• Title/Summary/Keyword: analytical solutions

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Comparison of a Groundwater Simulation-Optimization Numerical Model with the Analytical Solutions (해안지하수개발 최적화수치모델과 해석해의 비교연구)

  • Shi, Lei;Cui, Lei;Lee, Chan-Jong;Park, Nam-Sik
    • Proceedings of the Korea Water Resources Association Conference
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    • pp.905-908
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    • 2009
  • In the management of groundwater in coastal areas, saltwater intrusion associated with extensive groundwater pumping, is an important problem. The groundwater optimization model is an advanced method to study the aquifer and decide the optimal pumping rates or optimal well locations. Cheng and Park gave the analytical solutions to the optimization problems basing on Strack's analytical solution. However, the analytical solutions have some limitations of the property of aquifer, boundary conditions, and so on. A simulation-optimization numerical method presented in this study can deal with non-homogenous aquifers and various complex boundary conditions. This simulation-optimization model includes the sharp interface solution which solves the same governing equation with Strack's analytical solution, therefore, the freshwater head and saltwater thickness should be in the same conditions, that can lead to the comparable results in optimal pumping rates and optimal well locations for both of the solutions. It is noticed that the analytical solutions can only be applied on the infinite domain aquifer, while it is impossible to get a numerical model with infinite domain. To compare the numerical model with the analytical solutions, calculation of the equivalent boundary flux was planted into the numerical model so that the numerical model can have the same conditions in steady state with analytical solutions.

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Eddy-Current Loss Analysis in Rotor of Surface-Mounted Permanent Magnet Machines Using Analytical Method (해석적 방법을 이용한 표면부착형 영구자석 기기의 회전자 와전류 손실해석)

  • Choi, Jang-Young;Choi, Ji-Hwan;Jang, Seok-Myeong;Cho, Han-Wook;Lee, Sung-Ho
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.8
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    • pp.1115-1122
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    • 2012
  • This paper analyzes eddy-current loss induced in magnets of surface-mounted permanent magnet (SPM) machines by using an analytical method such as a space harmonic method. First, on the basis of a two-dimensional (2D) polar coordinate system and a magnetic vector potential, the analytical solutions for the flux density produced by armature winding current are obtained. By using derived field solutions, the analytical solutions for eddy current density distribution are also obtained. Finally, analytical solutions for eddy current loss induced in rotor magnets are derived by using equivalent electrical resistance calculated from magnet volume and analytical solutions for eddy-current density distribution. In particular, the influence of time harmonics in armature current on the eddy current loss is fully investigated and discussed. All analytical results are validated extensively by finite element analysis (FEA).

Analytical Prediction for Electromagnetic Characteristics of Tubular Linear Actuator with Halbach Array Using Transfer Relations

  • Jang, Seok-Myeong;Choi, Jang-Young
    • Journal of Electrical Engineering and Technology
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    • v.2 no.2
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    • pp.221-230
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    • 2007
  • This paper deals with analytical prediction for electromagnetic characteristics of a tubular linear actuator with Halbach array using transfer relations, namely, Melcher's methodology. Using transfer relations derived in terms of magnetic vector potential and a two-dimensional (2-d) cylindrical coordinate system, this paper derives analytical solutions for magnetic vector potential due to permanent magnets (PMs) and stator winding currents. On the basis of these analytical solutions, this paper also achieves analytical solutions for the magnetic fields distribution produced by PMs, stator windings current and axial thrust. The analytical results are validated extensively by finite element (FE) analyses. In particular, test results such as thrust measurements are given to confirm the analysis. Finally, this paper estimates control parameters using analytical solutions and test results such as thrust, back-emf, inductance and resistance measurements.

One-dimensional Analytical Solutions for Diffusion from a Low-permeability Layer (1차원 해석해를 이용한 저투수성 매체에서의 확산에 관한 연구)

  • Jang, Seonggan;Yang, Minjune
    • Economic and Environmental Geology
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    • v.53 no.1
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    • pp.11-21
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    • 2020
  • One-dimensional analytical solutions were used for forward and back diffusion of trichloroethylene (TCE) and tetrachloroethylene (PCE) in a single system with high- and low-permeability layers. Concentration profiles in a low-permeability layer, diffusive fluxes at the interface between the high- and low-permeability layers, and contaminant persistence in the high-permeability layer due to back diffusion were simulated with a comparison of semi-infinite and finite analytical solutions. In order to validate the analytical solutions used in this study, the results of one-dimensional analytical solutions developed by Yang et al. (2015) were compared with Nash-Sutcliffe model efficiency coefficient (NSE). When compared with Yang et al. (2015), the analytical solutions used in this study showed good agreements (NSE = 0.99). When compared with semi-infinite analytical solutions, TCE and PCE concentration profiles in the low-permeability layer, the diffusive fluxes, and the contaminant tailings of the high-permeability layer were underestimated. In order to determine the appropriate analytical solutions based on the effective diffusion coefficient, the thickness of the low-permeability layer, and the diffusion time in the TCE and PCE contaminated site, a term of dimensionless diffusion length (Zd) was used. If the Zd is less than 0.7, the semi-infinite solutions can be used to simulate accurate concentration profiles in low-permeability layers. If the Zd is greater than 0.7, the reliability of simulations may be improved by using the finite solutions.

Review on Analytical Solutions for Slump Flow of Cement Paste (시멘트 페이스트의 슬럼프 유동 모사를 위한 분석적 해의 검토)

  • Yun, Taeyoung
    • International Journal of Highway Engineering
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    • v.18 no.3
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    • pp.21-32
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    • 2016
  • PURPOSES : In this paper, the analytical solutions suggested to simulate the behavior of rheological fluids were rigorously re-derived and investigated for fixed conditions to evaluate the applicability for the solutions on a mini-cone slump test of cement paste. The selected solutions with proper boundary conditions can be used as reference solutions to evaluate the performance of numerical simulation approaches, such as the discrete element method. METHODS : The slump, height, and spread radius for the given boundary and yield stress conditions that are determined by five different analytical solutions are compared. RESULTS : The analytical solution based on fluid mechanics for pure shear flow shows similar results to that for intermediate flow at low yield stresses. The fluid mechanics-based analytical solution resulted in a very similar trend to the geometry-based analytical solution. However, it showed a higher slump at high yield stress and lower slump at low yield stress ranges than the geometry-based analytical model. The analytical solution based on the mini-cone geometry was not significantly affected by the yield criteria, such as von Mises and Tresca. CONCLUSIONS : Even though differences among the analytical solutions in terms of slump and spread radius existed, the difference can be considered insignificant when the solutions were used as reference to evaluate the appropriateness of numerical approaches, such as the discrete element method.

Dynamic Analysis of the Structures under Dynamic Distributed Loads Using Spectral Element Method (스펙트럴요소법을 이용한 동적분포하중을 받는 구조물의 동적해석)

  • Lee, U-Sik;Lee, Jun-Geun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.6
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    • pp.1773-1783
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    • 1996
  • Finite element method(FEM) is one of the most popularly used method analyzing the dynamic behaviors of structures. But unless number of finite elements is large enough, the results from FEM some what different from exact analytical solutions, especially at high frequency range. On the other hand, as the spectral analysis method(SAM) deals directly with the governing equations of a structure, the results from this melthod cannot but be exact regardless of any frequency range. However, the SAM can be applied only to the case where a structure is subjected to the concentrated loads, despite a structure could be unddergone distributed loads more generally. In this paper, therefore, new spectral analysis algorithm is introduced through the spectral element method(SEM), so that it can be applied to anlystructures whether they are subjected to the concentrated loads or to the distributed loads. The results from this new SEM are compared with both the results from FEM and the exact analytical solutions. As expected, the results from new SEM algorithm are found to be almost identical to the exact analytical solutions while those from FEM are not agreed well with the exact analytical solutions as the mode number increases.

One-dimensional nonlinear consolidation behavior of structured soft clay under time-dependent loading

  • Liu, Weizheng;Shi, Zhiguo;Zhang, Junhui;Zhang, Dingwen
    • Geomechanics and Engineering
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    • v.18 no.3
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    • pp.299-313
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    • 2019
  • This research investigated the nonlinear compressibility, permeability, the yielding due to structural degradation and their effects on consolidation behavior of structured soft soils. Based on oedometer and hydraulic conductivity test results of natural and reconstituted soft clays, linear log (1+e) ~ $log\;{\sigma}^{\prime}$ and log (1+e) ~ $log\;k_v$ relationships were developed to capture the variations in compressibility and permeability, and the yield stress ratio (YSR) was introduced to characterize the soil structure of natural soft clay. Semi-analytical solutions for one-dimensional consolidation of soft clay under time-dependent loading incorporating the effects of soil nonlinearity and soil structure were proposed. The semi-analytical solutions were verified against field measurements of a well-documented test embankment and they can give better accuracy in prediction of excess pore pressure compared to the predictions using the existing analytical solutions. Additionally, parametric studies were conducted to analyze the effects of YSR, compression index (${\lambda}_r$ and ${\lambda}_c$), and permeability index (${\eta}_k$) on the consolidation behavior of structured soft clays. The magnitude of the difference between degree of consolidation based on excess pore pressure ($U_p$) and that based on strain ($U_s$) depends on YSR. The parameter ${\lambda}_c/{\eta}_k$ plays a significant role in predicting consolidation behavior.

Analytical Prediction and Experimental Verification of Electromagnetic Performance of a Surface-Mounted Permanent Magnet Motor having a Fractional Slot/Pole Number Combination

  • Hong, Sang-A;Choi, Jang-Young;Jang, Seok-Myeong
    • Journal of Magnetics
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    • v.19 no.1
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    • pp.84-89
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    • 2014
  • This paper presents an analytical prediction and experimental verification of the electromagnetic performance of a parallel magnetized surface-mounted permanent magnet (SPM) motor having a fractional number of slots per pole combination. On the basis of a two-dimensional (2-D) polar coordinate system and a magnetic vector potential, analytical solutions for flux density produced by the permanent magnets (PMs) and stator windings are derived. Then, analytical solutions for back-electromotive force (emf) and electromagnetic torque are derived from these field solutions. The analytical results are thoroughly validated with 2-D nonlinear finite element (FE) analysis results. Finally, the experimental back-emf and electromagnetic torque measurements are presented to test the validity of the analysis.

Quasi-3D analysis of Axial Flux Permanent Magnet Rotating Machines using Space Harmonic Methods (공간고조파법을 이용한 축 자속 영구자석 회전기기의 준(準)-3D 특성 해석)

  • Choi, Jang-Young
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.5
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    • pp.942-948
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    • 2011
  • This paper deals with characteristic analysis of axial flux permanent magnet (AFPM) machines with axially magnetized PM rotor using quasi-3-D analysis modeling. On the basis of magnetic vector potential and a two-dimensional (2-D) polar-coordinate system, the magnetic field solutions due to various PM rotors are obtained. In particular, 3-D problem, that is, the reduction of magnetic fields near outer and inner radius of the PM is solved by introducing a special function for radial position. And then, the analytical solutions for back-emf and torque are also derived from magnetic field solutions. The predictions are shown in good agreement with those obtained from 3-D finite element analyses (FEA). Finally, it can be judged that analytical solutions for electromagnetic quantities presented in this paper are very useful for the AFPM machines in terms of following items : initial design, sensitivity analysis with design parameters, and estimation of control parameters.

Heat Transfer Optimization in a Tube with Circular-Sectored Fins (원관내 부채꼴 휜 주위에서의 열전달 최적화)

  • Yoo, Jae-Wook;Kim, Sung-Jin;Hyun, Jae-Min
    • Proceedings of the KSME Conference
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    • pp.57-64
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    • 2000
  • The present work investigates the heat transfer characteristics for laminar fully developed forced convection in an internally finned tube with axially uniform heat flux and peripherally uniform temperature through analytical models of convection in a porous medium. Using the Brinkman-extended Darcy flow model and the two equation model fur heat transfer, analytical solutions fur fluid flow and heat transfer are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer to validate the porous medium approach. Using the analytical solutions, parameters of engineering importance are identified and their effects on fluid flow and heat transfer are studied. Also, the expression fur total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of the internally finned tubes.

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