High-Rayleigh heat transfer flow: Thermal stratification analysis and assessment of Boussinesq approach

Abstract

Purpose - 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 liquidfilled domains. Design/methodology/approach - 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). Findings - 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. Research limitations/implications - The main limitation of the present research can be found in the shortage of experimental data for very high Rayleigh problems. Practical implications - 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. Originality/value - 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.