The purpose of this paper is to assess the Boussinesq approach for a wide range of Ra (10 × 6 to 10 × 11) in two-dimensional (square cavity) and three-dimensional (cubic cavity) problems for air- and liquid-filled domains.
The thermal behavior in “differentially heated cavities” filled with air (low and medium Rayleigh) and water (high Rayleigh) is solved using computational fluid dynamics (CFDs) (OpenFOAM) with a non-compressible (Boussinesq) and compressible approach (real water properties from the IAPWS database).
The results from the wide range of Rayleigh numbers allowed for the establishment of the limitation of the Boussinesq approach in problems where the fluid has significant density changes within the operation temperature range and especially when the dependence of density with temperature is not linear. For these cases, the symmetry behavior predicted by Boussinesq is far from the compressible results, thus inducing a transient heat imbalance and leading to a higher mean temperature.
The main limitation of the present research can be found in the shortage of experimental data for very high Rayleigh problems.
Practical implications of the current research could be use of the Boussinesq approach by carefully observing its limitations, especially for sensible problems such as the study of pressure vessels, nuclear reactors, etc.
The originality of this paper lies in addressing the limitations of the Boussinesq approach for high Rayleigh water systems. This fluid is commonly used in numerous industrial equipment. This work presents valuable conclusions about the limitations of the currently used models to carry out industrial simulations.
The authors would like to thank the CONICET (PIP 112 201101 00331) and ANPCyT (PICT 2013-830) and Universidad Nacional del Litoral (CAI + D 2011 PJ 500 201101 00015 and CAI + D PI 501 201101 00435) for giving the financial support for carrying out this research. Lastly, thanks should be given to Nicolas Schiliuk who contributed significantly to improve this study.
Corzo, S., Ramajo, D. and Nigro, N. (2017), "High-Rayleigh heat transfer flow: Thermal stratification analysis and assessment of Boussinesq approach", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 9, pp. 1928-1954. https://doi.org/10.1108/HFF-05-2016-0176Download as .RIS
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