Natural convection inside cubical cavities: numerical solutions with two boundary conditions

Padilla, Elie Luis Martínez; Lourenço, Marcos; Neto, Aristeu da Silveira

doi:10.1007/s40430-013-0033-y

Cited by 8 publications

(8 citation statements)

References 15 publications

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“…2. The numerical results from the present paper are slightly closer to those reported in the numerical work of Padilla et al [20] than those from the experimental work of Krane and Jessee [19]. The NOB results also presented good agreement with Krane and Jessee [19] and Padilla et al [20], as shown in Fig.…”

Section: Validation Of the Numerical Modelsupporting

confidence: 88%

“…where T east represents the temperature at the east wall and T west represents the temperature at the west wall. The simulations using OB demonstrated good agreement with the experimental data of Krane and Jessee [19] and with the numerical data of Padilla et al [20], as observed in Fig. 2.…”

Section: Validation Of the Numerical Modelsupporting

confidence: 86%

“…Natural convection simulations in a cubic cavity assuming a Rayleigh number of 1:89 Â 10 5 were performed using OB and NOB for validation purposes. Temperature profiles were plotted and then compared with the results of Krane and Jessee's experimental study [19] and the numerical results of Padilla et al [20].…”

Section: Validation Of the Numerical Modelmentioning

confidence: 99%

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An extension of Oberbeck–Boussinesq approximation for thermal convection problems

Duarte

Melo

Villar

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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An extension of the Oberbeck-Boussinesq approximation (OB) with expressive thermal effects is investigated to model specific mass with a temperature-dependent approach. An expansion of OB is proposed using a mathematical formulation with null velocity divergence in the continuity equation and variable specific mass in the momentum and energy equations (NOB). The NOB method has been previously tested in the literature, and the present paper aims to carry out a quantitative analysis between NOB and OB. The specific mass is calculated based on the temperature field and a divergence-free velocity is imposed on the NOB due to the small effects of variations of the specific mass in the continuity equation, as previously demonstrated by the OB. The purpose of the NOB is to overcome the OB's restriction to single-phase flows, as well as to model the effects of specific mass variations more accurately, especially in problems with prominent thermal transfer effects, as that occur in the turbulent regime. Since the effects of a variable specific mass in the momentum and energy equations were taken into account by the NOB, it was expected that the thermal transfer results of the NOB would be improved compared with those of the OB. Then, three-dimensional natural convection simulations for a large range of Rayleigh numbers were performed using OB and NOB in a cubic cavity. Turbulence modeling was performed using Large Eddy Simulation (LES). Numerical results from both approaches were validated and all the results presented good quality. Thermal transfer was evaluated by the calculation of the Nusselt number at the heated wall and compared to experimental data from the literature. The OB and NOB provided adequate thermal transfer rate results; however, the differences between the literature and OB were higher than for NOB. Therefore, NOB is presented as a useful mathematical formulation for modeling incompressible flows with a temperature-dependent specific mass approach in single-phase or multiphase problems instead of solving the full compressible mathematical formulation. In addition, the differences between the literature and OB results increased as the Rayleigh number was raised, especially in the turbulent regime. The results of the NOB were closer to the literature than were those of the OB for the entire range of Rayleigh numbers tested. Therefore, the numerical results confirmed the higher accuracy of NOB compared to OB despite the NOB's still being an approximate model. Lastly, flow visualization allowed the identification of coherent turbulent structures near the cavity walls in the simulation with Rayleigh number 10 10. The presence of hairpin and Tollmien-Schlichting instabilities revealed the importance of modeling the three-dimensional effects of natural convection in the turbulent regime.

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Section: Validation Of the Numerical Modelsupporting

confidence: 88%

Section: Validation Of the Numerical Modelsupporting

confidence: 86%

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An extension of Oberbeck–Boussinesq approximation for thermal convection problems

Duarte

Melo

Villar

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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“…where 'D' is the forth-order damping term and ' ' damping coeficient. This term is added expilicitly to the right hand side of Equaion (8). A negative sign is needed to produce positive dissipation.…”

Section: Numerical Schemementioning

confidence: 99%

A Characteristic-based Solution of Forced and Free Convection in Closed Domains with Emphasis on Various Fluids

Adibi

Razavi

2019

IJE

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“…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%

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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Natural convection inside cubical cavities: numerical solutions with two boundary conditions

Cited by 8 publications

References 15 publications

An extension of Oberbeck–Boussinesq approximation for thermal convection problems

An extension of Oberbeck–Boussinesq approximation for thermal convection problems

A Characteristic-based Solution of Forced and Free Convection in Closed Domains with Emphasis on Various Fluids

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

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