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.

scholarly journals Microbubble dynamics in a viscous compressible liquid near a rigid boundary

2019 ◽  
Vol 84 (4) ◽  
pp. 696-711 ◽  
Author(s):  
Qianxi Wang ◽  
WenKe Liu ◽  
David M Leppinen ◽  
A D Walmsley
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Compressible Liquid ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Rigid Boundary ◽  
Viscous Potential Flow ◽  
Viscous Compressible Liquid

Abstract This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

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.

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.

On the boundary integral method for the rebounding bubble

2007 ◽  
Vol 570 ◽  
pp. 407-429 ◽  
Author(s):  
M. LEE ◽  
E. KLASEBOER ◽  
B. C. KHOO
Keyword(s):  
Energy Loss ◽  
Integral Method ◽  
Bubble Radius ◽  
Experimental Studies ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Bubble Collapse ◽  
Solid Boundary ◽  
Bubble System ◽  
Toroidal Bubble

The formation of a toroidal bubble towards the end of the bubble collapse stage in the neighbourhood of a solid boundary has been successfully studied using the boundary integral method. The further evolution (rebound) of the toroidal bubble is considered with the loss of system energy taken into account. The energy loss is incorporated into a mathematical model by a discontinuous jump in the potential energy at the minimum volume during the short collapse–rebound period accompanying wave emission. This implementation is first tested with the spherically oscillating bubble system using the theoretical Rayleigh–Plesset equation. Excellent agreement with experimental data for the bubble radius evolution up to three oscillation periods is obtained. Secondly, the incorporation of energy loss is tested with the motion of an oscillating bubble system in the neighbourhood of a rigid boundary, in an axisymmetric geometry, using a boundary integral method. Example calculations are presented to demonstrate the possibility of capturing the peculiar entity of a counterjet, which has been reported only in recent experimental studies.

A BOUNDARY INTEGRAL METHOD FOR ACOUSTIC SOURCE LOCALIZATION IN A WAVEGUIDE WITH INCLUSIONS

1994 ◽  
Vol 02 (02) ◽  
pp. 133-145 ◽  
Author(s):  
YONGZHI XU ◽  
YI YAN
Keyword(s):  
Source Localization ◽  
Sound Source ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Rigid Boundary ◽  
Matched Field Processing ◽  
Acoustic Source Localization ◽  
Continuous Waves ◽  
Hydrophone Array ◽  
Computation Load

In this paper, we continue our study on combining the matched field processing with the boundary integral equation (BIE) method of scattering theory to solve a sound source localization problem in a shallow ocean with a large inclusion which has a rigid boundary. We consider an enviroment where continuous waves (CW) are produced by a sound source, scattered by the inclusion, and then received by a hydrophone array. The symmetry of the waveguide is destroyed by the existence of the inclusion, and a proper procedure is therefore required to avoid the mismatching. We present a numerical scheme which makes use of the separation of the source and the detection array, and a BIE method. The separation greatly reduces the computation load. The BIE method preserves a certain accuracy on one hand and minimizes arithmetic operations on the other. Some numerical simulations using this scheme are presented.

scholarly journals Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

2015 ◽  
Vol 784 ◽  
pp. 225-251 ◽  
Author(s):  
Ting Si ◽  
Tong Long ◽  
Zhigang Zhai ◽  
Xisheng Luo
Keyword(s):  
Shock Waves ◽  
Shock Tube ◽  
High Speed ◽  
Initial Conditions ◽  
Laser Sheet ◽  
Imaging Method ◽  
Gas Cylinder ◽  
Diaphragmless Shock Tube ◽  
Converging Shock Waves ◽  
Heavy Gas

The interaction of cylindrical converging shock waves with a polygonal heavy gas cylinder is studied experimentally in a vertical annular diaphragmless shock tube. The reliability of the shock tube facility is verified in advance by capturing the cylindrical shock movements during the convergence and reflection processes using high-speed schlieren photography. Three types of air/SF6 polygonal interfaces with cross-sections of an octagon, a square and an equilateral triangle are formed by the soap film technique. A high-speed laser sheet imaging method is employed to monitor the evolution of the three polygonal interfaces subjected to the converging shock waves. In the experiments, the Mach number of the incident cylindrical shock at its first contact with each interface is maintained to be 1.35 for all three cases. The results show that the evolution of the polygonal interfaces is heavily dependent on the initial conditions, such as the interface shapes and the shock features. A theoretical model for circulation initially deposited along the air/SF6 polygonal interface is developed based on the theory of Samtaney & Zabusky (J. Fluid Mech., vol. 269, 1994, pp. 45–78). The circulation depositions along the initial interface result in the differences in flow features among the three polygonal interfaces, including the interface velocities and the perturbation growth rates. In comparison with planar shock cases, there are distinct phenomena caused by the convergence effects, including the variation of shock strength during imploding and exploding (geometric convergence), consecutive reshocks on the interface (compressibility), and special behaviours of the movement of the interface structures (phase inversion).

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.

A model of sonoluminescence

1994 ◽  
Vol 445 (1924) ◽  
pp. 323-349 ◽  
Keyword(s):  
Shock Wave ◽  
Molecular Weight ◽  
Shock Waves ◽  
Bubble Radius ◽  
Bubble Surface ◽  
The Other ◽  
Sound Waves ◽  
Van Der Waals Gas ◽  
Trapped Gas ◽  
Spherical Container

A bubble of air, trapped at the centre of a spherical container of water on the surface of which spherical sound waves are maintained by transducers, may emit light, a phenomenon known as sonoluminescence. The surface of the bubble expands and contracts in obedience to the Rayleigh–Lamb equation, which requires knowledge of the gas pressure on the surface of the bubble. In many investigations of bubble pulsations, it is assumed that the air in the bubble moves adiabatically. To understand sonoluminescence, however, it is necessary to allow for the possibility that shocks are generated within the bubble. We couple the Rayleigh–Lamb equation governing the bubble radius to Euler’s equations governing the motion of air in the bubble, and solve the two equations simultaneously. The air is modelled by a van der Waals gas. Results are presented for a number of slightly different conditions of excitation, but in which the response of the system is widely different. If the frequency of the sound is high, the gas in the bubble moves adiabatically and no light is emitted. As the frequency is reduced (for the same ambient bubble radius and driving pressure), the incoming bubble surface acts as a piston that generates an ingoing shock wave that passes through the centre of the bubble, and then, when it strikes the bubble surface, halts and reverses its inward motion; a sequence of such inwardly and outwardly moving shocks occur. The shock waves generate such high temperatures that the air near the centre of the bubble is almost completely ionized, and emits light, which we attribute to bremmstrahlung. The light created by the second inwardly moving shock exceeds that created by the first but, as the frequency of the sound is further reduced, the energy from the first shock rises, and the overall luminosity of the bubble increases. When the sound frequency is further reduced, two shocks are launched successively by the inward moving bubble surface, the second colliding with the first after it has passed through the centre of symmetry but before it can collide with the bubble surface. Even higher temperatures are reached and the luminosity of the bubble continues to increase with decreasing frequency. Details of these solutions are presented, and estimates are made of the luminosity of the bubble in different conditions of excitation. Two other families of solutions are presented. In one, the frequency and ambient bubble radius are fixed and the driving amplitude is varied. In the other, the frequency and driving amplitude are fixed and the radius is varied. The effects of changing only the molecular weight of the trapped gas is also examined.

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.

Transient cavities near boundaries. Part 1. Rigid boundary

1986 ◽  
Vol 170 ◽  
pp. 479-497 ◽  
Author(s):  
J. R. Blake ◽  
B. B. Taib ◽  
G. Doherty
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relative Magnitude ◽  
Boundary Integral ◽  
Stagnation Point Flow ◽  
Boundary Integral Method ◽  
Physical Parameters ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Parameter Ranges

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.

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