3.18. Nomenclature

Subscript	Description
c	Coolant
e	Cladding
f	Fuel
g	Plenum gas
kz	Reflector zone
p	Gas plenum region
si	Structure inner node
so	Structure outer node
1	Beginning of the time step
2	End of the time step

Symbol	Description	Units
$A_{\text{c}}$	Coolant flow area	m2
$A_{\text{ep}}$	Cross sectional area of the clad in the gas plenum region	m2
$A_{\text{g}}$	Cross sectional area of the plenum gas	m2
$A_{\text{fr}}$, $b_{\text{fr}}$	Coefficients in the friction factor correlation: $f = A_{\text{fr}}\left( \text{Re} \right)^{b_{\text{fr}}}$	–
$c$	Specific heat	J/kg-K
$\overline{c}_{\text{c}}$	Coolant specific heat	J/kg-K
$c_{\text{e}}$	Cladding specific heat	J/kg-K
$\overline{c}_{\text{f}}$	Average fuel specific heat, averaged over a time step	J/kg-K
$c_{\text{m}}$	Modified specific heat in the melting range	J/kg-K
$c_{\text{mix}}$	Coolant specific heat in the mixing zone used for re-entry temperature calculation	J/kg-K
$c_1$, $c_2$, $c_3$	Correlation constants used in coolant heat-transfer coefficients	–
$D$	Right-hand-side terms in the matrix equations for radial temperature profiles	J/m
$D_{\text{h}}$	Hydraulic diameter	m
$d_{\text{sti}}$	Structure inner node thickness	m
$d_{\text{sto}}$	Structure outer node thickness	m
$E_{\text{ec}}$	Heat flux from clad to coolant, integrated over a time step	J/m2
$E_{\text{sc}}$	Heat flux form structure to coolant, integrated over a time step	J/m2
$f$	Friction factor	–
$f_{\text{i}}$	Fraction of the structure thickness represented by the inner node	–
$f_{\text{o}}$	Fraction of the structure thickness represented by the outer node	–
$g$	Acceleration of gravity	m/s2
$h_{\text{b}}$	Bond gap conductance	W/m2-K
$h_{\text{c}}$	Coolant-film heat-transfer coefficient	W/m2-K
$h_{\text{cond}}$	Condensation heat-transfer coefficient for sodium vapor	W/m2-K
$H_{\text{eg}}$	Heat-transfer coefficient form the gas in the gas plenum to the cladding	W/m2-K
$H_{\text{erc}}$	Heat-transfer coefficient from the cladding or reflector outer node to the coolant	W/m2-K
$h_{\text{r}}$	Equivalent radiation heat-transfer coefficient	W/m2-K
$H_{\text{rio}}$	Heat-transfer coefficient from the structure inner node to the reflector outer node	W/m2-K
$H_{\text{sic}}$	Heat-transfer coefficient from the structure inner node to the coolant	W/m2-K
$H_{\text{stio}}$	Heat-transfer coefficient from the structure inner node to the structure outer node	W/m2-K
$i$	Radial node number	–
$ic$	Core channel number	–
$I_1$	Inertial integral in the momentum equation	m-1
$I_2$	Acceleration integral in the momentum equation	m/kg
$I_3$	Friction integral in the momentum equation	m/kg
$I_4$	Orifice term in the momentum equation	m/kg
$I_5$	Density integral in the momentum equation	kg/m2
$j$	Fuel axial node number	–
$jc$	Coolant axial node number	–
$\text{JC}$	Axial node number	–
$k$	Thermal conductivity	W/m-K
$k_{\text{ep}}$	Cladding thermal conductivity in the gas plenum region	W/m-K
$\overline{k}_{\text{i~j}}$	Weighted average thermal conductivity for heat flow from node i to j	W/m-K
$K_{\text{or}}$	Orifice coefficient	–
$L$	1 for subassembly inlet, 2 for outlet	–
$\text{MZC}$	Total number of coolant axial nodes	–
$m_{\text{e}}$	Cladding mass	kg
$m_{\text{f}}$	Fuel mass	kg
$M_{\text{mix}}$	Mass of sodium in the mixing volume	kg
$\text{NC}$	Radial node number of the coolant node	–
$\text{NE}$	Radial node number for the cladding mid-point	–
$\text{NE}'$	Radial node number for the cladding outer surface node	–
$\text{NE}''$	Radial node number for the cladding inner surface node	–
$\text{NN}$	NT-1	–
$N_{\text{ps}}$	Number of fuel pins represented by a channel	–
$\text{NR}$	Radial node number for the fuel outer surface radius. (note $\text{NR}=\text{NE}''$)	–
$\text{NSI}$	Radial node number for the inner structure node	–
$\text{NSO}$	Radial node number for the outer structure node	–
$\text{NT}$	Radial node number for the fuel outer surface temperature node	–
$p$	Pressure	Pa
$p_{\text{b}}$	Pressure at the bottom of the subassembly	Pa
$p_{\text{b1}}$, $p_{\text{b2}}$	pb at beginning and end of a time step	Pa
$p_{\text{in}}$	Pressure in the coolant inlet plenum	Pa
$\overline{P}_{\text{j}}$	Heat production rate in axial node j	W
$P_{\text{r}}$	Radial power shape, per unit mass	–
$p_{\text{t}}$	Pressure at the top of the subassembly	Pa
$p_{\text{t1}}$, $p_{\text{t2}}$	pt at the beginning and end of a time step	Pa
$p_{\text{x}}$	Pressure in the coolant outlet plenum	Pa
$\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{fr}}$	Friction pressure drop	Pa/m
$\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{k}}$	Orifice pressure drop	Pa/m
$Q_{\text{c}}$	Coolant heat source due to direct heating by neutrons and gamma rays	W/m3
$Q_{\text{ct}}$	Total steady-state heat source per unit of coolant volume	W/m3
$Q_{\text{ec}}$	Heat flow from clad to coolant	W/m3
$q_{\text{fe}}$	Fuel-to-cladding heat flux	W/m2
$Q_{\text{sc}}$	Heat flow from structure to coolant	W/m3
$Q_{\text{sm}} \left( i \right)$	Sum of the heat sources for all radial nodes inside and including node i	W
$Q_{\text{st}}$	Structure heat source due to direct heating by neutrons and gamma rays	W/m2
$Q_{\text{v}}$	Heat source per unit volume	W/m3
$r$	Radius	m
$r_{\text{brp}}$	Clad inner radius in the gas plenum region	m
$\text{Re}$	Reynolds number	–
$R_{\text{ec}}$	Thermal resistance between clad and coolant	m2-K/W
$R_{\text{ehf}}$	Thermal resistance of the outer fourth of the cladding	m2-K/W
$r_{\text{erp}}$	Cladding outer radius in the gas plenum region	m
$R_{\text{g}}$	Thermal resistance of the gas in the plenum	m2-K/W
$r_{\text{o}} \left( i \right)$	Steady-state radial mesh	m
$S_{\text{er}}$	Perimeter of the cladding or reflector in contact with the coolant	m
$S_{\text{st}}$	Structure perimeter, heat-transfer area per unit height	m
$T$	Temperature	K
$t$	Time	s
$T_{\text{cin}}$	Coolant inlet temperature	K
$T_{\text{cout}}$	Coolant outlet temperature	K
$T_{\text{eex}}$	Extrapolated clad temperature	K
$T_{\text{eq}}$	Equilibrium temperature in the mixing volume	K
$\overline{T}_{\text{exp}}$	Temperature of the sodium expelled from the subassembly into a mixing volume, averaged over a time step	K
$\overline{T}_{\text{f}}$	Average fuel temperature at an axial node, mass-weighted average	K
$T_{\text{g}}$	Plenum gas temperature	K
$T_{\text{liq}}$	Liquidus temperature	K
$T_{\text{out}}$	Bulk temperature in the coolant outlet plenum	K
$t_{\text{p1}}$, $t_{\text{p2}}$	Times at the beginning and end of a PRIMAR time step	s
$T_{\text{ri}}$	Reflector inner node temperature	K
$T_{\text{ro}}$	Reflector outer node temperature	K
$T_{\text{sol}}$	Solidus temperature	K
$T_{\text{o}}$	Temperature at the beginning of a time step	K
$T_1$	Temperature at the beginning of a time step	K
${T'}_1$	Temperature of the coolant entering an axial node at the end of a time step	K
$T_2$	Temperature at the end of a time step	K
${T'}_2$	Temperature of the coolant entering an axial node at the end of a time step	K
$U_{\text{melt}}$	Heat of fusion	J/kg
$v$	Velocity	m/s
$w$	Coolant mass flow rate	kg/s
$w_{\text{e}}$	Estimated mass flow rate	kg/s
$w_{\text{fe}}$	Thickness of the liquid-sodium film left on the cladding after voiding occurs	m
$w_{\text{fr}}$	Thickness of the liquid-sodium film left on the reflector after voiding occurs	m
$w_{\text{fst}}$	Thickness of the liquid-sodium film left on the structure after voiding occurs	m
$w_1$, $w_2$	w at beginning and end of a time step	kg/s
$\Delta w$	Change in w during a time step	kg/s
$x$	Distance	m
$x_{\text{I1}} \left( \text{JC} \right)$	Nodal contribution to I1	m-1
$x_{\text{I2}} \left( \text{JC} \right)$	Nodal contribution to I2	m/kg
$x_{\text{I3}} \left( \text{JC} \right)$	Nodal contribution to I3
$x_{\text{I5}} \left( \text{JC} \right)$	Nodal contribution to I5	kg/m2
$z$	Axial position	m
$z$	Elevation	m
$\Delta z$	Node height	m
$z_{\text{pb}}$	Elevation at the bottom of the gas plenum	m
$z_{\text{pt}}$	Elevation at the top of the gas plenum	m
$z_{\text{pll}}$	Reference elevation of the coolant inlet plenum	m
$z_{\text{plu}}$	Reference elevation of the coolant outlet plenum	m
$\alpha$	Heat capacity terms in the matrix equations for radial temperature profiles	J/m-K
$\alpha_{\text{e}}$	Cladding thermal expansion coefficient	K-1
$\alpha_{\text{f}}$	Fuel thermal expansion coefficient	K-1
$\beta$	Thermal conductivity terms in the matrix equations for radial temperature profiles	J/m-K
$\gamma_{\text{c}}$	Fraction of the total heat production that goes directly into the coolant	–
$\gamma_{\text{e}}$	Fraction of the total heat production that goes directly into the cladding	–
$\gamma_{\text{s}}$	Fraction of the total heat production that goes directly into the structure	–
$\gamma_2$	Ratio of the structure perimeter to the cladding perimeter	–
$\Delta r$	Radial node size	m
$\Delta r_{\text{i,j}}$	Effective radial distance for heat flow from node I to node j	m
$\Delta t$	Time-step size	s
$\Delta z$	Axial node height	m
$\varepsilon$	Thermal emissivity	–
$\theta_1$, $\theta_2$	Degree of explicitness or implicitness in the solution	–
$\rho$	Density	kg/m3
$\rho_{\text{c}}$	Coolant density	kg/m3
$\rho_{\text{cin}}$	Coolant density in the inlet plenum	kg/m3
$\rho_{\text{cout}}$	Coolant density in the outlet plenum	kg/m3
$\left( \rho c_{\text{g}} \right)$	Density times specific heat of the plenum gas	J/m3-K
$\left( \rho c_{\text{r}} \right)$	Density times specific heat for the reflector	J/m3-K
$\rho_{\text{e}}$	Cladding density	kg/m3
$\sigma$	Stefan-Bolzmann constant	W/m2-K4
$\tau$	Time constant for flow rate changes	s
$\tau_{\text{c}}$	Condensation heat-transfer time constant	s
$\tau_{\text{ro}}$	Time constant for temperature changes in the outer reflector node	s
$\tau_{\text{sti}}$	Time constant for temperature changes in the inner structure node	s
$\mu$	Coolant viscosity	Pa-s
$\overline{\mu}\left( \text{JC} \right)$	Average value of $\mu$ for node JC	Pa-s
$\Psi$	Source terms in the matrix equations for radial temperature profiles	–