• 한국전산유체공학회지
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• 제22권1호
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• pp.110-115
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• 2017

Natural convection of a fluid with the Prandtl number of 7(water) in a horizontal annulus with constant temperature walls is numerically investigated. The inner cylinder is hotter than the outer cylinder. The flows are classified by the number of eddies in a half annulus. It is found that dual or triple solutions exists above a critical Rayleigh number for an annulus with a aspect ratio $D_i/L=4$. Transitions of $3{\rightarrow}1$ and $2{\rightarrow}1$ eddy flow occur with decrease of Rayleigh number. However, reverse transitions of $1{\rightarrow}3$ and $1{\rightarrow}2$ eddy flow do not occur with increase of Rayleigh number, and no hysteresis phenomenon is observed. In the regime of triple solutions, the 3 eddy flow has the largest mean Nusselt number value and the 1 eddy flow has the smallest value.

• 대한기계학회논문집B
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• 제22권12호
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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.

• 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.

• 대한기계학회논문집B
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• 제24권2호
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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.

• 한국전산유체공학회지
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• 제5권3호
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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.

• 한국전산유체공학회지
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• 제6권3호
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• pp.1-9
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• 2001

Mixed convection in a horizontal annulus is considered, and the effect of a forced flow on the natural convective flow is investigated. The inner cylinder is hotter than the outer cylinder, and the outer cylinder is rotating with constant angular velocity with its axis at the center of the annulus. The unsteady streamfunction-vorticity equation is solved with a finite difference method. For the fluid with Pr=0.7, there appear flows with two eddies, one eddy, or no eddy according the Rayleigh and Reynolds numbers. The rotation of the outer cylinder reduces the heat transfer rate at the wall of the annulus. The oscillatory multicellular flow of a low Prandtl number fluid with Pr=0.01 can be effectively suppressed by the forced flow.

• 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.

• 한국전산유체공학회지
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• 제4권2호
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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.

• 한국전산유체공학회지
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• 제16권3호
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• pp.52-58
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• 2011

This study investigates the bifurcation sequence to chaos in a horizontal annulus with a constant heat flux wall. After the first Hopf bifurcation from a steady to a simple time-periodic flow with a fundamental frequency, quasi-periodic flows with two or three incommensurable frequencies appear. A reverse transition from a quasi-periodic flow to a simple periodic flow is observed with increase of Rayleigh number. And finally, chaotic convection is established after appearance of three incommensurable frequencies at a high Rayleigh number. Simple periodic flows exist between quasi periodic flows. The transition route to chaos of the present simulations follows the Ruelle-Takens route.

• 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.