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. |