• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권2호
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• pp.89-107
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• 2017

In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. u-velocity, v-velocity, P, T, and C. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to compute the numerical solutions of the flow variables for Reynolds numbers Re = 10, 500, and 50000 in consonance with low, moderate, and high Reynolds numbers. We have also used appropriate Prandtl (Pr) and Schmidt (Sc) numbers in consistence with relevancy of the physical problem considered. We have executed this modified MAC algorithm with the aid of a computer program developed and run in C compiler. We have also computed numerical solutions of local Nusselt (Nu) and Sherwood (Sh) numbers along the horizontal line through the geometric center at low, moderate, and high Reynolds numbers for fixed Pr = 6.62 and Sc = 340 for two grid systems at time t = 0.0001s. Our numerical solutions for u and v velocities along the vertical and horizontal line through the geometric center of the square cavity for Re = 100 has been compared with benchmark solutions available in the literature and it has been found that they are in good agreement. The present numerical results indicate that, as we move along the horizontal line through the geometric center of the domain, we observed that, the heat and mass transfer decreases up to the geometric center. It, then, increases symmetrically.

• 대한기계학회논문집B
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• 제23권2호
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• pp.226-233
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• 1999

An experimental study has been performed on natural convection heat transfer with a rapid crust formation in the molten metal pool of a low Prandtl number fluid. Two types of steady state tests, a low and high geometric aspect ratio cases in the molten metal pool, were performed. The crust thickness by solidification was measured 88 a function of boundary surface temperatures. The experimental results on the relationship between the Nusselt number and Rayleigh number In the molten metal pool with a crust formation were compared with existing correlations. The experimental study has shown that the bottom surface temperature of the molten metal layer, in all experiments. is the major influential parameter in the crust formation, duo to the natural convection flow. The Nusselt number of the case without a crust formation in the molten metal pool is greater than that of the case with the crust formation at the same Rayleigh number. The present experimental results on the relationship between the Nusselt number and Rayleigh number In the molten metal pool match well with Globe and Dropkin's correlation. From the experimental results, a now correlation between the Nusslet number and Rayleigh number in the molten metal pool with the crust formation was developed as $Nu=0.0923(Ra)^{0.302}$ ($2{\times}10^4< Ra<2{\times}10^7$).

• 태양에너지
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• 제5권2호
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• pp.11-19
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• 1985

In this paper, the interface stability not to occur mixing and entrainment between the adjacent layers has been studied in the case of the selective withdrawal of a stratum and the injection in stratified fluid formed by the density difference in a small solar pond. There are stability parameter, Richardson number, Rayleigh number and Froude number as the parameters governing stability in order to measure the interface stability on the stratified fluid. The model which could measure the interface stability on the stratified fluid was the small solar pond composed by 1 meters wide, 2 meters high, and 5 meters long. In order to measure the interface stability on the stratified fluid at the inlet port, the middle section and the outlet port, Richardson number, Rayleigh number, and Froude number involved in the parameters governing the stability were calculated by means of the data resulted from the test of the study on hydrodynamic stability between the convective and nonconvective layers in that solar pond. Richardson number written by the ratio of inertia force to buoyancy force can be used in order to measure the stability on the stratified fluid related to the buoyancy force generated from the injection of fluid. Rayleigh number written by the product of Grashof number by Prandtl number can be used in order to measure the stability of the fluid related to the heat flux and diffusivity of viscosity. Froude number written by the ratio of gravity force to inertia force can be used in order to measure the stability of the nonhomogeneous fluid related to the density difference. As the result of calculating the parameters governing stability, the interface stability on the stratified fluid couldn't be identified below the 70cm height from the bottom of the solar pond, but it could be identified above the 70cm height from it at the inlet port, the middle section and the outlet port. When compared with such the three parameters as Richardson number, Rayleigh number, Froude number, the calculated result was in accord with them at inlet port, the middle section and the outlet port. Henceforth, it is learned that even though any of the three parameters is used for the purpose of measuring the interface stability on the stratified fluid, the result will be the same with them. It is concluded that all the use of Richardson number, Rayleigh number, and Froude number, is desirable and infallible to measure the interface stability on the stratified fluid in the case of considering the exist of the fluid flow and the heat flux like the model of the solar pond.

• 한국전산구조공학회논문집
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• 제20권5호
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• pp.661-669
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• 2007

바람에 저항하는 초고층 건물, 비행기나 자동차, 물에 저항하는 선박 등은 동일한 거동을 보여준다. 즉, 유속이 빨라 질경우, 건물 혹은 비행기, 자동차, 선박 뒤편에는 마이너스 압력과 와류가 발생하게 되는데 이로 인해 건물에서는 변위가 크게 발생하게 되고, 비행기나 자동차, 선박 등에서는 속력이 저하된다. 본 연구에서는 흡입과 방출이라는 기법을 이용하여 유체의 흐름을 우리가 원하는대로 적극적으로 제어하고자 한다. 그렇게 할 수만 있다면 초고층 건물에서의 변위를 대폭 줄일 수 있을 것이고, 자동차나 비행기 선박 등은 더 빠른 속도로 달릴 수 있을 것이다. 그렇다면 문제는 유체를 제어하기 위한 최적의 흡입 혹은 방출량을 구하는 것이고, 이 최적의 양들을 어떤 방법으로 구하는 것이냐 하는 것이다. 본 연구는 최적화 기법을 사용하여 Navier-Stokes 유체를 받는 물체의 표면에서 최적의 흡입, 그리고 방출량을 결정하려는 시도에서 출발하였다. 그러나 이 문제는 큰 Reynols Number 상태에서는 높은 비선형성으로 인하여 직접 한번에 Navier-Stokes 유체의 해석조차 불가능하였고, 더군다나 너무나 많은 변수로 인하여 기존의 방법으로는 최적화는 도저히 불가능 하였다. 본 연구에서는 이를 해결하기 위한 최적화 알고리즘을 제안하고, 또한 수렴속도도 대폭 증가시키기 위한 매우 효율적인 몇 가지 방법들을 제안하였다.

• 에너지공학
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• 제24권1호
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• pp.97-103
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• 2015

파이프의 길이(Length)와 직경(Diameter), 거칠기(Roughness)에 변화를 주면서 수직 원형관내 자연대류 열전달을 측정하였다. 고부력 조건에 대한 높은 Rayleigh수를 구현하기 위하여 상사성에 기초한 물질전달실험을 수행하였다. Pr수는 2,014였다. 수직 원형관의 길이(L)는 0.1m, 0.3m, 0.5m였으며 이는 Gr수 $4.2{\times}10^7$, $1.1{\times}10^9$, $5.5{\times}10^9$에 해당한다. 각 수직 원형관에 대하여 직경(D)을 0.005m, 0.01m, 0.03m로 변화시키면서 열전달을 측정하였다. 실험결과 모든 직경(D)에 대해서 높이(L) 0.1m에서의 열전달 계수는 Le Fevre의 수직평판에 대한 층류 자연대류상관식과 일치하였다. 동일한 직경(D)에 대해서 길이(L)가 감소할수록 열전달이 증가하였다. 그리고 동일한 길이(L)에 대하여 직경(D)이 증가하였을 때는 열전달이 감소하였다. 파이프 내부 표면에 거칠기를 주어 일반 수직원형관과 열전달을 비교하였을 때, 층류영역에서는 열전달의 차이가 있었으나, 천이영역에서는 열전달 차이가 없었다.