Modified correlations for the Nusselt numbers at the boundaries of a bottom-heated molten metal layer in a stratified corium melt pool and an assessment of heat transfer conditions during a severe accident

Abstract

The paper discusses new correlations for the Nusselt numbers at the side and bottom surfaces of a bottom-heated molten steel layer under the conditions of mixed natural convection of the melt at Rayleigh (Ra) numbers from ∼ 106 to 1012. The melt layer under consideration is characterized by radial non-uniformity of the temperature distribution, when the averaged temperatures of the top and side surfaces of the layer show a difference in value. This thermal pattern of the molten metal layer is typical when a stratified corium molten pool forms during a severe accident (SA). Upper metallic melt layer goes above the oxide phase of corium pool, and it is heated along its bottom surface. For an adequate prediction of heat transfer at the side and bottom surfaces of a layer in a SA, we developed special correlations for the Nu numbers. They take into account Rayleigh number and additional factors that determine geometric parameters of the layer and the temperature conditions at the bottom, side and top surfaces of the layer. Parameters in the developed correlations for the Nu numbers were determined via CFD simulation and mathematical processing of the simulation results. CFD simulations by means of the ANES code were completed in accordance with a specially developed experiments matrix. Two-parameter k-ω turbulence model by Wilcox, which includes Menter’s improved near wall functions, has been implemented in the CFD code and applied accordingly. To evaluate the accuracy and predictability of the developed correlations we ran a comparative analysis of the Nu numbers at the sidewall and bottom surfaces of the melt layer, as defined on the basis of the developed correlations for the Nu numbers and as defined in CFD simulation. The comparison showed a strong correspondence of the results within a wide range of Rayleigh number values of ∼ 106 < Ra < 1012. The analysis of the developed correlations allowed shaping a number of critical arguments that define heat transfer conditions at the melt layer boundaries. It was found that the Nu numbers at the side and bottom surfaces are largely dependent on the difference in the temperatures of the top and side surfaces of the layer. As the difference between the these temperatures widens, the Nu numbers increase drastically (by tens of percent or more) in comparison to similar Nu numbers defined on the basis of the well-known correlations. It is specified that when the temperatures at the top and side surfaces of the layer are equal, the heat transfer conditions at the side surface are defined by “Globe and Dropkin” correlation used for the horizontal surfaces of the layer. We also evaluated the significance of the geometric parameters on the Nu values for the sidewall and bottom surfaces of the melt layer. Multiplicative effect of this parameter and of the parameter for temperature conditions at the boundaries of the layer mentioned above may lead to a significant (by times) increase of the Nu values. That must be considered in the thermal analysis of the corium pool and the processes of the SA.