High-temperature ex-vessel corium spreading. Part 2: scaling principles for gravity-viscous spreading with slip at the melt–substrate interface

ABSTRACT

Promoting the spreading of molten corium represents a key strategy in the dissipation of decay heat and in the maintainence of containment integrity in the aftermath of a severe nuclear accident. Precise repeatability is difficult to achieve during high-temperature melt spreading experiments, and so scaling factors are necessary to correct for differences in flow rate, viscosity, and density between comparative experiments. A gravity-viscous momentum balance derived for spreading in the two-dimensional spreading geometry employed during recent $\approx 30$ kg-scale VE-U9 experiments on ceramic and sacrificial concrete substrates establishes that no-slip spreading length scales with the square root of the mass flow rate. Scaling for the reduced mass flow rate and enhanced viscosity implied that the melt spread 37% further on the sacrificial concrete than on the inert ceramic substrate. The possibility of a lubricating film of molten concrete and ablation gases reducing friction at the lower boundary is investigated through the imposition of a slip velocity proportional to the shear at the melt–substrate interface. Simulations over a range of Navier slip lengths implied that spreading length scales with the ratio of slip length to the melt thickness and that spreading length can be augmented by as much as 68% in the case of a virtually frictionless interface.

KEYWORDS:

• Severe accident
• ex-vessel
• corium
• spreading
• slip

This article is part of a series including:

High-temperature ex-vessel corium spreading. Part 1: experimental investigations on ceramic and sacrificial concrete substrates

Nomenclature

$D$	=	Channel width (m)
$O$	=	Error
$T$	=	Temperature (K)
$V$	=	Volume (m3)
$\varphi$	=	Distance between the start of the test section and a theoretical origin of wall convergence (m)
$\dot{V}$	=	Volumetric flow rate (m3s−1)
$\dot{m}$	=	Mass flow rate (kg s−1)
$\mathrm{\ell }$	=	Slip length
$\gamma$	=	Solid fraction
$\mu$	=	Dynamic viscosity (Pa s)
$\nu$	=	Kinematic viscosity (m2s−1)
$\varphi$	=	Porosity
$\rho$	=	Density (kg m−3)
$\theta$	=	Angle of channel wall divergence (°)
$g$	=	Gravitational acceleration (m s−2)
$h$	=	Melt depth (m)
$k,\alpha ,\beta$	=	Empirical constants
$k_{\mu },C$	=	Empirical coefficients for viscosity
$m$	=	Mass (kg)
$t$	=	Time (s)
$u$	=	Velocity (m s−1)
$x,y,z$	=	Spreading coordinates (m)
Acronyms	=
MCCI	=	Molten core-concrete interaction
PDE	=	Partial differential equation
Subscripts	=
$0$	=	no-slip ($\mathrm{\ell }=0$)
$cr$	=	Crucible
$f$	=	Final
$L$	=	Liquidus
$m$	=	Melt
$max$	=	Maximum
$N$	=	Melt front
$S$	=	Solidus
$sp$	=	Spreading section
$T$	=	Total
Dimensionless parameters	=
$\dot{\mathrm{{\rm Y}}}$	=	Dimensionless volumetric flow rate ($\frac{\dot{V}\nu }{D_0{\mathrm{\Phi }}^{3}g}$)
$\mathcal{L}$	=	Dimensionless slip length ($\frac{\mathrm{\ell }}{\mathrm{\Phi }}$)
$\tau$	=	Dimensionless time ($\frac{\mathrm{\Phi }gt}{\nu }$)
$H$	=	Dimensionless melt depth ($\frac{h}{\mathrm{\Phi }}$)
$U$	=	Dimensionless free-surface velocity ($\frac{u(x,h,t),t)}{{\bar{u}}_h(x,t)}$)
$X$	=	Dimensionless length ($\frac{x}{\mathrm{\Phi }}$)
$\mathrm{{\rm Y}}$	=	Dimensionless volume ($\frac{\dot{V}t}{D_0{\mathrm{\Phi }}^2}$)

Acknowledgments

The authors wish to thank Mitsubishi Heavy Industries for their financial support of the VE-U9 experiments and the PLINIUS team for their management of the VULCANO facility during this experimental program.

Disclosure statement

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