The immersed boundary method (IBM) was used for three-dimensional numerical simulations, and the results for natural convection in a rectangular channel with an inner hot circular cylinder are presented. This simulation used Rayleigh numbers spanning 3 orders of magnitude, from to . The Prandtl number considered in this study was 0.7. We investigated the effects of the inner cylinder's radius on the thermal convection and heat transfer in the space between the cylinder and rectangular channel. A map of the thermal and flow regimes is presented as a function of the cylinder's radius and the Rayleigh number.
Issue Section:
Natural and Mixed Convection
References
1.
Lipps
, F. B.
, 1976
, “Numerical Simulation of Three-Dimensional Bénard Convection in Air
,” J. Fluid Mech.
, 75
(1
), pp. 113
–148
.2.
Ozoe
, H.
, Yamamoto
, K.
, Churchill
, S. W.
, and Sayama
, H.
, 1976
, “Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below
,” ASME J. Heat Transfer
, 98
(2
), pp. 202
–207
.3.
Richter
, F. M.
, 1978
, “Experiments on the Stability of Convection Rolls in Fluids Whose Viscosity Depends on Temperature
,” J. Fluid Mech.
, 89
(3
), pp. 553
–560
.4.
Busse
, F. H.
, and Clever
, R. M.
, 1979
, “Instabilities of Convection Rolls in a Fluid of Moderate Prandtl Number
,” J. Fluid Mech.
, 91
(2
), pp. 319
–335
.5.
Grotzbach
, G.
, 1983
, “Spatial Resolution Requirements for Direct Numerical Simulation of the Rayleigh–Bénard Convection
,” J. Comput. Phys.
, 49
(2
), pp. 241
–264
.6.
Kerr
, R. M.
, 1996
, “Rayleigh Number Scaling in Numerical Convection
,” J. Fluid Mech.
, 310
, pp. 139
–179
.7.
Hartlep
, T.
, Tilgner
, A.
, and Busse
, F. H.
, 2005
, “Transition to Turbulent Convection in a Fluid Layer Heated From Below at Moderate Aspect Ratio
,” J. Fluid Mech.
, 554
, pp. 309
–322
.8.
Bailon-Cuba
, J.
, and Schumacher
, J.
, 2011
, “Low-Dimensional Model of Turbulent Rayleigh–Bénard Convection in a Cartesian Cell With Square Domain
,” Phys. Fluids
, 23
(7
), p. 077101
.9.
Moukalled
, F.
, and Acharya
, S.
, 1996
, “Natural Convection in the Annulus Between Concentric Horizontal Circular and Square Cylinders
,” J. Thermophys. Heat Transfer
, 10
(3
), pp. 524
–531
.10.
Ha
, M. Y.
, Kim
, I.
, Yoon
, H. S.
, Yoon
, K. S.
, Lee
, J. R.
, Balachandar
, S.
, and Chun
, H. H.
, 2002
, “Two-Dimensional and Unsteady Natural Convection in a Horizontal Enclosure With a Square Body
,” Numer. Heat Transfer, Part A
, 41
(1
), pp. 183
–210
.11.
Lee
, J. R.
, Ha
, M. Y.
, Balachandar
, S.
, Yoon
, H. S.
, and Lee
, S. S.
, 2004
, “Natural Convection in a Horizontal Layer of Fluid With a Periodic Array of Square Cylinders in the Interior
,” Phys. Fluids
, 16
(4
), pp. 1097
–1117
.12.
Lee
, J. R.
, Ha
, M. Y.
, and Balachandar
, S.
, 2007
, “Natural Convection in a Horizontal Fluid Layer With a Periodic Array of Internal Square Cylinders—Need for Very Large Aspect Ratio 2D Domains
,” Int. J. Heat Fluid Flow
, 28
(5
), pp. 978
–987
.13.
Lee
, J. R.
, and Ha
, M. Y.
, 2005
, “A Numerical Study of Natural Convection in a Horizontal Enclosure With a Conducting Body
,” Int. J. Heat Mass Transfer
, 48
(16
), pp. 3308
–3318
.14.
Lee
, J. R.
, and Ha
, M. Y.
, 2006
, “Numerical Simulation of Natural Convection in a Horizontal Enclosure With a Heat-Generating Conducting Body
,” Int. J. Heat Mass Transfer
, 49
(15–16
), pp. 2684
–2702
.15.
Angeli
, D.
, Levoni
, P.
, and Barozzi
, G. S.
, 2008
, “Numerical Predictions for Stable Buoyant Regimes Within a Square Cavity Containing a Heated Horizontal Cylinder
,” Int. J. Heat Mass Transfer
, 51
(3–4
), pp. 553
–565
.16.
Kim
, B. S.
, Lee
, D. S.
, Ha
, M. Y.
, and Yoon
, H. S.
, 2008
, “A Numerical Study on Natural Convection in a Square Enclosure With a Circular Cylinder at Different Vertical Locations
,” Int. J. Heat Mass Transfer
, 51
(7–8
), pp. 1888
–1906
.17.
Yoon
, H. S.
, Ha
, M. Y.
, Kim
, B. S.
, and Yu
, D. H.
, 2009
, “Effect of the Position of a Circular Cylinder in a Square Enclosure on Natural Convection at Rayleigh Number of 107
,” Phys. Fluids
, 21
(4
), p. 047101
.18.
Kang
, D. H.
, Ha
, M. Y.
, Yoon
, H. S.
, and Choi
, C.
, 2013
, “Bifurcation to Unsteady Natural Convection in Square Enclosure With a Circular Cylinder at Rayleigh Number of 107
,” Int. J. Heat Mass Transfer
, 64
, pp. 926
–944
.19.
Stevens
, R. J. A. M.
, Lohse
, D.
, and Verzicco
, R.
, 2011
, “Prandtl Number Dependence of Heat Transport in High Rayleigh Number Thermal Convection
,” J. Fluid Mech.
, 688
, pp. 1
–13
.20.
Chan
, A. M. C.
, and Banerjee
, S.
, 1979
, “A Numerical Study of Three-Dimensional Roll Cells Within Rigid Boundaries
,” ASME J. Heat Transfer
, 101
(2
), pp. 233
–237
.21.
Choi
, H.
, and Moin
, P.
, 1994
, “Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow
,” J. Comput. Phys.
, 113
(1
), pp. 1
–4
.22.
Kim
, J.
, Kim
, D.
, and Choi
, H.
, 2001
, “An Immersed-Boundary Finite Volume Method for Simulations of Flow in Complex Geometries
,” J. Comput. Phys.
, 171
(1
), pp. 132
–150
.23.
Kim
, J.
, and Choi
, H.
, 2004
, “An Immersed-Boundary Finite-Volume Method for Simulation of Heat Transfer in Complex Geometries
,” KSME Int. J.
, 18
(6
), pp. 1026
–1035
.24.
Park
, Y. G.
, Yoon
, H. S.
, and Ha
, M. Y.
, 2012
, “Natural Convection in Square Enclosure With Hot and Cold Cylinders at Different Vertical Locations
,” Int. J. Heat Mass Transfer
, 55
(25–26
), pp. 7911
–7925
.25.
Korenaga
, J.
, and Jordan
, T. H.
, 2001
, “Effects of Vertical Boundaries on Infinite Prandtl Number Thermal Convection
,” Geophys. J. Int.
, 147
(3
), pp. 639
–659
.26.
Maystrenko
, A.
, Resagk
, C.
, and Thess
, A.
, 2007
, “Structure of the Thermal Boundary Layer for Turbulent Rayleigh–Bénard Convection of Air in a Long Rectangular Enclosure
,” Phys. Rev. E
, 75
, p. 066303
.27.
Kaczorowski
, M.
, and Wagner
, C.
, 2009
, “Analysis of the Thermal Plumes in Turbulent Rayleigh–Bénard Convection Based on Well-Resolved Numerical Simulations
,” J. Fluid Mech.
, 618
, pp. 89
–112
.28.
Jakob
, M.
, 1949
, Heat Transfer
, Vol. 1
, Wiley
, New York
.29.
Wagner
, S.
, and Shishkina
, O.
, 2013
, “Aspect-Ratio Dependency of Rayleigh–Bénard Convection in Box-Shaped Containers
,” Phys. Fluids
, 25
(8
), p. 085110
.30.
Fiscaletti
, D.
, Angeli
, D.
, Tarozzi
, L.
, and Barozzi
, G. S.
, 2013
, “Buoyancy-Induced Transitional Flows Around an Enclosed Horizontal Cylinder: An Experiment
,” Int. J. Heat Mass Transfer
, 58
(1–2
), pp. 619
–631
.31.
Desrayaud
, G.
, and Lauriat
, G.
, 1993
, “Unsteady Confined Buoyant Plumes
,” J. Fluid Mech.
, 252
, pp. 617
–646
.32.
Belmonte
, A.
, Tilgner
, A.
, and Libchaber
, A.
, 1994
, “Temperature and Velocity Boundary Layers in Turbulent Convection
,” Phys. Rev. E
, 50
(1
), pp. 269
–279
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