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

SANTIAGO CORZO; RAMAJO DAMIAN; NORBERTO NIGRO

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW

EMERALD GROUP PUBLISHING LIMITED

Año: 2016

0961-5539

Natural convection heat transfer associated to fluid-dynamics phenomena has been extensively studied by means of experimental and numerical techniques in many scientific and industrial-related applications. High Rayleigh number (Ra) regimes are particularly challenging to be simulated in three-dimensional domains due to flow instability and the influence of turbulence models among others. Despite the efforts devoted to study these phenomena, the literature data remains scarce. Evidence shows that the Boussinesq approach, with constant thermal expansion coefficient, induces a body force that is linearly depending on the temperature. Therefore, the magnitude of the buoyancy force affectsequally both cold and hot walls, leading to perfectly antisymmetric solutions. On the other hand, for high Ra problems commonly found in liquid systems, compressible solvers allow introducing more realistic constitutive relationships for the density and the other properties. As a result of that, the buoyancy effect at the cold and hot walls becomes different, especially during the transient stage of the simulation. This induces transient heat imbalances leading to fluid averaged temperatures higher than the obtained fromBoussinesq. Consequently, the wall heat transfer is not the same as the that obtained from the Boussinesq solution. In this paper the Boussinesq approach is assessed for a wide range of Ra (106 < Ra < 1012)in two-dimensional (square cavity) and three-dimensional air and liquid-filled problems. The range of suitability of this approach was evaluated by comparing with the available experimental data and numerical results from a compressible solver. Moreover, the thermal and flow patterns and the stratification parameter S as well as the wall heat transfer were quantified while obtaining a correlation between Ra and S, which is useful to characterize the thermal pattern.