• Title/Summary/Keyword: Navier′s Equations of Motion

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Numerical Simulation of Body Motion Using a Composite Grid System (중첩 격자계를 이용한 물체운동의 수치 시뮬레이션)

  • 박종천;전호환;송기종
    • Journal of the Society of Naval Architects of Korea
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    • v.40 no.5
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    • pp.36-42
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    • 2003
  • A CFD simulation technique has been developed to handle the unsteady body motion with large amplitude by use of overlapping multi-block grid system. The three-dimensional, viscous and incompressible flow around body is investigated by solving the Navier-Stokes equations, and the motion of body is represented by moving effect of the grid system. Composite grid system is employed in order to deal with both the body motion with large amplitude and the condition of numerical wave maker in convenience at the same time. The governing equations, Navier-Stokes (N-S) and continuity equations, are discretized by a finite volume method, in the framework of an O-H type boundary-fitted grid system (inner grid system including test model) and a rectangular grid system (outer grid system including simulation equipments for generation of wave environments). If this study, several flow configurations, such as an oscillating cylinder with large KC number, are studied in order to predict and evaluate the hydrodynamic forces. Furthermore, the motion simulation of a Series 60 model advancing in a uniform flow under the condition of enforced roll motion of angle 20$^{\circ}$ is performed in the developed numerical wave tank.

Three-Dimensional Field Equations, Equations of Motion, and Energy Functionals for Thick Shells of Revolution with Arbitrary Curvature and Variable Thickness (임의의 곡률과 변두께를 갖는 두꺼운 축대칭 회전 셸의 3차원적 장방정식, 운동 방정식, 에너지 범함수)

  • 강재훈;이은택;양근혁
    • Journal of KSNVE
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    • v.11 no.1
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    • pp.156-166
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    • 2001
  • This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

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Optimization Design of Cascade with Rotor-Stator Interaction Effects (정익과 동익의 상호작용을 고려한 익렬의 공력 최적 설계)

  • Cho, J, K.;Jung, Y. R.;Park, W. G.
    • 유체기계공업학회:학술대회논문집
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    • 2001.11a
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    • pp.293-299
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    • 2001
  • Since the previous cut-and-try design algorithm require much cost and time, it has recently been concerned the automatic design technique using the CFD and optimum design algorithm. In this study, the Navier-Stokes equations is solved to consider the more detail viscous flow informations of cascade interaction and O-H multiblock grid system is generated to impose an accurate boundary condition. The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. To validate present procedure, the time averaged aerodynamic loads are compared with experiment and good agreement obtained. Once the N-S equations have been solved, the computed aerodynamic loads may be used to computed the sensitivities of the aerodynamic objective function. The Modified Method of feasible Direction(MMFD) is usef to compute the

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An original HSDT for free vibration analysis of functionally graded plates

  • Sidhoum, Imene Ait;Boutchicha, Djilali;Benyoucef, Samir;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • v.25 no.6
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    • pp.735-745
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    • 2017
  • This work presents a free vibration analysis of functionally graded plates by employing an original high order shear deformation theory (HSDT). This theory use only four unknowns, which is even less than the classical HSDT. The equations of motion for the dynamic analysis are determined via the Hamilton's principle. The original kinematic allows obtaining interesting equations of motion. These equations are solved analytically via Navier procedure. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

Mathematical modeling of concrete pipes reinforced with CNTs conveying fluid for vibration and stability analyses

  • Nouri, Alireza Zamani
    • Computers and Concrete
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    • v.19 no.3
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    • pp.325-331
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    • 2017
  • In this study, vibration and stability of concrete pipes reinforced with carbon nanotubes (CNTs) conveying fluid are presented. Due to the existence of CNTs, the structure is subjected to magnetic field. The radial fore induced with fluid is calculated using Navier-Stokes equations. Characteristics of the equivalent composite are determined using Mori-Tanaka model. The concrete pipe is simulated with classical cylindrical shell model. Employing energy method and Hamilton's principal, the motion equations are derived. Frequency and critical fluid velocity of structure are obtained analytically based on Navier method for simply supported boundary conditions at both ends of the pipe. The effects of fluid, volume percent of CNTs, magnetic field and geometrical parameters are shown on the frequency and critical fluid velocity of system. Results show that with increasing volume percent of CNTs, the frequency and critical fluid velocity of concrete pipe are increased.

Numerical Simulation of Cascade Flows with Rotor-Stator Interaction Using the Multiblocked Grid (중첩 격자계를 이용한 동익과 정익의 상호작용이 있는 익렬 유동해석)

  • Jung, Y. R.;Park, W. G.;Lee, S. W.
    • 유체기계공업학회:학술대회논문집
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    • 1999.12a
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    • pp.163-169
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    • 1999
  • The numerical procedure has been developed for simulating incompressible viscous flow around a turbine stage with rotor-stator interaction. This study solves 2-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system. The Marker-and-Cell concept is applied to efficiently solve continuity equation. To impose an accurate boundary condition, O-H multiblocked grid system is generated. O-type grid and H-type grid is generated near and outer rotor-stator The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. Turbulent flows have been modeled by the Baldwin- Lomax turbulent model. To validate present procedure, the time averaged pressure coefficients around the rotor and stator are compared with experiment and a good agreement obtained.

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Virtual Reality Technology for Multipurpose Numerical Simulation in Marine Environmental Engineering (해양환경공학의 다목적 수치시뮬레이션을 위한 Virtual Reality 기술)

  • Park, Jong-Chul
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.174-180
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    • 2002
  • A virtual reality technology for multipurpose numerical simulation is developed to reproduce and investigate a variety of ocean environmental problems in a 3D-Numerical Wave Tank. The governing equations for solving incompressible fluid motion are Navier-Stokes equation and continuity equation, and the Marker-Density function technique is adopted to implement the fully-nonlinear free-surface kinematic condition. The marine environmental situations, i.e. waves, currents, wind, etc., are reproduced by use of multi-segmented wavemaker on the basis of the so-called "snake-principle". In this paper, some numerical reproduction techniques for regular and irregular waves, multi-directional waves, Bull's-eye wave, wave-current, and solitary wave are presented, and a model test in motion with large amplitude of roll angle is conducted in the developed 3D-NWT, using a overlaid grid system.

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FLUID-BODY INTERACTION ANALYSIS OF FLOATING BODY IN THREE DIMENSIONS (3차원 부유체의 유체-물체 연성해석)

  • Go, G.S.;Ahn, H.T.
    • Journal of computational fluids engineering
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    • v.20 no.2
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    • pp.103-108
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    • 2015
  • Fluid-body interaction analysis of floating body with six degree-of-freedom motion is presented. In this study, three-dimensional incompressible Navier-Stokes equations are employed as a governing equation. The numerical method is based on a finite-volume approach on a cartesian grid together with a fractional-step method. To represent the body motion, the immersed boundary method for direct forcing is employed. In order to simulate the coupled six degree-of-freedom motion, Euler's equations based on rigid body dynamics are utilized. To represent the complex body shape, level-set based algorithm is utilized. In order to describe the free surface motion, the volume of fluid method utilizing the tangent of hyperbola for interface capturing scheme is employed. This study showed three different continuums(air, water and body) are simultaneously simulated by newly developed code. To demonstrate the applicability of the current approach, two different problems(dam-breaking with stationary obstacle and water entry) are simulated and all results are validated.

Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory

  • Safa, Abdelkader;Hadji, Lazreg;Bourada, Mohamed;Zouatnia, Nafissa
    • Earthquakes and Structures
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    • v.17 no.3
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    • pp.329-336
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    • 2019
  • An efficient shear deformation beam theory is developed for thermo-elastic vibration of FGM beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the on the surfaces of the beam without using shear correction factors. The material properties of the FGM beam are assumed to be temperature dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity are considered through the beam thickness. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. The closed-form solutions of functionally graded beams are obtained using Navier solution. Numerical results are presented to investigate the effects of temperature distributions, material parameters, thermal moments and slenderness ratios on the natural frequencies. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Vibration analysis of FGM beam: Effect of the micromechanical models

  • Hadji, Lazreg
    • Coupled systems mechanics
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    • v.9 no.3
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    • pp.265-280
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    • 2020
  • In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.