A numerical study of radiation heat transfer in sodium pool combustion and response surface modeling of luminous flame emissivity

A response surface model of the luminous flame emissivity of sodium pool fire has been proposed for use in safety analysis computer codes of a liquid metal fast reactor. The liquid sodium burns in air resulting in not only heat generation but also release of sodium oxide aerosols of sub-micron diameters. Aerosols levitating in air are radiative and they influence the allocation of combustion heat from the flame to atmospheric gas or sodium pool. The emissivity of the flame needs to be quantified, as it is one of user-specified parameters of the computer codes for the sodium fire analysis. The response surface model of the flame emissivity is developed based on numerical experiments on the physics of mass and heat transfer and behavior of the aerosol. Thermal-hydraulic equations have been solved coupled with aerosol dynamics and chemical reaction. Three influential variables on the emissivity are identified as pool temperature, gas temperature and oxygen molar fraction in the air. It has been found that the emissivity is calculated reasonably as a function of the three variables. The proposed response surface model can be easily employed in the sodium fire analysis codes because it is a simple quadratic expression. For the safety evaluation of the sodium fire, combined use is recommended of the proposed model and the lumped-mass zone model code.