• Title/Summary/Keyword: Algebraic Equation

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Study of the Secondary Flow Effect on the Turbulent Flow Characteristics in Fuel Rod Bundles (핵연료봉 주위의 난류 유동장 특성에 미치는 이차 유동의 영향에 대한 연구)

  • Lee, Kye-Bock;Jang, Ho-Cheol;Lee, Sang-Keun
    • Nuclear Engineering and Technology
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    • v.26 no.3
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    • pp.345-354
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    • 1994
  • Numerical Predictions including secondary flows have been Performed for fully developed turbulent single-phase rod bundle flows. The k-$\varepsilon$ turbulence model(two equation model) for the isotropic eddy viscosity, together with an algebraic stress model for generating secondary velocities, enabled the prediction of mean axial velocities, secondary velocities, and turbulent kinetic energy and turbulent stresses. Comparisons with experiment hate shown that the influence of secondary motion on mean flow and turbulence is dearly evident. The convective transport effects of secondary flow on the velocity field have been identified.

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An Acoustic Analysis of Mufflers with a Concentric Extended Pipe (동심 연장관형 소음기의 음향해석)

  • Lee, Jun-Shin;Lee, Jeong-Guon
    • The Journal of the Acoustical Society of Korea
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    • v.14 no.1
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    • pp.108-114
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    • 1995
  • Cylindrical chamber mufflers with an extended inlet or outlet are extensively used in many application fields to reduce the propagated noise in ducts. The basic attenuation effectivencess in the low frequency region can be explained by the reactive wave action inside the expansion chamber associated with the geometric configurations of the inlet and outlet locations, and the area expansion of the jacket. In this study, an acoustic analysis is carried out for a concentric extended pipe inserted into a simple expansion chamber. An algebraic equation is derived by using the eigenfuction expansion and orthogonality principle in which the acoustic pressures and particle velocities defined on each subdivided surface are expressed by the separable coordinates. By using the proposed analytical method, transmission losses are predicted for several configurations of the concentric extended systems and they agree very well with experimental results.

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A Study on the Robust Compensator of An Inverted Pendulum Using $H_{\infty}$ Optimal Control Theory ($H_{\infty}$ 최적제어 이론을 이용한 도립진자의 견실한 보상기 설계에 관한 연구)

  • 김대현;정규홍;이석재;이교일
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.213-218
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    • 1991
  • A new model which contains the dynamics of the motor system and the kinematics of the timing belt system is derived for an inverted pendulum system in FAPA Lab. Generalized standard compensator configuration(SCC) which contains the variable design parameters Kl, K2, .., K5 is proposed so that any desired design specification can be achieved. The robust controller which has robust property against the influence of sensor noise, system parameter variation and model uncertainty is designed minimizing the H$_{\infty}$-norm of transfer function from exogenous input to controlled output. The method of solving the two Riccati equations in state space and determining the controller uses on iteration method where the unique stabilizing solution to two algebraic Riccati equation must be positive definite and the spectral radius of their product less than .gamma.$^{2}$. Some cases are derived by varying the design parameter for simulation on a digital computer and experimenting the H$_{\infty}$- controller on an analog computer. The design parameters of controller which satisfies the desired control specification is selected on the basis of the simulation result and experimenting. The reasonableness and validity of the simulation and the robustness of the controller is established.d.

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A new and simple analytical approach to determining the natural frequencies of framed tube structures

  • Mohammadnejad, Mehrdad;Kazemi, Hasan Haji
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.111-120
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    • 2018
  • This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

A Numerical Study of Shock Wave/Boundary Layer Interaction in a Supersonic Compressor Cascade

  • Song, Dong-Joo;Hwang, Hyun-Chul;Kim, Young-In
    • Journal of Mechanical Science and Technology
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    • v.15 no.3
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    • pp.366-373
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    • 2001
  • A numerical analysis of shock wave/boundary layer interaction in transonic/supersonic axial flow compressor cascade has been performed by using a characteristics upwind Navier-Stokes method with various turbulence models. Two equation turbulence models were applied to transonic/supersonic flows over a NACA 0012 airfoil. The results are superion to those from an algebraic turbulence model. High order TVD schemes predicted shock wave/boundary layer interactions reasonably well. However, the prediction of SWBLI depends more on turbulence models than high order schemes. In a supersonic axial flow cascade at M=1.59 and exit/inlet static pressure ratio of 2.21, k-$\omega$ and Shear Stress Transport (SST) models were numerically stables. However, the k-$\omega$ model predicted thicker shock waves in the flow passage. Losses due to shock/shock and shock/boundary layer interactions in transonic/supersonic compressor flowfields can be higher losses than viscous losses due to flow separation and viscous dissipation.

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Derivation of New Box Model to Analyze the Air Pollution Trends in a Metropolitan Area (대도시 대기오염 추세 분석을 위한 새로운 박스모델의 유도)

  • Kim Seogcheol;Joh Seunghun
    • Journal of Korean Society for Atmospheric Environment
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    • v.21 no.3
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    • pp.377-397
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    • 2005
  • A new box model is proposed to describe the dynamic trend of the spatially averaged concentrations of pollutants over a large urban area such as metropolitan Seoul. Being averaged temporally and spatially over a thresh-hold scales, the dynamics of the pollutant concentration becomes simple enough that the governing equation can be expressed in an explicit algebraic form as a function of several meteorological factors and the pollutant emission rate. The single most important meteorological factor is the wind speed dominating the daily variations of the pollutant concentrations. Given the meteorological data from the surface station in the metropolitan Seoul, the model concentration shows excellent agreement with observations from January 1, 1990 to December 31, 2000: the modeling uncertainty, for example, of $NO_2$ concentrations, defined as mean differences between the model concentrations and observations is $16\%$ of the model concentrations. Even for $PM_{10}$ of which secondary sources are considered to be very important and simple box model is irrelevant to, the model performance turns out good, modeling uncertainty being about $32\%$.

Development of an Effective Method for Extracting Eigenvalues of Arbitrarily Shaped Acoustic Cavities (임의 형상 음향 공동의 효율적인 고유치 해석 기법 개발)

  • Kang, S.W.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2011.10a
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    • pp.124-129
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    • 2011
  • An improved NDIF method is introduced to efficiently extract eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods (FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn't take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

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Development of an Improved NDIF Method for Efficiently Extracting Eigenvalues and Eigenmodes of Arbitrarily Shaped Acoustic Cavities (임의 형상 음향 공동의 효율적인 고유치 및 고유모드 추출을 위한 개선된 NDIF법 개발)

  • Kang, S.W.;Yon, J.I.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.10
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    • pp.960-966
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    • 2011
  • An improved NDIF method is introduced to efficiently extract eigenvalues and eigenmodes of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn's take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues and mode shapes can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

Design of a Low-Order Sensorless Controller by Robust H∞ Control for Boost Converters

  • Li, Xutao;Chen, Minjie;Shinohara, Hirofumi;Yoshihara, Tsutomu
    • Journal of Power Electronics
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    • v.16 no.3
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    • pp.1025-1035
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    • 2016
  • Luenberger observer (LO)-based sensorless multi-loop control of a converter requires an iterative trial-and-error design process, considering that many parameters should be determined, and loop gains are indirectly related to the closed-loop characteristics. Robust H∞ control adopts a compact sensorless controller. The algebraic Riccati equation (ARE)-based and linear matrix inequality (LMI)-based H∞ approaches need an exhaustive procedure, particularly for a low-order controller. Therefore, in this study, a novel robust H∞ synthesis approach is proposed to design a low-order sensorless controller for boost converters, which need not solve any ARE or LMI, and to parameterize the controller by an adjustable parameter behaving like a "knob" on the closed-loop characteristics. Simulation results show the straightforward closed-loop characteristics evaluation and better dynamic performance by the proposed H∞ approach, compared with the LO-based sensorless multi-loop control. Practical experiments on a digital processor confirmed the simulation results.

A TWO-DIMENSIONAL FINITE VOLUME METHOD FOR TRANSIENT SIMULATION OF TIME- AND SCALE-DEPENDENT TRANSPORT IN HETEROGENEOUS AQUIFER SYSTEMS

  • Liu, F.;Turner, I.;Ahn, V.;Su, N.
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.215-241
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    • 2003
  • In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.