• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.06a
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• pp.197-201
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• 1997

The momentum, heat and mass trasfer phenomena in the silicon melt of the Czochralki crystal growth system are calculated using a three dimensional numerical simulation thechnique. Even though axisymmetrical boundary conditions are imposed to all calculations in a 3cm diameter crucible, several types of non-axisymmetric profiles of velocities, temperature and oxygen concentration appeared in the melt. Because of the non-axisymmetric profiles of velocities, temperature and oxygen concentration appeared in the melt. Because of the non-axisymmetric profiles and rotations of fluid induced by the crucible rotation, temperatures and oxygen concentrations in the silicon melt fluctuate. The rotating velocity of the profile is calculated from the phase shift of the data of temperature or oxygen at two different points which have same radius from center but 90 degree angular difference. From this calculation, it is found that the rotating veolocity of the oxygen and temperature is different from the crucible rotation rates. Therefore the frequencies of the oscillating temperature and oxygen concentrations are not same to the frequencies of the crucible rotations. Futhermore, the components of the frequencies of the temperature and oxygen concentration at the same point are not same. The fluctuation behaviors of the temperature or oxygen themselves are also different when the points are different. The calculation show that the temperature and the oxygen concentration near the interface also fluctuate. The results suggest that the striation pattern found in the grown silicon single crystals may ben generated by the oxygen concentration and the temperature oscillations of the melt occurred near the interface.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.5
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• pp.1383-1393
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• 2014

Recently, with rapid improvement in computer hardware and theoretical development in the field of computational fluid dynamics, high-order accurate schemes also have been applied in the realm of computational hydraulics. In this study, numerical solutions of 1D shallow water equations are presented with TVD Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The transcritical flows such as dam-break flows due to instant dam failure and transcritical flow with bottom elevation change were studied. As a formulation of approximate Riemann solver, the local Lax-Friedrichs (LLF), Roe, HLL flux schemes were employed and MUSCL slope limiter was used to eliminate unnecessary numerical oscillations. The developed model was applied to 1D dam break and transcritical flow. The results were compared to the exact solutions and experimental data.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• v.y2005m4
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• pp.281-287
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• 2005

Nonlinear behaviors such as steep-fronted wave motions and a finite amplitude limit cycle often accompanying combustion instabilities have been numerically investigated using a characteristic-based approximate Riemann solver and the well-known ${\eta}-{\tau}$ model. A resonant pipe initially subjected to a harmonic pressure disturbance described the natural steepening process that leads to a shocked N-wave. For a linearly unstable regime, pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions. For the 1.5 MW gas generator under development in KARI, the numerical results show good agreement with experimental data from hot-firing tests.

• Journal of Energy Engineering
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• v.12 no.4
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• pp.259-266
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• 2003

Load reduction ring (LRR) was installed on the ABB-Atom sparger to reduce the oscillatory loadings due to the air bubble clouds in the water pool in case of safety relief system operations. In order to investigate the effect of LRR on the pressure field, a numerical simulation on the behavior of air bubble clouds discharging into a water pool through a ABB-Atom sparser without LRR was performed by using a commercial thermal hydraulic analysis code, FLUENT 4.5. Among the multi-phase models contained in the code, the VOF (Volume Of Fluid) model was used to simulate the interface of water, air and steam flows. By comparing the analysis results with the previous ones, the load reduction ring has an effect on reducing the oscillatory loads at the wall. It also includes the effect of air mass and inlet boundary conditions of the pipe on the pressure oscillations at the wall.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.10
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• pp.973-978
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• 2010

In this paper, we studied the shimmy phenomena of an aircraft nose landing gear considering free-play. Shimmy is a self-excited vibration in lateral and torsional directions of a landing gear during either the take-off or landing. This phenomena is caused by a couple of conditions such as low torsional stiffness of the strut, friction and free-play in the gear, wheel imbalance, or worn parts, and it may make an aircraft unstable. Free-play non-linearity is linearized by the described function for a stability analysis in a frequency domain, and time marching is performed using the fourth-order Runge-Kutta method. We performed the numerical simulation of the nose landing gear shimmy and investigated its linear and nonlinear characteristics. From the numerical results, we found limit-cycle-oscillations at the speed under linear shimmy speed for the case considering free-play and it can be concluded that the shimmy stability can be decreased by free-play.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.6
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• pp.15-20
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• 2005

Two-dimensional incompressible Navier-Stokes flow solver is developed using SIMPLER method to study the unsteady viscous flow physics over two-dimensional ellipses. Unsteady viscous flows over various thickness-to-chord ratios of 0.6, 0.8, 1.0, and 1.2 elliptic cylinders are simulated at different Reynolds numbers of 200, 400, and 1,000. This study is focused on the understanding the effects of Reynolds number and elliptic cylinder thickness on the drag and lift forces. The present numerical solutions are compared with available experimental and numerical results and show a good agreement. Through this study, it is observed that the Reynolds number and the cylinder thickness affect not only the frequency of the force oscillations but also the mean values and the amplitudes of the total drag and lift forces significantly.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.7
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• pp.683-693
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• 2013

In this study, the mixing characteristics in lid-driven cavity flows were studied numerically by using a hybrid lattice Boltzmann method (HLBM). First, we compared the numerical results from single-relaxation-time (LB-SRT) and multi-relaxation-time (LB-MRT) models to examine their reliability. In most of the cavity flow, the results from both the LB-SRT and the LB-MRT models were in good agreement with those using a Navier-Stokes solver for Re=100-5000. However, the LB-MRT model was superior to the LB-SRT model for the simulation of higher Reynolds number flows having a geometrical singularity with much lesser spatial oscillations. For this reason, the LB-MRT model was selected to study the mass transport in lid-driven cavity flows, and it was demonstrated that mass transport in the fluid was activated by a recirculation zone in the cavity, which is connected from the top to the bottom surfaces through two boundary layers. Various mixing characteristics such as the concentration profiles, mean Sherwood (Sh) numbers, and velocity were computed. Finally, the detailed transport mechanism and solutions for the concentration profile in the cavity were presented.

• The KSFM Journal of Fluid Machinery
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• v.11 no.1
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• pp.9-17
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• 2008

A numerical study for three-dimensional laminar flow in the entrance region of helical tubes connected with straight ones is carried out to investigate the effects of Reynolds number, pitch and curvature ratio on the oscillation periods of the flow. The fully elliptic governing equations were solved by means of a finite volume method. The fully developed laminar flow boundary condition was applied at the straight tube inlet. This results cover a curvature ratio range of 1/10${\sim}$1/320, a pitch range of 0.0${\sim}$3.2, and a Reynolds number range of 62.5${\sim}$2000. A comparison is made with previous experimental correlations and numerical data. The developments of velocity, local and average friction factors are discussed. The average friction factors are oscillatory in the entrance region of helical pipes. It has been found that the angle required for the flow to be similarly developed is most affected by the curvature ratio. The pitch and Reynolds number do not have any significant effect on the angle. The characteristic angle ${\phi}_c(={\phi}/sqrt{\delta})$, or the characteristic length to diameter ratio $s_c(=l\sqrt{\delta} cos(atan{\lambda})/d)$, can be useful to represent the development of flow in helical tubes. As the pitch increases and as the curvature ratio and Reynolds number decrease, the amplitude and the number of flow oscillations along the main streamwise direction decrease.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.45-56
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• 1994

A computationally efficient numerical method based on potential flow is developed for time-domain simulation of the nonlinear free-surface flows around a 2-dimensional hydrofoil. This numerical method, namely, spectral/boundary-element method, is a mixed one of the high-order spectral method and the boundary-element method in time-domain. The high-order spectral method is used to calculate the nonlinear evolution of free-surface, and the boundary-element method is used to calculate the effects of the hydrofoil and the shed vortex. As application examples, nonlinear free-surface flows around a 2-dimensional hydrofoil which starts from the rest and translates near the free-surface with or without harmonic oscillations are calculated. Nonlinear/unsteady results of free-surface waves and hydrodynamic farces are shown and discussed. Particularly, the results of steady-state which are obtained as a special case of the present unsteady solution are compared with others' calculated and experimental results, and good agreements are observed.

• 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