A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure

Fusegi, Toru; Hyun, Jae Min; Kuwahara, Kunio; Farouk, Bakhtier

doi:10.1016/0017-9310(91)90295-p

Cited by 509 publications

(230 citation statements)

References 11 publications

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“…It is concluded that 2100-10500 number of control volumes depending on aspect ratio and the Rayleigh number is suitable for this study. The numerical procedure is validated with the benchmark solution of De Vahl Davis [10] and Fusegi et al [11]. As seen in Table, the numerical procedure shows a very good agreement with the benchmark solutions for entire range of the Rayleigh number where the discrepancy is less than 8%.…”

Section: Problem Description and Numerical Methodsmentioning

confidence: 80%

Effect of Aspect Ratio on Natural Convection in a Cavity with Wavy Walls

2015

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In this study, flow characteristics and natural convection in a cavity with two wavy walls is studied numerically. The wavy walls of the cavity are isothermal and at different temperatures while other straight walls are adiabatic. The fluid considered inside the cavity is air having Prandtl number of 0.71. A parametric study is conducted for various aspect ratios (1 ≤ AR ≤ 5), Rayleigh numbers (10 3 ≤ RaH ≤ 10 6 ) and inclination angles (0 • ≤ θ ≤ 180 • ). Streamlines, isotherms and local and mean Nusselt numbers are presented to show the effect of the investigated parameters on the flow field and heat transfer.

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Section: Problem Description and Numerical Methodsmentioning

confidence: 80%

Effect of Aspect Ratio on Natural Convection in a Cavity with Wavy Walls

2015

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“…Tables 7 and 8 give the average Nusselt number on the wall, the maximum horizontal velocity along the vertical centerline and the maximum vertical velocity along the horizontal centerline at different mesh sizes and Rayleigh numbers. It is observed that, be refining the mesh resolution, both USTLBM and STLBM can converge to the reference data [30][31][32][33][34]. Such performance indicates the robustness of USTLBM and STLBM on non-uniform mesh in three-dimensional scenarios.…”

Section: D Natural Convection In a Cubic Cavitymentioning

confidence: 78%

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

2017

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An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman-Enskog (C-E) expansion analysis are resolved in a predictor-corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM). Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

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“…Resorting on the YZ adiabatic walls configuration, Fusegi et al (1991a) reported that even for low Ra , the flow within the cavity is three-dimensional, where the modulus of the velocity component in the transverse direction w is one order of magnitude smaller than the other components. For higher Ra , the vertical velocity component v becomes more important than the horizontal component u .…”

Section: Resultsmentioning

confidence: 99%

“…One of the first threedimensional investigations was made by Aziz and Hellums (1967), where the computational capacity at that time limited the study to relatively coarse grids, but allowed a closer approximation of the real flow (which is three-dimensional in nature). Later, due to the rapid development of computer technologies and numerical methodologies, new studies have been conducted (Fusegi et al, 1991a;Janssen et al, 1993, Tric et al, 2000Wakashima and Saitoh, 2004;Trias et al, 2010;Padilla et al, 2013) to better characterize and evaluate the heat transfer rate. Fusegi et al (1991a) aimed to show the three-dimensional nature of the various flow fields induced by the thermal conditions imposed on the walls of a cubic cavity for Ra between 10 3 and 10 6 .…”

Section: Introductionmentioning

confidence: 99%

“…Later, due to the rapid development of computer technologies and numerical methodologies, new studies have been conducted (Fusegi et al, 1991a;Janssen et al, 1993, Tric et al, 2000Wakashima and Saitoh, 2004;Trias et al, 2010;Padilla et al, 2013) to better characterize and evaluate the heat transfer rate. Fusegi et al (1991a) aimed to show the three-dimensional nature of the various flow fields induced by the thermal conditions imposed on the walls of a cubic cavity for Ra between 10 3 and 10 6 . These authors used a finite difference scheme with third order accuracy and the numerical results were compared with two-dimensional experimental and numerical data, where inconsistencies with experimental data were found.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Analysis of Natural Convection inside Cubical Cavities Exposed to Diverse Boundary Conditions

Padilla

Lourenço²,

Campo³

2016

AJHMT

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This paper presents a numerical study of fluid flow and natural convection inside cubical cavities using the finite volume method with second order schemes. Cubical cavities of various sizes with three different thermal configurations were considered, where two opposite vertical walls are isothermal and the other walls are either adiabatic or conducting (with linear temperature variation). The numerical simulations were performed for air and gases with Prandtl number 0.71 under the influence of variable Rayleigh numbers covering the range 10 3 -10 7 . The effects of the three thermal configurations in terms of velocities and temperatures were investigated for both steady and unsteady flow regimes. Additionally, the magnitudes of local and average Nusselt numbers in each direction of the cubical cavity were scrutinized. Using conducting walls, the heat transfer analysis in different directions divulged that the heat flow through the top/bottom walls surpasses 1/3 of the total heat flow of the cubical cavity. Overall, the collection of numerical results demonstrates good agreement when compared with experimental-based and numerical-based publications.

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A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure

Cited by 509 publications

References 11 publications

Effect of Aspect Ratio on Natural Convection in a Cavity with Wavy Walls

Effect of Aspect Ratio on Natural Convection in a Cavity with Wavy Walls

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Numerical Analysis of Natural Convection inside Cubical Cavities Exposed to Diverse Boundary Conditions

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