4.10. Nomenclature

Symbol	Description	Units
$A$	Coefficient in EBR-II bowing reactivity.	$
$A_{\text{cr}}$	Control rod driveline heat transfer area.	m2
$A_{\text{e}}$	Nominal cross-sectional area of cladding.	m2
$A_{\text{f}}$	Nominal cross-sectional area of fuel.	m2
$a$	Above-core load pad elevation.	m
$a_{\text{cr}}$	Coefficient in control rod driveline reactivity feedback.	$/m
$B$	Coefficient in EBR-II bowing reactivity.	$
$b_{\text{cr}}$	Coefficient in control rod driveline reactivity feedback.	$/m2
$C_{\text{cr}}$	Control rod driveline specific heat.	J/kg-K
$C_{\text{i}}$	Delayed neutron precursor group $i$ population.
$C_{\text{rc}}$	Coefficient in simple radial core expansion reactivity feedback.	$/K
$D$	Hex can flat-to-flat dimension.	m
$D_{\text{z}}$	Nominal axial node height in simple axial expansion reactivity feedback model.	m
$E$	Modulus of elasticity.	N/m2
$F_{\text{cr}}$	Temperature multiplier in EBR-II control rod bank expansion model.
$F_{\text{LowBU}}$	Fraction of fuel elements with burnup less than 2.9% in EBR-II.
$f_{\text{e}}$	Cladding mesh height expansion factor.
$f_{\text{f}}$	Fuel mesh height expansion factor.
$f_{\text{i}}$	Channel flag in simple radial expansion reactivity model.
$H$	Fuel height in EBR-II.	m
$h_{\text{cr}}$	Coolant to control rod driveline heat transfer coefficient.	W/m2-k
$H_{\text{n}}$	Normalized decay heat energy fraction for group $n$.
$I$	Moment of inertia of beam cross-sectional area.	m4
$k$	Reactor effective multiplication constant.
$\delta k$	Reactivity, or change in the effective reactor multiplication constant.
$\delta k_{\text{cl}}$	Cladding relocation reactivity.
$\delta k_{\text{cr}}$	Control rod drive expansion reactivity.
$\delta k_{\text{cs}}$	Control system reactivity.
$\delta k_{\text{D}}$	Fuel Doppler reactivity.
$\delta k_{\text{d}}$	Fuel and cladding axial expansion reactivity.
$\delta k_{\text{fu}}$	Fuel relocation reactivity.
$\delta k_{\text{Na}}$	Coolant density or voiding reactivity.
$\delta k_{\text{p}}$	User-programmed reactivity.
$\delta k_{\text{re}}$	Core radial expansion reactivity.
$L$	Elevation of top load pad.	m
$L_{\text{cr}}$	Control rod driveline length.	m
$L_{\text{k}}$	Reactor vessel wall length represented by compressible volume $k$ or element $k$.	m
$M$	Bending moment.	N-m
$M_{\text{cr}}$	Control rod driveline mass.	kg
$M_{\text{GR}}$	Applied moment at grid plate.	N-m
$M_{1}$	Thermally induced bending moment in the core region.	N-m
$M_{2}$	Thermally induced bending moment above the core region.	N-m
$m_{\text{ij}}$	Fuel or cladding mass at node $j$ in channel $i$ in fuel and cladding relocation reactivity.	kg
$N$	Fuel, sodium, or steel atom density in EBR-II reactivity model.	atm/m3
$N_{\text{c}}$	Number of channels.
$N_{\text{s}}$	Number of subassemblies per channel.
$P$	Radial force at the above core load pad.	N
$P_{\text{t}}^{k}$	Normalized power in interval $k$ of irradiation history for decay heat precursor initial condition.
$Q$	Space and time dependent nodal power.	W
$Q_{\text{t}}$	Total recoverable energy per fission	MeV
$R_{\text{e}}$	Cladding nodal reactivity worth in simple axial expansion reactivity model.	kg-1
$R_{\text{f}}$	Fuel nodal reactivity worth in simple axial expansion reactivity model.	kg-1
$R_{\text{i}}$	Radial fuel reactivity worth shape factor in EBR-II reactivity model.
$R_{1}$	Minimum core radius at above-core load pad in detailed radial expansion model.	m
$R_{2}$	Minimum core radius at top load pad in detailed radial expansion model.	m
$R_{3}$	Maximum core radius at restraint ring in detailed radial expansion.	m
$\overrightarrow{r}$	Reactor spatial position vector.
$S$	Space-dependent steady-state nodal power.	W
$S_{\text{GR}}$	Subassembly slope with respect to vertical at the grid plate.	m/m
$S_{\text{GRMAX}}$	Maximum subassembly slope with respect to vertical at the grid plate.	m/m
$T$	Temperature.	K
$\overline{T}$	Average temperature.	K
$\Delta T$	Hexcan flat-to-flat temperature difference.	K
$T_{\text{by}}$	Bypass region temperature.	K
$T_{\text{ch}}$	Reflector steel temperature.	K
$T_{\text{cr}}$	Control rod driveline temperature.	K
$T_{\text{cv}1}$	Inlet plenum coolant temperature.	K
$T_{\text{cv}2}$	Outlet plenum coolant temperature.	K
$T_{\text{e}}$	Cladding temperature.	K
$T_{\text{f}}$	Fuel temperature.	K
${\overline{T}}_{\text{f}}$	Average fuel temperature.	K
$\Delta T_{f}$	Fuel temperature change.	K
$\Delta{\overline{T}}_{\text{favg}}$	Average fuel temperature change.	K
${\overline{T}}_{\text{floc}}$	Average fuel temperature for a channel.	K
$T_{\text{i}}$	Plenum coolant temperature.	K
$T_{\text{in}}$	Coolant inlet temperature.	K
$\Delta T_{\text{in}}$	Coolant inlet temperature change.	K
$T_{\text{j}}$	Reflector coolant temperature.	K
${\overline{T}}_{\text{k}}$	Average vessel wall temperature in $k$-th compressible volume or element.	K
${\overline{T}}_{\text{lr}}$	Average coolant temperature in lower reflector.	K
$T_{\text{mm}}$	Mixed mean coolant core outlet temperature.	K
${\overline{T}}_{\text{Na}}$	Average coolant temperature.	K
${\overline{T}}_{\text{rr}}$	Average radial reflector coolant temperature.	K
$T_{\text{SLP}}$	Space and time dependent structure temperature.	K
${\overline{T}}_{\text{SLP}}$	Space-average, time dependent structure temperature.	K
${\Delta\overline{T}}_{\text{SLP}}$	Change in space-averaged structure temperature.	K
$\Delta T_{\text{ss}}$	Cladding temperature change.	K
${\overline{T}}_{\text{ss}}$	Average cladding temperature.	K
$T_{\text{ui}}$	Coolant temperature in the upper internal structure region.	K
${\overline{T}}_{\text{ur}}$	Average coolant temperature in the upper reflector.	K
$t$	Time.	s
$\Delta t$	Change in time.	s
$V_{\text{by}}$	Bypass region volume.	m3
$V_{\text{c}}h$	Channel steel volume.	m3
$V_{\text{cv}1}$	Inlet plenum volume.	m3
$V_{\text{cv}2}$	Outlet plenum volume.	m3
$V_{\text{f}}$	Fuel volume.	m3
$V_{\text{GR}}$	Radial reaction at the grid plate.
$V_{\text{i}}$	Plenum coolant volume.	m3
$V_{\text{i}}$	Channel volume.	m3
$V_{\text{j}}$	Reflector coolant volume.	m3
$V_{\text{k}}$	Nodal volume at $k$ in channel.	m3
$V_{\text{Na}}$	Sodium volume in fuel/cladding gap.	m3
$V_{\text{ss}}$	Cladding volume.	m3
$V_{\text{ui}}$	Coolant volume in upper internal structure.	m3
$w_{\text{c}}$	Core outlet flow rate.	kg/s
$w_{\text{k}}$	Core volume weighting for decay heat curve $k$.
$\text{XAC}$	Distance from subassembly nozzle support to above core load pad.	m
$\text{XMC}$	Distance from subassembly nozzle support to core midplane.	m
$x$	Axial elevation in detailed radial core expansion model.	m
$x_{1}$	Elevation of lower axial blanket/lower reflector interface.	m
$x_{\text{i}}$	Fraction of total fission power from isotope $i$.
$Y$	Fraction of full power temperature rise.
$Y_{\text{e}}$	Cladding Young’s modulus.
$Y_{\text{f}}$	Fuel Young’s modulus.
$Y_{\text{ss}}$	Cladding Young’s modulus.
$y$	Radial displacement with respect to the core radius at the grid plate.	m
$Z_{\text{k}}$	Axial fuel reactivity worth shape.
$\Delta z_{\text{cr}}$	Control rod driveline expansion.	m
$z_{0}$	Unexpanded axial mesh elevation.	m
$\Delta z_{\text{n}}$	Net control rod movement.	m
$z_{\text{ne}}$	Expanded cladding mesh elevation.	m
$z_{\text{nf}}$	Expanded fuel mesh elevation.	m
$\Delta z_{\text{v}}$	Reactor vessel expansion.	m
$\alpha$	Subassembly hex can thermal expansion coefficient.	1/K
$\alpha_{\text{cr}}$	Control rod driveline thermal expansion coefficients.	1/K
$\alpha_{\text{D}}$	Local fuel Doppler coefficient.
$\alpha_{\text{e}}$	Cladding thermal expansion coefficient.	1/K
$\alpha_{\text{f}}$	Fuel thermal expansion coefficient.	1/K
$\alpha_{\text{jI}}$	Average coolant void fraction in axial node $j$ of channel $I$.
$\alpha_{\text{k}}$	Reactor vessel thermal expansion coefficient.	1/K
$\alpha_{\text{Lf}}$	Fuel thermal expansion coefficient.	1/K
$\alpha_{\text{Lss}}$	Cladding thermal expansion coefficient.	1/K
$\alpha_{\text{VNa}}$	Sodium volumetric thermal expansion coefficient.	1/K
$\alpha_{\text{n}}$	Contribution of group $n$ to immediate decay heat from a single fission event	MeV
$\beta$	Total effective delayed-neutron fraction
$\beta_{\text{n}}$	Effective decay-heat power fraction for group $n$.
$\beta_{\text{i}}$	Effective delayed-neutron precursor group $i$ fraction.
$\delta_{\text{e}}$	Cladding axial expansion.	m
$\delta_{\text{f}}$	Fuel axial expansion.	m
$\epsilon_{\text{d}}$	Sodium density multiplier.
$\epsilon_{\text{e}}$	Cladding fractional thermal expansion.
$\epsilon_{\text{ex}}$	Effective axial expansion multiplier.
$\epsilon_{\text{f}}$	Fuel fractional thermal expansion.
$\zeta$	EBR-II reactivity parameter.	$
$\zeta_{\text{bw}}$	EBR-II bowing reactivity parameter.	$
$\zeta_{\text{c}}$	EBR-II coolant reactivity parameter.	$
$\zeta_{\text{cr}}$	EBR-II control rod driveline reactivity parameter.	$
$\zeta_{\text{fa}}$	EBR-II axial fuel expansion reactivity parameter.	$
$\zeta_{\text{fr}}$	EBR-II radial fuel expansion reactivity parameter.	$
$\zeta_{\text{lr}}$	EBR-II lower reflector reactivity parameter.	$
$\zeta_{\text{rr}}$	EBR-II radial reflector reactivity parameter.	$
$\zeta_{\text{ssa}}$	EBR-II axial cladding expansion reactivity parameter.	$
$\zeta_{\text{ssr}}$	EBR-II radial cladding expansion reactivity parameter.	$
$\zeta_{\text{ur}}$	EBR-II upper reflector reactivity parameter.	$
$\Lambda$	Prompt neutron lifetime.	s
$\lambda_{\text{n}}$	Decay heat group effective decay constant for group $n$.	1/s
$\lambda_{\text{i}}$	Delayed neutron precursor group $i$ decay constant.	1/s
$\rho_{\text{c}}$	Local coolant void reactivity worth.	g-1
$\Delta\rho_{\text{e}}$	Cladding axial expansion reactivity.
$\Delta\rho_{\text{f}}$	Fuel axial expansion reactivity.
$\rho_{\text{u}}$	Sodium density in outlet plenum.	kg/m3
$\phi$	Normalized fission power amplitude.
$\phi_{1}$	First order coefficient in normalized fission power amplitude expansion.	s-1
$\phi_{2}$	Second order coefficient in normalized fission power amplitude expansion.	s-2
$\psi_{\text{f}}$	Normalized fission power.
$\psi_{\text{h}}$	Normalized decay heat power.
$\psi_{\text{t}}$	Normalized total power.