• 대한공업교육학회지
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• 제33권2호
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• pp.300-311
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• 2008

두 벽면이 서로 다른 평균 온도와 일정한 위상 차이 하에서 작은 파동수의 정현적인 온도 분포를 갖는 시스템에서의 자연 대류를 조사한다. 벽면 온도 분포의 파동수 k=0.5이고 위상차는 ㄱ/2 이며, 고려하는 유체는 Pr =0.7인 공기이다. 작은 Rayleigh 수의 전도 영역에서는 한 주기에 걸쳐 약간 기울어진 형태의 두 개의 큰 셀이 형성된다. 그러나 Rayleigh 수가 증가하면 열적으로 불안정한 영역에서 여러 개의 셀이 형성되는 다수 셀 유동이 일어난다. 다수 셀 영역에서 과도기적인 기간에서는 일시적으로 공간적인 점대칭성이 깨어지기도 하지만 정상 상태의 유동장은 언제나 대칭성을 만족한다. 유동 형태의 천이가 일어나는 임계 Rayleigh 수 부근에서는 Nusselt 수가 급격하게 증가한다.

• 대한공업교육학회지
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• 제30권2호
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• pp.123-129
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• 2005

A Rayleigh-Benard problem with non-uniform wall temperatures of the form, $T_L=T_1+{\delta}{\Delta}T{\sin}kx$ and $T_U=T_2-{\delta}{\Delta}{\sin (kx)$, is numerically investigated. In the conduction-dominated regime with small a Rayleigh number, a two-tier structure appears with two counter-rotating rolls stacked on the top of each other. 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 approximetely square-shape cells. Four multiple flows and dual flows classified by the number of cells are found at k=0.5 and k=1, respectively.

• 한국전산유체공학회지
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• 제9권4호
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• pp.1-6
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• 2004

This study investigates the transition of flows in a natural convection problem with periodic wall temperatures of the form, T/sub L/=T₁＋δ Tsinκχ and T/sub L/=T₂＋δ Tsinκχ .The fluid considered is air with P/sub γ/=0.7. In the conduction-dominated regime with a small Rayleigh number, two large cells are formed over one wave length, for all wave numbers. When k≤1.8, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The flow patterns are classified by the number of eddies over one wave length, and several kinds of transition phenomena, such as 2→3→4, 4→3→2, and 2→4 eddy flow, occur with increase( or decrease) of the Rayleigh number. Dual solutions are found above a critical Rayleigh number, and an anomalous bifurcation is observed.

• 설비공학논문집
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• 제5권4호
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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.

• 대한설비공학회지:설비저널
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• 제12권4호
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• pp.234-239
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• 1983

수직관내에서 공기의 자연대류 열전달 연구가 유체의 지배방정식에 대한 이론해석과 실험에 의하여 수행되었다. 관내에서 공기의 대류열전달 특성을 조사하기 위하여 무차원 Rayleigh수가 도입되었으며, 이 Rayleigh 수와 Nusselt수 사이의 관계를 유한차분법의 수치해석과 실험으로 서로 비교하였다. 실험에서 얻은 결과와 이론치가 서로 잘 일치하고 있음을 알았으며, 또한 Nusselt와 Rayleigh수 사이의 관계식을 얻었다.

• Advances in aircraft and spacecraft science
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• 제5권4호
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• pp.411-430
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• 2018

This computational study examines the augmentation of classic 2-D Rayleigh-$B{\acute{e}}nard$ convection by the addition of periodically-spaced transverse fins. The fins are attached to the heated base of the cavity and serve to partition the cavity into 'units' with different aspect ratios. The respective impacts upon heat transfer of the fin configuration parameters - including spacing, height, thickness and thermal conductivity - are systematically examined through numerical simulations for a range of laminar Rayleigh numbers (0 < Ra < $2{\times}10^5$) and reported in terms of an average Nusselt number. The selection of the low Rayleigh number regime is linked to likely scenarios within aerospace applications (e.g. avionics cooling) where the cavity length scale and/or gravitational acceleration is small. The net heat transfer augmentation is found to result from a combination of competing fin effects, most of which are hydrodynamic in nature. Heat transfer enhancement of up to $1.2{\times}$ that for a Rayleigh-$B{\acute{e}}nard$ cavity without fins was found to occur under favorable fin configurations. Such configurations are generally characterized by short, thin fins with half-spacings somewhat less than the convection cell diameter from classic Rayleigh-$B{\acute{e}}nard$ theory. In contrast, for unfavorable configurations, it is found that the introduction of fins can result in a significant reduction in the heat transfer performance.

• 한국전산유체공학회지
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• 제21권3호
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• 대한기계학회논문집B
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• 제28권11호
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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.

• Nuclear Engineering and Technology
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• 제54권9호
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• pp.3540-3550
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• 2022

The supercritical carbon dioxide (S-CO₂) Brayton cycle is an important energy conversion technology for the fourth generation of nuclear energy. Since the printed circuit heat exchanger (PCHE) used in the S-CO₂ Brayton cycle has narrow channels, Rayleigh-Bénard (RB) convection is likely to exist in the tiny channels. However, there are very few studies on RB convection in supercritical fluids. Current research on RB convection mainly focuses on conventional fluids such as water and air that meet the Boussinesq assumption. It is necessary to study non-Boussinesq fluids. PRB convection refers to RB convection that is affected by horizontal incoming flow. In this paper, the computational fluid dynamics simulation method is used to study the PRB convection phenomenon of non-Boussinesq fluid-supercritical carbon dioxide. The result shows that the inlet Reynolds number (Re) of the horizontal incoming flow significantly affects the PRB convection. When the inlet Re remains unchanged, with the increase of Rayleigh number (Ra), the steady-state convective pattern of the fluid layer is shown in order: horizontal flow, local traveling wave, traveling wave convection. If Ra remains unchanged, as the inlet Re increases, three convection patterns of traveling wave convection, local traveling wave, and horizontal flow will appear in sequence. To characterize the relationship between traveling wave convection and horizontal incoming flow, this paper proposes the relationship between critical Reynolds number and relative Rayleigh number (r).

• 설비공학논문집
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• 제13권3호
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• pp.145-152
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• 2001

Low Rayleigh number thermal convection in a fluid layer confined between two-infinite horizontal walls kept at spatially sinusoidal temperature distributions, T_L=T_m+\Delta T\sin \kappax,\;T_U=T_m+\Delta T\sin(\kappax-\beta)$, is theoretically investigated by a regular perturbation expansion method. For small wave numbers, an upright cell is formed between the two walls at $\beta$=0. The cell is tilted, as the phase difference increases, and a flow with tow counter-rotating eddies occurs at $\beta=\pi$. when the wave number is large, isolated eddies are formed near the lower and upper walls, for all the phase differences. There exists a wave number at which maximum heat transfer rate at the walls occurs, at each of the phase differences. And the wave number increases with increase of the phase difference. for a fixed wave number, the heat transfer rate decrease with increase of the phase difference.