• Title/Summary/Keyword: Peclet Number

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Comparison of the Results of Finite Difference Method in One-Dimensional Advection-Dispersion Equation (유한차분 모형에 의한 일차원 이송-확산방정식 계산결과의 비교)

  • 이희영;이재철
    • Water for future
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    • v.28 no.4
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    • pp.125-136
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    • 1995
  • ELM, a characteristic line based method, was applied to advection-dispersion equation, and the results obtained were compared with those of Eulerian schemes(Stone-Brian and QUICKEST). The calculation methods consisted of Lagrangian interpolation scheme and cubic spline interpolation scheme for the advection calculation, and the Crank-Nicholson scheme for the dispersion calculation. The results of numerical methods were as follows: (1) for Gaussian hill: ELM, using Lagrangian interpolation scheme, gave the most accurate computational result, ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical damping for Peclet number 50. Stone-Brian scheme gave phase shift introduced in the numerical solution for Peclet number 10 and 50. (2) for advanced front: All schemes gave accurate computational results for Peclet number 1 and 4. ELM, Lagrangian interpolation scheme, and Stone,Brian scheme gave dissipation error and ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical oscillation for Peclet number 50.

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An Experimental Study on Enhancement of the Filter Efficiency by the Image Effect of Charged Particle (대전된 입자의 영상효과에 의한 필터효율 향상에 관한 실험적 연구)

  • Lee, Chang-Sun;Jeong, Hae-Young;Kim, Sang-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.24 no.6
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    • pp.760-768
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    • 2000
  • Filter efficiency of electrically charged particle in uncharged fibrous filter was measured. In previous studies, the effect of charged particle on filter efficiency was investigated but there was difficulty in measuring of image effect that is appeared at the charged small particle. We could easily measure the image effect with charging small particles by photoelectric charging. The spark discharge aerosol generator and a differential mobility analyzer (DMA) were used to generate sub-micron monodisperse particles (${\leq}200$ nm). The generated particles were charged in photoelectric charging process using ultraviolet lamp and electric field. The filter efficiency of the charged particles, classified by another DMA, was measured in filter tester using a condensation nucleus counter (CNC) as function of particle diameter, particle charge and airflow velocity. It is shown that the filter efficiency increases with increasing charge number of the particle and is affected by particle size and flow velocity. Single fiber filter efficiency mainly depends on image force parameter and peclet number. The peclet number was not considered at previous other papers. We propose a modi fied experimental correlation as function of image force parameter and peclet number.

Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe(I) Analytical approach- thermally fully developed flow and thermally develping flow(the Graetz problem extended) (원관내 Bingham Plastic의 층류 대류 열전달(1)해석적 연구-완전발달유동과 온도분포 발달유동(확장된 그래츠문제))

  • Min, Tae-Gi;Yu, Jeong-Yeol;Choe, Hae-Chun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.12
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    • pp.3991-4002
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    • 1996
  • Thermally fully developed and thermally developing laminar flows of a Bingham plastic in a circular pipe have been studied analytically. For thermally fully developed flow, the Nusselt numbers and temperature profiles are presented in terms of the yield stress and Peclet number, proposing a correlation formula between the Nusselt number and the Peclet number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet and Brinkman numbers on the Nusselt number are discussed.

A Numerical Study on Characteristics of Solute Transport in a Rough Single Fracture with Spatial Correlation Length and Effect of Effective Normal Stress (공간적 상관길이와 유효수직응력의 효과에 따른 거친 단일 균열내의 용질이동특성에 관한 수치적 연구)

  • Jeong, Woochang
    • Journal of the Korean GEO-environmental Society
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    • v.10 no.1
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    • pp.5-14
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    • 2009
  • This study is to analyze numerically the spatial behaviors of the solute transport in a spatially correlated variable-aperture fracture under the effective normal stress conditions. Numerical results show that the solute transport in a fracture is strongly affected by the spatial correlation length of apertures and applied effective normal stress. According to increasing spatial correlation length, the mean residence time of solute is decreased and the tortuosity and Peclet number (is a dimensionless number relating the rate of advection of a flow to its rate of diffusion) is also decreased. These results mean that the geometry of the aperture distribution is favorable to the solute transport as the spatial correlation length is increased. However, according to the applied effective normal stress is increased, the mean residence time and tortuosity have a tendency to increase but the Peclet number is decreased. The main reason that the Peclet number is decreased, is that the solute is displaced by one or two channels with relatively higher local flow rate due to the increment of contact areas by increasing effective normal stress. Moreover, based on numerical results of the solute transport in this study, the exponential-type correlation formulae between the mean residence time and the effective normal stress are proposed.

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Comparison of ELLAM and LEZOOMPC for Developing an Efficient Modeling Technique (효율적인 수치 모델링 기법 개발을 위한 ELLAM과 LEZOOMPC의 비교분석)

  • Suk Hee-Jun
    • Journal of Soil and Groundwater Environment
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    • v.11 no.1
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    • pp.37-44
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    • 2006
  • This study summarizes advantages and disadvantages of numerical methods and compares ELLAM and LEZOOMPC to develop an efficient numerical modeling technique on contaminant transport. Eulerian-Lagrangian method and Eulerian method are commonly used numerical techniques. However Eulerian-Lagrangian method does not conserve mass globally and fails to treat boundary in a straightforward manner. Also, Eulerian method has restrictions on the size of Courant number and mesh Peclet number because of time truncation error. ELLAM (Eulerian Lagrangian Localized Adjoint Method) which has been popularly used for past 10 years in numerical modeling, is known for overcoming these numerical problems of Eulerian-Lagrangian method and Eulerian method. However, this study investigates advantages and disadvantages of ELLAM and suggests a change for the better. To figure out the disadvantages of ELLAM, the results of ELLAM, LEZOOMPC (Lagrangian-Eulerian ZOOMing Peak and valley Capturing), and visual MODFLOW are compared for four examples having different mesh Peclet numbers. The result of ELLAM generates numerical oscillation at infinite of mesh Peclet number, but that of LEZOOMPC yields accurate simulations. The simulation results suggest that the numerical error of ELLAM could be alleviated by adopting some schemes in LEZOOMPC. In other words, the numerical model which combines ELLAM with backward particle tracking, forward particle tracking, adaptively local zooming, and peak/valley capturing of LEZOOMPC can be developed for not only overcoming the numerical error of ELLAM, but also keeping the numerical advantage of ELLAM.

Analysis of microstructural evolutions during advanced ceramics processing : I. Phase behavior of colloidal dispersion (세라믹 제조시 미세구조 변화의 해석 : I. 콜로이드 분산의 상거동)

  • Kim, Hern
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.7 no.4
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    • pp.599-609
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    • 1997
  • The phase behavior and dynamics of colloid suspensions and the resulting structures and properties of powder compacts were examined by a computer experimental method for cooperative packing processes. A wide range of properties and process conditions such as arbitrary particle size, medium densities, field strength, and temperature could be examined using the Peclet number (Pe). We demonstrated that an optimum range of Peclet number for the ordering of sediments was present and that the phenomena related to the ordering such as the onset of crystallization, the phase behavior, etc. strongly depend on process conditions. The present work appears to be useful to design the processing method of ceramic spherical submicron powders for the preparation of high-density green compacts.

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Thermo-hydraulic Modeling in Fault Zones (단층대에서의 열-수리적 거동 모델링)

  • Lee, Young-Min;Kim, Jong-Chan;Koo, Min-Ho;Keehm, Young-Seuk
    • Economic and Environmental Geology
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    • v.42 no.6
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    • pp.609-618
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    • 2009
  • High permeable faults are important geological structures for fluid flow, energy, and solute transport. Therefore, high permeable faults play an important role in the formation of hydrothermal fluid (or hot spring), high heat flow, and hydrothermal ore deposits. We conducted 2-D coupled thermal and hydraulic modeling to examine thermohydraulic behavior in fault zones with various permeabilities and geometric conditions. The results indicate discharge temperature in fault zones increases with increasing fault permeability. In addition, discharge temperature in fault zones is linearly correlated with Peclet number ($R^2=0.98$). If Peclet number is greater than 1, discharge temperature in fault zones can be higher than $32^{\circ}C$. In this case, convection is dominant against conduction for the heat transfer in fault zones.

Dynamic Characteristics Analysis Considering the Effect of the Vortexes of Flux in a LIM for Railway Propulsion System (맴돌이 자속의 영향을 고려한 철도추진용 선형유도전동기의 동특성 연구)

  • Park, Chan-Bae;Lee, Byung-Song;Lee, Ju
    • Journal of the Korean Society for Railway
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    • v.12 no.3
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    • pp.437-442
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    • 2009
  • In the case of a Linear Induction Motor (LIM), numerical analysis method like Finite Element Method (FEM) has been mainly used to analyze the travelling magnetic field problem which includes the velocity-induced electromotive force. If the problem including the velocity-induced electromotive force is analyzed by FEM using the Galerkin method, the solution can be oscillated according to the Peclet Number, which is determined by conductivity, permeability, moving velocity and size of mesh. Consequently, the accuracy of the solution can be low and the vortexes of flux can be occurred at the secondary back-iron. These vortexes of the flux occurred at the secondary back-iron does not exist physically, but it can be occurred in the analysis. In this case, the vortexes of the flux can be generally removed by using Up-Wind method which is impossible to apply a conventional S/W tool (Maxwell 2D). Therefore, in this paper, authors examined the vortexes of the flux occurred at the secondary back-iron of the LIM according to variations of the Peclet Number, and analyzed whether these vortexes of the flux affect on the dynamic force characteristics of the LIM or not.

A Study on the Transport of Soil Contaminant (A Development of FDM Model for 3-D Advection-Diffusion Equation with Decay Term) (토양 오염원의 이동에 관한 연구 (감쇠항이 있는 3차원 이송-확산 방정식의 수치모형 개발))

  • Kim, Sang-Jun
    • Journal of Korea Water Resources Association
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    • v.45 no.2
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    • pp.179-189
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    • 2012
  • To simulate the transport of pollutant, a numeric model for the advection-diffusion equation with the decay term is developed. This is finite-difference model using the implicit method (with the weight factor ${\alpha}$) and Gauss-Seidel SOR(successive over-relaxation). This model is compared to the analytical solutions (of simpler dimensional or boundary conditions), and in the condition of Peclet number < 5~20, the result shows stable condition, and Crank-Nicolson method (${\alpha}$=0.5) shows the more accurate results than fully-implicit method (${\alpha}$=1). The mass of advection, diffusion and decay is calculated and the error of mass balance is less than 3%. This model can evaluate the 3-D concentrations of the advection-diffusion and decay problems, but this model uses only the finite-difference method with the fixd grid system, so it can be effectively used in the problems with small Peclet numbers like the pollutant transport in groundwater.

Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

  • Jeong Ho-Eyoul;Jeong Jae-Tack
    • Journal of Mechanical Science and Technology
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    • v.20 no.1
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    • pp.158-166
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    • 2006
  • Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.