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In order to simulate flows in an MHD pump, a three-dimensional, steady-state, incompressible, liquid metal magnetohydrodynamic(MHD) flow has been investigated under the influence of applied magnetic and electric fields. Governing equations including the viscous and inertial effects are solved by means of the finite volume method. At an intermediate interaction parameter and Hartmann number, the distributions of axial velocity, pressure and electric current are obtained under, the assumption that magnetic Reynolds number is very small. In the vicinity of electrodes, the axial velocity distribution is generally flatted and the velocities near the electrodes become larger, yielding M shape profile. Here, the velocity gradients near the duct walls are very steep, forming side layers and Hartmann layers. As the fluid passes the electrodes, the pressure becomes lager and the peculiar pressure behavior near the edge of the electrodes is seen. The transverse electrical currents are concentrated in the Hartmann layers. This study has shown the intrinsic three-dimensional effect of the MHD flow which was not reported yet by one-.and two- dimensional approaches.
The charcteristics of melt flows, temperatures and concentrations of oxygen are numerically studied for various intensities of cusp magnetic fields in the Czochralski furnace. Cusp magnetic fields can suppress buoyancy force due to the heating of crucible wall and centrifugal force due to the rotations of the crucible and crystal. As the magnetic fields are increased, velocities of the flow are greatly diminished, the average oxygen concentration is lowered and the radial uniformity of oxygen concentration at melt/crystal interface is improved.
A numerical study has been carried out on the evaluation of performance of extruded heat sink in electronic equipment. Heat transfer characteristics have been analyzed for various design parameters including the shape of heat sink, thickness of fin base and fin pitches. A commercial program called Flotherm has been employed for the numerical calculation. Optimal design of the heat sink has been persued which is closely related with the reduction of heat resistance involved in conduction and convection of heat.
Numerical analysis are focused on the flow patterns and wall shear stress under unsteady pusaltile flow condition with wall motion. Flow is considered as a non-Newtonian fluid and the constitute equation of blood is used for numerical analysis. Distributions of velocity and wall shear stress in the parallel channel model are calculated to investigated the differences of flow characteristics of unsteady pulsatile flow and to compare flow characteristics of a Newtonian fluid with that of a non-Newtonian fluid. The numerical results may be used to correlation the clinical observations.
Flow Characteristics 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 corner 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.
For various angular velocities of crucible and crystal, the characteristics of melt flows, temperatures and concentrations of oxygen are numerically studied in the Czochralski furnace with a uniform axial magnetic field. With an assumption that two velocity components in the meridional plane and circumferential velocity, temperature, electric current intensity have reached the steady state, unsteady concentration field of oxygen has been analyzed with an initially uniform oxygen concentration. when the angular velocities of crucible and crystal are remarkable, oxygen cannot be easily transported to the area close to the bottom of crystal due to the noticeable centrifugal force. Therefore absorption rate of oxygen to the surface of crystal growth is small and is nearly uniform in the radial direction. On the contrary, when the angular velocities are small, the absorption rate of oxygen shows large gradient in the radial direction.
A numerical simulation has been carried out for the performance characterization of heat sinks in electronic equipment. Heat transfer characteristics have been analyzed for various design parameters including the shape of heat sink, thickness of fin base and fin pitches. A commercial program called Flotherm has been employed for the numerical calculation. Optimal design of the heat sink has been persued which is closely related with the reduction of heat resistance involved in conduction and convection of heat.
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The characteristics of the flow and energy conversion in OMACON liquid-metal MHD system are investigated. Numerical simulation of two-phase flow in the OMACON system without magnetic field was carried out by the Phoenics code and the energy conversion characteristics are studied in association with the fact that the mechanical energy loss at the nozzle of the OMACON system are to be converted into electrical energy. In this system, working fluid (gas) is injected through the mixer located at the bottom of the riser, and is mixed with hot liquid metal. Therefore in the riser two-phase flow is developed under the influence of the gravity. In this study, the interaction between the gas and liquid is considered by the use of IPSA(InterPhase Slip Algorithm) where standard drag coefficient has been used. It has been assumed that in the flow regime the liquid is continuous and the gas is dispersed. For the liquid and gas, the continuity equations, momentum equations and energy equations are solved respectively in association with void fraction in the flow field. In order to calculate the energy conversion efficiency, firstly the ratio of the mechanical energy loss of liquid metal flow at the nozzle to the input thermal energy is considered. Secondly flow pattern of liquid metal in the generator has been analyzed, and the characteristics of the conversion of the mechanical energy into the electrical energy has been investigated. For an representative case where Hartmann number is 540 and magnetic field is 0.35 T, the present analysis shows that the energy conversion efficiency is 0.653. This result is considered to be reasonable in comparison with published experimental results.
비균일 자장이 도가니에 인가되어 있는 상황에서 정상상태의 Czochralski 유동장과 비정상상태의 산소농도장에 대한 연구가 수치해석적인 방법으로 연구되었다. 여기에서 기준 자장의 세기가 B=0.1T, 0.2T, 0.3T의 경우에 대한 연구가 수행되었다. 가열에 의한 부력의 효과와 자유표면의 표면장력에 의한 열모세관 효과에 의하여 유발되는 자오면 유동은 비균일 자장에 의하여 차등적으로 억제되고 있다. 자자의 세기가 증가하면 자오면 유동에서 발생하는 순환류의 중심은 결정으로 접근하며, 순환류의 크기도 작아진다. 결정으로 흡수되는 산소의 세기가 클수록 낮아지며 농도분포는 균일해지는 경향을 갖는다. Under the influence of non-uniform magnetic field, melt flow in steady state and oxygen concentration in unsteady state are numerically investigated. The strength of the applied characteristic magnetic fields are B=0.1T, 0.2T, and 0.3T, respectively. The buoyancy effects due to the crucible wall heating and the thermocapillary effects due to the surface tention at the free surface are suppressed differentially by the non-uniform magnetic fields. As the intensity of characteristic magnetic fields is increasing, the recirculation region in the meridional plane is moving toward the growing crystal, and is diminishing. The oxygen concentration on the growing surface of crystals is decreasing and the uniformity of the oxygen concentration is increasing as the intensity of the magnetic fields is increasing.
The effect of the buyancy and thermocapillarity for differnent aspect ratio of flow field on melt motion and mass transfer has been numerically investigated in magnetic Czochralski crystal growth of silicon. During the process of crystal growth, the melt depth of crucible reduces so the aspect ratio of flow field also reduces. Therefore the shape of magnetic field of the flow field changes and the flow pattern also changes significantly. Together with the melt flow which forms the Marangoni convection (or thermocapillary flow) that comes from the inside the flow field, a flow circulation is observed near the corner close both to the crucible wall and the free surface. Due to this circulation, buoyancy effect has been turned out to be local rather than global. As the aspect ratio decreases, the radial component of the magnetic field prevails compared with the axial component in the flow field. Under the influence of this magnetic field, the melt flow and the temperature distribution in a meridional plane tend to depend on the radial position. As the aspect ratio decreases, the temperature gradient near the edge of the crystal decreases yielding smaller thermocapillarity, and the oxygen concentration near the crystal and the oxygen incorporation rate also decrease. 약한 cusp 자장이 가하여진 Czochralski실리콘 단결정 성장에서 유동장의 종횡비에 따라 부력과 열모세관 현상이 용융물질의 유동과 물질(산소)전달에 미치는 영향이 수치적인 방법으로 연구되었다. 실리콘 단결정 성장이 진행됨에 따라 도가니안의 용융물질의 깊이가 즐어들어 유동장의 종횡비가 감소하고, 이에 따라 현존하는 유동장에 작용하는 자장의 상대적인 형태가 변화하므로 유동의 형태가 계속 변화한다. 유동장 내부에서 자유표면으로 접근하여 Marangoni 대류를 구성하는 용융물질의 흐름(열모세관 현상)과 함께 도가니 벽 근처의 자유표면 바로 아래에서 순환류가 발생하는데, 이 순환류의 존재로 인하여 부력의 효과가 “전반적으로”나타나지 않고 도리어 “국소적으로”나타나는 특성을 갖는다. 종횡비가 작아질수록 유동장의 대부분에서 자장의 반경방향 성분이 축방향 성분보다 우세하여 용융물질의 유동은 횡방향 성분(수평성분)이 현저해지므로 자오면에서의 온도분포는 점차 반경방향에 의존하는 특성을 갖게 된다 종횡비가 작아질수록 결정의 가장자리에서 온도구배가 작아지며 따라서 열모세관 현상포 약화된다 또 이때 결정주위의 산소의 농도가 작아지며 따라서 흡수되는 산소의 양도 작아진다.