• Korean Journal of Mathematics
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• v.20 no.3
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• pp.323-331
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• 2012

We present a high-order potential ow model for the motion of the impulsively accelerated unstable interface of infinite density jump. The Layzer model for the evolution of the interface is extended to high-order. The time-evolution solutions of the bubble and the spike in the interface are obtained from the high-order model. We show that the high-order model gives improvement on the prediction of the evolution of the bubble and the spike.

• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1575-1588
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• 2019

Fracture near the U-10Mo/cladding material interface impacts fuel service life. In this work, a mesoscale stress model is developed with the fuel foil considered as a porous medium having gas bubbles and bearing bubble pressure and surface tension. The models for the evolution of bubble volume fraction, size and internal pressure are also obtained. For a U-10Mo/Al monolithic fuel plate under location-dependent irradiation, the finite element simulation of the thermo-mechanical coupling behavior is implemented to obtain the bubble distribution and evolution behavior together with their effects on the mesoscale stresses. The numerical simulation results indicate that higher macroscale tensile stresses appear close to the locations with the maximum increments of fuel foil thickness, which is intensively related to irradiation creep deformations. The maximum mesoscale tensile stress is more than 2 times of the macroscale one on the irradiation time of 98 days, which results from the contributions of considerable volume fraction and internal pressure of bubbles. This study lays a foundation for the fracture mechanism analysis and development of a fracture criterion for U-10Mo monolithic fuels.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.663-673
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• 2017

We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.

• Journal of The Korean Astronomical Society
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• v.40 no.4
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• pp.161-164
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• 2007

We calculate the evolution of multiple supernova (SN) explosions inside a pre-exiting bubble blown up by winds from massive stars, using one-dimensional hydrodynamic simulations including radiative cooling and thermal conduction effects. First, the development of the wind bubble driven by collective winds from multiple stars during the main sequence is calculated. Then multiple SN explosion is loaded at the center of the bubble and the evolution of the SN remnant is followed for $10^6$ years. We find the size and mass of the SN-driven shell depend on the structure of the pre-existing wind bubble as well as the total SN explosion energy. Most of the explosion energy is lost via radiative cooling, while about 10% remains as kinetic energy and less than 10% as thermal energy of the expanding bubble shell. Thus the photoionization and heating by diffuse radiation emitted by the shock heated gas is the most dominant form of SN feedback into the surrounding interstellar medium.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.225-234
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• 2012

We present two high-order potential flow models for the evolution of the interface in the Rayleigh-Taylor instability in two dimensions. One is the source-flow model and the other is the Layzer-type model which is based on an analytic potential. The late-time asymptotic solution of the source-flow model for arbitrary density jump is obtained. The asymptotic bubble curvature is found to be independent to the density jump of the fluids. We also give the time-evolution solutions of the two models by integrating equations numerically. We show that the two high-order models give more accurate solutions for the bubble evolution than their low-order models, but the solution of the source-flow model agrees much better with the numerical solution than the Layzer model.

• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.226-233
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• 2022

In the present work, a phase-field model was developed to investigate the influence of recrystallization on bubble evolution during irradiation. Considering the interaction between bubbles and grain boundary (GB), a set of modified Cahn-Hilliard and Allen-Cahn equations, with field variables and order parameters evolving in space and time, was used in this model. Both the kinetics of recrystallization characterized in experiments and point defects generated during cascade were incorporated in the model. The bubble evolution in recrystallized polycrystalline of U-Mo alloy was also investigated. The simulation results showed that GB with a large area fraction generated by recrystallization accelerates the formation and growth of bubbles. With the formation of new grains, gas atoms are swept and collected by GBs. The simulation results of bubble size and distribution are consistent with the experimental results.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.779-791
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• 2000

The nonlinear stage of the evolution of free boundary between a light fluid and a heavy fluid driven by an external force is studied by a potential flow model with a source singlarity. The potential flow model is applied to a bubble and spije evolution for constantly accelerated interface (Rayleigh-Taylor instability) and impulsively accelerated interface (Richtmyer-Meshkow instability). The numerical results of the model show that, in constantly accelerated intergace, bubble grows with constant velocity and the spike falls with gravitational acceleration at later times, while the velocity of the bubble in impulsively accelerated interface decay to zero asymp flow model for the bubble and spike for constantly accelerated interface and impulsively accelerated interface.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.566-574
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• 2021

The process of cavitation involves generation, growth, coalescence, and collapse of small bubbles and is tremendously influenced by bubble-bubble interactions. To understand these interactions, a new cavitation model based on the transport equation is proposed herein. The modified Rayleigh-Plesset equation is analyzed to determine the bubble growth rate by assuming equal-sized spherical bubble clouds. The source term in the transport equation is then derived according to the bubble growth rate with the bubble-bubble interaction. The proposed model is validated by various test simulations, including microscopic bubble cloud evolution as well as macroscopical two- and three-dimensional cavitating flows. Compared with previous models, namely the Kunz and Zwart cavitation models, the newly proposed model does not require adjustable parameters and generally results in better predictions both microscopic and macroscopical cases. This model is more physical.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.418-426
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• 1995

A bubble-powered microactuator is designed conceptually. And the actuation mechanism due to bubble growth and collapse is studied numerically and analytically. In this analysis, it is estimated that the time lag for bubble formation on micro line heater, the duration of the bubble growth and collapse and the pressure change in actuator due to the bubble evolution. Based on these calculations, the actuator control scheme is visualized. This actuator may be applicable to the system which needs to pump liquid correctly and regularly.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.9
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• pp.1317-1326
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• 2003

The maximum temperature limit at which liquid boils explosively is called the superheat limit of liquids. The superheat limits of hydrocarbon liquids and their mixtures were measured by the droplet explosion technique. Also the fully evaporated droplet at the superheat limit and subsequent bubble evolution from the fully evaporated droplet were visualized. The pressure wave emanating from the evaporating droplet and subsequent bubble evolution process were measured by a piezoelectric transducer.