CFD Modeling and Analysis of a Heat-Generating Melt Pool Under External Vessel Cooling and Top Flooding

Abstract

In some nuclear reactors, under accidental conditions, core debris forms a molten pool, which is later located in a core catcher. The core catcher proposed by the authors uses special refractory material to absorb enthalpy of corium so that temperatures are within 1500 K, which is possible to cool with side cooling and top flooding. Since performing a full-scale prototypic experiment is extremely challenging and complex because of the involvement of very high temperatures and the presence of radioactive materials, it is important to develop a Computational Fluid Dynamics (CFD) model capable of simulating coolability of the melt pool with the above cooling strategy. In the present work, a CFD model was developed for the above purpose and was benchmarked with experiments conducted under simulated conditions by the authors. The experiment involved the melting of about 25 L of sodium borosilicate glass at about 1473 K and cooling it in a scaled-down core catcher model. In the presence of decay heat inside the melt pool, turbulent natural convection plays an important role in the temperature distribution inside the melt pool and on the vessel walls. For this, we used different turbulence models. Comparisons among the Standard k-ε, Shear Stress Transport (SST) k-ω, and two-dimensional (2D) Large Eddy Simulation (LES) turbulence models show that SST k-ω and 2D LES turbulences are found to be in good agreement with the experimental results for the temperature distribution in the melt pool, and SST k-ω is found to be computationally less expensive than 2D LES. In general, the CFD model is capable of simulating heat transfer with phase changes inside the heat-generating melt pool. In view of this, the model can be further extended to include cooling of the melt pool in the prototype core catcher. The evolution of crust formation has been investigated in detail using a CFD model.

Keywords:

• Severe accident simulation
• core catcher simulation
• melt pool coolability
• heat transfer
• CFD

Nomenclature

$C_p$ =	=	specific heat (J/kg∙K)
$\mathit{E}$ =	=	Young’s modulus (GPa)
$\mathit{g}$ =	=	acceleration due to gravity (m/s2)
$\mathit{H}$ =	=	specific enthalpy
$\mathit{h}$ =	=	heat transfer coefficient (W/m∙K)
k =	=	kinetic energy
$\mathit{k}$ =	=	thermal conductivity (W/m∙K)
$\mathit{m}$ =	=	mass (kg)
$\mathrm{Nu}$ =	=	Nusselt number
$\mathit{q}{ }^{\prime \mathrm{\prime \prime }}$ =	=	heat per volume (W/m3)
$\mathrm{Ra}$ =	=	Rayleigh number
Raʹ =	=	Rayleigh number with volumetric heat generation
$\mathit{T}$ =	=	temperature (K)
$\mathit{t}$ =	=	time (s)
u, v =	=	velocity components (m/s)
$\mathit{V}$ =	=	volume (m3)
$\mathit{x}$ =	=	thickness (m)

Greek

$\mathit{\alpha }$ =	=	thermal diffusivity (m2/s)
$\mathit{\beta }$ =	=	volumetric thermal expansion coefficient (1/k)
$\mathrm{\Delta }\mathit{H}$ =	=	latent heat
ε =	=	dissipation rate
$\mathrm{M}$ =	=	dynamic viscosity (Pa∙s)
$\mathit{\nu }$ =	=	kinematic viscosity (m2/s)
$\mathit{\rho }$ =	=	density (kg/m3)
$\mathit{\sigma }$ =	=	strength of corium (MPa)
ω =	=	dissipation per unit kinetic energy

Subscripts

$\mathit{d}$ =	=	downward direction
$\mathit{eff}$ =	=	effective
$\mathit{Experimental}\mathit{Facility}$ =	=	experimental facility
$\mathit{l}$ =	=	liquidous
$\mathit{prototype}$ =	=	prototype
$\mathit{Prototypic}\mathit{Facility}$ =	=	prototype
$\mathit{s}$ =	=	solidus
$\mathit{simulant}$ =	=	simulant material
$\mathit{t}$ =	=	turbulent
$\mathit{u}$ =	=	upward direction

Authors’ Contributions

AKN conceived of the presented idea. SSM developed the theory and performed the simulations. AKN and JBJ guided in the CFD computations. SSM analyzed the results under the supervision of AKN and JBJ. SSM wrote the manuscript under the supervision of AKN and JBJ. All authors reviewed the manuscript.

Disclosure Statement

No potential conflict of interest was reported by the author(s).