• Title/Summary/Keyword: Viscosity Equation

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Scaling law in MHD turbulence small-scale dynamo

  • Park, Kiwan;Ryu, Dongsu
    • The Bulletin of The Korean Astronomical Society
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    • v.39 no.2
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    • pp.74.2-74.2
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    • 2014
  • Magnetohydrodynamics(MHD) dynamo depends on many factors such as viscosity ${\gamma}$, magnetic diffusivity ${\eta}$, magnetic Reynolds number $Re_M$, external driving source, or magnetic Prandtl number $Pr_M$. $Pr_M$, the ratio of ${\gamma}$ to ${\eta}$ (for example, galaxy ${\sim}10^{14}$), plays an important role in small scale dynamo. With the high PrM, conductivity effect becomes very important in small scale regime between the viscous scale ($k_{\gamma}{\sim}Re^{3/4}k_fk_f$:forcing scale) and resistivity scale ($k_{\eta}{\sim}PrM^{1/2}k_{\gamma}$). Since ${\eta}$ is very small, the balance of local energy transport due to the advection term and nonlocal energy transfer decides the magnetic energy spectra. Beyond the viscous scale, the stretched magnetic field (magnetic tension in Lorentz force) transfers the magnetic energy, which is originally from the kinetic energy, back to the kinetic eddies leading to the extension of the viscous scale. This repeated process eventually decides the energy spectrum of the coupled momentum and magnetic induction equation. However, the evolving profile does not follow Kolmogorov's -3/5 law. The spectra of EV (${\sim}k^{-4}$) and EM (${\sim}k^0$ or $k^{-1}$) in high $Pr_M$ have been reported, but our recent simulation results show a little different scaling law ($E_V{\sim}k^{-3}-k^{-4}$, $EM{\sim}k^{-1/2}-k^{-1}$). We show the results and explain the reason.

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Wave Breaking Characteristics due to Shape and Plane Arrangement of the Submerged Breakwaters (잠제 제원 및 평면배치에 따른 쇄파특성)

  • Lee, Woo-Dong;Hur, Dong-Soo;Huh, Jung-Won
    • Journal of Ocean Engineering and Technology
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    • v.24 no.1
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    • pp.116-122
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    • 2010
  • The aim of this study is to examine the effects of shape and plane arrangement of submerged breakwaters on 3-D wave breaking characteristics over them. First, the numerical model, which is able to consider the flow through a porous medium with inertial, laminar, and turbulent resistance terms, i.e. simulate directly WAve Structure Seabed/Sandy beach interaction, and can determine the eddy viscosity with a LES turbulent model in a 3-Dimensional wave field (LES-WASS-3D), has been validated by a comparison with Goda's equation for breaking wave heights. And then, using the numerical results, the wave breaking points over the crest of submerged breakwaters have been examined in relation to the shape and plane arrangement of submerged breakwaters. Moreover, the wave height distribution and upper flow around submerged breakwaters have been also discussed, as well as the distribution of the wave breaking points over the beach.

Prediction and Measurement of Residual Stresses in Injection Molded Parts

  • Kwon, Young-Il;Kang, Tae-Jin;Chung, Kwansoo;Youn, Jae Ryoun
    • Fibers and Polymers
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    • v.2 no.4
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    • pp.203-211
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    • 2001
  • Residual stresses were predicted by a flow analysis in the mold cavity and residual stress distribution in the injection molded product was measured. Flow field was analyzed by the hybrid FEM/FDM method, using the Hele Shaw approximation. The Modified Cross model was used to determine the dependence of the viscosity on the temperature and the shear rate. The specific volume of the polymer melt which varies with the pressure and temperature fields was calculated by the Tait\`s state equation. Flow analysis results such as pressure, temperature, and the location of the liquid-solid interface were used as the input of the stress analysis. In order to calculate more accurate gap-wise temperature field, a coordinate transformation technique was used. The residual stress distribution in the gap-wise temperature field, a coordinate transformation technique was used. The residual stress distribution in the gap-wise direction was predicted in two cases, the free quenching, under the assumption that the shrinkage of the injection molded product occurs within the mold cavity and that the solid polymer is elastic. Effects of the initial flow rate, packing pressure, and mold temperature on the residual stress distribution was discussed. Experimental results were also obtained by the layer removal method for molded polypropylene.

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Analysis of Filling in Injection Molding with Compressibility (압축성을 고려한 사출성형 충전과정에 관한 연구)

  • Han, Kyeong-Hee;Im, Yong-Taek
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.735-745
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    • 1997
  • In this study, the compressibility of resin was considered in filling analysis to account for the possible packing type flow. A numerical simulation program employing a hybrid finite element/finite difference scheme was developed to solve Hele-Shaw flow of the compressible viscous fluid at non-isothermal conditions. To advance the melt front, a control volume approach was adopted. Thin complex 3-D shapes of cavities, runners, and sprues were discretized by employing triangular, cylindrical and/or rectangular strip elements. Mass conservation was applied to each control volume to solve for the pressure distribution. Directly applying a constant mass flow rate at the inlet removes calculation of the apparent pressure boundary conditions, resulting in better simulation condition. The Cross model was used to model viscosity and the Tait equation was employed to represent density as a function of temperature and pressure. The validity of the developed program was verified through comparisons with available data in the literature and the effect of compressibility on the pressure distribution was discussed. To reduce computation time, 1-D and 2-D elements were used instead of applying triangular elements and the numerical results were compared to each other.

Three-Dimensional Transition in the Wake of a Circular Cylinder By Direct Numerical Simulation (DNS에 의한 원주 후류에서의 3차원 천이)

  • Knag, S.J.;Tanahashi, M.;Miyauchi, T.;Mo, J.O.;Lee, Y.H.
    • Proceedings of the KSME Conference
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    • 2001.11b
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    • pp.570-577
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    • 2001
  • Three-dimensional time-dependent flow past a circular cylinder is numerically investigated using direct numerical simulation for Reynolds number 280 and 300. The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. In x-y plane, the convection term is applied by the 5th order upwind scheme and the pressure and viscosity terms are applied by the 4th order central difference. And in spanwise, Navier-Stokes equation is distributed using of Spectral Method. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength about 1.0 diameters at onset (B-mode). Present results of three-dimensional effects of in wake of a circular cylinder is represented with spanwise and streamwise vorticity contours as Reynolds numbers.

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Rheological Characteristics of Thermal Gelatinized Corn Starch Solution (옥수수 전분 호화액의 리올로지 특성)

  • Kim, Ju-Bong;Lee, Shin-Young;Kim, Sung-Kon
    • Korean Journal of Food Science and Technology
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    • v.24 no.1
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    • pp.54-58
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    • 1992
  • The reological properties of commercial corn starch solutions at various concentrations($4{\sim}9%$) and temperatures($30{\sim}60^{\circ}C$) were investigated. The rheological behavior of corn starch solutions was illustrated by Herschel-Bulkley equation and exhibited pseudoplastic behavior with yield stress. The degree of pseudoplasticity of starch solution increased as the starch concentration increased but was independent on temperature. Apparent viscosity and yield stress of starch solutions were exponentially dependent on concentration and temperature. The critical concentrations for sol-gel transition and for the onset of close-packing of the starch granules were $6.22{\sim}6.52%\;and\;2.68{\sim}2.78%$ respectively.

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Analysis of Anisotropic Turbulent Heat Transfer in Nuclear Fuel Bundles (핵연료 집합체내의 비등방성 난류 열전달에 관한 해석적 연구)

  • Kim, Sin;Park, Goon-Cherl
    • Nuclear Engineering and Technology
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    • v.20 no.1
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    • pp.35-46
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    • 1988
  • The prediction of clad surface temperatures is important to the design and the safety anlaysis of nuclear reactor. The accurate prediction requires the detailed knowledge of the flow structure and heat transfer, which is complicate due to anisotropic turbulent phenomena. A two-equation model including anisotropic eddy viscosity model is applied to forecast the velocity distribution. And the temperature field is calculated with uniform wall heat flux. The Galerkin's weighted residual finite element method has been used to calculate the turbulent quantities right up to the wall. The numerical results show good agreement with available data and that turbulence anisotropy strongly affects on the mean flow and thus the temperature field. And Nu-P/D correlation is established for sodium coolant in close-packed equilateral triangular bundle in the P/D range of 1.05 to 1.30.

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Analysis of Secondary Flow Effects on Turbulent Flow in Nuclear Reactor Fuel Rod Bundles (핵연료 집합체 내에서의 이차유동이 난류에 미치는 영향에 대한 해석적 분석)

  • Shon, Jae-Yeong;Park, Goon-Chul
    • Nuclear Engineering and Technology
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    • v.23 no.3
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    • pp.275-284
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    • 1991
  • It is important to predict the main feature of fully developed turbulent secondary flow through infinite triangular arrays of parallel rod bundles. One-equation turbulence model which include anisotropic eddy viscosity model was applied to predict the exact velocity field. For a constant properties, Reynolds equations were solved by the finite element method. Mean axial velocity near the wall is simulated by the law of the wall. The numerical results showed good agreement with avaiable experimental data. The strength of the secondary flow increased with Reynolds number but decreased with rod spacing, P/D (pitch-to-diameter). The secondary flow affects remarkably the distribution of the axial velocity, wall shear stress and turbulent kinetic energy in the closely packed rod array bundles.

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Analysis of the Dynamic Characteristics of a HDD Spindle System Supported by Asymmetrically Grooved Journal Bearings (비대칭 그루브 저널 베어링으로 지지되는 하드디스크 스핀들 시스템의 동특성 해석)

  • 이상훈;김학운;장건희;김철순
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.05a
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    • pp.748-752
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    • 2004
  • Fluid dynamic bearings (FDBs) have been replacing ball bearings of the HDD spindle motor very rapidly. But there are several demerits of HDB, such as high friction torque, variable viscosity of the fluid lubricant depending on operating temperature, low stiffness, and etc. Eccentricity is one of the major parameters which affects the static and dynamic characteristics. As the static eccentricity is larger, the stiffness and the damping coefficients become bigger. But friction torque is relatively unaffected by the static eccentricity. This research proposes a new type of journal bearing with asymmetric journal grooves which results in better dynamic characteristics. The static and dynamic characteristics of the new journal bearing are investigated by solving the Reynolds' equation with FEM, and the transient analysis is performed to predict the dynamic behavior of rotor by solving the equations of motion of a HDD spindle system with Runge-Kutta method. The result shows that the proposed Journal bearings have much bigger stiffness and damping coefficients compared with the conventional symmetric ones. And consequently, it has smaller whirl radius and tilting angle.

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Studies on the Retrogradation Properties of Rice Starch (쌀 전분의 노화 특성에 관한 연구)

  • Lee, Chan
    • The Korean Journal of Food And Nutrition
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    • v.16 no.2
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    • pp.105-110
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    • 2003
  • The effect of varietal differences of rice starches by amylose content and gel consistency on the retrogradation behavior was studied. The gel consistency test, which is designed to detect differences in the texture of cooked rice of varieties that have a similar amylose content, had been turned out to be useful in this study. Both Suwon 232 and San Li Cun had higher amylose content, but were greatly different in gel consistency values. The results showed that setback viscosity of rice flour measured in a Brabender amylograph was significantly affected by amylose content as well as gel consistency. Increase in the rigidity modulus (E) of rice starch gels during storage determined by using Texture analyzer indicated that amylose content was an important factor in terms of hardness development The study of Avrami kinetics of retrogradation showed that time constant of rice starch gels was influenced by amylose content, but not by gel consistency.