• Title, Summary, Keyword: analytical solutions

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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.

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.

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.

Parametric Analysis and Experimental Testing of Radial Flux Type Synchronous Permanent Magnet Coupling Based on Analytical Torque Calculations

  • Kang, Han-Bit;Choi, Jang-Young
    • Journal of Electrical Engineering and Technology
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    • v.9 no.3
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    • pp.926-931
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    • 2014
  • This paper presents the torque calculation and parametric analysis of synchronous permanent magnet couplings (SPMCs). Based on a magnetic vector potential, we obtained the analytical magnetic field solutions produced by permanent magnets (PMs). Then, the analytical solutions for a magnetic torque were obtained. All analytical results were extensively validated with the non-linear a two-dimensional (2D) finite element analysis (FEA). In particular, test results such as torque measurements are presented that confirm the analysis. Finally, using the derived analytical magnetic torque solutions, we carried out a parametric analysis to determine the influence of the design parameters on the SPMC's behavior.

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.

A Theoretical Study on the Analytical Solutions for Laterally Loaded Pile (횡방향 하중을 받는 말뚝의 해석해에 대한 이론적 고찰)

  • Lee, Seung-Hyun
    • Journal of the Korean Society of Hazard Mitigation
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    • v.11 no.3
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    • pp.111-116
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    • 2011
  • Analytical solutions for laterally loaded piles were derived. Critical pile length which can be considered as the length for behaving as long pile was investigated varying with densities of sandy soils. Lateral behaviors obtained from analytical solution and numerical solution were also investigated. Non-dimensional critical pile lengths obtained from analytical solutions for three types of pile head boundary conditions were 2.3~3.2. By comparing analytical solutions with numerical solutions, distribution of pile deflection and that of moment were similar and it can be seen that pile head deflection obtained by analytical method is conservative. And the values of moments were not too different between analytical solution and numerical solution.

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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Brief and accurate analytical approximations to nonlinear static response of curled cantilever micro beams

  • Sun, Youhong;Yu, Yongping;Liu, Baochang
    • Structural Engineering and Mechanics
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    • v.56 no.3
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    • pp.461-472
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    • 2015
  • In this paper, the nonlinear static response of curled cantilever beam actuators subjected to the one-sided electrostatic field is focused on. By assuming the deflection function of electrostatically actuated beam, analytical approximate solutions are established via using Galerkin method to solve the equilibrium equation. The Pull-In voltages which determine the stability of the curled beam actuators are also obtained. These approximate solutions show excellent agreements with numerical solutions obtained by the shooting method and the experimental data for a wide range of beam length. Expressions of these analytical approximate solutions are brief and could easily be used to derive the effects of various physical parameters on MEMS structures.