Shock propagation in liquids containing bubbly clusters: a continuum approach

2012 ◽  
Vol 701 ◽  
pp. 304-332 ◽  
Author(s):  
H. Grandjean ◽  
N. Jacques ◽  
S. Zaleski
Keyword(s):  
Bubble Dynamics ◽  
Cluster Structure ◽  
Computation Time ◽  
Shock Propagation ◽  
Bubbly Liquid ◽  
Global Response ◽  
Bubbly Liquids ◽  
Single Bubble Dynamics ◽  
Shock Profile ◽  
Typical Length

AbstractThe present work investigates the influence of bubble clustering on the propagation of shock waves in bubbly liquids. A continuum model is developed to describe the macroscopic response of a bubbly liquid with a cluster structure, using a two-step homogenization technique. The proposed methodology allows us to simulate shock wave propagation over long distances with a small computation time and to study the effect of bubble clustering on the shock structure. It is shown that the typical length of the shock profile is related to the global response of the clusters instead of the single-bubble dynamics, as in homogeneous bubbly flows. The accuracy of the proposed modelling is assessed through comparisons with axisymmetric simulations, in which clusters are directly specified, with given positions and sizes, and with experimental data.

Influence of Parametric Resonance on a Bubble Driven by Intensive Sound During Stable Cavitation

2008 ◽  
Author(s):  
Ruimin Wang ◽  
Fengde Zong ◽  
Yang Yang
Keyword(s):  
Bubble Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Ultrasonic Cavitation ◽  
Single Bubble ◽  
Forced Oscillations ◽  
Bubbly Liquid ◽  
Physical Parameters ◽  
Frequency Spectra ◽  
Starting Point ◽  
Single Bubble Dynamics

Ultrasonic cavitation is a well-known phenomenon that plays an important role in several physical systems and its applications are commonly utilized in different fields of physics and technology. The cavitation phenomena can be described by means of a field theory that should be able to predict the values of the macroscopic quantities, introducing physical parameters specifically for the bubbly liquid to be considered as a continuum; while on the other hand, the goal is to solve the problem of single bubble dynamics in an ultrasonic field as a starting point towards a multibubble theory. Usually the theory of single bubble dynamics in ultrasonic cavitation is constructed by primarily imposing the conditions of spherical symmetry on the bubble interface and a viscoelastic liquid, thus obtaining a significant simplification of the equations of motion and a single nonlinear equation for the interface. This approach can be satisfactory in several cases, but the situations in which the bubble deviates from its spherical shape (i.e. the collapse on a rigid boundary) and the problem of the stability of the interface motion, which turns out to be very important in sonoluminescence, cannot be treated by this theory. In the field of ultrasonic cavitation numerical analysis is a further means of investigation besides the analytical approach and experimental measurements, and it is necessary at least for two reasons. Specifically, an exact analytical treatment of the equations that model this phenomenon is substantially impossible due to their high nonlinearity; and furthermore the typical order of magnitude of the measurable quantities (object sizes in the range of microns, time intervals in the range of microseconds with nanosecond resolution) makes experiments difficult to perform. Hence we numerically analyze the relationships between amplitude and frequency by the use of SPECTRA PLUS software. The method is tested analyzing forced oscillations of cavitation bubbles excited by ultrasonic standing waves at different pressure amplitudes, showing characteristic behaviour of nonlinear dynamical systems; frequency spectra are obtained, stability analysis is performed. It is important to note that we observe subharmonic behaviour of the volume mode of the bubble prior to the instabilities due to shape modes. If one further increases the value of pressure amplitudes, one can clearly observe surface instabilities and deformations that lead to the destruction of the bubble. This evidence may suggest that the subharmonic behaviour leads to chaos in ultrasonic cavitation.

A PHASE-PLANE DESCRIPTION OF NONLINEAR TRAVELING WAVES IN BUBBLY LIQUIDS

1999 ◽  
Vol 07 (02) ◽  
pp. 71-82
Author(s):  
A. NADIM ◽  
D. GOLDMAN ◽  
J. J. CARTMELL ◽  
P. E. BARBONE
Keyword(s):  
Equation Of State ◽  
Fixed Points ◽  
Traveling Wave ◽  
Phase Plane ◽  
Volume Fraction ◽  
Low Frequency ◽  
Traveling Wave Solutions ◽  
Bubbly Liquid ◽  
Phase Plane Analysis ◽  
Bubbly Liquids

One-dimensional traveling wave solutions to the fully nonlinear continuity and Euler equations in a bubbly liquid are considered. The elimination of velocity from the two equations leaves a single nonlinear algebraic relation between the pressure and density profiles in the mixture. On assuming the bubbles to have identical size and taking the volume fraction of bubbles in the medium to be small, an equation of state which relates the mixture pressure to the density and its first two material time-derivatives is derived. When this equation of state is linearized and combined with the laws of conservation of mass and momentum, a nonlinear, second-order, ordinary differential equation is obtained for the density as a function of the single traveling wave coordinate. A phase-plane analysis of this equation reveals the existence of two fixed points, one of which is a saddle and the other a node. A single trajectory connects the two fixed points and corresponds to a traveling shock wave solution when the Mach number of the wave, defined as the ratio of traveling wave speed to the low-frequency speed of sound in the bubbly liquid, exceeds unity. The analysis provides a qualitative explanation of the oscillations behind shocks seen in experiments on bubbly liquids.

scholarly journals Numerical simulations of non-spherical bubble collapse

2009 ◽  
Vol 629 ◽  
pp. 231-262 ◽  
Author(s):  
ERIC JOHNSEN ◽  
TIM COLONIUS
Keyword(s):  
Bubble Dynamics ◽  
High Pressures ◽  
Pressure Ratio ◽  
Free Field ◽  
Water Hammer ◽  
Incident Shock ◽  
Bubble Collapse ◽  
Shock Propagation ◽  
Potential Damage ◽  
Very High

A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring surface is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse occurs is determined.

Pressure and Shock Waves in Bubbly Liquids

2015 ◽  
Author(s):  
Shahid Mahmood ◽  
Yungpil Yoo ◽  
Ho-Young Kwak
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Sound Propagation ◽  
Relaxation Oscillation ◽  
Bubbly Flow ◽  
Gas Bubbles ◽  
Bubbly Liquid ◽  
Bubbly Liquids ◽  
Pressure Profiles

It is well known that sound propagation in liquid media is strongly affected by the presence of gas bubbles that interact with sound and in turn affect the medium. An explicit form of a wave equation in a bubbly liquid medium was obtained in this study. Using the linearized wave equation and the Keller-Miksis equation for bubble wall motion, a dispersion relation for the linear pressure wave propagation in bubbly liquids was obtained. It was found that attenuation of the waves in bubbly liquid occurs due to the viscosity and the heat transfer from/to the bubble. In particular, at the lower frequency region, the thermal diffusion has a considerable affect on the frequency-dependent attenuation coefficients. The phase velocity and the attenuation coefficient obtained from the dispersion relation are in good agreement with the observed values in all sound frequency ranges from kHz to MHz. Shock wave propagation in bubbly mixtures was also considered with the solution of the wave equation, whose particular solution represents the interaction between bubbles. The calculated pressure profiles are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow. Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factor to affect the relaxation oscillation behind the the shock front.

Numerical Investigation of Single Bubble Dynamics Passing a Mesh-Based Structure

2020 ◽  
Author(s):  
Fadi Alnaimat ◽  
Bobby Mathew ◽  
Omar Alhammadi
Keyword(s):  
Bubble Dynamics ◽  
Cfd Simulation ◽  
Single Bubble ◽  
Separation Mechanism ◽  
Mesh Structure ◽  
Flow Restriction ◽  
Complex Interactions ◽  
Vof Model ◽  
Single Bubble Dynamics ◽  
Physical Features

Abstract In this article, investigations of the dynamic behaviors of a single bubble flowing across a mesh-based structure domain was conducted using the volume of fluid (VOF) model. The study was investigated in various mesh structure sizes, including hole size and gap distance. The fundamental behavior of bubble deformation and the effects of gap sizes were analyzed. Subsequently, the predicted dynamics of the deforming bubble area and the effect of the surface tension were examined inside the mesh holes. The discharging bubbles from the mesh structure resulted in a slight difference in the physical features from the original bubble dynamics before entering the mesh (flow restriction). This drafted the bubbles in different trajectories and led to behave differently based on the mesh characteristics. The complex interactions and the subsequent deformations were observed between different mesh sizes. For the validation of the bubble dynamics, the results of computational fluid dynamics (CFD) simulation were tested under different mesh sizes detailing the velocity field, exiting trajectory, bubbles deformation, and residence time, which helps to reveal the affected parameters on the separation mechanism of the original bubble.

Bubble transport theory with application to the upper ocean

1973 ◽  
Vol 59 (1) ◽  
pp. 187-206 ◽  
Author(s):  
G. A. Garrettson
Keyword(s):  
Bubble Dynamics ◽  
Transport Theory ◽  
Gas Diffusion ◽  
Ocean Model ◽  
Upper Ocean ◽  
General Description ◽  
Source Mechanisms ◽  
Bubble Transport ◽  
Single Bubble Dynamics ◽  
Moving Fluid

The formalism of transport theory is adapted to a general description of bubble populations in a moving fluid. The bubble distribution, as a function of position, velocity, radius and time, satisfies a Boltzmann-type transport equation that is derived and then formally solved by the method of characteristics. In order to apply this new analytical tool to the specific problem of gas bubble transport in the upper ocean, an ocean model and a bubble dynamics model must be chosen. For the purpose of illustration, explicit solutions are written, for distributed sources in a stationary ocean with simple expressions for bubble gas diffusion and drag. Calculated results clarify the relations between observed bubble distributions at sea, proposed bubble source mechanisms and known models of single-bubble dynamics.

scholarly journals Effects of injection pressure on cavitation and spray in marine diesel engine

2016 ◽  
Vol 9 (3) ◽  
pp. 186-198 ◽  
Author(s):  
Fei Yan ◽  
Yuchen Du ◽  
Lihui Wang ◽  
Wenxian Tang ◽  
Jian Zhang ◽  
...  
Keyword(s):  
Diesel Engine ◽  
Bubble Dynamics ◽  
Pressure Fluctuations ◽  
Injection Pressure ◽  
Spray Angle ◽  
Marine Diesel Engine ◽  
Sauter Mean Diameter ◽  
Two Phase ◽  
Marine Diesel ◽  
Single Bubble Dynamics

Numerical simulation of the cavitation and spray in a marine diesel engine is performed to investigate the effects of injection pressure on the cavitation flow and spray characteristics in the marine diesel engine, which in turn influence atomization and combustion in the cylinder. A two-phase flow model combined with single bubble dynamics and a droplet break-up model are used to simulate cavitation and spray, respectively, and the results are compared to the experimental data. With increasing injection pressure, the pressure fluctuations inside the nozzle become more intense. The spray penetration is proportional to time at the beginning of injection. Higher injection pressure increases the spray angle. In addition, massive structures on spray edge can return to the spray body, whereas the massive structures on the spray head remain unchanged throughout its lifetime. Each additional 20 MPa of injection pressure reduces the Sauter mean diameter by approximately 9%.

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