• Title/Summary/Keyword: Governing equation

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Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams

  • Ebrahimi, Farzad;Shafiei, Navvab
    • Smart Structures and Systems
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    • v.17 no.5
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    • pp.837-857
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    • 2016
  • In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen's nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton's principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.

A Numerical Analysis of Three-Dimensional Flow Within a Transonic Fan (천음속 팬의 3차원 유동에 관한 수치해석)

  • Chung, Juhyun;Ko, Sungho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.1
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    • pp.82-91
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    • 1999
  • A numerical analysis based on the three-dimensional Reynolds-averaged Navier-Stokes equation has been conducted to investigate the flow within a NASA rotor 67 transonic fan. General coordinate transformations are used to represent the complex blade geometry and an H-type grid is used. The governing equations are solved using implicit LU-SGS scheme for the time-marching integration and a standard ${\kappa}-{\varepsilon}$ model is used with wall functions for the turbulence modeling. The computations are compared with the experimental data and a detailed study of the flow structures near peak efficiency and near stall is presented. The calculated overall aerodynamic efficiency and three-dimensional shock system agree well with the laser anemometer data.

A Study on the Flow Behavior of Magnetic Fluids in a Circular Pipe with a Vertical Magnetic Field (수직자장하에서 원관내 자성유체의 거동에 관한 연구)

  • Park, Joung-Woo;Ryu, Shin-Oh;Seo, Lee-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.1
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    • pp.25-32
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    • 1999
  • In the present paper, we theoretically analyze the flow of magnetic fluids in a circular pipe with a vertical magnetic field and investigate the magnetic response by the external magnetic field. Theoretical study through the governing equation derived by Siliomis is carried out with numerical analysis by the Gauss Elimination Method. Using polar and magnetic effect parameters, theoretical equations and distributions for the velocity, vorticity, internal angular momentum and induced magnetization as the magnetic response are shown. Especially, in the region of strong magnetic field the specific property is appeared by finding a critical magnetic effect parameter for a polar effect parameter.

A Thermal Conductivity Model for Hydrating Concrete Pavements

  • Jeong Jin-Hoon;Kim Nakseok
    • Journal of the Korea Concrete Institute
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    • v.16 no.1 s.79
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    • pp.125-129
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    • 2004
  • Hydrating concrete pavement is typically subjected to temperature-induced stresses that drive cracking mechanisms at early concrete ages. Undesired cracking plays a key role in the long-term performance of concrete pavement systems. The loss of support beneath the concrete pavement due to curling caused by temperature changes in the pavement may induce several significant distresses such as punch out pumping, and erosion. The effect of temperature on these distress mechanisms is both significant and intricate. Because thermal conductivity dominates temperature flow in hydrating concrete over time, this material property is back-calculated by transforming governing equation of heat transfer and test data measured in laboratory. Theoretically, the back- calculated thermal conductivity simulates the heat movements in concrete very accurately. Therefore, the back- calculated thermal conductivity can be used to calibrate concrete temperature predicted by models.

Application of k-w turbulence model to the analysis of the flow through a single stage axial-flow compressor (단단 축류압축기 유동해석에 대한 k-w 난류모델의 응용)

  • Lee, Joon-Suk;Kim, Kwang-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.3 no.3 s.8
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    • pp.7-11
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    • 2000
  • A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit fout-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations we discretized with explcit finite difference method. Mired-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-w turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.

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Analysis on Characteristic of Pressure Fluctuation in Hydraulic Turbine with Guide Vane

  • Shi, FengXia;Yang, JunHu;Wang, XiaoHui
    • International Journal of Fluid Machinery and Systems
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    • v.9 no.3
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    • pp.237-244
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    • 2016
  • An unsteady three-dimensional simulation based on Reynolds time-averaged governing equation and RNG $k-{\varepsilon}$ turbulence model, was presented for pump-as-turbine, the pressure fluctuation characteristic of hydraulic turbine with guide vane was obtained. The results show that the time domains of pressure fluctuation in volute change periodically and have identical cycles. In volute tongue and inlet pressure fluctuations are light, while in dynamic and static coupling interface pressure fluctuations are serious; In impeller blade region the pressure fluctuation of pressure surface are lighter than that of suction surface. The dominant frequencies of pressure fluctuation concentrate in low frequency region, and concentrate within 2 times of the blade passing frequency.

Characteristic of High Speed Synchronous Reluctance Motor(SynRM) (고속용 동기 릴럭턴스 전동기 특성)

  • Joo, S.W.;Hahn, S.C.;Koo, D.H.;Hong, J.P.
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.55 no.4
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    • pp.203-208
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    • 2006
  • This paper presents characteristics of SynRM(Synchronous Reluctance Motor) that is compared with a high speed induction motor. SynRM is much suitable for high speed electric machines because of structural robustness. There are many kinds of SynRM according to the shape of rotors. Particularly, axially laminated anisotropic (ALA) rotor is suitable for high speed instruments. Characteristics of SynRM with ALA rotor is obtained from a governing voltage and torque equation mainly composed of d-axis and q-axis inductance that will be identified with finite element method.

Simulation of Fuel Injection System and Model of Spray Behavior in Liquefied Butane (액상부탄 분사시스템의 수치시뮬레이션 및 분무특성 예측)

  • Kim, J.H.;Koo, J.Y.
    • Journal of ILASS-Korea
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    • v.3 no.2
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    • pp.24-33
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    • 1998
  • The characteristics of liquefied butane spray are expected to be different from conventional diesel fuel spray, because a kind of flash boiling spray is expected when the back pressure is below the saturation vapor pressure of the butane(0.23MPa at $25^{\circ}C$). An accumulator type pintle injector and its fuel delivery system has been simulated in ruder to give injection pressure, needle lift and rate of fuel injected. The governing equation were solved by finite difference metho. The injection duration was controlled by solenoid valve. Spray behaviors such as a transient spray tip penetration, spray angle and SMD were calculated based on the empirical correlations in case that the back pressure is both above the vapor pressure of the butane and below that of butane. When the back preassure is below the vapor pressure of the fuel, conventional correlation is modified to represent the effect of flash boiling.

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Numerical Investigation of the Stability of Flows induced by a Surface Acoustic Wave along a Slab

  • Chu W. Kwang-Hua
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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    • pp.77-79
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    • 2003
  • The stability of flows induced by a surface acoustic wave (SAW) propagating along the deformable walls in a confined parallel-plane microchannel or slab in the laminar flow regime is investigated. The governing equation which was derived by considering the nonlinear coupling between the deformable or waving interface and viscous fluids is linearized and then the problem is solved by a verified code based on the spectral method together with the associated interface and boundary conditions. The value of the critical Reynolds number was found to be near 1439 which is much smaller than the rigid-wall case: 5772 for conventional pressure-driven flows.

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CHAOTIC MIXING IN THREE-DIMENSIONAL MICRO CHANNEL (삼차원 마이크로 채널 내 카오스 혼합)

  • Le, T.H.V.;Kang, S.;Suh, Y.K.;Wang, Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2007.10a
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    • pp.49-55
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    • 2007
  • The quality of chaotic mixing in three-dimensional micro channel flow has been numerically studied using Fractional-step method (FSM) and particle tracking techniques such as $Poincar{\acute{e}}$ section and Lyapunov exponents. The flow was driven by pressure distribution and the chaotic mixing was generated by applying alternating current to electrodes embedded on the bottom wall at a first half period and on the top wall at a second half period. The equations governing the velocity and concentration distributions were solved using FSM based on Finite Volume approach. Results showed that the mixing quality depended significantly on the modulation period. The modulation period for the best mixing performance was determined based on the mixing index for various initial conditions of concentration distribution. The optimal values of modulation period obtained by the particle tracking techniques were compared with those from the solution of concentration distribution equation using FSM and CFX software and the comparison showed their good match.

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