• Proceedings of the Korea Association of Crystal Growth Conference
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• 1996.06a
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• pp.179-200
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• 1996

The intrinsic instabilities of fluid flow occurred in the melt of the Czochralski crystal growth system Czochralski method, asymmetric flow patterns and temperature profiles in the melt have been studied by many researchers. The idea that the non-symmetric structure of the growing equipment is responsible for the asymmetric profiles is usually accepted at the first time. However further researches revealed that some intrinsic instabilities not related to the non-symmetric equipment structure in the melt could also appear. Ristorcelli had pointed out that there are many possible causes of instabilities in the melt. The instabilities appears because of the coupling effects of fluid flow and temperature profiles in the melt. Among the instabilities, the B nard type instabilities with no or low crucible rotation rates are analyzed by the visualizing experiments using X-ray radiography and the 3-D numerical simulation in this study. The velocity profiles in the Silicon melt at different crucible rotation rates were measured using X-ray radiography method using tungsten tracers in the melt. The results showed that there exits two types of fluid flow mode. One is axisymmetric flow, the other is asymmetric flow. In the axisymmetric flow, the trajectory of the tracers show torus pattern. However, more exact measurement of the axisymmetrc case shows that this flow field has small non-axisymmetric components of the velocity. When fluid flow is asymmetric, the tracers show random motion from the fixed view point. On the other hand, when the observer rotates to the same velocity of the crucible, the trajectory of the tracer show a rotating motion, the center of the motion is not same the center of the melt. The temperature of a point in the melt were measured using thermocouples with different rotating rates. Measured temperatures oscillated. Such kind of oscillations are also measured by the other researchers. The behavior of temperature oscillations were quite different between at low rotations and at high rotations. Above experimental results means that the fluid flow and temperature profiles in the melt is not symmetric, and then the mode of the asymmetric is changed when rotation rates are changed. To compare with these experimental results, the fluid flow and temperature profiles at no rotation and 8 rpm of crucible rotation rates on the same size of crucible is calculated using a 3-dimensional numerical simulation. A finite different method is adopted for this simulation. 50×30×30 grids are used. The numerical simulation also showed that the velocity and flow profiles are changed when rotation rates change. Futhermore, the flow patterns and temperature profiles of both cases are not axisymmetric even though axisymmetric boundary conditions are used. Several cells appear at no rotation. The cells are formed by the unstable vertical temperature profiles (upper region is colder than lower part) beneath the free surface of the melt. When the temperature profile is combined with density difference (Rayleigh-B nard instability) or surface tension difference (Marangoni-B nard instability) on temperature, cell structures are naturally formed. Both sources of instabilities are coupled to the cell structures in the melt of the Czochralski process. With high rotation rates, the shape of the fluid field is changed to another type of asymmetric profile. Because of the velocity profile, isothermal lines on the plane vertical to the centerline change to elliptic. When the velocity profiles are plotted at the rotating view point, two vortices appear at the both sides of centerline. These vortices seem to be the main reason of the tracer behavior shown in the asymmetric velocity experiment. This profile is quite similar to the profiles created by the baroclinic instability on the rotating annulus. The temperature profiles obtained from the numerical calculations and Fourier transforms of it are quite similar to the results of the experiment. bove esults intend that at least two types of intrinsic instabilities can occur in the melt of Czochralski growing systems. Because the instabilities cause temperature fluctuations in the melt and near the crystal-melt interface, some defects may be generated by them. When the crucible size becomes large, the intensity of the instabilities should increase. Therefore, to produce large single crystals with good quality, the behavior of the intrinsic instabilities in the melt as well as the effects of the instabilities on the defects in the ingot should be studied. As one of the cause of the defects in the large diameter Silicon single crystal grown by the

• Journal of the Korean Society for Nondestructive Testing
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• v.29 no.6
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• pp.570-578
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• 2009

Excitation and propagation of guided waves are very complex problems in pipes due to their dispersive nature. Pipes are commonly used in the oil, chemical or nuclear industry and hence must be inspected regularly to ensure continued safe operation. The normal mode expansion(NME) method is given for the amplitude with which any propagating waveguide mode is generated in the pipes by applied surface tractions. Numerical results are calculated based on the NME method using different sources, i.e., non-axisymmetric partial loading and quasi-axisymmetric loading sources. The sum of amplitude coefficients for 0~nineth order of the harmonic modes are calculated based on the NME method and the dispersion curves in pipes. The superimposed total field which is namely the angular profile, varies with propagating distance and circumferential angle. This angular profile of guided waves provides information for setting the transducer position to find defects in pipes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.6
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• pp.1407-1414
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• 1988

Deviation angles are predicted by numerical calculation of three-dimensional compressible flow through the rotating blade row in axial flow compressor. Three-dimensional flow fields are analyzed by the quasi three-dimensional combination of blade-to blade surfaces and hub-to shroud stream surfaces and calculated by the finite element method in the cyclic calculation of both stream surfaces. In the blade-to blade calculations the method of boundary stream line correction is used and in the hub-to shroud calculations the loss effects due to viscous flow are included. The computational results are compared with the available experimental one. It is shown that the computational results from blade-to-blade flow calculation are correct for incompressible, compressible low subsonic and high subsonic flow at the inlet, and the loss effects on the deviation angle can be neglected in the range of the subsonic flow less than the critical Mach number for the axisymmetric flow and even for 3-D non-axisymmetric flow with loss. And it is found that the present results are better agreed with the experimental data than Lieblein's one.

• Journal of the Korean Society of Safety
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• v.13 no.3
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• pp.11-23
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• 1998

In this study, collapse test of thin-walled structure is performed under axially quasi-static and impact load in collapse characteristic to develop the optimum structural member for a light-oriented automobile. Furthermore, the energy-absorbing capacity is observed according to the variety of configuration(circular, square), aspect ratio in aluminum specimen to obtain basic data for the improved member of vehicle. In both quasi-static and impact collapse test, Al circular specimens collapse, in general, with axisymmetric mode in case of thin thickness while collapse with non-axisynmetric mode according to the thickness increase. For Al rectangular specimens, they collapse with axisymmetric mode in case of thin thickness, with mixed collapse mode according to the increase of thickness. In terms of initial max. load, Al square specimen turns out the best member among specimens, and then Al square, circular and circular with large scaling ratio, respectively. In case of quasi-static compression test, the absorbed energy per unit volume and mass shows higher in Al circular specimen, and then Al square, circular with large scaling ratio, respectively, according to shape ratio the absorbed energy per unit volume and mass in case of max. impact compression load is higher than that of static load. But the absorbed energy per unit volume and mass shows that Al circular specimen is the best member. Especially, unlike max. compression loan, the absorbed energy per unit volume and mass in impact test turns out the low value.

• Nuclear Engineering and Technology
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• v.40 no.1
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• pp.77-86
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• 2008

This paper describes the nonlinear analyses of a 1:4 scale model of a prestressed concrete containment vessel (PCCV) using an axisymmetric model and a three-dimensional model. These two models are refined by comparison of the analysis results and with testing results. This paper is especially focused on the analysis of behavior under pressure and the temperature effects revealed using an axisymmetric model. The temperature-dependent degradation properties of concrete and steel are considered. Both geometric and material nonlinearities, including thermal effects, are also addressed in the analyses. The Menetrey and Willam (1995) concrete constitutive model with non-associated flow potential is adopted for this study. This study includes the results of the predicted thermal and mechanical behaviors of the PCCV subject to high temperature loading and internal pressure at the same time. To find the effect of high temperature accident conditions on the ultimate capacity of the liner plate, reinforcement, prestressing tendon and concrete, two kinds of analyses are performed: one for pressure only and the other for pressure with temperature. The results from the test on pressurization, analysis for pressure only, and analyses considering pressure with temperatures are compared with one another. The analysis results show that the temperature directly affects the behavior of the liner plate, but has little impact on the ultimate pressure capacity of the PCCV.

• Computers and Concrete
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• v.31 no.5
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• pp.443-455
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• 2023

This is a research analyses on the bearing capacity at a pile tip embedded in rock. The aim is to propose a shape coefficient for an analytical solution and to investigate the influence of the plastic flow law on the problem. For this purpose, the finite difference method is used to analyze the bearing capacity of various types and states of rock masses, assuming the Hoek & Brown failure criterion, by considering both plane strain and an axisymmetric model. Different geometrical configurations were adopted for this analysis. First, the axisymmetric numerical results were compared with those obtained from the plane strain analytical solution. Then the pile shape influence on the bearing capacity was studied. A shape factor is now proposed. Furthermore, an evaluation was done on the influence of the plastic flow law on the pile tip bearing capacity. Associative flow and non-associative flow with null dilatancy were considered, resulting in a proposed correlation. A total of 324 cases were simulated, performing a sensitivity analysis on the results and using the graphic output of vertical displacement and maximum principal stress to understand how the failure mechanism occurs in the numerical model.

• Transactions of Materials Processing
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• v.11 no.8
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• pp.682-690
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• 2002

The formation of adiabatic shearband in tungsten heavy alloys(WHA) was studied in this investigation. Five prismatic specimens were loaded by high velocity impacts and treated as plane strain problems. To find out the effect of particle's volume ratio, specimens containing 81%, 93% and 97% volume percents of tungsten particles were used. Also the effects of particle's geometry and size on the formation of shearband were studied for 81% volume percent alloys by small size particle model, large size particle model and undulated particle models, and the results were discussed.be used to diagnose the causes of necking and fracture in industrial practice and to investigate whether these defects were caused by material property variation, changes in lubrication, or incorrect press settings. In non-axisymmetric deep drawing, three modes of forming regimes are found: draw, stretch, plane strain. The stretch mode for non-axisymmetric deep drawing could be defined when the major and minor strains are positive. The draw mode could be defined when the major strain is positive and minor strain is negative, and plane strain mode could be defined when the major strain is positive and minor strain is zero. Through experiments the draw mode was shown on the wall and flange are one of a drawn cup, while the plane strain and the stretch mode were on the punch head and the punch corner area respectively, We observed that the punch load of elliptical deep drawing was decreased according to increase of die corner radius and the thickness deformation of minor side was more large than major side.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2492-2502
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• 2002

A rubber-like material model is generally characterized by hyperelasticity and formulated by a total stress-total strain relationship because the material shows nonlinear elastic behaviour under large deformation. In this study, a pressure potential obtained by a separately interpolated pressure is introduced to the non-linear finite element formulation incorporating with incompressible or almost incompressible condition of the material. The present formulation is somewhat different from the general formulation using the pressure computed in the displacement field. A non-linear finite element analysis program is developed for the plane strain and the axisymmetric contact problems of a rubber-like material. Various examples with rubber material are analyzed for its verification. The results about deformed shapes and stress distributions thought to be meaningful in comparison with a commercial program, MARC.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.583-584
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• 2015

In this paper, the numerical results concerning different orbits of a 3D axisymmetric non-rotating galactic potential are presented. We use $Paczy{\acute{n}}ski^{\prime}s$ gravitational potential with different birth velocity distributions for the isolated old Neutron Star (NS) population. We note some smooth non-constant segments corresponding to regular orbits as well as the characterization of their chaoticity. This is strongly related to the effect of different kick velocities due to supernovae mass-loss and natal kicks to the newly-formed NS. We further confirm that the dynamical motion of the isolated old NSs in the gravitational field becomes obvious, with some significant diffraction in the symmetry of their orbital characteristics.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.6
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• pp.544-552
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• 1984

A non-steady group combustion model of a spherical droplets cloud has been developed to access the non-steady effects of collective behavior of fuel droplets on combustion characteristics and cloud structure. A system of conservation equations of droplets cloud in axisymmetric spherical coordinate was solved by numerical methods for n-Butylbenzene(C$_{10}$ / $H_{14}$) It was found that the effect of initial droplet size on combustion characteristics is dominated compare with effects of cloud size and number density of droplets. For dense droplets cloud, external group combustion mode is established during main part of cloud life time, and internal and single droplet combustion modes are simultaneously established for the dilute droplets cloud. Radius of cloud and external envelope flame are slowly decreased during main part of cloud life time, and suddenly decreased at end of combustion period.d.