antinode at higher acoustic pressures, the bubble loses its spherical shape at the end of the collapse phase after only a few oscillations. A high-speed liquid bubble jet forms and is directed towards the node, impacting the opposite bubble surface and penetrating through the bubble to form a toroidal bubble. The bubble first rebounds in a toroidal form but re-combines to a singly connected bubble, expanding continuously and gradually returning to a near spherical shape. These processes are repeated in the next oscillation.

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