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 |