• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.9
• /
• pp.1210-1218
• /
• 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
• /
• v.3 no.1
• /
• pp.73-81
• /
• 1998

The effect of vertical or horizontal throughflow on natural convection in horizontal porous layer was investigated. The computations were performed by employing Darcy-Brinkman-Forchheimer equation to consider the effect of inertia and viscous effect. The patterns of streamlines and isotherms are observed by changing the strength of throughflow. The vertical throughflow stabilizes the natural convection in porous layer. It also disturbs the developing vertical and horizontal velocity component of natural convection cell and increases the critical modified Rayleigh number. The horizontal throughflow influences the stabilization of natural convection in porous layer much more than the vertical throughflow. And it changes a stable convection into a oscillatory convection.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.10
• /
• pp.1963-1970
• /
• 1992

An oscillatory motion of the natural convection in a two dimensional, partially divided square enclosure heated from below, and fitted with a partition is 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 mid-height of the one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were performed with the variation of the length and the thermal conductivity of the partition, and Rayleigh number based on the temperature difference between horizontal walls and the enclosure height with water(Pr=4.95). also, the effect of the inclination angles was studied for the transition to the oscillating flow. As the results, it was found that the intensity and frequency of oscillatory motion were affected significantly by the Rayleigh number and the length of partition. The effect of oscillatory motion was weaken with the increase of the thermal conductivity of partition. The inclination angle for the transition was raised with the increase of Rayleigh number and the length of partition.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.9
• /
• pp.2304-2314
• /
• 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.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.1560-1565
• /
• 2003

Thermocapillary convection in an open cylindrical annulus heated from the inside wall is investigated by two-dimensional numerical simulations. The deformable free surface is obtained as a solution of the coupled transport equations at fixed Prandtl and aspect ratio. Only steady convection can be realized in this axisymmetric computations with either non-deformable or deformable surfaces. Dynamic free-surface deformations do not induce transitions to oscillatory convection even at large Reynolds numbers. Free surfaces are convex near the cold wall due to the stagnation point, and concave near the hot wall. Free surface deformation increases with increasing Ca at a fixed Re. Two peaks appear at the free surface with low Re, while additional ripples, four peaks, occur at larger Re. Thermocapillary convection in the open annulus interior is insensitive to variations in Ca.

• Proceedings of the KSME Conference
• /
• 2008.11b
• /
• pp.2248-2253
• /
• 2008

A numerical study on oscillatory thermocapillary flow in half-zone has performed to understand the effect of axial rotation. 2d unsteady code is developed to observe the onset of oscillation. 2cs Silicone oil with Prandtl number of 26.5 is used as a working fluid. The critical temperature difference at onset of oscillation is investigated under the different aspect ratios and rotation modes. It is shown that the onset of oscillation is delayed when aspect ratio reduces and rotating speed increases. The oscillatory flow is strongly reduced under top rotation and co-rotation modes, while it is augmented under bottom rotation and counter-rotation modes. It is thought that interaction between return flow and bottom wall is important to explain the oscillatory flow.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.3
• /
• pp.360-372
• /
• 1998

This study deals with the interaction between buoyancy-induced convection and externally imposed excitation in the form of harmonic rocking and the effect of the interaction upon heat transfer in low-Pr liquids. A wide array of system responses are discussed using the spectral collocation numerical technique. The superposition of buoyancy and Coriolis forces leads to complex fluid flow and heat transfer. The transition to chaotic convection is accelerated, and heat transfer rates are reduced as the enclosure is excited at the fundamental frequency of oscillation associated with the pure buoyancy-driven case. Average heat transfer rates are correlated for Pr=0.02 and 0.03. The heat transfer is affected more in the Pr=0.03 liquid than the case of Pr=0.02.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.26 no.4
• /
• pp.622-628
• /
• 2002

Numerical analysis has been carried out for two-dimensional steady and unsteady mixed convection in the annulus between co-rotating horizontal cylinders with a heated inner cylinder. The ratio of annulus gap($\sigma$) is taken from 1 to 10 and the order of mixed-convection parameter B(=Gr/(1+Re)$^2$) varies from 10$^4$to $10^0$. The flow patterns over this parameter range are steady multicellular, oscillatory multicellular or steady unicellular. The addition of co-rotating of both cylinders stabilizes the flow in the annulus and weakens the unsteadiness. Even in the large values of rotating parameter such as of $10^0$/($\sigma$=2) and 10$^2$($\sigma$=10), the flow pattern becomes asymptotic to the steady unicellular flow, like as in the rigid-body rotating flow.

• Journal of computational fluids engineering
• /
• v.16 no.3
• /
• pp.52-58
• /
• 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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.13 no.2
• /
• pp.88-95
• /
• 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.