• 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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.4
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• pp.285-294
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• 1993

An oscillatory motion of natural convection in a two-dimensional square enclosure fitted with a horizontal 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 positioned perpendicularly at the mid-height of 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 the partition length 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 has perfectly shown the periodicity with the decrease of Rayleigh number, and the stability was reduced to a chaotic state with the increase of Rayleigh number. The period of oscillation gets shorten with the decrease of the partition length and the increase of Rayleigh number. The frequency of oscillation obtained by the variations of stream function is more similar to the experimental results than that of the average Nusselt number. The stability of oscillation grows worse with the increase of Rayleigh number. The transition Rayleigh number for the chaos is gradually decreased with the increase of the partition length.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2397-2408
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• 1996

A numerical study was made of the control of transient oscillatory flow modes in Czochralski convection. The reduction of temperature oscillation was achieved by changing the rotation rate of crystal rod, .OMEGA.$_{S}$=.OMEG $A_{S0}$(1+ $A_{S}$sin(2.pi. $f_{S}$/ $t_{p}$t)). The temporal behavior of oscillation flow was scrutinized over broad ranges of two parameters, i.e., the rotation amplitude( $A_{S}$.leq.0.5) and the nondimensional frequency (0.9.leq. $f_{S}$.leq.1.5). The mixed convection parameter was ranged 0.225.leq.Ra/PrR $e^{2}$.leq.0.929, which encompassed the buoyancy-and forced-dominant convection regimes. Computational results revealed that the temperature oscillations could be reduced effectively by a proper adjustment of the control parameters. The uniformity of temperature distribution near the crystal rod was examined. The control of oscillatory flow modes was also made for a realistic, low value of Pr.

• Journal of computational fluids engineering
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• v.11 no.2 s.33
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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.

• 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.

• Fisheries and Aquatic Sciences
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• v.7 no.2
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• Journal of computational fluids engineering
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• v.6 no.3
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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.

• 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.

• Nuclear Engineering and Technology
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• v.44 no.3
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.10a
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• pp.148-148
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• 1998