Turbulence modelling for large volumetrically heated liquid pools Original Research Article

In this paper, the natural convection heat transfer in a volumetrically heated liquid pool under high Rayleigh number (up to 1015) conditions is investigated. The available turbulence modelling techniques are first reviewed, with particular emphasis on selecting models capable of treating the mechanisms of turbulence that are relevant to high Rayleigh number natural convection. As a practical exercise, numerical analyses are performed for experiments that simulate a molten corium pool in the lower head of an externally cooled VVER-440 reactor pressure vessel (COPO) and Steinberner-Reineke experiments in a square cavity. It is shown that standard forms of the low Reynolds number k-ε model fail to describe the turbulent natural convection heat transfer regimes of interest. Phenomenological corrections for the near-wall turbulent viscosity and turbulent Prandtl number, based on the local Richardson number, are proposed to model the stratification-induced non-isotropy of turbulence in the eddy diffusivity approach. With such corrections, a reasonable agreement is achieved with the experimental data (averaged and local heat fluxes) obtained in the Finnish COPO and Steinberner-Reineke experiments, which involve two-dimensional turbulent convection of water at Rayleigh numbers that range from 1012 to 1015. However, it is considered that reliable computations of the reactor conditions in question require at least second-order corrections to the two-equation turbulence models. The physical aspects related to developing such models are also discussed in the present paper.