• Title/Summary/Keyword: Moment balance equation

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The Numerical Simulation of Ultrafine $SiO_2$ Particle Fabrication and Deposition by Using the Tube Furnace Reactor (튜브형 가열로 반응기를 이용한 초미립 $SiO_2$ 입자의 제조 및 증착에 대한 수치모사)

  • 김교선;현봉수
    • Journal of the Korean Ceramic Society
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    • v.32 no.11
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    • pp.1246-1254
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    • 1995
  • A numerical model for fabrication and deposition of ultrafine SiO2 particles were proposed in the simplified horizontal MCVD apparatus using tube furnace reactor. The model equations such as energy and mass balance equations and the 0th, 1st and 2nd moment balance equations of aerosols were considered in the reactor. The phenomena of SiCl4 chemical reaction, SiO2 particle formation and coagulation, diffusion and thermophoresis of SiO2 particles were included in the aerosol dynamic equation. The profiles of gas temperature, SiCl4 concentration and SiO2 particle volume were calculated for standard conditions. The concentrations, sizes and deposition efficiencies of SiO2 particles were calculated, changing the process conditions such as tube furnace setting temperature, total gas flow rate and inlet SiCl4 concentration.

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Numerical Study of Aggregation and Breakage of Particles in Taylor Reactor (테일러 반응기 내의 입자응집과 분해에 관한 수치 연구)

  • Lee, Seung Hun;Jeon, Dong Hyup
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.40 no.6
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    • pp.365-372
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    • 2016
  • Using the computational fluid dynamics (CFD) technique, we simulated the fluid flow in a Taylor reactor considering the aggregation and breakage of particles. We calculated the population balance equation (PBE) to determine the particle-size distribution by implementing the quadrature method-of-moment (QMOM). It was used that six moments for an initial moments, the sum of Brownian kernel and turbulent kernel for aggregation kernel, and power-law kernel for breakage kernel. We predicted the final mean particle size when the particle had various initial volume fraction values. The result showed that the mean particle size and initial growth rate increased as the initial volume fraction of the particle increased.

Design of Cam Contour for Constant Hangers (등하중지지대의 캠 윤곽 설계)

  • Lee, Gun-Myung;Park, Mun-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.35 no.6
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    • pp.669-675
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    • 2011
  • A constant hanger is a device for supporting pipes in plants. It supplies a constant force to a supporting pipe even if the pipe moves because of thermal expansion. In this paper, we propose a method for designing the contour of a cam for a constant hanger. It has been shown that the contour of a cam must satisfy the geometrical relation of the cam, the force balance equation for the load tube, the relation between the side spring compression and the cam rotation angle, and the moment balance equation for the cam. A calculation procedure to solve these equations simultaneously is proposed, and a constant hanger is designed successfully.

Numerical analysis of particle transport in low-pressure, low-temperature plasma environment

  • Kim, Heon Chang
    • Particle and aerosol research
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    • v.5 no.3
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    • pp.123-131
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    • 2009
  • This paper presents simulation results of particle transport in low-pressure, low-temperature plasma environment. The size dependent transport of particles in the plasma is investigated with a two-dimensional simulation tool developed in-house for plasma chamber analysis and design. The plasma model consists of the first two and three moments of the Boltzmann equation for ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The particle transport model takes into account all important factors, such as gravitational, electrostatic, ion drag, neutral drag and Brownian forces, affecting the motion of particles in the plasma environment. The particle transport model coupled with both neutral fluid and plasma models is simulated through a Lagrangian approach tracking the individual trajectory of each particle by taking a force balance on the particle. The size dependant trap locations of particles ranging from a few nm to a few ${\mu}m$ are identified in both electropositive and electronegative plasmas. The simulation results show that particles are trapped at locations where the forces acting on them balance. While fine particles tend to be trapped in the bulk, large particles accumulate near bottom sheath boundaries and around material interfaces, such as wafer and electrode edges where a sudden change in electric field occurs. Overall, small particles form a "dome" shape around the center of the plasma reactor and are also trapped in a "ring" near the radial sheath boundaries, while larger particles accumulate only in the "ring". These simulation results are qualitatively in good agreement with experimental observation.

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Theoretical Analysis on the Synthesis of Ultrafine TiO2 Particles by Combustion Reaction (연소반응을 이용한 TiO2 초미립자 제조 공정에 대한 이론적 연구)

  • Chae, Bum-San;Kim, Kyo-Seon
    • Journal of Industrial Technology
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    • v.17
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    • pp.241-247
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    • 1997
  • A numerical model has been proposed for a diffusion flame reactor to manufacture ultrafine $TiO_2$ powders. The model equations such as mass balance equation, the 0th, 1st, and 2nd moment equations of aerosols were considered. The phenomena such as $TiCl_4$ reaction rate, $TiO_2$ nucleation rate and the coagulation of $TiO_2$ powders were included in the aerosol dynamic equation. It is found that the $TiO_2$ particle concentration becomes higher, as the inlet $TiCl_4$ concentration and the total gas flow rate increase, and also as the flame temperature decreases. The $TiO_2$ particle size increases, as the flame temperature and the inlet $TiCl_4$ concentration increase and the total gas flow rate decreases.

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Biodynamic Characteristics of Korean Male in Twenties-Mass, Center of Mass and Moment of Inertia Characteristics of Body Segments (한국인 20대 청년 인체분절의 관성특성에 관한 연구)

  • 이영신;임현균;김철중
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.8
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    • pp.1952-1966
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    • 1994
  • The body segment parameters of twelve young male Korean were measured to compare with the results of foreign cadaver studies. A human body was assumed to have fourteen body segments. The mass of each segment was measured with a water immersion test and the mass center of a segment was determined on the balance platform by changing postures. In the case of Korean, because of the difference in body proportion, the mass center of whole-body is located further from the distal end of head(Korean : 44.9% vs. Caucasian : 41.2%), and the mass center of each segment also located in different proportional locations. The existing regression equations, which can estimate segment mass based upon the anthropometric dimensions, estimates segment mass (the mass of shank) for Korean with 13% error. Therefore, it is not recommended to estimate the mass, and the moment of inertia of body segment of Korean based on the existing equations. However, the density information of body constituents was similar enough to apply it to Korean density. It was validated by the comparison between the results of the direct immersion method and 3-dimensional volume reconstruction of segment form the cross sectional images of CT-scan. The average body density measured form twelve subjects was $1.035{\;}kg/m^3$ and showed deceasing trendency.

The multiple Control Law Design of the Variable Structure Control for Angular Position Control of the Robot Arm with an Indirect Driving Joint Using Balance of the Inertial Moment (관성모멘트의 균형을 이용하는 간접구동관절을 갖는 로보트아암의 각위치 제어를 위한 가변구조제어기의 다중 제어법칙 설계)

  • Kim, Joong-Wan;Kang, Dae-Ki
    • Journal of the Korean Society for Precision Engineering
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    • v.13 no.2
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    • pp.76-83
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    • 1996
  • We have developed the unconventional robot arm which is composed of the two main parts, one is a ball screw and the other is a robot arm. The dynamic systems of the robot arm and ball screw are unstable systems coupled with each other. The ball screw mechanism is unstable system but controllable system. The robot arm's dynamics is quasi stable system when ball screw's angular position is zero, else, unstable system. Our system has the duality between stability and controllability at the view point of control. This duality causes difficulty to control of the robot arm using normal control law. We have investigated the location of the characteristic roots of the dynamic equation. And we have found out that the best condition for the control of the arm is quasi stable state. In this paper, we have proposed multiple control laws which are consist of three components to guarantee the stability and controllability simultaneously. The computer simulations were carried out based on VSC about the angular position control of the robot arm, and it is confirmed that the good performances could be obtained by using new controller.

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A Lubrication Design Optimization of Mechanical Face Seal (미케니컬 페이스 실의 유활 최적설계)

  • Choe, Byeong-Ryeol;Lee, An-Seong;Choe, Dong-Hun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.12
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    • pp.2989-2994
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    • 2000
  • A mechanical face seal is a tribo-element intended to control leakage of working fluid at the interface of a rotating shaft and its housing. Leakage of working fluid decreases drastically as the clearance between mating seal faces gets smaller. But the very small clearance may result in an increased reduction of seal life because of high wear and heat generation. Therefore, in the design of mechanical face seals a compromise between low leakage and acceptable seal life is important, ant it present a difficult and practical design problem. A fluid film or sealing dam geometry of the seal clearance affects seal lubrication performance very much, and thereby is optimization is one of the main design consideration. in this study the Reynolds equation for the sealing dam of mechanical face seals is numerically analyzed, using the Galerkin finite element method, which is readily applied to various seal geometries, to give lubrication performances, such as opening force, restoring moment, leakage, and axial and angular stiffness coefficients. Then, to improve the seal performance an optimization is performed, considering various design variables simultaneously. For the tested case the optimization ha successfully resulted in the optimal design values of outer and inner seal radii, coning, seal clearance, and balance radius while satisfying all the operation subjected constraints and design variable side-constraints, and improvements of axial and angular stiffness coefficients by 16.8% and 2.4% respectively and reduction of leakage by 38.4% have been achieved.