Turbulent natural convection (Ra = 1.58·109) in a confined 3D square cavity with two differentially heated side walls are simulated numerically using the in-house EDF code (Code_Saturne) based on the unstructured finite volume solver. The objective of the present work is to investigate the performance of the low-Reynolds-number models known by their good suitability for the near-wall treatment. The low-Reynolds-number models, shear stress transport (SST) k–ω model, φ–f model which is a developed version of the original \({\overline{\upsilon }}^{2}\) f model, and the LES (large-eddy simulation) technique are used, and the results of their using are compared with the experimental benchmark data. The numerical results show quantitative and qualitative agreements. In general, the SST k–ω model gives good predictions for the temperature profiles, and the φ –f model is more accurate for the velocity profile prediction. This is mainly due to the good resolution of the turbulence properties in the near-wall region and to the ability to mimic the physical flow features in this type of geometries.
Similar content being viewed by others
References
S. Mergui and F. Penot, Natural convection in a differentially heated square cavity: Experimental investigation at Ra = 1.69 · 109, Int. J. Heat Mass Transf., 39, No. 3, 563–574 (1996); https://doi.org/10.1016/0017-9310(95)00133-T.
P. L. Betts and I. H. Bokhari, Experiments on turbulent natural convection in an enclosed tall cavity, Int. J. Heat Fluid Flow, 21, No. 6, 675–683 (2000); https://doi.org/https://doi.org/10.1016/S0142-727X(00)00033-3.
Y. S. Tian and T. G. Karayiannis, Low turbulence natural convection in an air filled square cavity. Part I: The thermal and fluid flow fields, Int. J. Heat Mass Transf., 43, No. 6, 849–866 (2000); https://doi.org/10.1016/S0017-9310(99)00199-4.
Y. S. Tian and T. G. Karayiannis, Low turbulence natural convection in an air filled square cavity. Part II: The turbulence quantities, Int. J. Heat Mass Transf., 43, No. 6, 867–884 (2000); https://doi.org/10.1016/S0017-9310(99)00200-8.
J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, and P. Le Quéré, Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity, Int. J. Heat Fluid Flow, 25, No. 5, 824–832 (2004); https://doi.org/https://doi.org/10.1016/j.ijheatfluidflow.2004.04.003.
F. Ampofo, Turbulent natural convection of air in a non-partitioned or partitioned cavity with differentially heated vertical and conducting horizontal walls, Exp. Therm. Fluid Sci., 29, Issue 2, 137–157 (2005).
F. Ampofo and T. G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transf., 46, No. 19, 3551–3572 (2003); https://doi.org/https://doi.org/10.1016/S0017-9310(03)00147-9.
G. de Vahl Davis, Natural convection of air in a square cavity: A benchmark numerical solution, Int. J. Numer. Methods Fluids, 3, No. 3, 249–264 (1983); http://dx.doi.org/https://doi.org/10.1002/fld.1650030305.
N. C. Markatos and K. A. Pericleous, Laminar and turbulent natural convection in an enclosed cavity, Int. J. Heat Mass Transf., 27, No. 5, 755–772 (1984); http://dx.doi.org/https://doi.org/10.1016/0017-9310(84)90145-5.
R. A. W. M. Henkes, F. F. van der Vlugt, and C. J. Hoogendoorn, Natural convection flow in a square cavity calculated with low-Reynolds-number turbulence models, Int. J. Heat Mass Transf., 34, No. 2, 377–388 (1991); https://doi.org/https://doi.org/10.1016/0017-9310(91)90258-g.
K. Hanjalić, S. Kenjereš, and F. Durst, Natural convection in partitioned two-dimensional enclosures at higher Rayleigh number, Int. J. Heat Mass Transf., 39, No. 7, 1407–1427 (1996); https://doi.org/https://doi.org/10.1016/0017-9310(95)00219-7.
P. Le Quéré and M. Behnia, From onset of unsteadiness to chaos in a differentially heated square cavity, J. Fluid Mech., 359, 81–107 (1998); https://doi.org/https://doi.org/10.1017/S0022112097008458.
S. H. Peng and L. Davidson, Computation of turbulent buoyant flows in enclosures with low-Reynolds-number k–ω models, Int. J. Heat Fluid Flow, 20, No. 2, 172–184 (1999); https://doi.org/https://doi.org/10.1016/S0142-727X(98)10050-4.
H. S. Dol and K. Hanjalić, Computational study of turbulent natural convection in a side-heated near-cubic enclosure at a high Rayleigh number, Int. J. Heat Mass Transf., 44, No. 12, 2323–2344 (2001); https://doi.org/https://doi.org/10.1016/S0017-9310(00)00271-4.
K. J. Hsieh and F. S. Lien, Numerical modelling of buoyancy-driven flows in enclosures, Int. J. Heat Fluid Flow, 25, No. 4, 659–670 (2004); https://doi.org/https://doi.org/10.1016/j.ijheatfluidflow.2003.11.023.
H. S. Peng and L. Davidson, Large eddy simulation for turbulent buoyant flow in a confined cavity, Int. J. Heat Fluid Flow, 22, No. 3, 323–331 (2001); https://doi.org/https://doi.org/10.1016/S0142-727X(01)00095-9.
J. Pallares, I. Cuesta, and F. X. Gran, Laminar and turbulent Rayleigh–Bénard convection in perfectly conducting cubical cavity, Int. J. Heat Fluid Flow, 23, No. 3, 346–358 (2002); https://doi.org/https://doi.org/10.1016/S0142-727X(02)00182-0.
A. Sergent, P. Joubert, and P. Le Quéré, Development of a local subgrid diffusivity model for large-eddy simulation of buoyancy-driven flows: Application to a square differentially heated cavity, Numer. Heat Transf. A: Appl., 44, No. 8, 789–810 (2003); https://doi.org/https://doi.org/10.1080/716100524.
J. Z. Zhai, Z. Zhang, W. Zhang, and Q. Chen, Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: Part 1 — Summary of prevalent turbulence models, HVAC&R Res., 13, No. 6, 853–870 (2007); http://dx.doi.org/https://doi.org/10.1080/10789669.2007.10391459.
Z. Zhang, W. Zhang, Z. J. Zhai, and Q. Y. Chen, Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: Part 2 — Comparison with experimental data from literature, HVAC&R Res., 13, No. 6, 871–886 (2007); http://dx.doi.org/https://doi.org/10.1080/10789669.2007.10391460.
L. El Moutaouakil, Z. Zrikem, and A. Abdelbaki, Performance of various RANS eddy-viscosity models for turbulent natural convection in tall vertical cavities, Heat Mass Transf., 50, No. 8, 1103–1113 (2014); https://doi.org/https://doi.org/10.1007/s00231-014-1322-4.
P. C. Walsh and W. H. Leong, Effectiveness of several turbulence models in natural convection, Int. J. Numer. Methods Heat Fluid Flow, 14, No. 5, 633–648 (2004); https://doi.org/https://doi.org/10.1108/09615530410539955.
C. E. Clifford and M. L. Kimber, Assessment of RANS and LES turbulence models for natural convection in a differentially heated square cavity, Numer. Heat Transf. A: Appl., 78, No. 10, 1–35 (2020); https://doi.org/https://doi.org/10.1080/10407782.2020.1803592.
F. R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J., 32, No. 8, 1598–1605 (1994); https://doi.org/https://doi.org/10.2514/3.12149.
Laurence, J. C. Uribe, and S. Utyuzhnikov, A robust formulation of the \({\overline{\upsilon }}^{2}\)– f model, Flow Turbul. Combust., 73, No. 3, 169–185 (2004); https://doi.org/10.1007/s10494-005-1974-8.
P. A. Durbin, Near-wall turbulent closure modeling without damping functions, Theor. Comput. Fluid Dyn., 3, No. 1, 1–13 (1991); https://doi.org/https://doi.org/10.1007/BF00271513.
P. A. Durbin, Separated flow computations with the k–ε–υ2 model, AIAA J., 33, No. 4, 659–664 (1995); https://doi.org/https://doi.org/10.2514/3.12628.
J. Smagorinsky, General circulation experiments with the primitive equations. I: The basic experiment, Mon. Weather Rev., 91, No. 3, 99–165 (1963); https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.
E. R. van Driest, On turbulent flow near a wall, J. Aeronaut. Sci., 23, No. 11, 1007–1011 (1956); https://doi.org/https://doi.org/10.2514/8.3713.
F. Archambeau, N. Méchitoua, and M. Sakiz, Code_Saturne: A finite volume code for the computation of turbulent incompressible flows — Industrial applications, Int. J. Finite Vol., 1, No. 1, 1–62 (2004); https://hal.archives-ouvertes.fr/hal-01115371.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 4, pp. 1017–1027, July–August, 2023
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Belharizi, M., Khorsi, A., Yahiaoui, T. et al. RANS and LES Computations of Natural Convection in a Square Cavity. J Eng Phys Thermophy 96, 1017–1027 (2023). https://doi.org/10.1007/s10891-023-02765-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-023-02765-2