• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권1호
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• pp.121-131
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• 2000

Melt flow, heat and mass transfer of oxygen have been analyzed numerically in the process of Czochralski single crystal growth of silicon under the influence of misaligned cusp magnetic fields. Since the silicon melt in a crucible for crystal growth is of high temperature and of highly electrical-conducting, experimentation method has difficulty in analyzing the behavior of the melt flow. A set of simultaneous nonlinear equations including Navier-Stokes and Maxwell equations has been used for the modelling of the melt flow which can be regarded as a liquid metal. Together with the melt flow which forms the Marangoni convection, a flow circulation is observed near the comer close both to the crucible wall and the free surface. The melt flow tends to follow the magnetic lines instead of traversing the lines. These flow characteristics helps the flow circulation exist. Mass transfer characteristics influenced by the melt flow has been analyzed and the oxygen absorption rate to the crystal has been calculated and turned out to be rather uniform than in the case of an aligned magnetic field.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권3호
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• pp.257-268
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• 2014

The objective of the present study is to investigate thermal diffusion and radiation effects on unsteady MHD flow past a linearly accelerated vertical porous plate with variable temperature and also with variable mass diffusion in presence of heat source or sink under the influence of applied transverse magnetic field. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. At time t > 0, the plate is linearly accelerated with a velocity $u=u_0t$ in its own plane. And at the same time, plate temperature and concentration levels near the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the closed analytical method. The velocity, temperature, concentration, skin-friction, the rate or heat transfer and the rate of mass transfer are studied through graphs in terms of different physical parameters like magnetic field parameter (M), radiation parameter (R), Schmidt parameter (Sc), Soret number (So), Heat source parameter (S), Prandtl number (Pr), thermal Grashof number (Gr), mass Grashof number (Gm) and time (t).

• 한국전산유체공학회지
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• 제6권3호
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• pp.41-50
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• 2001

Effects of rotor-stator blade count ratio on the unsteady aerodynamic characteristics of a cascade was studied by using a Navier-Stokes code. Present Navier-Stokes code is a parallel code and works on a multi-cpu machine. It is based on the SIMPLE algorithm and uses QUICK scheme for convection terms and second order back difference for all temporal derivatives. Computations were carried out for two cases : case 1 is for 3 stator cascade passages subjected to two upstream wakes while case 2 is for 2 stator cascade passages subjected to three upstream wakes. Numerical solutions show that rotor-stator blade count ratio plays a significant role in the unsteady aerodynamic characteristics of the stator cascade. Case 2 shows smaller unsteady fluctuation than case 1, even if they show the same time averaged value. The smaller fluctuation of case 2 is believed due to strong interaction between unsteady vortices. The unsteady lift variation of case 2 is shown to have many high frequency fluctuations as more unsteady vortices travel around the cascade. The unsteady turbulent kinetic energy due to the upstream wake is also shown to decay faster through the cascade passage than in the free stream.

• 대한기계학회논문집B
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• 제25권7호
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• pp.915-922
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• 2001

A new phase-average technique using instantaneous velocity fields obtained by a PIV method has been developed. The technique tracks vorticity centers and estimates the value of circulation for a chosen domain. The locations of vortex-centers and the magnitudes of circulation are matched together then showing a sine wave feature due to the periodic vortex shedding from the circular cylinder. Ensemble averaged and phase averaged velocity fields are successfully measured for the circular cylinder wake where Reynolds number is 3900 based on free stream velocity and cylinder diameter. The convection velocities of the vortices center and the vortex shedding frequency were measured by a single hot-wire probe.

• 대한기계학회논문집B
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• 제20권10호
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• pp.3322-3333
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• 1996

A numerical analysis has been conducted to investigate a modified floating-zone crystal growth process in which most of the melt surface is covered with a heated ring. The crystal rod is not only pulled downward but rotated around its axisymmetric line during crystal growth process in order to produce the flat interface of crystal growth and the single crystal growth of NaNO3 is considered in 6mm diameter. The present study is made from a full-equation-based analysis considering a pulling velocity in all of solid and liquid domains and both of solid-liquid interfaces are tracked simultaneously with a governing equation in each domain. Numerical results are mainly presented for the comparison of the surface shape of rotational crystal rod with that of no-rotational crystal rod and the effects of revolution speeds of the crystal rod. Results show that the rotation of crystal rod produces more its flat surface. In addition, the shape of crystal growth near the centerline is more concaved with the increase in the revolution speed of crystal rod. The flow pattern and temperature distribution is analyzed and presented in each case. As the pulling velocity of crystal rod is increasing, the free surface of the melt below the heated ring is enlarged due to the crystal interface migrating downward.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집B
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• pp.610-615
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• 2001

Effects of rotor-stator blade count ratio on the unsteady aerodynamic characteristics of a cascade was studied by using a Navier-Stokes code. Present Navier-Stokes code is a parallel code and works on a multi-cpu machine. It is based on the SIMPLE algorithm and uses QUICK scheme for convection terms and second order back difference for all temporal derivatives. Computations were carried out for two cases : case 1 is for 3 stator cascade passages subjected to two upstream wakes while case 2 is for 2 stator cascade passages subjected to three upstream wakes. Numerical solutions show that rotor-stator blade count ratio plays a significant role in the unsteady aerodynamic characteristics of the stator cascade. Case 2 shows smaller unsteady fluctuation than case 1, even if they show the same time averaged value. The smaller fluctuation of case 2 is believed due to strong interaction between unsteady vortices. The unsteady lift variation of case 2 is shown to have many high frequency fluctuations as more unsteady vortices travel around the cascade. The unsteady turbulent kinetic energy due to the upstream wake is also shown to decay faster through the cascade passage than in the free stream.

• 대한기계학회논문집B
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• 제25권11호
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• pp.1527-1534
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• 2001

Phase averaged velocity fields in the near wake region behind a square cylinder have been (successfully) obtained using randomly sampled PIV data sets. The Reynolds number based on the flow velocity and the vertex height was 3,900. To identify the phase information, we examined the magnitude of circulation and the center of peak vorticity. The center of vorticity was estimated from lowpass filtered vorticity contours (LES decomposition) adopting a sub-pixel searching algirithm. Due to the sinusoidal nature of firculation which is closely related to the instantaneous vorticity, the location of peak voticity fits well with a sine curve of the circulation magnitude. Conditionally-averaged velocity fields represent the barman vortex shedding phenomenon very well within 5 degrees phase uncertainty. The oscillating nature of the separated shear layer and the separation bubble at the top surface are clearly observed. With the hot-wire measurements of Strouhal frequency, we found thats the convection velocity changes its magnitude very rapidly from 25 to 75 percent of the free stream velocity along the streamwise direction when the flow passes by the recirculation region.

• 대한기계학회논문집B
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• 제31권3호
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• pp.225-233
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• 2007

The growth of GaN on the patterned substances has proven favorable to achieve thick, crack-free GaN layers. In this paper, numerical modeling of transport and reaction of species is performed to estimate the growth rate of GaN from tile reaction of TMG(trimethly-gallium) and ammonia. GaN growth rate was estimated through the model analysis including the effect of species velocity, thermal convection and chemical reaction, and thermal condition for the uniform deposition was to be presented. The effect of shape and construction of microscopic pattern was also investigated using a simulator to perform surface analysis, and a review was done on the quantitative thickness and shape in making GaN layer on the pattern. Quantitative analysis was especially performed about the shape of reactor geometry, periodicity of pattern and flow conditions which decisively affect the quality of crystal growth. It was found that the conformal deposition could be obtained with the inclination of trench ${\Theta}>125^{\circ}$. The aspect ratio was sensitive to the void formation inside trench and the void located deep in trench with increased aspect ratio.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2002년도 춘계 학술대회논문집
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• pp.8-15
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• 2002

For the large scale computation of turbulent flows around an arbitrarily shaped body, a parallel LES (large eddy simulation) code has been recently developed in which domain decomposition method is adopted. METIS and MPI (message Passing interface) libraries are used for domain partitioning and data communication between processors, respectively. For unsteady computation of the incompressible Wavier-Stokes equation, 4-step splitting finite element algorithm [1] is adopted and Smagorinsky or dynamic LES model can be chosen fur the modeling of small eddies in turbulent flows. For the validation and performance-estimation of the parallel code, a three-dimensional laminar flow generated by natural convection inside a cube has been solved. Then, we have solved the turbulent flow around MIRA (Motor Industry Research Association) model at $Re = 2.6\times10^6$, which is based on the model height and inlet free stream velocity, using 32 processors on IBM SMP cluster and compared with the existing experiment.

• 한국환경과학회지
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• 제2권1호
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• pp.17-26
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• 1993

The layer that is directly influenced by ground surface is called the atmospheric boutsdary layer in comparison with the free atmosphere of higher layer. In the boundary layer, the changes of wind, temperature and coefficient of turbulent diffusion in altitude are large and have great influences an atmospheric diffusion. The purpose of this paper is to express the structure and characteristics of development of mixed layer by using laboratory experiment and numerical simulation. Laboratory experiment using water tank are performed that closely simulate the process of break up of nocturnal surface inversion above heated surface and its phenomena are analyzed by the use of horizontally averaged temperature which is observed. The result obtained from the laboratory experiment is compared with theoretical ones from ; \textsc{k}-\varepsilon numerical model. The results are summarized as follows. 1) The horizontally averaged temperature was found to vary smoothly with height and the mixed layer developed obviously being affected by the convection. 2) The mean height of mixed layer may be predicted as a function of time, knowing the mean initial temperature gradient. The experimental values are associated well with the theoretical values computed for value of the universal constant $C_r$= 0.16, our $C_r$ value is little smaller than the value found by Townsend and Deardoru et al.