• Title/Summary/Keyword: Two-fluid equation

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Bubble and Liquid Velocities for a Bubbly Flow in an Area-Varying Horizontal Channel (유로단면이 변하는 수평관 내 기포류에서의 기포 및 액체 속도)

  • Tram, Tran Thanh;Kim, Byoung Jae;Park, Hyun Sik
    • Journal of the Korean Society of Visualization
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    • v.15 no.3
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    • pp.20-26
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    • 2017
  • The two-fluid equations are widely used to simulate two-phase flows in a nuclear reactor. For the two-fluid momentum equation, the wall and interfacial drag terms play an important role in predicting a two-phase flow behavior. Since the bubble density is much smaller than the water density, the bubble accelerates faster than the liquid in a nozzle. As a result, the bubble phase becomes faster than the liquid phase in the nozzle. In contrast, the opposite phenomena occur in the diffuser. The purpose of our study is to experimentally show these behaviors in an area-varying channel such as nozzle and diffuser. Experiments were made of turbulent bubbly flows in an area-varying horizontal channel. The velocities of the bubble and liquid phases were measured by the PIV technique. It was shown that the two-phase velocities were no longer close to each other in the area-varying regions. The bubble was faster than the liquid in the nozzle; in contrast, the bubble was slower than the liquid in the diffuser. Code simulations were also performed using the MARS code. By replacing the original wall drag model in the MARS code with Kim (1)'s wall drag partition model, we obtained the simulation results being consistent with experimental observations.

THERMAL INSTABILITY IN REACTIVE VISCOUS PLANE POISEUILLE / COUETTE FLOWS FOR TWO EXTREME THERMAL BOUNDARY CONDITIONS

  • Ajadi, Suraju Olusegun
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.2
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    • pp.73-86
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    • 2009
  • The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using the variational method technique. The problem is characterized by two parameters: the Nusselt number(N) and the dynamic parameter($\Lambda$). We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.

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A Study on the Numerical Simulation Method of Two-dimensional Incompressible Fluid Flows using ISPH Method (ISPH법을 이용한 2차원 비압축성 유체 유동의 수치시뮬레이션 기법 연구)

  • Kim, Cheol-Ho;Lee, Young-Gill;Jeong, Kwang-Leol
    • Journal of the Society of Naval Architects of Korea
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    • v.48 no.6
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    • pp.560-568
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    • 2011
  • In SPH(Smoothed Particle Hydrodynamics) method, the fluid has been assumed that it is weakly compressible to solve the basic equations composed of Navier-Stokes equations and continuity equation. That leads to some drawbacks such as non-physical pressure fluctuations and a restriction as like small time steps in computation. In this study, to improve these problems we assume that the fluid is incompressible and the velocity-pressure coupling problem is solved by a projection method(that is, by ISPH method). The two-dimensional computation results of dam breaking and gravitational wave generation are respectively compared with the results of finite volume method and analytical method to confirm the accuracy of the present numerical computation technique. And, the agreements are comparatively acceptable. Subsequently, the green water simulations of a two-dimensional fixed barge are carried out to inspect the possibility of practical application to ship hydrodynamics, those correspond to one of the violent free surface motions with impact loads. The agreement between the experimental data and the present computational results is also comparatively good.

Eulerian-Lagrangian Modeling of One-Dimensional Dispersion Equation in Nonuniform Flow (부등류조건에서 종확산방정식의 Eulerian-Lagrangian 모형)

  • 김대근;서일원
    • Journal of Environmental Science International
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    • v.11 no.9
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    • pp.907-914
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    • 2002
  • Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

Computation of Dynamic Fluid-Structure Interaction in a 2-Dimensional Laminar Channel Flow Divided by a Plate (판으로 나뉘어진 2차원 충류 채널유동에서 동적 유체-구조물 상호작용 수치해석)

  • Namkoong, Kak;Choi, Hyoung-Gwon;Yoo, Jung-Yul
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.12
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    • pp.1738-1746
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    • 2002
  • In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.

Fluid-Structure Interaction Study on Diffuser Pump With a Two-Way Coupling Method

  • Xu, Huan;Liu, Houlin;Tan, Minggao;Cui, Jianbao
    • International Journal of Fluid Machinery and Systems
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    • v.6 no.2
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    • pp.87-93
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    • 2013
  • In order to study the effect of the fluid-structure interaction (FSI) on the simulation results, the external characteristics and internal flow features of a diffuser pump were analyzed with a two-way flow solid coupling method. And the static and dynamic structure analysis of the blade was also caculated with the FEA method. The steady flow field is based on Reynolds Averaged N-S equations with standard $k-{\varepsilon}$ turbulent model, the unsteady flow field is based on the large eddy simulation, and the structure response is based on elastic transient structural dynamic equation. The results showed that the effect of FSI on the head prediction based on CFD really exists. At the same radius, the van mises stress on the nodes closed shroud and hub was larger than other nodes. A large deformation region existed near inlet side at the middle of blades. The strength of impeller satisfied the strength requirement with static stress analysis based on the fourth strength theory. The dynamic stress varied periodically with the impeller rotating. It was also found that the fundamental frequency of the dynamic stress is the rotating frequency and its harmonic frequency. The frequency of maximum stress amplitude at node 1626 was 7 times of the rotating frequency. The frequency of maximum stress amplitude at node 2328 was 14 times of the rotating frequency. No matter strength failure or fatigue failure, the root of blades near shroud is the key region to analyse.

Stability Analysis of Pipe Conveying Fluid with Crack (크랙을 가진 유체유동 파이프의 안정성 해석)

  • Son, In-Soo;Ahn, Tae-Su;Yoon, Han-Ik
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.1 s.118
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    • pp.10-16
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    • 2007
  • In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid is investigated. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid due to the coupled mode(modes combined) is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Galerkin method. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The stiffness of the spring depends on the crack severity and the geometry of the cracked section. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. This results of study will contribute to the safety test and a stability estimation of the structures of a cracked pipe conveying fluid.

Effects of Attached Mass on Stability of Pipe Conveying Fluid with Crack (크랙을 가진 유체유동 파이프의 안정성에 미치는 부가질량의 영향)

  • Son, In-Soo;Cho, Jeong-Rae;Yoon, Han-Ik
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.10
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    • pp.1002-1009
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    • 2007
  • In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid with an attached mass is investigated. Also, the effect of attached mass on the dynamic stability of a simply supported pipe conveying fluid is presented for the different positions and depth of the crack. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by the energy expressions using extended Hamilton's principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of a fracture and to be always opened during the vibrations. Finally, the critical flow velocities and stability maps of the pipe conveying fluid are obtained by changing the attached mass and crack severity.

Stability Analysis of Pipe Conveying Fluid with Crack and Attached Masses (크랙과 부가질량들을 가진 유체유동 파이프의 안정성 해석)

  • Son, In-Soo;Yoon, Han-Ik
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.5
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    • pp.121-131
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    • 2008
  • In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid with an attached mass is investigated. Also, the effect of attached masses on the dynamic stability of a simply supported pipe conveying fluid is presented for the different positions and depth of the crack. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by the energy expressions using extended Hamilton's principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of a fracture and to be always opened during the vibrations. Finally, the critical flow velocities and stability maps of the pipe conveying fluid are obtained by changing the attached masses and crack severity. As attached masses are increased, the region of re-stabilization of the system is decreased but the region of divergence is increased.

Two Linked-Robot Actuated by ER-Valve Systems (ER-Valve 작동기를 이용한 Two link Robot의 위치제어)

  • 이호근;김휘동
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2001.04a
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    • pp.165-170
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    • 2001
  • This paper presents performance analysis of two-linked robot system using ER (electro rheological) valve actuators. An ER fluid consisting of soluble chemical starches (particles) and silicone oil is made and its field-dependent yield stress is experimentally distilled using electro-viscometer. From this result, the design parameters of ER valve are determined. Based on parameter study, an ER valve system is designed and manufactured. Furthermore, the measured pressure drop is compared with predicted one obtained from the Bingham model. Following the evaluation of field-dependent pressure drop of ER valve, a two-linked robot system with two ER valve actuators is then constructed and its governing equation of motion is derived. From this equation, PID controller is established. Consequently, control performances of the proposed two-linked robot system featuring ER valve are evaluated.

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