• Journal of the Korean Statistical Society
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• 제28권2호
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• pp.151-165
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• 1999

This paper considers the trimmed least squares estimator of the autoregression parameter in the unstable AR(1) model: X\ulcorner=ØX\ulcorner+$\varepsilon$\ulcorner, where $\varepsilon$\ulcorner are iid random variables with mean 0 and variance $\sigma$$^2$> 0, and Ø is the real number with │Ø│=1. The trimmed least squares estimator for Ø is defined in analogy of that of Welsh(1987). The limiting distribution of the trimmed least squares estimator is derived under certain regularity conditions.

• 대한토목학회논문집
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• 제29권3B호
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• pp.231-237
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• 2009

본 연구에서는 2-방정식 난류모형인 ${\kappa}-{\varepsilon}$ 모형을 이용하여 2차원적으로 발달하는 하층 밀도류를 모의하기 위한 수치모형을 제시하였다. 타원형 편미분 방정식으로 흐름에 대한 지배방정식을 구성하였으며, 수치기법으로는 유한체적법을 사용하였다. 연구를 통해 개발된 수치모형을 기존의 실험결과와 비교하여 적용성을 검토하였다. 불연속 유입조건 밀도류의 시간별 진행에서 흐름의 불안정에 의한 와(渦)의 발생을 확인하였으며, 진행중인 불연속 유입 밀도류의 진행단계 변화와 선단부 속도의 관계를 살펴보았다. 또한, 무거운 유체 위로 이동하던 주변수체가 벽면을 접하면서 발생된 단파가 밀도류의 진행에 미치는 영향을 수직구조를 통해 살펴보았다. 한편, 개발된 모형을 이용한 수치모의에서 선단부의 진행 속도가 실험보다 느리게 모의되었다. 이는 3차원 현상인 난류의 불안정성을 모의하는 2차원 모형의 한계인 것으로 판단된다.

• Wind and Structures
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• 제4권3호
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• pp.177-196
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• 2001

At present the most popular turbulence models used for engineering solutions to flow problems are the $k-{\varepsilon}$ and Reynolds stress models. The shortcoming of these models based on the isotropic eddy viscosity concept and Reynolds averaging in flow fields of the type found in the field of Wind Engineering are well documented. In view of these shortcomings this paper presents the implementation of a non-linear model and its evaluation for flow around a building. Tests were undertaken using the classical bluff body shape, a surface mounted cube, with orientations both normal and skewed at $45^{\circ}$ to the incident wind. Full-scale investigations have been undertaken at the Silsoe Research Institute with a 6 m surface mounted cube and a fetch of roughness height equal to 0.01 m. All tests were originally undertaken for a number of turbulence models including the standard, RNG and MMK $k-{\varepsilon}$ models and the differential stress model. The sensitivity of the CFD results to a number of solver parameters was tested. The accuracy of the turbulence model used was deduced by comparison to the full-scale predicted roof and wake recirculation zone lengths. Mean values of the predicted pressure coefficients were used to further validate the turbulence models. Preliminary comparisons have also been made with available published experimental and large eddy simulation data. Initial investigations suggested that a suitable turbulence model should be able to model the anisotropy of turbulent flow such as the Reynolds stress model whilst maintaining the ease of use and computational stability of the two equations models. Therefore development work concentrated on non-linear quadratic and cubic expansions of the Boussinesq eddy viscosity assumption. Comparisons of these with models based on an isotropic assumption are presented along with comparisons with measured data.

• 설비공학논문집
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• 제11권2호
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• pp.157-166
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• 1999

Numerical calculations of turbulent natural convection in an enclosure of the 20 kYA oil-immersed transformer model are presented. The transformer is modelled as two concentric cylinders with different heights and diameters. The thermal boundary layers are well represented in the temperature distributions along the wall of the transformer model. The flow stratification between the hot and cold walls can not be seen in the transformer model. The turbulence eddy viscosity has its maximum at the center of the core and its maximum values at the top of the core are larger than those at the bottom of the core.

• 한국해양공학회지
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• 제22권3호
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• pp.24-33
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• 2008

In this study, flow and creation and dissipation of vorticity around rectangular floating breakwater is investigated both experimentally and numerically. The PIV system(Particle image velocimetry) is employed to obtain the velocity field in the vorticity of rectangular structure. The numerical model, combined with ${\kappa}-{\varepsilon}$ turbulence model and the VOF method based on RANS equation, is used to analyze the turbulence structure. In the results of this study, the vorticity is found around conner of rectangular structure at all time domain, and creation and dissipation of vorticity are closely related to wave period. Separation points of phase of vortex due to flow separation for longer period waves are faster then for shorter period waves.

• Ocean Systems Engineering
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• 제4권3호
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• pp.185-200
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• 2014

The objective of the present simulations is to evaluate the applicability of the standard $k-{\varepsilon}$ turbulence model in engineering practice in the subcritical to supercritical flow regimes. Two-dimensional numerical simulations of flow around a circular cylinder at $Re=1{\times}10^5$, $5{\times}10^5$ and $1{\times}10^6$, had been performed using Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the standard $k-{\varepsilon}$ turbulence model. Solution verification had been studied by evaluating grid and time step size convergence. For each Reynolds number, several meshes with different grid and time step size resolutions were chosen to calculate the hydrodynamic quantities such as the time-averaged drag coefficient, root-mean square value of lift coefficient, Strouhal number, the coefficient of pressure on the downstream point of the cylinder, the separation angle. By comparing the values of these quantities of adjacent grid or time step size resolutions, convergence study has been performed. Solution validation is obtained by comparing the converged results with published numerical and experimental data. The deviations of the values of present simulated quantities from those corresponding experimental data become smaller as Reynolds numbers increases from $1{\times}10^5$ to $1{\times}10^6$. This may show that the standard $k-{\varepsilon}$ model with enhanced wall treatment appears to be applicable for higher Reynolds number turbulence flow.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.13-14
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• 2003

Two different ${\kappa}-{\varepsilon}-\overline{{\nu}{\nu}}-f$ turbulence models together with the two-layer model are evaluated for natural convection in a rectangular cavity. The numerical problem and accuracy of the turbulence models are discussed. The original $\overline{{\nu}{\nu}}-f$ model suffers from the numerical stiffness problem when used with the segregate solution procedure like the SIMPLE algorithm, and a remedy for this problem is proposed. It is shown that original $\overline{{\nu}{\nu}}-f$ model best predicts the mean velocity, Reynolds stresses and the turbulent heat flux while the modified $\overline{{\nu}{\nu}}-f$ model (N=6) overpredicts the turbulent quantities.

• 한국수자원학회논문집
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• 제50권2호
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• pp.89-97
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• 2017

만곡수로에서의 흐름 구조는 나선형 운동을 갖는 이차 재순환 흐름 그리고 만곡부 측벽으로부터 발생하는 흐름분리로 인한 전단층 등으로 복잡하다. 이 연구에서는 3개의 통계학적 난류모형($k-{\varepsilon}$, RNG $k-{\varepsilon}$, $k-{\omega}$ SST) 그리고 자유수면 변동 해석을 위한 VOF 기법을 적용한 비정상 Reynolds-averaged Navier-Stokes (RANS) 계산을 수행하여 고진폭 만곡수로인 키노시타(Kinoshita) 수로에서의 이차류와 편수위를 해석하였다. 2차 정확도의 유한체적법을 이용하여 구한 해석결과를 기존 수리실험 자료와 비교하여 각 난류모형의 적용성을 평가하였다. 비정상 RANS 계산에서 적용한 3개의 통계학적 난류모형의 해석 결과를 분석해 보면 키노시타 수로에서 발생하는 만곡부 편수위는 3개 모형 모두 유사하게 모의하는 한편, 전반적인 이차류 분포는 $k-{\omega}$ SST상대적으로 잘 모의하는 것으로 나타났다. 하류에 위치한 만곡부 흐름에 영향을 미쳐 국부적으로 발생한 이차류와 이전의 만곡부 중앙 수면 부근에서 발생하는 한 쌍의 이차 와류가 존재하는 현상을 관측하였으며, $k-{\omega}$ SST 난류모형은 이러한 복잡한 와류 변화를 양호하게 모의했다. $k-{\varepsilon}$ 모형을 기반으로 개발된 두 모형으로 모의한 결과에서는 실험에서 관측된 중앙 만곡부에 존재하는 두 개의 이차류 중, 시계방향 와류가 재현되지 않는다. VOF기법을 이용해서 계산한 만곡부에서의 편수위 해석결과는 적용한 모든 난류모형에 대해서 전반적으로 실험값을 양호하게 재현하는 것으로 나타났다.

• Wind and Structures
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• 제5권2_3_4호
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• pp.317-328
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• 2002

A numerical investigation on the turbulent flows over a three-dimensional steep hill is presented. The numerical model developed for the present work is based on the finite volume method and the SIMPLE algorithm with a non-staggered grid system. Standard $k-{\varepsilon}$ model and Shih's non-linear model are tested for the validation of the prediction accuracy in the 3D separated flow. Comparisons of the mean velocity and turbulence profiles between the numerical predictions and the measurements show good agreement. The Shih's non-linear model is found to predict mean flow and turbulence better than the Standard $k-{\varepsilon}$. Flow patterns have also been examined to explain the difference in the cavity zone between 2D and 3D hills.

• 한국자동차공학회논문집
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• 제2권5호
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• pp.48-57
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• 1994

The specific power output and thermal effeciency of any two-stroke engine are dependent on its scavenging behavior. Among the many factors which influence on the scavenging process, the cylinder head shape is one of the important factor. Hence in this study three different type models of cylinder head shape which are the cylindrical, the spherical and the arbitrary shape are studied to show the effects of the turbulent scavenging process in the cylinder with one inlet port, two side ports and one exhaust port. A modified version of KIVA-II which strip out of or add planes of cells across the mesh above the piston for flow simulation of two-stroke engine is used. The $k-{\varepsilon}$ turbulent model is used. The results show that the flow in a two-stroke engine cylinder of the spherical head shape among the three different type model is a desirable for efficient scavenging.