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Three-dimensional numerical simulation of periodic natural convection in a differentially heated cubical enclosure

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Abstract

A high-resolution, finite-difference numerical study is carried out of three-dimensional unsteady periodic natural convection of air in a cubical enclosure at the Rayleigh number of 8.5×106. The enclosure is subjected to differential heating at the two vertical side walls. The other vertical walls are insulated. A linear temperature profile is specified at the thermally-conducting horizontal walls. Flow details in the three-dimensional field are captured by elaborate post-processing of the computational results, for which the state-of-the-art numerical visualization techniques are utilized. The three-dimensionality of the mean flow fields is observed to be confined into narrow regions near the end walls. The time-dependent solutions clearly indicate the periodic nature of the flow. The oscillation frequency is in close agreement with the previous experimental measurements reported in the literature.

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Abbreviations

c p :

specific heat at constant pressure

Fr:

Froude number, u 20 /g*L 0

f ND :

normalized frequency, f*/N where f* is the dimensional frequency

g :

gravitational acceleration

k :

thermal conductivity

L 0 :

reference length (enclosure height)

N :

Brunt-Väisälä frequency, [g * β *(T H −T C )L 0]1/2

p :

pressure

p 0 :

reference pressure (hydrostatic pressure)

Pr:

Prandtl number, c * p μ*/k*

Ra:

Rayleigh number, g * β * c * p ρ *2 L 30 (T H −T C )/µ * k *

Re:

Reynolds number, ρ* 0 L 0 μ*

t :

time

T :

temperature

T 0 :

reference temperature, (T C +T H )/2

T C , T H :

cooled and heated side wall temperatures

u 0 :

reference velocity, [g * β * L 0(T H −T C )]1/2

u, v, w :

velocity components in the x, y and z directions

x, y, z :

Cartesian coordinates

β :

thermal expansion coefficient

δ :

overheat ratio, (T H −T C )/T 0

μ :

viscosity

ρ :

density

*:

dimensional quantities

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Author information

Authors and Affiliations

  1. Institute of Computational Fluid Dynamics, 1-22-3 Haramachi, Meguro, 152, Tokyo, Japan

    Toru Fusegi

  2. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Chong Ryang, 131, Seoul, Korea

    Jae Min Hyun

  3. Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, 229, Sagamihara, Kanagawa, Japan

    Kunio Kuwahara

Authors
  1. Toru Fusegi
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  2. Jae Min Hyun
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  3. Kunio Kuwahara
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Fusegi, T., Hyun, J.M. & Kuwahara, K. Three-dimensional numerical simulation of periodic natural convection in a differentially heated cubical enclosure. Applied Scientific Research 49, 271–282 (1992). https://doi.org/10.1007/BF00384627

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  • DOI: https://doi.org/10.1007/BF00384627

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