• Title/Summary/Keyword: 오일러 방정식

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Development of 2DH hydrodynamic and scalar transport model based on hybrid finite volume/finite difference method (하이브리드 FVM/FDM 기반의 2차원 흐름 및 스칼라 이송 모형 개발)

  • Hwang, Sooncheol;Son, Sangyoung
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.105-105
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    • 2021
  • 본 연구에서는 2차원 비선형 천수모형과 수심평균된 스칼라 이송모형을 해석하는 수치모형에 대해 기술하였다. 수치모형의 정확성을 보장함과 동시에 안정성을 높이기 위해 유한체적법, 플럭스 재구성 및 minmod 제한자를 사용하였다. 비선형 천수방정식의 이송항과 바닥 경사항은 계산된 수심의 양수 보존과 흐름의 정상 상태를 보장하기 위한 second order well-balanced positivity preserving central-upwind method를 이용하여 수치적으로 이산화되었다. 마찬가지로, 이송-확산 방정식 내 이송항은 동일한 2차 풍상차분법을 통해 수치적으로 풀이하였다. 격자점 경계면에서의 불연속으로 인한 수치진동을 방지하기 위해 이송항의 계산에 포함된 보존항의 차이로 인해 발생하는 스칼라의 수치확산을 최소화하기 위해 무차원의 비소산함수를 도입하였다. 또한, 확산항은 유한차분법을 이용하여 이산화하였다. 제안된 수치모형은 시간미분항의 계산을 위해 오일러 기법을 적용하여 계산된 수심 및 스칼라의 양수 보존여부와 함께 정지된 흐름의 정상 상태의 보존여부를 확인하였다. 제안된 수치모형의 해석 정확성을 평가하기 위해 1, 2차원 공간 내 다양한 흐름 조건에서의 해석해를 이용한 3개의 벤치마크 테스트를 수행하였다. 평균 제곱근 오차(Root Mean Squared Error, RMSE)를 산정하여 수치모형의 성능을 정량적으로 평가하였으며, 비소산함수를 적용함에 따라 스칼라의 수치확산이 감소하게 되었음을 확인하였다. 또한, 세 차례의 벤치마크 테스트 결과는 공통적으로 수치모형에 의해 계산된 결과값이 비소산함수를 고려함에 따라 해석해와 잘 일치함을 확인하였다.

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Dynamic Elastic Constants of Composite Material using Resonance Frequencies, Euler and Timoshenko Beam Equations (공진주파수, 오일러 티모센코 빔 방정식을 이용한 복합재료의 동적탄성계수 측정에 관한 연구)

  • Lee, Jae-Hyeok;Park, Se-Man;Kim, Hyeong-Sam
    • Korean Journal of Materials Research
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    • v.9 no.7
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    • pp.670-674
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    • 1999
  • Accurate measurements of elastic constants are important from the view points of both science and engineering. The measurement can be viewed from scientific principle as a service tools for analyzing and improving the understanding of the nature of bondings between atoms and between ions. Also, from engineering perspective it would became an important factor to be definitely considered for the design of machinery equipments. In this investigation, two dynamic experimental methods of vibrations (acoustic method and Impulse technique method) are utilized and the results from the both methods are compared to obtain elastic constants data with a high degree of accuracy. The resonance frequencies obtained from the two methods are applied to both Euler and Timoshenko beam equations respectively, to determine the sources for possible differences.

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The Control of Flexible Robot Arm using Adaptive Control Theory (적응제어 이론을 이용한 유연한 로봇팔의 제어)

  • Han, Jong-Kil
    • The Journal of the Korea institute of electronic communication sciences
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    • v.7 no.5
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    • pp.1139-1144
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    • 2012
  • The ration of payload to weight of industrial robot amounts form 1:10 to 1:30. Compared with man who have a ration of 3:1, it is very low. One of the goals for the next generation of robots will be a ration. This might be possible only by developing lightweight robots. When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}-2C$ is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed by using Lyapunov stability theory. We propose deterministic and adaptive control laws for two link flexible arm, and the validity of the proposed control scheme is shown in computer simulation for two-link flexible arm.

Numerical Simulation of Shallow Water Flow Using Multi-dimensional Limiting Process (MLP) (MLP기법을 적용한 천수흐름의 수치모의)

  • An, Hyunuk;Yu, Soonyoung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.2B
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    • pp.123-130
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    • 2012
  • MLP (Multi dimensional Limiting Process) is implemented to simulate shallow water flows, and its performance over conventional TVD limiters in multidimensional flows is verified through several numerical simulations. MLP was developed to control oscillations for multi-dimensional compressible flows and proved to improve accuracy, efficiency and robustness in compressible flows. In this study, we applies MLP to modeling shallow water equations(SWEs) given that the SWEs are amenable to be solved using the large range of numerical methods developed to deal with compressible flows and MLP has been yet used for SWEs. Simulation results through the benchmark tests show that MLP has favorable features such as numerical oscillation control and convergence behaviors comparable to the conventional limiters. Both numerical accuracy and stability are improved in multi-dimensional discontinuous flows.

Velocities Induced by Stator Arrays in a Class of Shear Flows (전단 유동중에 놓인 스테이터에 의한 유기속도)

  • E.D.,Park
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.2
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    • pp.13-20
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    • 1990
  • The interaction of the flows induced by stator blades with a ship-like wake is discussed to obtain the flow components of each with and without radial shear. The flow induced by stator blades is modeled by lifting line theory and the shear is taken to be provided by the radial gradient of the peripheral mean axial flow approximated by a logarithmic function of radius for a class of vessels. And the theory is based on the linearized Euler equations in the absence of viscosity. The results show that shear effects are relatively large at inner radii and the distribution of blade pitch angles is most effective in reducing non-uniformity.

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Computational analysis of coupled fluid-structure for a rotor blade in hover (정지 비행하는 로터 블레이드의 전산 유체-구조 결합 해석)

  • Kim, Hae-Dong
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.12
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    • pp.1139-1145
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    • 2008
  • numerical study on the coupled fluid-structure for a rotor blade in hover was conducted. Computational fluid dynamics code with enhanced wake-capturing capability is coupled with a simple structural dynamics code based on Euler-Bernoulli's beam equation. The numerical results show a reasonable blade structural deformation and aerodynamic characteristics.

Theoretical Analysis of Carbon Nanotube Actuators (탄소나노튜브 작동기의 이론적 해석)

  • Park C.H.;Park H.C.;So H.K.;Jung B.B.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2005.06a
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    • pp.927-931
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    • 2005
  • Carbon nanotube actuator, working under physical conditions (in aqueous solution) and converting electrical energy into mechanical energy directly, can be a good substitute for artificial muscle. The carbon nanotube actuator simulated in this paper is an isotropic cantilever type with an adhesive tape which is sandwiched between two single-walled carbon nanotubes. For predicting the static and dynamic characteristic parameters, the analytical model for a 3 layer bimorph carbon nanotube actuator is developed by using Euler-Bernoulli beam theory. The governing equation and boundary conditions are derived from energy principles. The induced displacements of the theoretical model are presented in order to investigate the performance of the carbon nanotube actuator with different control voltages. The developed model presents invaluable means for designing and predicting the performance of carbon nanotube actuator that can be used in artificial muscle applications.

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A Computational Study of the Aerodynamics of a Projectile Launched from a Ballistic Range (Ballistic Range로 부터 발사되는 Projectile 공기역학에 관한 수치해석적 연구)

  • Jun Gu-Sik;Lim Chae-Min;Kim Heuy-Dong;Lee Jeong-Min
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2006.05a
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    • pp.371-375
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    • 2006
  • A computational work has been performed to investigate the aerodynamics of a projectile which is launched from a ballistic range. A moving coordinate method for a multi-domain technique is employed to simulate unsteady projectile flows with a moving boundary. The variation of a virtual mass and the shape of projectile are added to the axisymmetric unsteady Euler equation systems. The present computational results properly predict the velocity, acceleration, drag histories and the major flow characteristics of the projectile.

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Performance analysis of mixed-flow fans considering the low flow characteristics (저유량 특성을 고려한 사류 송풍기의 성능 해석)

  • Oh, Hyoung Woo;Kim, Kwang-Yong
    • 유체기계공업학회:학술대회논문집
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    • 2000.12a
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    • pp.110-115
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    • 2000
  • The mean streamline analysis using the empirical loss correlations has been developed for performance prediction of industrial mixed-flow fan impellers in the present study. New simple, but effective, models for the additional Euler input work characteristic and an internal recirculation loss due to internal flow reversal under the low flowrate conditions are proposed in this paper. Comparison of overall performance predictions with six sets of test data of mixed-flow fans is accomplished to demonstrate the accuracy of the proposed models. Predicted performance curves by the present set of loss models agree fairly well with experimental data for a variety of mixed-flow fan impellers over the entire operating conditions. The prediction method presented herein can be used efficiently in the conceptual design phase of mixed-flow fan impellers.

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Historical Background for Derivation of the Differential Equation mẍ+kx = f(t) (미분방정식 mẍ + kx = f(t)의 역사적 유도배경)

  • Park, Bo-Yong
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.4
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    • pp.315-324
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    • 2011
  • This paper presents a historical study on the derivation of the differential equation of motion for the single-degree-of-freedom m-k system with the harmonic excitation. It was Euler for the first time in the history of vibration theory who tackled the equation of motion for that system analytically, then gave the solution of the free vibration and described the resonance phenomena of the forced vibration in his famous paper E126 of 1739. As a result of the chronological progress in mechanics like pendulum condition from Galileo to Euler, the author asserts two conjectures that Euler could apply to obtain the equation of motion at that time.