• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.1 s.256
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• pp.40-50
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• 2007

The present contribution describes the application of elliptic-blending second moment closure to predict the gas cooling process of turbulent super-critical carbon dioxide flow in a square cross-sectioned duct. The gas cooling process under super-critical state experiences a drastic change in thermodynamic and transport properties. Redistributive terms in the Reynolds stress and turbulent heat flux equations are modeled by an elliptic-blending second moment closure in order to represent strongly non-homogeneous effects produced by the presence of walls. The main feature of Durbin's elliptic relaxation second moment closure that accounts for the nonlocal character of pressure-velocity gradient correlation and the near-wall inhomogeneity guaranteed by the elliptic blending second moment closure.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.12
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• pp.831-841
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• 2007

This work is to extend the elliptic operator, which has been already adopted in turbulent stress model, to fully developed turbulent buoyant channel flows with changing the orientation of the buoyancy vector to be perpendicular to the channel walls. The turbulent heat flux models based on the elliptic concept are employed and closely linked to the elliptic blending second moment closure which is used for the prediction of Reynolds stresses. In order to reflect the stable or unstable stratification conditions, the present model introduces the gradient Richardson number into the thermal to mechanical time scale ratio and model coefficients. The present model has been applied for the computation of stably and unstably stratified turbulent channel flows and the prediction results are directly compared to the DNS data.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.11 s.242
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• pp.1265-1276
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• 2005

The elliptic conceptual second moment models for turbulent heat fluxes, which are proposed on the basis of elliptic-blending and elliptic-relaxation equations, are applied to calculate the combined forced and natural turbulent convection in a vertical plane channel. The models satisfy the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also have the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. Also the models are closely linked to the elliptic blending model which is used for the prediction of Reynolds stress. In order to calibrate the heat flux models, firstly, the distributions of mean temperature and scala flux in fully developed channel flow with constant wall difference temperature are solved by the present models. The buoyancy effect on the turbulent characteristics including the mean velocity and temperature, the Reynolds stress tensor, and the turbulent heat flux vector are examined. In the opposing flow, the turbulent transport is greatly enhanced with both the Reynolds stresses and the turbulent heat fluxes being remarkably increased; whereas, in the aiding flow, the opposite change is observed. The results of prediction are directly compared to the DNS to assess the performance of the model predictions and show that the behaviors of the turbulent heat transfer in the whole flow region are well captured by the present models.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.9
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• pp.741-753
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• 2007

The elliptic conceptual second moment model for turbulent heat fluxes, which was proposed on the basis of elliptic-relaxation equation, was applied to calculate the turbulent heat transfer in an axially rotating pipe flow. The model was closely linked to the elliptic blending model which was used for the prediction of Reynolds stress. The effects of rotation on the turbulent characteristics including the mean velocity, the Reynolds stress tensor, the mean temperature and the turbulent heat flux vector were examined by the model. The numerical results by the present model were directly compared to the DNS as well as the experimental results to assess the performance of the model predictions and showed that the behaviors of the turbulent heat transfer in the axially rotating pipe flow were satisfactorily captured by the present models.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.39.2-40
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• 2021

본 연구는 《숭전역서》 혹은 《서양신법역서》 이후, 하국종(何國宗, ? -1767)과 매각성(梅殼成, 1681-1764) 등에 의해 기술된 《역상고성》 상하편에 실린 <일전역리>, <일전역법>, <일전표>를 바탕으로 태양의 운동을 자세히 살펴보았다. 《숭전역서》 <일전역리>에서는 티코브라헤의 혼합모형을 기반에 두었지만 태양의 운동은 톨레미(Ptolemy)의 이심모델(Eccentric model)과 차이가 없다. 그러나 <일전표>에 수록된 가감차의 값은 이퀀트모델(Equant model)을 기초로 한 것이었다. 《신법산서》 <일전표>에는 이 모델에 의한 계산법을 소개하고 있으나 계산의 오류를 범하였다. 태양 실측과의 어긋남, 태양의 운동을 기술하는 여러 상수들이 다시 얻어짐에 따라 《역상고성》 상하편의 <일전역리>에서는 코페르니쿠스 모델을 기초로 한 본륜-균륜 모델을 채택하고 있다. 이 모델을 기초로 한 가감차 계산 과정에 조금의 수학적 오류가 있지만 계산 결과에는 영향을 미치지 않았다. 그리고 <일전표>에 제시된 가감차값은 바로 이 모델을 기반으로 한 값들이다. <일전역법>에 제시된 동지 이후 태양의 실제 경도를 구하는 방법이 매우 구체적이다. 이 방법은 이후 《역상고성후편》의 <일전역법>도 그대로 따르고 있는데 다만 《역상고성후편》의 <일전역리>는 케플러의 타원모델을 채택하고 있다. 태양의 황경을 구하는 현재의 방법과 비교해보면 《역상고성》 <일전역법>에서는 그 기준이 동지이고 현재의 방법은 춘분점이라는 것만 다를 뿐이고, 방법은 동일하다. 다만 필요한 상수 값들이 시간에 따라 아주 느리게 변하기에 이 값들의 보정이 필요할 뿐이다. 이 방법은 조선에서 집필된 《세초류휘》, 《시헌기요》, 《추보속해》, 《추보첩례》에도 사용한 모델과 상수들은 다르지만 동일한 방법을 요약하고 있다.