13.6. Nomenclature

Symbol	Definition	Units
$A_{\text{c}}$	Moving cladding cross-sectional area	m2
$\text{AFRV}$	Input constant in single-phase friction factor formula, Eq. (13.2-5)
$A_{\text{f}}$	Total area allowed for cladding by the fuel	m2
$A_{\text{max}}$	Available area for molten cladding	m2
$A_{\text{s}}$	Refrozen steel cross-sectional area	m2
$A_{\text{v}}$	Vapor flow area	m2
$a$	Constant in viscosity Eq. (13.2-21)	K
$\text{BFRV}$	Input constant, see AFRV	–
$b_{\text{f}}$	Molten cladding/pin turbulent friction factor, Eq. (13.2-19)	–
$C$	Liquid-steel volumetric coefficient of thermal expansion, Eq. (13.2-47)	K-1
$C_{\text{a}}$	Mass convection term	kg/m-s
$C_{\text{f}}$	Terms in the outer-fuel-node energy Eq. (13.3-21)	W/m
$C_{\text{m}}$	Momentum convection term	m/s2
$C_{\text{v}}$	Energy convection term, Eq. (13.3-9)	W/m
$C_{1}, C_{2}, C_{3}$	Input constants in the correlation of liquid metal heat transfer,
$c_{\text{f}}$	Eq. (13.2-33)	–
$c_{\text{pc}}$	Coefficient of friction with fuel pin, Eq. (13.2-17)	–
$c_{\text{pf}}$	Molten cladding specific heat capacity	J/kg-K
$c_{\text{ps}}$	Fuel specific heat capacity	J/kg-K
$D_{\text{c}}$	Solid steel specific heat capacity	J/kg-K
$D_{\text{c}}$	Molten cladding hydraulic diameter	m
$D_{\text{h}}$	Hydraulic diameter for bare fuel or fuel pin	m
$D_{\text{v}}$	Hydraulic diameter for the vapor	m
$e_{\text{c}}$	Moving cladding internal energy	J/kg
$e_{\text{c}}^{o}$	Constant, Eq. (13.2-50)	J/kg
$e_{\text{s}}$	Refrozen steel internal energy	J/kg
$F_{\text{p}}$	Pin/molten-cladding friction force per unit volume of molten cladding	N/m3
$F_{\text{v}}$	Cladding/vapor interfacial force per unit volume of channel	N/m3
$f$	Melt fraction	–
$\text{fps}$	Full-power seconds from initial cladding motion	s
$\left( \text{fps} \right)_{0}$	Constant in incoherence factor on friction, Eq. (13.2-12)	s
$f_{\text{sf}}$	Single-phase friction factor for vapor	–
$g$	Gravitational constant	m/s2
$h$	Coefficient of heat transfer to the molten cladding from the solid interface	W/m2-K
$I$	Incoherence multiplier on friction	–
$j$	Index for axial segment	–
$\Delta K$	Reactivity change due to cladding relocation	δk/k
$k_{\text{c}}$	Molten cladding thermal conductivity	W/m-K
$k_{\text{f}}$	Fuel thermal conductivity	W/m-K
$M$	Friction multiplier due to flooding (M is also the total steel mass in channel)	–
$m_{\text{j}}$	Mass of cladding in segment $j$	kg
$m_{\text{j}}^{o}$	Initial mass of cladding in segment $j$	kg
${\dot{m}}_{\text{c}}$	Mass rate of cladding melting per unit length of channel	kg/m-s
${\dot{m}}_{\text{v}}$	Rate of vapor generation per unit length of channel	kg/m-s
$n$	Index for time step	–
$P_{\text{e}}$	Outer perimeter of intact cladding	m
$P_{\text{r}}$	Perimeter of the cladding solid/liquid interface	m
$P/D$	Pitch-to-diameter ratio for fuel pins	–
$\frac{\partial\text{p}}{\partial\text{z}}$	Channel axial pressure gradient	Pa/m
$Q_{\text{j}}$	Cumulative pin segment heat loss from beginning of heat transfer time step	J
$Q_{\text{NT}}$	Volumetric heat generation in outer fuel segment	W/m3
$q$	Input constant, Eq. (13.2-22)	–
$\text{Re}$	Molten cladding Reynolds number, Eq. (13.2-20)	–
$\left( \text{Re} \right)_{\text{break}}$	Turbulent transition Reynolds number, Eq. (13.2-18)	–
$\left( \text{Re} \right)_{\text{v}}$	Reynolds number for vapor	–
$r$	Radius (from fuel pin axis)	m
$r_{\text{NR}}, r_{\text{NT}}$	Fuel radii defined in Figure 13.3.1	m
$\Delta r_{\text{c}}$	Half-thickness of molten cladding layer	m
$\Delta r_{\text{i}}$	Half-thickness of the intact cladding	m
$\Delta r_{\text{s}}$	Half-thickness of the refrozen cladding	m
$\Delta r_{\text{w}}$	Half-thickness of the structure	m
$T_{\text{c}}$	Moving cladding temperature	K
$T_{\text{f}}$	Fuel surface temperature	K
$T_{\text{i}}$	Intact cladding temperature	K
$T_{\text{m}}$	Cladding melting temperature	K
$T_{\text{ref}}$	Reference temperature in density Eq. (13.2-46)	K
$T_{\text{s}}$	Refrozen cladding temperature	K
$T_{\text{w}}$	Structure temperature	K
$t$	Time	s
$t^{*}$	Time at beginning of current heat-transfer time step	s
$\Delta t$	CLAP (coolant) time step	s
$\Delta t^{*}$	Heat-transfer time step	s
$v_{\text{c}}$	Moving cladding velocity	m/s
$v_{\text{flood}}$	Flooding velocity	m/s
$W_{\text{j}}$	Cladding reactivity worth distribution	∂k/k-kg
$w$	Vapor mass flowrate	kg/s
$w_{\text{j}}$	Segment midpoint mass flow, Eq. (13.3-16)	kg/s
$w_{\text{j}}^{*}$	Segment boundary mass flow, Eq. (13.3-10)	kg/s
$w_{\text{m,j}}$	Segment mean mass flow, Eq. (13.3-11)	kg/s
$x$	Constant in incoherence factor on friction, Eq. (13.2-12)	–
$y_{1}, y_{2}$	Constants in linearized pin friction equation	N/m3
$z$	Elevation	m
$z_{\text{j}}$	Segment boundary elevation	m
$z_{\text{m,j}}$	Nodal elevation, Eq. (13.3-15)	m
$\Delta z_{\text{j}}$	Segment length	m
$\alpha$	Vapor fraction based on area available for molten steel and vapor	–
$\alpha_{\text{crit}}$	Input constant in two-phase multiplier, Eq. (13.2-10)	–
$\beta$	Steel (solid) coefficient of linear thermal expansion, Eq. (13.2-46)	K-1
$\Gamma$	Factor in correction of cladding area for overfilled segments	m3
$\gamma_{\text{c}}$	Computer coefficient, Eq. (13.3-26)
$\gamma_{\text{f}}$	Computed coefficient, Eq. (13.3-23)
$\varepsilon$	Input constant in two-phase multiplier, Eq. (13.2-10)	–
$\theta$	Multiplier on heat loss to structure (usually = 1)	–
$\lambda$	Effective heat-of-fusion, Eq. (13.2-31)	J/kg
$\lambda_{\text{o}}$	Thermodynamic heat-of-fusion	J/kg
$\mu_{\text{c}}$	Moving cladding viscosity	Pa-s
$\mu_{\text{m}}$	Cladding viscosity at the liquidus temperature	Pa-s
$\mu_{\text{s}}$	Solid cladding pseudo-viscosity, Eq. (13.2-23)	Pa-s
$\mu_{\text{t}}$	Cladding viscosity at the solidus temperature	Pa-s
$\mu_{\text{v}}$	Vapor viscosity	Pa-s
$\xi_{\text{f}}, \xi_{\text{w}}$	Computed coefficients	–
$\xi_{1}, \xi_{2}, \xi_{3}$	Computed coefficients	–
$\rho_{\text{c}}$	Molten cladding density	kg/m3
$\rho_{\text{c}}^{\circ}$	Density of cladding at the liquidus temperature	kg/m3
$\rho_{\text{f}}$	Fuel density	kg/m3
$\rho_{\text{s}}$	Refrozen steel density	kg/m3
$\rho_{\text{s}}^{\circ}$	Solid cladding density at the reference temperature	kg/m3
$\rho_{\text{v}}$	Vapor density	kg/m3
$\phi$	Sensible heat flux from refrozen cladding to the molten interface	W/m2
$\phi_{\text{c}}$	Flux of sensible heat into the moving cladding layer	W/m2
$\phi_{\text{hf}}$	Fusion heat flux, Eq. (13.2-29)	W/m2
$\phi_{\text{r}}$	Heat flux at interface of intact and refrozen cladding	W/m2
$\phi_{\text{trial}}$	Trail heat flux, Eq. (13.2-43)	W/m2
$\phi_{1}$	Heat flux, Eq. (13.2-41)	W/m2
$\phi_{2}$	Heat flux, Eq. (13.2-42)	W/m2
$\overline{\psi}$	Mean ratio of thermal-to-momentum eddy diffusivities	–