822 research outputs found
Bubble models and real bubbles: Rayleigh and energy-deposit cases in a Tait-compressible liquid
No full textIn analytical and numerical studies on bubbles in liquids often the Rayleigh initial condition
of a spherical bubble at maximum radius is used, the Rayleigh case.
This condition cannot be realized in practice, instead the bubbles need first to be generated
and expanded. The energy-deposit case with its initial condition of a small, spherical bubble
of high internal pressure that expands into water at atmospheric pressure is studied
for comparison with the Rayleigh case. From the many possible configurations a single bubble
near a flat solid boundary is chosen as this is a basic configuration to study erosion and
cleaning phenomena. The bubble contains a small amount of non-condensable gas
obeying an adiabatic law. The water is compressible according to the Tait equation.
The Euler equations in axial symmetry are solved with the help of the open source software
package OpenFOAM, based on the finite volume method.
The volume of fluid method is used for interface capturing.
Rayleigh bubbles of m and energy-deposit bubbles
that reach m after expansion in an unbounded liquid are compared
with respect to microjet velocity, microjet impact pressure and microjet impact times,
when placed or being generated near a flat solid boundary.
Velocity and pressure fields from the impact zone are given to demonstrate
the sequence of phenomena from axial liquid microjet impact via annular gas-jet-
and annular liquid-nanojet formation to the Blake splash and the first torus-bubble splitting.
Normalized distances ( = initial distance of the bubble centre
from the boundary) between 1.02 and 1.5 are studied.
Rayleigh bubbles show a stronger collapse
with about 50\% higher microjet impact velocities
and also significantly higher microjet impact pressures
Pressure and tension waves from bubble collapse near a solid boundary: A numerical approach
No full textThe acoustic waves being generated during the motion of a bubble in water
near a solid boundary are calculated numerically.
The open source package OpenFOAM is used for solving the Navier-Stokes equation and extended
to include nonlinear acoustic wave effects via the Tait equation for water.
A bubble model with a small amount of gas is chosen, the gas obeying an adiabatic law.
A bubble starting from a small size with high internal pressure
near a flat, solid boundary is studied.
The sequence of events from bubble growth via axial microjet formation, jet impact,
annular nanojet formation, torus-bubble collapse, and bubble rebound
to second collapse is described.
The different pressure and tension waves with their propagation properties are demonstrated
Ring Vortex Dynamics Following Jet Formation of a Bubble Expanding and Collapsing Close to a Flat Solid Boundary Visualized via Dye Advection in the Framework of OpenFOAM
Full text linkA bubble expanding and collapsing near a solid boundary develops a liquid jet toward the boundary. The jet leaves a torus bubble and induces vortices in the liquid that persist long after the bubble oscillations have ceased. The vortices are studied numerically in axial symmetry and compared to experiments in the literature. The flow field is visualized with different methods: vorticity with superimposed flow-direction arrows for maps at a time instant and colored-liquid-layer flow-field maps (dye advection) for following the complete long-term fluid flow up to a chosen time since bubble generation. Bubbles with equal energy—maximum radius in a free liquid Rmax∞= 500 µm—are studied for different distances Dinit from the solid boundary. The interval of normalized distances D* = Dinit/Rmax∞ from 0.4 to 1.8 is covered. Two types of vortices were reported in experiments, one moving toward the solid boundary and one moving away from it. This finding is reproduced numerically with higher resolution of the flow field and in more detail. The higher detail reveals that the two types of vortices have different rotation directions and coexist with individually varying vorticity amplitude throughout the interval studied. In a quite narrow part of the interval, the two types change their strength and extent with the result of a reversal of the dominating rotational direction of the fluid flow. Thereby, the experimentally found transition interval could be reproduced and refined. It is interesting to note that in the vortex transition interval, the erosion of a solid surface is strongly augmented
Jet formation from bubbles near a solid boundary in a compressible liquid: Numerical study of distance dependence
No full textA small spherical bubble of high internal pressure is inserted into water at constant ambient pressure as a model of a laser-induced bubble. Its subsequent dynamics near a flat solid boundary is studied in dependence on the distance of the bubble to the boundary by numerically solving the Navier-Stokes equations with the help of the open source software environment OpenFOAM. Implemented is the finite-volume method for discretization of the equations of motion and the volume-of-fluid method for capturing the interface between the bubble interior and exterior. The bubble contains a small amount of noncondensable gas that is treated as an ideal gas. The liquid is water obeying the Tait equation. Surface tension is included where necessary. The evolution of the bubble shape and a selection of pressure and velocity fields are given for normalized distances D∗=D/Rmax between 0 and 3 (D is the initial distance of the bubble center to the boundary and Rmax is the maximum radius the bubble would attain without any boundary). The value Rmax= 500 μm is chosen for the study. Normal axial-jet formation (∼100 m/s) by axial flow focusing is found for 0.24≤D∗≤3 and the change to a different type of axial-jet formation (∼1000 m/s) by annular-liquid-flow collision for bubbles very close to the solid boundary (0≤D∗≤0.2). The transition region (0.2<D∗<0.24) is characterized by additional inbound and outbound annular jets. Remarkably, the inclusion of the viscosity of the water is decisive to get the fast jets
Fast, thin jets from bubbles expanding and collapsing in extreme vicinity to a solid boundary: A numerical study
No full textA bubble expanding and collapsing in water near a flat solid boundary is studied
numerically. According to current knowledge, it develops a high-speed liquid jet towards
the boundary of typically ∼100 m/s. However, the character of jet formation and the jet
properties alter strongly when the bubble expands and collapses very close to a solid
boundary. In this case, a much thinner and much faster jet of typically ∼1000 m/s
is generated. The respective mechanism is demonstrated by solving the Navier-Stokes
equations for a model of a laser-induced bubble. The results add substantially to the
understanding of the erosion process caused by imploding cavitation bubbles near solid
boundaries
A new transition between discrete and continuous self-similarity in critical gravitational collapse
Full text linkWe analyze a bifurcation phenomenon associated with critical gravitational
collapse in a family of self-gravitating SU(2) ? models. As the
dimensionless coupling constant decreases, the critical solution changes
from discretely self-similar (DSS) to continuously self-similar (CSS).
Numerical results provide evidence for a bifurcation which is analogous
to a heteroclinic loop bifurcation in dynamical systems, where two fixed
points (CSS) collide with a limit cycle (DSS) in phase space as the
coupling constant tends to a critical value
Ethics of the other and the Hypo case : moments of blindness in the conduct of business of a failed bank
No full textauthor: Christiane MittererMasterarbeit University of Innsbruck 201
Ethics of the other and the Hypo case : moments of blindness in the conduct of business of a failed bank
No full textauthor: Christiane MittererMasterarbeit University of Innsbruck 201
The London Market Excess of Loss Spiral
No full textThis thesis explores the London Market Excess of Loss Spiral (“LMX Spiral”), a phenomenon based upon excess of loss reinsurance contracts that developed within the London reinsurance market of the 1980s. The unwinding of the LMX Spiral was a key factor in the crisis the Lloyd’s insurance market had to face in the early 1990s. However, whilst the crisis resulted in a wave of litigation in the English courts, there is no legal appraisal of the additional element of risk brought by the LMX Spiral itself. The case law instead focuses on the duties of the underwriters and various agents that fuelled its development.This situation is unsatisfactory for two reasons. Firstly, reinsurance spirals are a potential side-effect of XL reinsurance markets and therefore other spirals may develop in the future. Secondly, this thesis shows that once a reinsurance spiral reaches a certain point, it becomes unsustainable, generating instability within the relevant reinsurance market.This thesis provides a detailed legal appraisal of reinsurance spirals and a new analysis of excess of loss reinsurance contracts. The first part sets out the relevant legal principles and describes the LMX Spiral and its impact; listing, for the first time, the “Spiral Effects” identified through reports and actuarial models. The second part reviews the case law and assesses the legal nature of the excess of loss “Spiral Contracts” at the core of any reinsurance spiral, concluding that the Spiral Effects can distort the Spiral Contracts to the point where they become simple contracts of indemnity. The third part explores the nature of excess of loss reinsurance in light of the review of the Spiral Contracts, submitting that excess of loss reinsurance contracts cover both the liability of the reinsured and the relevant insured peril
Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM
No full textLaser generated cavitation bubbles are numerically modeled with the finite volume method using the open source software package OpenFOAM. The alterations applied to the native code are described and validated by solving the spherical bubble collapse problem and comparing the solution with the Gilmore model and experiments. Problems of spherical stability and their connection with the mesh are discussed. Shock wave emission upon laser bubble generation and bubble collapse is modeled by inserting the Tait equation for the liquid (water) into the code. The results are compared with calculations by Hickling and Plesset and experiments. The calculations are extended to the problem of cavitation bubble collapse in front of a solid boundary. (C) 2015 Elsevier Ltd. All rights reserved
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