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Title: Turbulent Natural Convection in a Square Cavity with a Circular Cylinder

Abstract

In this paper, numerical simulations of high Rayleigh number flows (10 8-10 10) were conducted to investigate the turbulent fluid flow and thermal characteristics of natural convection induced by a centrally placed hot cylinder in a cold square enclosure. The effect of the aspect ratio (radius of the cylinder to the side of the cavity) was investigated for three values (0.1, 0.2, and 0.3) for each Rayleigh number. Effects of turbulence induced by the high Rayleigh number (>10 7) were computed by using the unsteady k-ω model. A spectral-element method with high polynomial order (high resolution) was used to solve the system of unsteady time-averaged equations of continuity, momentum, and energy, along with the turbulence equations. Detailed comparison with other numerical work is presented. Contours of velocity, temperature, and turbulence quantities are presented for various high Rayleigh numbers. Also presented is the influence of the Rayleigh number on the local Nusselt number on the centrally placed hot cylinder and the cold enclosure walls. Time-marching results show that the steady-state solutions can be obtained even for high Rayleigh numbers considered in this study. The results also show that the average and peak Nusselt numbers roughly double for each order of magnitudemore » increase of the Rayleigh number for all radii considered. Finally, a correlation for the average Nusselt number as a function of Rayleigh number and aspect ratio is also presented.« less

Authors:
 [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1339154
Grant/Contract Number:
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Thermophysics and Heat Transfer
Additional Journal Information:
Journal Volume: 30; Journal Issue: 4; Journal ID: ISSN 0887-8722
Publisher:
American Institute of Aeronautics and Astronautics, Inc.
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; natural convection; high Rayleigh number; turbulence; k-ω model

Citation Formats

Aithal, S. M. Turbulent Natural Convection in a Square Cavity with a Circular Cylinder. United States: N. p., 2016. Web. doi:10.2514/1.T4873.
Aithal, S. M. Turbulent Natural Convection in a Square Cavity with a Circular Cylinder. United States. doi:10.2514/1.T4873.
Aithal, S. M. 2016. "Turbulent Natural Convection in a Square Cavity with a Circular Cylinder". United States. doi:10.2514/1.T4873. https://www.osti.gov/servlets/purl/1339154.
@article{osti_1339154,
title = {Turbulent Natural Convection in a Square Cavity with a Circular Cylinder},
author = {Aithal, S. M.},
abstractNote = {In this paper, numerical simulations of high Rayleigh number flows (108-1010) were conducted to investigate the turbulent fluid flow and thermal characteristics of natural convection induced by a centrally placed hot cylinder in a cold square enclosure. The effect of the aspect ratio (radius of the cylinder to the side of the cavity) was investigated for three values (0.1, 0.2, and 0.3) for each Rayleigh number. Effects of turbulence induced by the high Rayleigh number (>107) were computed by using the unsteady k-ω model. A spectral-element method with high polynomial order (high resolution) was used to solve the system of unsteady time-averaged equations of continuity, momentum, and energy, along with the turbulence equations. Detailed comparison with other numerical work is presented. Contours of velocity, temperature, and turbulence quantities are presented for various high Rayleigh numbers. Also presented is the influence of the Rayleigh number on the local Nusselt number on the centrally placed hot cylinder and the cold enclosure walls. Time-marching results show that the steady-state solutions can be obtained even for high Rayleigh numbers considered in this study. The results also show that the average and peak Nusselt numbers roughly double for each order of magnitude increase of the Rayleigh number for all radii considered. Finally, a correlation for the average Nusselt number as a function of Rayleigh number and aspect ratio is also presented.},
doi = {10.2514/1.T4873},
journal = {Journal of Thermophysics and Heat Transfer},
number = 4,
volume = 30,
place = {United States},
year = 2016,
month = 7
}

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  • Numerical results are presented for two-dimensional laminar mixed convection flows around a heated horizontal square cylinder rotating slowly within a concentric circular enclosure. The time evolution of the rotation and buoyancy-induced mixed convection flows are analyzed over a range of the radius ratio {chi}, the Gr, and the rotational Re. The radius ratio considered ranged from 0.2 to 0.55. The Gr range is taken from 10{sup 3} to 2{times}10{sup 4}, and the rotational Re varied from 0 to 24. The flow and temperature fields and heat transfer characteristics are presented over this parameter range. The effect of the rotating noncircularmore » geometry of the inner cylinder on the flow field and heat transfer characteristics are considered in detail and compared with those previously studied for differentially heated concentric circular annuli.« less
  • Because of its importance in industrial processes, overall natural convective heat transfer from horizontal cylinders has been the subject of many experimental and analytical studies. However, because of the dispersions in these results, there is still uncertainty about the value of the Nusselt number Nu at a particular Rayleigh number Ra, especially for Ra > 10{sup 3}. The values of Nu obtained from the most commonly used correlations do not reduce this uncertainty because of their own dispersion. To avoid the effect of higher Prandtl numbers Pr on the heat transfer, a review is made of the results from 34more » experimental studies in air (Pr = 0.7) in the range 10 {le} Ra {le} 10{sup 7}. A review is also made of 23 analytical and numerical studies. It is concluded that the mean values of Nu within each of the two groups agree to within 4% in the range 10 {le} Ra {le} 10{sup 4}. At higher Ra, the mean of the experimental values of Nu is higher than the mean of the analytical and numerical values, the difference increasing from 7.86% at Ra = 10{sup 5} to 11.3% at Ra = 10{sup 7}. Possible reasons for this discrepancy are discussed.« less
  • The purpose of this is to report the results of experimental investigations on the effects of natural convection on the ice formation over an isothermally cooled vertical circular cylinder involving laminar, transitional, and turbulent flow regimes. Further details and one-dimensional analysis of the transient development of the interface for the present study can be found in Cheng and Sabhapathy (1985).
  • The objective of the present study is to clarify the heat transfer characteristic of natural convection around a horizontal circular cylinder immersed in liquid metals. Experimental work concerning liquid metals sometimes involves such a degree of error that is impossible to understand the observed characteristics in measurement. Numerical analysis is a powerful means to overcome this experimental disadvantage. In the present paper the authors first show that the Boussinesq approximation is more applicable heat transfer rates, even for a cylinder with a relatively large temperature difference (>100K) between the heat transfer surface and fluid. It is found from a comparisonmore » of the present results with previous work that the correlation equations that have already been proposed predict values lower than the present ones.« less
  • Steady, laminar natural convection flow from a horizontal circular cylinder with a heated core region has been theoretically analyzed by taking account of the thermal conduction of the core region. The problem is conjugate, and the main focus of the study is to examine the effect of conduction in the core region on the natural convection flow from the cylinder. The governing equations were solved numerically using a finite difference technique. The effects of various parameters are presented in graphical form. Approximate solutions for the average boundary temperature at the surface of the cylinder and for the average Nusselt numbermore » are also found. In the parametric range investigated, both the theoretical and numerical results predict nearly the same values for the average boundary temperature at the surface of the cylinder and the sum evaluates for the average Nusselt number, showing the validity of the present analysis.« less