• 한국전산유체공학회지
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• 제11권2호
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• pp.49-55
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• 2006

This study investigates the oscillatory thermal convection of a fluid with Pr=0.02 in a wide-gap horizontal annulus with constant heat flux inner wall. When Pr=0.02, dual steady-state flows are not found. After the first Hopf bifurcation from a steady to a time-periodic flow, five successive period-doubling bifurcations are recorded before chaos. The power spectrum shows the $period-2^4\;and\;2^5$ flows clearly, and a window of period $3{\times}2^3$ flow is found in the chaotic regime. The approximate value of the Feigenbaum number for the last three period-doubling bifurcations is 4.76. The transition route to chaos of the present simulations is consistent with the period-doubling route of Feigenbaum.

• Nuclear Engineering and Technology
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• 제44권3호
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• pp.283-296
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• 2012

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body in the center is studied. Three different Prandtl numbers (0.01, 0.7 and 7) are considered for the investigation of the effect of the Prandtl number on natural convection. Adiabatic boundary conditions are employed for the side walls. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10_3$ to $10_6$. It had been experimentally reported that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. It was found that when Ra=$10_6$, only the case for intermediate Pr (=0.7) reached a non-changing steady state and the low and high Pr number cases (Pr=0.01 and 7) showed a periodically oscillatory fashion hydrodynamically and thermally. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers are presented to show the overall heat transfer characteristics in the system. Further, the isotherms and streamline distributions are presented in detail to compare the physics related to their thermal behavior.

• 대한기계학회논문집B
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• 제24권9호
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• pp.1210-1218
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• 2000

Thermal convection in a horizontal annulus is considered, and the bifurcation phenomena of flows from time-periodic to chaotic convection are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady flow bifurcates to a time-periodic flow with a fundamental frequency, and afterwards a period-tripling bifurcation occurs with further increase of the Rayleigh number. Chaotic convection is established after a period-doubling bifurcation. A periodic convection with period 4 appears after the first chaotic convection. At still higher Rayleigh numbers, chaotic flows reappear.

• 대한기계학회논문집
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• 제17권9호
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• pp.2304-2314
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• 1993

Natural convective flow and heat transfer in a two-dimensional square enclosure fitted with a horizontal partition are investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was situated perpendicularly at the one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were carried out with the variations of length, position and thermal conductivity of the partition, and Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height with water(Pr=4.95). As the results, an oscillatory motion of natural convection is resulted in a sudden rise of overall heat transfer, but the increase of length of partition is significantly restrained the increase of Nusselt number. The maximum heat transfer was shown just before the transition of the direction of oscillating flow. An oscillatory motion of flow was perfectly shown the stability with the decrease of the length of partition and Rayleigh number. Also, the heat transfer was raised with the increase of the thermal conductivity in proportion to the increase of the length of partition. The stability and oscillation of flow are affected by the position of partition.

• 대한기계학회논문집
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• 제16권10호
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• pp.1963-1970
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• 1992

본 연구에서는 Fig.1에 나타낸 정 등의 모델을 사용하여 공간내의 자연대류 유동을 수치적으로 해석하고 실험결과와 비교하여 수평격판에 의해서 발생하는 진동유 동의 특성을 규명하고자 한다. 본 수치해석에서는 물(Pr=4.95)을 내부유체로 하여 Rayleigh수, 공간의 폭에 대한 격판길이(L/W)및 격판의 열전도율의 변화가 자연대류 진동유동에 미치는 영향을 밝히고, 밀폐공간의 경사에 의해 진동유동이 사라지는 각 도, 즉 천이 경사각도를 찾아 내고자 한다. 이러한 유동특성을 파악하기 위하여 본 연구에서는 지배방정식을 Galerkin method를 사용한 2차원 유한요소법(FEM)으로 수치 해석하였다.

• 설비공학논문집
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• 제13권2호
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• pp.88-95
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• 2001

Transition to chaotic convection is investigated for natural convection of a fluid with Pr=0.1 in a wide-gap horizontal annuls. The unsteady two-dimensional stream-function-vorticity equation is solved with finite difference method. As the Rayleigh number is increased, the steady 'downward flow' bifurcates to a time-periodic flow with a fundamental frequency, and afterwards a period-doubling bifurcation occurs. As the Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. The route to chaos shows the Ruelle-Takens-Newhouse scenario. The flow of chaotic regime displays complex coalescence and separation of eddies in the side and lower region of the annulus.

• 대한기계학회논문집B
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• 제25권3호
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• pp.433-441
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• 2001

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

• 대한기계학회논문집
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• 제18권2호
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• pp.456-466
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• 1994

Experimental investigation was made to study the mechanism of fluid and thermal oscillation phenomena of surface-tension driven flow in a cylindrical liquid column heated from above which is the low-gravity floating zone simulated on earth. Hexadecane, octadecane, silicon oil (10cs), FC-40 and water are used as the test liquids. The onset of the oscillatory thermocapillary convection appears when Marangoni number exceeds its criteria value and is found to be due to the coupling among velocity and temperature field with the free surface deformation. The frequency of temperature oscillation decreases with increasing aspect ratio for a given diameter and Marangoni number and the oscillation level increases with Marangoni number. The flow pattern in the liquid column appears either as symmetric or asymmetric 3-D flow due to the oscillatory flow in the azimuthal direction. The free surface deformation also occurs either as symmetric or asymmetric mode and its frequency is consistent with those of flow and temperature oscillations. The amplitude of surface deformation also increases with Marangoni number.

• 한국전산유체공학회지
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• 제16권3호
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• pp.29-36
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• 2011

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body at its centered area was studied. Three different Prandtl numbers (0.01, 0.7 and 7) were considered for an effect of the Prandtl number on natural convection. A two-dimensional solution for unsteady natural convection was obtained, using Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10^4$ to $10^6$. It had been experimentally and numerically reported [1,2] that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers was presented to show the overall heat transfer characteristics in the system. And also, the isotherms and streamline distributions were presented in detail to compare the physics related to their thermal behavior.

• 대한기계학회논문집B
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• 제20권9호
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• pp.2953-2964
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• 1996

왕복유동에 의한 순간 열전달현상은, 왕복유동의 두가지 특성인 왕복주파수와 왕복거리를 나타내는 .betha.와 .gamma.에 의하여 결정되고, 그 특성에 따라 세영역으로 나누어짐을 확인하였다. 영역 I에서는 일방향유동에서와 마찬가지로 열유속이 평균온도차에 비례하고, 영역 II에서는 열유속과 평균온도차간에 약 45.deg.의 위상차가 발생하지만 모두 1차 조화성분이 주로 나타났다. 한편 영역 III의 경우에는 위상차가 생길뿐만 아니라 평균온도차에 고차 조화성분이 나타났다. 기존의 방법인 복소 Nusselt수를 고차 조화성분까지 확장하면 열유속을 평균온도차로 나타낼 수 있지만 각 조화성분의 정보를 다 알아야하므로 실제 적용이 불가능하였다.