• Proceedings of the KSME Conference
• /
• 2001.11b
• /
• pp.545-550
• /
• 2001

A two-dimensional laminar flow through a channel, on which a couple of symmetric vertical fins are attached, is investigated. The stokes flow for this channel flow is investigated analytically and laminar flow numerically. For analytic solution, the method of eigen function expansion and collocation method are employed. For numerical solution, finite difference method(FDM) is used to obtain vorticity and stream function. From the results, streamline patterns are shown and the pressure drop due to the attached fins is calculated, which depends on the length of fins and Reynolds number. While $Re, streamline pattern is symmetric, a pair of additional asymmetric solutions appear for $Re>Re_c$, where the critical Reynolds number $Re_c$ depends on the length of the fin.

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

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.3
• /
• pp.339-346
• /
• 2001

The impulsive spin-up flow in a shallow rectangular container is analyzed numerically by quasi 3-D unsteady laminar flow. In the non-inertia coordinates, the flow is generated by the virtual forces as Coriolis force, etc.. After the boundary layers grow up near sidewalls, primary vortexes separate from the sidewalls. As the Reynolds number increases, the subsidiary vortexes take place in the boundary layer. The rigid body rotation is started from the inner region and propagated to the outer region, finally all the fluid reaches the rigid body rotation. According to the Reynolds number and the aspect ratio, the development of vortex pattern is symmetric or asymmetric.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.1466-1471
• /
• 2004

In this paper, we report the numerical and experimental solutions of the axi-symmetric flows in the axial plane driven by an impingement of fluid from the bottom wall of a circular cylinder. We managed to visualize successfully the flow pattern shown on the vertical plane through the container axis. The numerical results are not show to compare well with the experimental results for the case of the Rossby number 3. Because the numerical results calculate on the assumption that vortex flows are axi-symmetric flow on the other hand real experimental results are show asymmetric flow. The numerical solutions reveal that inertial oscillation plays an important role at small Rossby numbers, or at a larger background rotation.

• Proceedings of the KSME Conference
• /
• 2007.05b
• /
• pp.2951-2954
• /
• 2007

Tumor hemodynamics in vascular state is numerically simulated using pressure node solution. The tumor angiogenesis pattern in our previous study is used for the geometry of vessel networks. For tumor angiogenesis, the equation that governed angiogenesis comprises a tumor angiogenesis factor (TAF) conservation equation in time and space, which is solved numerically using the Galerkin finite element method. A stochastic process model is used to simulate vessel formation and vessel. In this study, we use a two-dimensional model with planar vessel structure. Hemodynamics in vessel is assumed as incompressible steady flow with Newtonian fluid properties. In parent vessel, arterial pressure is assigned as a boundary condition whereas a constant terminal pressure is specified in tumor inside. Kirchhoff's law is applied to each pressure node to simulate the pressure distribution in vessel networks. Transient pressure distribution along with angiogenesis pattern is presented to investigate the effect of tumor growth in tumor hemodynamics.

• Journal of computational fluids engineering
• /
• v.21 no.2
• /
• pp.81-89
• /
• 2016

Numerical simulations are carried out for the fluid flow and particle transport around two nearby circular cylinders in a side-by-side arrangement. The present study aims to understand the effects of the particle Stokes number and the spacing between two cylinders on particle dispersion and deposition characteristics. Simulations are based on an Eulerian-Lagrangian approach where the motion of particles is calculated by a Lagrangian approach based on one-way coupling. Results show that the flow structure is very different depending on the cylinder spacing, eventually affecting the overall pattern of particle dispersion significantly. It is also found that particles with smaller Stokes number tend to be distributed more uniformly in the wake of two cylinders, being located even inside the vortex cores. Meanwhile, particle deposition is analyzed in terms of the deposition efficiency and deposition location. The deposition efficiency of particles strongly depends on the Stokes number, whereas it is slightly affected by the cylinder spacing. The deposition location gets wider as the Stokes number increases, and it becomes asymmetric about the center of each cylinder as the cylinders get close.

• Journal of the Korean Society of Marine Environment & Safety
• /
• v.12 no.4 s.27
• /
• pp.261-266
• /
• 2006

In this study, a scaled model chamber was built to investigate ventilation characteristics of the hood room in LNG carrier. Experimental study was performed in model by visualization equipment with laser apparatus. Four different kinds of measuring area were selected as experimental condition Instant simultaneous velocity vectors at whole field were measured by 2-D PIV system and its software adopting two-frame grey-level cross correlation algorithm. The flow pattern reveals the large scale counter-clockwise forced-vortex rotation at center area.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.36 no.6
• /
• pp.663-668
• /
• 2012

Fly ash erosion is a leading cause of boiler tube failure in PC boilers. Therefore, shields or baffle plates are installed in specific areas to mitigate fly ash erosion and prevent boiler tube failure. However, the tube failure problems caused by fly ash erosion cannot be eliminated with this solution alone, because each PC boiler has a different flue-gas flow pattern and erosion can become severe in unexpected zones. This problem is caused by an asymmetric internal flow velocity and local growth of the flue gas velocity. For these reasons, clearly defining the flow pattern in PC boilers is important for solving the problem of tube failure caused by fly ash erosion. For this purpose, the cold air velocity technique (CAVT) can be applied to the fly ash erosion problem. In this study, CAVT was carried out on the Hadong #2 PC boiler and the feasibility of application of CAVT to conventional PC boilers was validated.

• Journal of Korean Society of Water and Wastewater
• /
• v.23 no.5
• /
• pp.573-581
• /
• 2009

In the case that the average velocity within rectangular-shaped sedimentation basin is less than 1.5cm/sec, and Froude number less than $10^{-6}$, it can not be expected that the longitudinal baffle improves the sedimentation efficiency. Also, since relatively lower velocity increases the effect of geostrophic body force, asymmetric flow pattern on a plane occurs within the basin. From the results of CFD (Computational Fluid Dynamics) simulation, in the case that the highest velocity within rectangular-shaped sedimentation basin is over 1.5cm/sec, and Froude number over $10^{-6}$, it can be expected that the longitudinal baffle installed within rectangular-shaped sedimentation basin improves the sedimentation efficiency.

• 한국전산유체공학회:학술대회논문집
• /
• 2008.03a
• /
• pp.92-96
• /
• 2008

For the Mach reflection of symmetric shock waves, only the wave configuration of an oMR(DiMR+DiMR) is theoretically admissible. For asymmetric shock waves, an oMR(DiMR+InMR) will be possible if the two slip layers assemble a convergent-divergent stream tube while an oMR(InMR+InMR) is absolutely impossible. In this paper, an overall Mach reflection configuration with double inverse MR patterns is confirmed using the CFD technique. Classical two- and three-shock theories are also applied for the theoretical analysis. In addition, oscillations of shock wave patterns are computed for the interaction of a hypersonic flow and double-wedge-like geometries.