• Journal of Mechanical Science and Technology
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• 제15권5호
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• pp.656-664
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• 2001

A theoretical analysis is performed to describe the qualitative behavior of transient buoyant flows in a vertical channel. Consideration is given to the case of a fluid with a pre-existing stratification. The fluid motion is generated by giving impulsive anti-symmetric step-changes in temperature at the vertical left ad right sidewalls. The qualitative character of the flow is shown to be classified in the Rayleigh number (Ra)-Prandtl number ($sigma$) diagram. The transitory approach to the steady state can be monotonic or oscillatory, depending on ($sigma$-1)$^2$$pi$$^4$ 4$sigma$$R_a$. The prominent characteristics of time-dependent flow are discussed for large $R_a$. The profiles of temperature and velocity in the transient phase are depicted, which disclose distinctive time scales of motion. The transient process is shown to be sensitive to the Prandtl number. The detailed evolutions of flow and temperature fields are illustrated for large $R_a$.

• Nuclear Engineering and Technology
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• 제30권6호
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• pp.496-506
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• 1998

This paper deals with the computational modeling of buoyancy-driven turbulent heat transfer involving spatially uniform volumetric heat sources in semicircular geometry. The Launder & Sharma low-Reynolds number k-$\varepsilon$ turbulence model without any modifications and the SIMPLER computational algorithm were used for the numerical modeling, which was incorporated into the new computer code CORE-TNC. This computer code was subsequently benchmarked with the Mini-ACOPO experimental data in the modified Rayleigh number range of 2$\times$10$^{13}$ $\times$10$^{14}$ . The general trends of the velocity and temperature fields were well predicted by the model used, and the calculated isotherm patterns were found to be very similiar to those observed in previous experimental investigations. The deviation between the Mini-ACOPO experimental data and the corresponding numerical results obtained with CORE-TNC for the average Nusselt number was less than 30% using fine grid in the near-wall region and the three-point difference formula for the wall temperature gradient. With isothermal pool boundaries, heat was convected predominantly to the upper and adjacent lateral surfaces, and the bottom surface received smaller heat fluxes.

• 대한기계학회논문집B
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• 제21권2호
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• pp.235-251
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• 1997

A numerical simulation on the combined natural convection and radiation is carried out in a partially open rectangular enclosure with a heater by using the finite volume and the S-8 discrete ordinate methods. The fluid inside the enclosure is considered as an absorbing, emitting and anisotropic scattering media. The heater causes a natural circulation of the fluid (10$^{5}$ $^{9}$ ) which results in significant in-flow of the ambient cold fluid through the partially open wall. Comparing the results of pure convection with those of the combined convection- radiation, the combined heat transfer results with small Planck numbers (P$_{l}$ <1.0) show much stronger circulation than those of the pure convection, and the fluid circulation is more evident for larger Rayleigh numbers. When one of three radiative properties - the medium absorption coefficient, the wall reflectivity, and the scattering albedo - increases, the fluid circulation and the heat transfer in the enclosure are reduced. The location of the heater and the open ratio of the right wall are also shown to affect the fluid circulation and heat transfer significantly. However, the anisotropy of the scattering phase function is shown to be unimportant for the fluid circulation and heat transfer within the enclosure considered in this study.

• 태양에너지
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• 제7권2호
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• pp.86-97
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• 1987

Natural convection in the annulus between a horizontal conducting tube and a cylinder with spacers has been studied by 2-dimensional numerical method with finite difference techniques. The effects of Rayleigh number, conductivities of conducting tube and spacer, and position of spacers were studied analytically. In case of vertical spacers, the maximum local Nusselt number appears at ${\theta}{\approx}50^{\circ}$ in a conducting tube and ${\theta}{\approx}30^{\circ}$ in an outer cylinder, The local Nusselt numbers show positive values on the lower spacer, but negative values on the surface of the upper spacer. In case of horizontal spacers, the flow over the spacer is more active than that of under the spacer as the Rayleigh number increases. The maximum local Nusselt appeares at ${\theta}=180^{\circ}$ in a conducting tube and at ${\theta}=0^{\circ}$ in an outer cylinder. The local Nusselt numbers show positive values on the upward surface, but negative values on the downward surface of spacer. As the dimensionless conductivity increases, the mean Nusselt number remarkably increases at $K_w/K_f<48$ and show almost even at $K_w/K_f{\ge}48$. The mean Nusselt number of a conducting tube with vertical spacers is 5.12 percent less and with horizontal spacers is 11.33 percent less than that of a conducting tube without spacer at $Ra=10^4$, Pr = 0.7 and $K_w/K_f=48$.

• Nuclear Engineering and Technology
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• 제49권7호
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• pp.1405-1413
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• 2017

To investigate the heat loads imposed on a reactor vessel through the natural convection of core melts in severe accidents, mass transfer experiments were performed based on the heat transfer/mass transfer analogy, using two- (2-D) and three-dimensional (3-D) facilities of various heights. The modified Rayleigh numbers ranged from $10^{12}$ to $10^{15}$, with a fixed Prandtl number of 2,014. The measured Nusselt numbers showed a trend similar to those of existing studies, but the absolute values showed discrepancies owing to the high Prandtl number of this system. The measured angle-dependent Nusselt numbers were analyzed for 2-D and 3-D geometries, and a multiplier was developed that enables the extrapolation of 2-D data into 3-D data. The definition of $Ra^{\prime}_H$ was specified for 2-D geometries, so that results could be extrapolated for 3-D geometries; also, heat transfer correlations were developed.

• 대한기계학회논문집
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• 제19권7호
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• pp.1720-1730
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• 1995

Finite-difference analysis was conducted to study the natural convection of a stably stratified salt-water solution in an annulus due to lateral heating. The main purpose of this study is to examine in detail the multi-layered flow structure. Calculation was thus made for R $a_{\eta}$=2*10$^{5}$ and 6.5*10$^{5}$ . Formation of layered flow structure, merging process of layers, the corresponding temperature and concentration distributions, Nusselt number variations with time are examined. Numerical results show that in each layer, the temperature profile looks 'S`-shaped and the concentration profile is uniform due to the convective mixing. The formation of the roll and the layer is governed by natural convection due to the temperature gradient and the merging process of the layer by diffusion of the concentration.ation.

• 설비공학논문집
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• 제16권3호
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• pp.211-217
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• 2004

Effect of a solid insert on thermal stratification in the natural convection enclosure is numerically investigated. The enclosure consists of two differently heated vertical walls and two adiabatic horizontal walls. A solid insert is located in the middle of the enclosure. The non-dimensional governing equations are solved by using the SIMPLER algorithm. The computations are carried out with the variations of thermal conductivity, width and height of the solid insert. The Prandtl number of the fluid in an enclosure is fixed at Pr=0.71, Two cases of Rayleigh number are considered in the present study, i.e., Ra:10$^3$ and 10$^{6}$ . The thermal stratification attenuates as thermal conductivity, width, and height of the solid insert are increased. As the thermal conductivity ratio of a solid insert to fluid increases beyond (equation omitted)10$^3$, the thermal stratification ratio shows an asymptotic value.

• 설비공학논문집
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• 제24권3호
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• pp.247-255
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• 2012

Numerical calculations are carried out for the natural convection in a square enclosure with two hot cylinders induced by temperature difference between a cold outer rectangular cylinder and two hot circular cylinders. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model two inner circular cylinders based on finite volume method, for different Rayleigh numbers varying over the range of $10^3$ to $10^5$. The study goes further to investigate the effect of the location of two cylinders on the heat transfer and fluid flow. The location of inner circular cylinders is changed vertically along the center-line of square enclosure. The changes of heat transfer quantities have been presented.

• 설비공학논문집
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• 제3권4호
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• pp.222-230
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• 1991

Conjugate heat transfer by steady laminar natural convection from a conducting tube with two vertical axial fins has been studied by a finite difference numerical procedure under basic conditions; $Ra=10_6$, Pr = 5 and $L_F=0.15$. The maximum local tube Nusselt number appears at ${\theta}=140^{\circ}$ for $L_F=0.06$, at ${\theta}=130^{\circ}$ for $L_F=0.30$ and at ${\theta}=120^{\circ}$ for $L_F=0.30$, $L_F=0.06$, respectively. The maximum mean Nusselt number shows at $L_F=0.18$ for the downward fin and at $L_F=0.12$ for the upward fin. Therefore the optimized fin length is $L_F{\approx}0.15$ under these conditions. At $L_F=0.15$, the mean Nusselt number by increasing Rayleigh number is remarkably increased for downward fin and then is slowly increased except for downward fin, it by increasing Prandtl number is apparently increased at $Pr{\leq}2$, and slightly increased at Pr>2.

• 한국수소및신에너지학회논문집
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• 제34권3호
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• pp.274-282
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• 2023

This study conducted direct numerical simulations of the natural convection phenomena of gaseous hydrogen in a physical storage container containing four circular cylinders. Rayleigh numbers (Ra) in the range of 10⁴≤Ra≤10⁶ and a Prandtl number (Pr)=0.69 (gaseous hydrogen) were considered. The main parameter is a horizontal distance of four circular cylinders and the values of ε_h=0.1, 0.2, 0.3, 0.4, and 0.5 are considered. The flow and thermal structures and corresponding heat transfer characteristics are investigated with respect to the transition of the flow regime. The time- and surface-averaged Nusselt number on the cylinder surface and the wall of physical storage container increased by about 57% and 69% according to the Ra and ε_h, respectively. Thus, the horizontal distance has an influence on the heat transfer characteristics on natural convection of gaseous hydrogen.