• Title/Summary/Keyword: Third-order equation

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Numerical Study of the blade dynamics for a cross-flow turbine

  • Sato Yuko;Kawamura Tetuya
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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    • pp.230-231
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    • 2003
  • Two and three-dimensional flows around a cross-flow wind turbine are investigated by the numerical simulation. The turbine studied in this paper has cylindrical shape with many small blades along its periphery. Incompressible Navier-Stokes equation is used for this simulation. A rotating coordinate system, which rotates at the same speed of the turbine, is used in order to simplify the boundary conditions on the blades of the turbine. Additionally, a boundary fitted coordinate system is employed in order to express the shape of the blades precisely. A third order upwind scheme is chosen for the approximation of the non-linear terms. When the number of blades is about 10, the highest torque is obtained.

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A Study on an Effective Higher-Order Taylor-Galerkin Method for the Analysis of Structural Dynamics (동적 해석을 위한 효과적 고차 Taylor Galerkin법에 관한 연구)

  • 윤성기;박상훈
    • Journal of KSNVE
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    • v.3 no.4
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    • pp.353-359
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    • 1993
  • In this study, the Taylor-Galerkin method is modified to take into consideration the third order term in the Taylor series of the fundamental variable. In the Taylor-Galerkin method, after expressing the governing equation of motion in conservation form, the temporal discretization is done first and then spatial discretization follows in contrast to the conventional approaches. A predictor-corrector type algorithm has been developed previously by the same author. A new computationally efficient direct algorithm is proposed in this study. A study on convergency and accuracy of the solution is carried out. Numerical examples show that this new algorithm exhibits the same order of accuracy with less computational effort.

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Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations

  • Asgari, Gholamreza;Payganeh, Gholamhassan;Fard, Keramat Malekzadeh
    • Structural Engineering and Mechanics
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    • v.72 no.4
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    • pp.525-540
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    • 2019
  • The purpose of the present work was to study the dynamic instability of a three-layered, symmetric sandwich beam subjected to a periodic axial load resting on nonlinear elastic foundation. A higher-order theory was used for analysis of sandwich beams with soft core on elastic foundations. In the higher-order theory, the Reddy's third-order theory was used for the face sheets and quadratic and cubic functions were assumed for transverse and in-plane displacements of the core, respectively. The elastic foundation was modeled as nonlinear's type. The dynamic instability regions and free vibration were investigated for simply supported conditions by Bolotin's method. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the coefficients of foundation, the core thickness, the dynamic and static load factor. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.

A Numerical Method for Longitudinal Dispersion Equation for Nonconservative Contaminants (비보존성 오염물질에 대한 종확산 방정식의 수치해법)

  • Yu, Myeong-Gwan;Jeon, Gyeong-Su
    • Journal of Korea Water Resources Association
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    • v.32 no.6
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    • pp.607-616
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    • 1999
  • A fractional step finite difference model for the longitudinal dispersion of nonconservative contaminants is developed. It is based on splitting the longitudinal dispersion equation into a set of three equations each to be solved over a one-third time step. The fourth-order Holly-Preissmann scheme, an analytic solution, and the Crank-Nicholson scheme are used to solve the equations for the pure advection, the first-order decay, and the diffusion, respectively. To test the model, it is applied to simulate the longitudinal dispersion of continuous source released into a nonuniform flow field as well as the dispersion of an instantaneous source in a uniform flow field. The results are compared with the exact solution and those computed by an existing model. Compared to the existing model which uses Euler method for the first-order decay equation, the present model yield more accurate results as the decay coefficient increases.

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Study on corrosion fatigue of high strength steel (고장력강의 부식피로에 관한 연구)

  • 유헌일;천기정;택목양삼
    • Journal of the korean Society of Automotive Engineers
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    • v.5 no.1
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    • pp.32-44
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    • 1983
  • In case of $K_{Imax}$ < $K_{Iscc}$, the corrosion fatigue of high strength steel in 0.1N $H_{2}$S $O_{4}$ solution and 3.5% salt water is as follows. 1. The fatigue life shortens in order of 3.5% salt water and 0.1N $H_{2}$S $o_{4}$ solution. 2. The fatigue crack growth rate in air is obtained as the following equation. (dc/dN)$_{atr}$=7.23*10$^{-6}$ (.DELTA. K)$^{2.23}$ 3. The corrosion fatigue crack growth rate in environment is divided into three regions, that is, First Region, Second Region and Third Region from the small cyclic stress intensity. 4. The formation rate of the active surface on metal is slower than the mechano-chemical reaction rate in First Region. The crack growth rate depends on time and the cyclic stress intensity and is expressed as the following equation. (dc/dN)$_{I}$=C(/DELTA. K)$^{\delta}$ 5. The formation rate of the active surface is faster than the mechano-chemical reaction rate in Second Region and the synergistic effect by stress and corrosion becomes slow. In case the fatigue load is large, we have the critical crack growth rate which is not related to the cyclic stress intensity. 6. The corrosion crack growth rate by the mechano-chemical reaction is the same in $H_{2}$S $O_{4}$ solution and salt water, so Hydrogen accelerates the crack growth. 7. The environment has no effect on the corrosion fatigue crack growth rate in Third Region. 8. In First Region and Second Region, dimple is observed on the fatigue fracture surface in 0.1N $H_{2}$S $O_{4}$ solution. 9. The striation is observed in any environment as in air in Third Region and its interval approximately coincide with the crack growth rate.ate.e.e.

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Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories

  • Sy, Ngoc Nguyen;Lee, Jaehun;Cho, Maenghyo
    • International Journal of Aeronautical and Space Sciences
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    • v.13 no.4
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    • pp.458-467
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    • 2012
  • In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

Incompressible Viscous Flow Analysis Around a Three Dimensional Minivan-Like Body (3차원 미니밴 형상 주위의 비압축성 점성 유동 해석)

  • Jung Y. R.;Park W. G.;Park Y. J.;Kim J. S.;Hong S. H.
    • Journal of computational fluids engineering
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    • v.2 no.1
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    • pp.46-53
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    • 1997
  • The flow field around a three dimensional minivan-like body has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. A H-H type of multi-block grid system is generated around a three dimensional minivan-like body. Turbulent flows have been modeled by the Baldwin-Lomax turbulent model. To validate present procedure, the flows around the Ahmed body with 12.5° of slant angle are simulated. A good agreement with other numerical results is achived. After code validation, the flows around a mimivan-like body are simulated. The simulation shows three dimensional vortex-pair just behind body. The flow separation is also observed on the rear of the body. It has concluded that the results of present study properly agreed with physical flow phenomena.

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Passive Control of Condensation Shock Wave in a Transonic Nozzle (천음속 노즐에서 발생하는 응축충격파의 피동제어)

  • Kim, Hui-Dong;Baek, Seung-Cheol;Gwon, Sun-Beom
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.5
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    • pp.666-674
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    • 2002
  • A rapid expansion of the moist air or stream through transonic nozzle often leads to not-equilibrium condensation shock, causing a considerable amount of energy loss to the entire flow field. Depending on amount of heat released, condensation shock wave occurs in the nozzle and interacts with the boundary layer flow. In the current study, a passive control technique using a porous wall with a plenum cavity underneath is applied for purpose of alleviation the condensation shock wave in a transonic nozzle. A droplet growth equation is incorporated into two-dimensional wavier-Stokes equation systems. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. An experiment using an indraft transonic wind tunnel is made to validate the present computational results. The results obtained show that the magnitude of condensation shock wave is reduced by the current passive control method.

Detonation Wave Propagation Through a T-type Branch Tube in Combustion Wave Rocket Igniter (연소파 로켓 점화기의 T형 분기관내 데토네이션파 전파)

  • ;Vigor Yang
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2003.05a
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    • pp.221-224
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    • 2003
  • A numerical study is carried out for the detonation wave propagation through a T-branch. The T-branch is a crucial part of the combustion wave igniter, a novel concept of rocket ignition system aimed for the simultaneous ignition of multiple combustion chambers by delivering detonation waves. Euler equation and induction parameter equation are used as governing equations with a reaction term modeled from the chemical kinetics database obtained from a detailed chemistry mechanism. Second-order accurate implicit time integration and third-order space accurate TVD algorithm were used for solution of the coupled equations. Over two-million grid points enabled the capture of the dynamics of the detonation wave propagation including the degeneration and re-initiation phenomena, and some of the design factors were be obtained for the CWI flame tubes.

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Passive Control of the Condensation Shock Wave Oscillation in a Supersonic Nozzle (초음속 노즐에서 발생하는 응축충격파 진동의 피동제어)

  • Baek, Seung-Cheol;Kwon, Soon-Bum;Kim, Heuy-Dong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.7
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    • pp.951-958
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    • 2002
  • Rapid expansion of a moist air or a stream through a supersonic nozzle often leads to non-equilibrium condensation shock wave, causing a considerable energy loss in flow field. Depending on amount of latent heat released due to non-equilibrium condensation, the flow is highly unstable or a periodical oscillation accompanying the condensation shock wave in the nozzle. The unsteadiness of the condensation shock wave is always associated with several kinds of instabilities as well as noise and vibration of flow devices. In the current study, a passive control technique using a porous wall with a plenum cavity underneath is applied for the purpose of alleviation of the condensation shock oscillations in a transonic nozzle. A droplet growth equation is coupled with two-dimensional Navier-Stokes equation system. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. An experiment using an indraft wind tunnel is made to validate the present computational results. The results show that the oscillations of the condensation shock wave are completely suppressed by the current passive control method.