8.9. Nomenclature

Symbols	Definition	Units
$A, A_{\text{h}}$	Axial segment length	m
$B$	Burnup	atom %
$D$	Grain size	m
$C_{\text{r}}$	Calibration constant for metal fuel bubble radius
$E$	Modulus of elasticity	Pa
$E_{\text{c}}$	Energy of the cladding	J/kg
$E_{\text{f}}$	Modulus of Elasticity of the fuel	Pa
$F_{\text{as}}$	Fraction of volume change occurring axially
$F_{\text{f}}$	Failure fraction
$f$	Mole fraction
$G_{\text{f}}$	Fission gas retained in fuel cell	kg
$G_{\text{r}}$	Fission gas released from fuel cell	kg
$G_{\text{t}}$	Total fission gas produced in fuel cell	kg
$g$	Thermal jump distance	m
$F$	Force	N
$H$	Hardness of cladding	Pa
$H_{\text{sp}}$	Height of sodium in the plenum	m
$h$	Heat-transfer coefficient	W m-2K-1
$K$	Bulk modulus	Pa
$k$	Thermal conductivity	W m-1K-1
$M$	Molecular weight, g mole, or Mass	kg
$M_{\text{s,j}}$	Mass of sodium in fuel-cladding gap in axial segment j	kg
$M_{\text{s1}}$	Mass of sodium loaded into the fuel pin	kg
$M_{\text{sp}}$	Mass of sodium in the plenum region	kg
$M_{\text{st}}$	Total mass of sodium in the fuel-cladding gap	kg
$n$	Number of moles
$P$	Pressure	Pa
$P_{\text{cav}}$	Molten cavity pressure	Pa
$P_{\text{ext}}$	Coolant channel pressure	Pa
$P_{\text{fci}}$	Fuel-Cladding interface pressure	Pa
$p$	Porosity fraction
$R$	Universal gas constant	J K-1g-mole-1
$R_{\text{B}}$	Fission gas bubble radius	m
$R_{\text{c}}$	Fuel creep rate	s-1
$R_{\text{f}}$	Fission gas release fraction
$r$	Radius	m
$r_{\text{cav}}$	Radius of central molten cavity	m
$r_{\text{ci}}$	Inner radius of the cladding	m
$r_{\text{co}}$	Outer cladding radius	m
$r_{\text{cl}}$	Outer boundary of SAS4A inner cladding cell	m
$r_{\text{c2}}$	Outer boundary of SAS4A central cladding cell	m
$r_{\text{fo}}$	Outer fuel radius	m
$r_{\text{p}}$	Inner cladding radius in the plenum	m
$r_{\text{ci}}$	Volumetric swelling fraction
$r_{\text{co}}$	Temperature	K
$r_{\text{ci}}$	Average temperature	K
$r_{\text{cz}}$	Temperature of cladding center	K
$r_{\text{fo}}$	Inner cladding temperature	K
$r_{\text{p}}$	Outer cladding temperature	K
$s_{\text{f}}$	Temperature of PLUTO2/LEVITATE inner cladding node	K
$T$	Temperature	K
$T_{\text{a}}$	Average temperature	K
$T_{\text{cc}}$	Temperature of cladding center	K
$T_{\text{ci}}$	Inner cladding temperature	K
$T_{\text{co}}$	Outer cladding temperature	K
$T_{\text{cl}}$	Temperature of PLUTO2/LEVITATE inner cladding node	K
$T_{\text{eut}}$	Eutectic temperature	°C
$T_{\text{f}}$	Time to failure	s
$t$	Time	s
$U$	Velocity	m s-1
$U_{\text{ts}}$	Ultimate tensile strength	Pa
$u$	Radial displacement	m
$V$	Volume	m3
$V_{\text{c}}$	Volume of a cell	m3
$V_{\text{f}}$	Volume of fission gas in closed porosity	m3
$V_{\text{r}}$	Volume of fission gas moved from closed to open porosity	m3
$\Delta V_{\text{a}}$	Axial volume change	m3
$\Delta V_{\text{exc}}$	Volume of excess radial fuel swelling	m3
$\Delta V_{\text{r}}$	Radial volume change	m3
$V_{\text{th}}$	Theoretical volume of material in a cell	m3
$v$	Circumferential displacement	m
$W$	Weighting factor
$z_{\text{o}}$	Radially constant axial strain
$Z$	Axial elevation	m
$\alpha$	Thermal-expansion coefficient	K-1
$\gamma$	Surface tension	N m-1
$\Delta t$	Time-step length	s
$\delta$	Mean surface roughness	m
$\varepsilon$	Strain or emissivity
$\eta$	Outer radius of solid fuel annulus	m
$\rho$	Inner radius of solid fuel annulus or density	m kg m-3
$\rho s,j$	Density of sodium in fuel-cladding gap in axial segment j	kg m-3
$\rho sp$	Density of sodium in the plenum	kg m-3
$v$	Poisson’s ratio
$\phi$	Neutron flux	n m-2s-1
$\sigma$	Stress, Pa, or Stefan-Boltzmann constant	J s-1m-2k-4
$Y$	Time constant, s-1, or incubation parameter	n/m2
$\Sigma$	Negative fractional density change in the cladding

Superscripts
$f$	Force component
$th$	Thermal component
$p$	Plenum
$v$	Central fuel void

Subscripts
$r$	Radial or reference
$\theta$	Circumferential
$z$	Axial
$f$	Force or fuel
$th$	Thermal
$\rho$	Inner radius of the solid fuel annulus
$\eta$	Outer radius of the solid fuel annulus
$g$	Plenum gas or fuel-cladding gap
$FC$	Fuel-cladding interface
$c$	Cladding
$m$	Maximum
$k$	Iteration counter
$i$	Time step or radial node
$j$	Axial node
$B$	Bubble
$fg$	Fission gas
$s$	Swelling
$v$	Central fuel void
$p$	Plenum or pore
$He$	Helium
$T$	Total
$R$	Reference
$cav$	Molten cavity
$mc$	Melting of cladding