This work is focused on the simulation and prediction of turbulent natural convection flows by means of two-equation eddy-viscosity models. In order to show the generality, precision, and numerical issues related to these models under natural convection, three different buoyancy-driven cavities have been simulated: a tall cavity with a 30:1 aspect ratio, a cavity with a 5:1 aspect ratio, and, finally, a 4:1 aspect ratio cavity. All cases are solved under moderate and∕or transitional Rayleigh numbers (, , and , respectively) and all simulations are compared to experimental and∕or direct numerical simulation data available in literature. These different situations allow to check the applicability of two-equation eddy-viscosity models in buoyancy-driven flows, giving criteria on computational effort∕precision and their physical behavior.
Issue Section:
Natural and Mixed Convection
Keywords:
flow simulation,
natural convection,
turbulence,
viscosity,
turbulence,
buoyancy,
natural convection,
two equation,
k-ϵ,
k-ω
1.
Pope
, S.
, 2000, Turbulent Flows
, Cambridge University Press
, Cambridge
.2.
Peng
, S.
, and Davidson
, L.
, 1999, “Computation of Turbulent Buoyant Flows in Enclosures With Low-Reynolds Number k‐ω Models
,” Int. J. Heat Fluid Flow
0142-727X, 20
, pp. 172
–184
.3.
Davidson
, L.
, 1990, “Calculation of the Turbulent Buoyancy-Driven Flow in a Rectangular Cavity Using an Efficient Solver and Two Different Low Reynolds Number k‐ϵ Models
,” Numer. Heat Transfer, Part A
1040-7782, 18
, pp. 129
–147
.4.
Hanjalić
, K.
, and Vasić
, S.
, 1993, “Computation of Turbulent Natural-Convection in Rectangular Enclosures With an Algebraic Flux Model
,” Int. J. Heat Mass Transfer
0017-9310, 36
, pp. 3603
–3624
.5.
Hanjalić
, K.
, Kenjereš
, S.
, and Durst
, F.
, 1995, “Natural Convection in Partitioned Two-Dimensional Enclosures at Higher Rayleigh Numbers
,” Int. J. Heat Mass Transfer
0017-9310, 39
(7
), pp. 1407
–1427
.6.
Kenjereš
, S.
, Gunarjo
, S. B.
, and Hanjalić
, K.
, 2005, “Contribution to Elliptic Relaxation Modelling of Turbulent Natural and Mixed Convection
,” Int. J. Heat Fluid Flow
0142-727X, 26
(7
), pp. 569
–586
.7.
Ince
, N.
, and Launder
, B.
, 1989, “Computation of Buoyancy-Driven Turbulent Flows in Rectangular Enclosures
,” Int. J. Heat Fluid Flow
0142-727X, 10
(1
), pp. 110
–117
.8.
Pérez-Segarra
, C. D.
, Oliva
, A.
, Costa
, M.
, and Escanes
, F.
, 1995, “Numerical Experiments in Turbulent Natural and Mixed Convection in Internal Flows
,” Int. J. Numer. Methods Heat Fluid Flow
0961-5539, 5
(1
), pp. 13
–33
.9.
Wilcox
, D. C.
, 1988, “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,” AIAA J.
0001-1452, 26
, pp. 1299
–1310
.10.
Wilcox
, D. C.
, 1994, “Simulation of Transition With a Two-Equation Turbulence Model
,” AIAA J.
0001-1452, 32
, pp. 247
–255
.11.
Goldberg
, U.
, Peroomian
, O.
, and Chakravarthy
, S.
, 1998, “A Wall-Distance-Free k‐ϵ Model With Enhanced Near-Wall Treatment
,” ASME J. Fluids Eng.
0098-2202, 120
, pp. 457
–462
.12.
Markatos
, N.
, Malin
, M.
, and Cox
, G.
, 1982, “Mathematic Modelling of Buoyancy-Induced Smoke Flow in Enclosures
,” Int. J. Heat Mass Transfer
0017-9310, 25
, pp. 63
–75
.13.
Markatos
, N.
, and Pericleous
, K.
, 1984, “Laminar and Turbulent Natural Convection in an Enclosed Cavity
,” Int. J. Heat Mass Transfer
0017-9310, 27
, pp. 755
–772
.14.
Heindel
, T.
, Ramadhyani
, S.
, and Incropera
, F.
, 1994, “Assessment of Turbulence Models for Natural Convection in an Enclosure
,” Numer. Heat Transfer, Part B
1040-7790, 26
, pp. 147
–172
.15.
Dafa’alla
, A.
, and Betts
, P.
, 1996, “Experimental Study of Turbulent Natural Convection in a Tall Air Cavity
,” Exp. Heat Transfer
0891-6152, 9
, pp. 165
–194
.16.
Cheeswright
, R.
, King
, K.
, and Ziai
, S.
, 1986, “Experimental Data for the Validation of Computer Codes for the Prediction of Two-Dimensional Buoyant Cavity Flows
,” Proceedings of Significant Questions in Buoyancy Affected Enclosure or Cavity Flows
, pp. 75
–81
.17.
Henkes
, R.
, van Der Vlugt
, F.
, and Hoogendoorn
, C.
, 1991, “Natural Convection Flow in a Square Cavity Calculated With Low Reynolds-Number Turbulence Models
,” Int. J. Heat Mass Transfer
0017-9310, 34
, pp. 377
–388
.18.
Rodi
, W.
, 1984, “Turbulence Models and Their Application in Hydraulics: A State-of-the-Art Review
,” University of Karlsrhue, Germany.19.
Patankar
, S. V.
, 1980, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, Washington, DC
.20.
Cadafalch
, J.
, Pérez-Segarra
, C. D.
, Cónsul
, R.
, and Oliva
, A.
, 2002, “Verification of Finite Volume Computations on Steady State Fluid Flow and Heat Transfer
,” ASME J. Fluids Eng.
0098-2202, 124
, pp. 11
–21
.21.
Roache
, P.
, 1997, “Quantification of Uncertainty in Computational Fluid Dynamics
,” Annu. Rev. Fluid Mech.
0066-4189, 29
, pp. 123
–160
.22.
Roache
, P.
, 1998, Verification and Validation in Computational Science and Engineering
, Hermosa
, Albuquerque, NM
.23.
Roache
, P.
, 1972, “On Artificial Viscosity
,” J. Comput. Phys.
0021-9991, 10
, pp. 169
–184
.24.
Trias
, F. X.
, Soria
, M.
, Oliva
, A.
, and Pérez-Segarra
, C. D.
, 2007, “Direct Numerical Simulation of Two and Three-Dimensional Turbulent Natural Convection Flows in a Differentially Heated Cavity of Aspect Ratio 4
,” J. Fluid Mech.
0022-1120, 586
, pp. 259
–293
.25.
Murakami
, S.
, Kato
, S.
, Chiakamoto
, T.
, and Laurence
, D.
, 1996, “New Low-Reynolds-Number k‐ϵ Model Including Damping Effect due to Buoyancy in a Stratified Flow Field
,” Int. J. Heat Mass Transfer
0017-9310, 39
(16
), pp. 3483
–3496
.26.
Liu
, F.
, and Wen
, J.
, 1999, “Development and Validation of an Advanced Turbulence Model for Buoyancy Driven Flows in Enclosures
,” Int. J. Heat Mass Transfer
0017-9310, 42
, pp. 3967
–3981
.27.
Launder
, B.
, and Sharma
, B.
, 1974, “Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc
,” Lett. Heat Mass Transfer
0094-4548, 1
(2
), pp. 131
–138
.28.
So
, R.
, and Sommer
, T.
, 1994, “A Near-wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers
,” ASME J. Fluids Eng.
0098-2202, 116
, pp. 844
–854
.29.
Xin
, S.
, and Quere
, P.
, 1995, “Direct Numerical Simulations of Two-Dimensional Chaotic Natural Convection in a Differentially Heated Cavity of Aspect Ratio 4
,” J. Fluid Mech.
0022-1120, 304
, pp. 87
–118
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