Technical Note Estimation of radiation coupling factors in film boiling around spheres by mean of Computational Fluid Dynamics (CFD) tools R. Arévalo a,⇑ , D. Antúnez a , L. Rebollo b , A. Abánades b a Mechanical Engineering Department, UNET, San Cristóbal 5001, Venezuela b ETSII/Universidad Politécnica de Madrid, J. Gutiérrez Abascal, 2-28006 Madrid, Spain article info Article history: Received 15 January 2014 Received in revised form 15 May 2014 Accepted 22 June 2014 Keywords: Film boiling Radiation CFD simulation abstract In this paper, the CFD (Computational Fluid Dynamics) analysis of the pool film boiling heat transfer on a sphere at saturated conditions is presented. The simulation was performed, in first place, in absence of radiation, and subsequently incorporating it, to determine how the radiation affects to convection and the value of the coupling factor between both mechanisms. The VOF (Volume-of-fluid) method was used to model the multiphase flow and the P-1 method for the treatment of the radiation. A User Defined Function (UDF) was added to the CFD code for the treatment of the mass and energy transfer between the liquid and vapor phases. The results for the convective heat transfer were consistent with the exper- imental data reported in the literature and with two of the most widely used correlations. The coupling factor between radiation and convection obtained from the simulation analysis was similar to that proposed by known models. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Among heat transfer mechanisms, film boiling presents a rather special treatment complexity as far as radiation, convection, and phase change are coupled. It is the heat transfer phenomenon that occurs when heat fluxes between a hot surface and a saturated liquid overcome the critical heat flux of the nucleate boiling regime. Heat transfer change from liquid boiling in contact with a surface to radiation combined with convection trough a vapor film. Therefore, film boiling is characterized by the formation of a continuous vapor film on a hot surface which obstructs the heat transfer to the bulk of a cooling liquid. Film boiling is generally an unwanted heat transfer mode as it implies high temperature differences and a high risk of material damage, even reaching to melting. In nuclear reactors, massive film boiling might appear during the very abnormal operating conditions that took place in the extremely low probability case of having an accident with the additional simultaneous total failure of the emergency core cooling systems. Residual nuclear heat should be evacuated, being maxi- mal in the first stage of such event, leading to departure of nuclear boiling. During film boiling very high temperatures are reached exceeding the melting temperature of the nuclear fuel cladding and of the nuclear fuel, and so producing a severe accident with core melting. Different correlations have been proposed to evaluate the heat transfer under film boiling around various geometries. Bromley [1] was the first to study the pool film boiling at satu- rated conditions systematically. Using a boundary layer approxi- mation, predicted the Nusselt number for a horizontal cylinder as Nu ¼ 0:62ðGr=Sp 0 Þ 1=4 ð1Þ where the constant was adjusted through experimental data. This prediction is valid only when the cylinder diameter is much larger than the thickness of the vapor film. For the case of spheres, Frederking and Clark [2], using a similar analysis of Bromley, proposed a correlation, given by Nu ¼ 0:586ðGr=SpÞ 1=4 ð2Þ Grigoriev et al. [3] combined 1=4 and 1=3 power laws, to account the diameter effect and the turbulence effect in the film boiling around spheres. They used the 1=4 power law for laminar film boiling when the diameter is small and 1=3 power law for turbulent film boiling when the diameter is large. Its correlation provides: Nu ¼ CGr n Pr 1=3 m f K ð3Þ http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.06.063 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +58 2763565767; fax: +58 4268107486. E-mail addresses: rarevalo@unet.edu.ve (R. Arévalo), daniel.antunez@unet.edu. ve (D. Antúnez), lrebollo@unionfenosa.es (L. Rebollo), abanades@etsii.upm.es (A. Abánades). International Journal of Heat and Mass Transfer 78 (2014) 84–89 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt