• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.6
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• pp.804-810
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• 2001

Transition of flows in natural convection in a horizontal cylindrical annulus is investigated for the fluid with Pr=0.2. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped eddy flow bifurcates to a time-periodic flow with like-rotating eddies. After the first Hopf bifurcation, however, a reverse transition from oscillatory to a steady flow occurs by the flow pattern variation. Hysteresis phenomenon occurs between the solution branches of up-scan and down-scan stages, and dual solutions with one steady and one oscillatory flow are found. Overall Nusselt of the flows at the flows at the down-scan stage is greater than that at the up-scan stage.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1440-1448
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• 2004

Multiple solutions in natural convection of air (Pr=0.7) between two horizontal walls with mean temperature difference and the same periodic nob-uniformities are investigated. An analytical solution is found for small Rayleigh number, and the general solution is investigated by using a numerical method. In the conduction-dominated regime, two upright cells are formed between two walls over one wave length. When the wave number is small, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximately square-shape cells. And several kinds of multiple flows classified by the number of cells are found.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.6
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• pp.435-442
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• 2009

Three-dimensional heat transfer characteristics for natural convection flows are numerically investigated in the doubly-inclined cubical-cavity according to the variation of a newly defined orientation angle �� of the hot wall surface from horizontal plane at moderate Rayleigh numbers. Numerical simulations of laminar flows are conducted in the range of Rayleigh numbers($10^4{\leq}Ra{\leq}10^5$) and $0^{\circ}{\leq}{\alpha}90^{circ}$ with a solution code(PowerCFD) employing unstructured cell-centered method. Comparisons of the average Nusselt number at the cold face are made with benchmark solutions and experimental results found in the literature. It is found that the average Nusselt number at the cold wall has a maximum value around the specified orientation ${\alpha}$ at each Rayleigh number. Special attention is also paid to three-dimensional thermal characteristics in natural convection according to new orientation angles at Ra��= $1{\times}10^5$, in order to investigate a new additional heat transfer characteristic found in the range of above Ra = $6{\times}10^4$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.9
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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.

• Journal of computational fluids engineering
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• v.4 no.2
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• pp.1-8
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• 1999

Natural convection in a horizontal annulus with the inner cylinder heated by the application of a constant heat flux and the isothermally cooled outer cylinder is considered, and the transition of flows and the bifurcation phenomenon are numerically investigated for air with Pr=0.7. The zero initial condition always induces a crescent-sheped eddy flow. A bicellular flow in which the fluid descends along the vertical central plane of the annulus can be obtained at high Rayleigh number by introducing artificial numerical disturbances. Dual solutions are found above a certain critical Rayleigh number. Hysteresis phenomena have not been observed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.4 s.247
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• pp.337-342
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• 2006

Natural convection flows in a cubical air-filled cavity that has one pair of opposing faces isothermal at different temperatures, $T_h\;and\;T_c$, respectively, the remaining four faces having a linear variation from $T_c\;to\;T_h$ are numerically simulated by a solution code(PowerCFD) using unstructured cell-centered method. Special attention is paid to three-dimensional flow and thermal characteristics according to the variation of inclination angle $\theta$ of the isothermal faces from horizontal: namely $\theta=0^{\circ},\;15^{\circ},\;30^{\circ},\;45^{\circ},\;50^{\circ},\;60^{\circ},\;75^{\circ}\;and\;90^{\circ}$. Comparisons of the average Nusselt number at the cold face are made with experimental benchmark results found in the literature. It is demonstrated that the average Nusselt number at the cold face has a maximum value around the inclination angle of $50^{\circ}$. It is also found that the code is capable of producing accurately the nature of the laminar convection in a cubical air-filled cavity with differentially heated walls.

• Journal of computational fluids engineering
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• v.5 no.3
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• pp.40-46
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• 2000

Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows from steady to oscillatory convection is investigated for the fluid with Pr=0.1. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped flow bifurcates to a time-periodic flow with like-rotating eddies. And afterwards, a transition to an oscillatory multicellular flow with a counter-rotating eddy on the top of the annulus occurs. A transition from steady to an oscillatory flow occurs, but dual solutions and hysteresis phenomena are not observed.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.94-101
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• 2002

Convection-dominated melting in a rectangular cavity is analyzed numerically with particular attention to the multi-cellular flows in the melt. At the earlier stage of the melting, the melt region is quite similar to a cavity with high aspect rati71, where the multi-cellular natural convection appears. Numerical results show that the formation and evolution of the multiple flow cells in the melt region is approximately similar to t]tat of a single-phase flow in a tall cavity with the same aspect ratio; however, the continuous change of the melt region due to the melting affects the detailed process. Also, numerical aspects for the prediction of the detailed flow structure in the melt are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1784-1795
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• 1998

Natural convection of low Prandtl number fluids with $Pr{\leq}0.2$ in a narrow horizontal annulus is numerically investigated. For $Pr{\leq}0.2$, hydrodynamic instability induces oscillatory multicellular flows consisting of multiple like-rotating cells. For a fluid with $Pr{\approx}0$, the region in which instability of conduction regime first forms is near the vertical section of annulus, and the multiple cells are distributed uniformly in the lower and upper regions of annulus. As Pr increases, however, the cells are shifted upwards. The like-rotating cells drift downward, as time goes on, and the speed of travel increases with increase of Pr. For a fluid with Pr=0.1, a flow with period-4 solution is observed between chaotic states.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.2
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• pp.169-176
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• 2000

Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows and the bifurcation phenomenon are investigated for the fluids with Pr=0.2 and 0.3. At Pr=0.2, a bicellular flow pattern is observed at high Rayleigh number, and the solution is unique. At Pr=0.3, both the steady unicellular and bicellular flows exist above a certain critical Rayleigh number. For the fluids of Pr=0.2, the bicellular flow can be obtained by the impulsive heating of the inner cylinder, but it is not obtained from the zero initial condition for Pr=0.3. Hysteresis phenomena have not been observed. A transition from a bicellular flow to a unicellular flow occurs for Pr=0.3.