• Title/Summary/Keyword: equilibrium equation

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Estimation of Density of Methane and Ethane and Vapor-Liquid Equilibrium Predictions for Methane-Ethane Binary System Using PR and PC-SAFT Equations of State (PR 및 PC-SAFT 상태방정식을 이용한 메탄과 에탄의 기상과 액상의 밀도 추산 및 이성분계의 기-액 상평형 계산)

  • Park, Jong-Kee;Choi, Kun-Hyung;Lee, Sang-Gyu;Yang, Young-Myung;Cho, Jung-Ho
    • Journal of the Korean Institute of Gas
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    • v.14 no.2
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    • pp.22-26
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    • 2010
  • In this study, experimental vapor pressures and densities of vapor and liquid phases versus temperature were estimated using PC-SAFT equation. The estimated results were compared with those using PR equation of state. For the vapor phase densities, both equations well predicted the literature data. However, PC-SAFT equation showed better prediction capability for liquid phase densities. In the comparison of vapor-liquid equilibrium prediction capability for the binary systems of methane and ethane, PC-SAFT equation was better than the PR equation.

An Analytical Approach for Structural Synthesis of Substructures

  • Eun, Hee-Chang;Park, Sang-Yeol;Lee, Eun-Taik
    • Journal of Mechanical Science and Technology
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    • v.18 no.9
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    • pp.1529-1536
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    • 2004
  • A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

Estimation of diffusion coefficient at the interface between liquid and vapor phases using the equilibrium molecular dynamics simulation (분자 동역학 모사를 이용한 액상과 기상 계면에서의 확산계수의 예측)

  • Kim, Kyeong-Yun;Choi, Young-Ki;Kwon, Oh-Myoung;Park, Seung-Ho;Lee, Joon-Sik
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.1584-1589
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    • 2003
  • This work applies the equilibrium molecular dynamics simulation method to study a Lennard-Jones liquid thin film suspended in the vapor and calculates diffusion coefficients by Green-Kubo equation derived from Einstein relationship. As a preliminary test, the diffusion coefficients of the pure argon fluid are calculated by equilibrium molecular dynamics simulation. It is found that the diffusion coefficients increase with decreasing the density and increasing the temperature. When both argon liquid and vapor phases are present, the effects of the system temperature on the diffusion coefficient are investigated. It can be seen that the diffusion coefficient significantly increases with the temperature of the system.

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Dynamic Stability and Semi-Analytical Taylor Solution of Arch With Symmetric Mode (대칭 모드 아치의 준-해석적 테일러 해와 동적 안정성)

  • Pokhrel, Bijaya P.;Shon, Sudeok;Ha, Junhong;Lee, Seungjae
    • Journal of Korean Association for Spatial Structures
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    • v.18 no.3
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    • pp.83-91
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    • 2018
  • In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

Uniform metal droplet generation using laser (레이저를 이용한 균일 금속 액적 생성)

  • 강대현;양영수;김용욱;조성규;박성민
    • Laser Solutions
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    • v.5 no.1
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    • pp.23-31
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    • 2002
  • The uniform metal droplet generation using Nd-YAG laser was studied and experiment was carried out. The shape and volume of developed droplet was measured and the Young-Laplace equation and equilibrium condition of force were applied this model. The differential equation predicting shape of droplet using equilibrium condition of force instead of Navier-stokes equation was induced and numerical solution of differential equation compared with experimentation data. The differential equation was solved by Runge-Kutta method. Surface tension coefficient of droplet was determined with numerical solution relate to experimental result under the statical condition. In case of dynamic vibration, metal droplet shape and detaching critical volume are predicted by recalculating proposed model. The result revealed that this model could reasonably describe the behavior of molten metal droplet on vibration.

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Numerical Analysis of Cavitation Flow Around Hydrofoils (3차원 수중익형 주위의 캐비테이션 유동 전산해석)

  • Kim, S.H.;Koo, T.K.;Park, W.G.;Kim, D.H.
    • The KSFM Journal of Fluid Machinery
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    • v.11 no.3
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    • pp.7-13
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    • 2008
  • The cavitating flow simulation is of practical importance for many engineering systems, such as pump, turbine, nozzle, Infector, etc. In the present work, a solver for two-phase flows has been developed and applied to simulate the cavitating flows past hydrofoils. The governing equation is the two-phase Navier-Stokes equation, comprised of the continuity equation of liquid and vapor phase. The momentum and energy equation is in the mixture phase. The solver employs an implicit, dual time, preconditioned algorithm using finite difference scheme in curvilinear coordinates. An experimental data and other numerical data were compared with the present results to validate the present solver. It is concluded that the present numerical code has successfully accounted for two-phase Navier-Stokes model of cavitation flow.

Vibration Analysis and Non-linear Equilibrium Equations of a Curved Pipe Conveying Fluid (유체가 흐르는 곡선관의 진동 해석과 비선형 평형 방정식)

  • Jung, Du-Han;Chung, Jin-Tai
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.983-986
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    • 2005
  • Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

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Moisture Sorption and Desorption Characteristics of Tobacco Types. (담배종류별 흡습 및 방습 특성)

  • 김용옥;정한주;공판임;장기철
    • Journal of the Korean Society of Tobacco Science
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    • v.26 no.1
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    • pp.43-49
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    • 2004
  • This study was carried out to investigate moisture sorption and desorption characteristics followed by tobacco type. Experiments were performed at various temperature(5, 15, 25, 40 $^{\circ}C$) and relative humidity range (11~84 %) controlled by saturated salt solution. Regression equation was obtained to predict equilibrium moisture according to various relative humidity, temperature and tobacco types. The obtained regression equation showed high $R^2$(above 0.95) and predicted accurate equilibrium moisture. Equilibrium moisture contents declines in the following order when a relative humidity is 50 % or above: expanded stem, flue-cured, expanded tobacco, reconstituted tobacco, USA flue-cured, orient, burley. To maintain 13 % moisture of each tobacco type in the range of 5~40 $^{\circ}C$ it is recommendable to control relative humidity 49~56 % for expanded stem, 50~57 % for flue-cured, 54~61 % for USA flue-cured, 56~60 % for reconstituted tobacco, 57~62 % for expanded tobacco, 58~64 % for orient and 58~65 % for burley, respectively. It means that the relative humidity of each tobacco type should be differently controlled to maintain the same moisture under the same temperature. In the range of 5~25 $^{\circ}C$, the lower temperature showed the higher equilibrium moisture content.

An Experimental Study on Vapor-Liquid Equilibria of HFC and HC Refrigerant Mixtures (탄화수소 및 불화탄화수소 혼합냉매의 기상-액상 평형에 관한 실험적 연구)

  • 강병복;김민수;김영일
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.12 no.11
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    • pp.1031-1037
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    • 2000
  • Isothermal vapor-liquid equilibrium(VLE) data have been obtained for the systems of propane(R290)+1,1,1,2-tetrafluoroethane(R134a) and 1,1,1,2-tetrafluoroethane(R134a)+isobutane(R60A) in the temperature range of 253.15 to 323.15K. Experiments were performed in a circulation type apparatus by injecting vapor through liquid pool using a magnetic pump. Both systems form azeotropes in the temperature range of this study. The experimental results were estimated with the Peng-Robinson equation of state. When the temperature-dependent binary interaction parameter was used in the Peng-Robinson equation of state, the absolute average deviation of the measured bubble point pressures from the values correlated by the Peng-Robinson equation was 0.65% and 0.78% for R290+R134a and R134a+600a, respectively. Azeotropic compositions for both systems were presented.

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Salt-Induced Protein Precipitation in Aqueous Solution: Single and Binary Protein Systems

  • Kim, Sang-Gon;Bae, Young-Chan
    • Macromolecular Research
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    • v.11 no.1
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    • pp.53-61
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    • 2003
  • A molecular-thermodynamic model is developed for the salt-induced protein precipitation. The protein molecules interact through four intermolecular potentials. An equation of state is derived based on the statistical mechanical perturbation theory with the modified Chiew's equation for the fluid phase, Young's equation for the solid phase as the reference system and a perturbation based on the protein-protein effective two body potential. The equation of state provides an expression for the chemical potential of the protein. In a single protein system, the phase separation is represented by fluid-fluid equilibria. The precipitation behaviors are simulated with the partition coefficient at various salt concentrations and degree of pre-aggregation effect for the protein particles. In a binary protein system, we regard the system as a fluid-solid phase equilibrium. At equilibrium, we compute the reduced osmotic pressure-composition diagram in the diverse protein size difference and salt concentrations.