================================================================================ Nomenclature ================================================================================ .. list-table:: :header-rows: 1 :align: center :widths: auto * - **Symbols** - **Definition** - **Units** * - :math:`A, A_{\text{h}}` - Axial segment length - m * - :math:`B` - Burnup - atom % * - :math:`D` - Grain size - m * - :math:`C_{\text{r}}` - Calibration constant for metal fuel bubble radius - * - :math:`E` - Modulus of elasticity - Pa * - :math:`E_{\text{c}}` - Energy of the cladding - J/kg * - :math:`E_{\text{f}}` - Modulus of Elasticity of the fuel - Pa * - :math:`F_{\text{as}}` - Fraction of volume change occurring axially - * - :math:`F_{\text{f}}` - Failure fraction - * - :math:`f` - Mole fraction - * - :math:`G_{\text{f}}` - Fission gas retained in fuel cell - kg * - :math:`G_{\text{r}}` - Fission gas released from fuel cell - kg * - :math:`G_{\text{t}}` - Total fission gas produced in fuel cell - kg * - :math:`g` - Thermal jump distance - m * - :math:`F` - Force - N * - :math:`H` - Hardness of cladding - Pa * - :math:`H_{\text{sp}}` - Height of sodium in the plenum - m * - :math:`h` - Heat-transfer coefficient - W m\ :sup:`-2`\ K\ :sup:`-1` * - :math:`K` - Bulk modulus - Pa * - :math:`k` - Thermal conductivity - W m\ :sup:`-1`\ K\ :sup:`-1` * - :math:`M` - Molecular weight, g mole, or Mass - kg * - :math:`M_{\text{s,j}}` - Mass of sodium in fuel-cladding gap in axial segment j - kg * - :math:`M_{\text{s1}}` - Mass of sodium loaded into the fuel pin - kg * - :math:`M_{\text{sp}}` - Mass of sodium in the plenum region - kg * - :math:`M_{\text{st}}` - Total mass of sodium in the fuel-cladding gap - kg * - :math:`n` - Number of moles - * - :math:`P` - Pressure - Pa * - :math:`P_{\text{cav}}` - Molten cavity pressure - Pa * - :math:`P_{\text{ext}}` - Coolant channel pressure - Pa * - :math:`P_{\text{fci}}` - Fuel-Cladding interface pressure - Pa * - :math:`p` - Porosity fraction - * - :math:`R` - Universal gas constant - J K\ :sup:`-1`\ g-mole\ :sup:`-1` * - :math:`R_{\text{B}}` - Fission gas bubble radius - m * - :math:`R_{\text{c}}` - Fuel creep rate - s\ :sup:`-1` * - :math:`R_{\text{f}}` - Fission gas release fraction - * - :math:`r` - Radius - m * - :math:`r_{\text{cav}}` - Radius of central molten cavity - m * - :math:`r_{\text{ci}}` - Inner radius of the cladding - m * - :math:`r_{\text{co}}` - Outer cladding radius - m * - :math:`r_{\text{cl}}` - Outer boundary of SAS4A inner cladding cell - m * - :math:`r_{\text{c2}}` - Outer boundary of SAS4A central cladding cell - m * - :math:`r_{\text{fo}}` - Outer fuel radius - m * - :math:`r_{\text{p}}` - Inner cladding radius in the plenum - m * - :math:`r_{\text{ci}}` - Volumetric swelling fraction - * - :math:`r_{\text{co}}` - Temperature - K * - :math:`r_{\text{ci}}` - Average temperature - K * - :math:`r_{\text{cz}}` - Temperature of cladding center - K * - :math:`r_{\text{fo}}` - Inner cladding temperature - K * - :math:`r_{\text{p}}` - Outer cladding temperature - K * - :math:`s_{\text{f}}` - Temperature of PLUTO2/LEVITATE inner cladding node - K * - :math:`T` - Temperature - K * - :math:`T_{\text{a}}` - Average temperature - K * - :math:`T_{\text{cc}}` - Temperature of cladding center - K * - :math:`T_{\text{ci}}` - Inner cladding temperature - K * - :math:`T_{\text{co}}` - Outer cladding temperature - K * - :math:`T_{\text{cl}}` - Temperature of PLUTO2/LEVITATE inner cladding node - K * - :math:`T_{\text{eut}}` - Eutectic temperature - °C * - :math:`T_{\text{f}}` - Time to failure - s * - :math:`t` - Time - s * - :math:`U` - Velocity - m s\ :sup:`-1` * - :math:`U_{\text{ts}}` - Ultimate tensile strength - Pa * - :math:`u` - Radial displacement - m * - :math:`V` - Volume - m\ :sup:`3` * - :math:`V_{\text{c}}` - Volume of a cell - m\ :sup:`3` * - :math:`V_{\text{f}}` - Volume of fission gas in closed porosity - m\ :sup:`3` * - :math:`V_{\text{r}}` - Volume of fission gas moved from closed to open porosity - m\ :sup:`3` * - :math:`\Delta V_{\text{a}}` - Axial volume change - m\ :sup:`3` * - :math:`\Delta V_{\text{exc}}` - Volume of excess radial fuel swelling - m\ :sup:`3` * - :math:`\Delta V_{\text{r}}` - Radial volume change - m\ :sup:`3` * - :math:`V_{\text{th}}` - Theoretical volume of material in a cell - m\ :sup:`3` * - :math:`v` - Circumferential displacement - m * - :math:`W` - Weighting factor - * - :math:`z_{\text{o}}` - Radially constant axial strain - * - :math:`Z` - Axial elevation - m * - :math:`\alpha` - Thermal-expansion coefficient - K\ :sup:`-1` * - :math:`\gamma` - Surface tension - N m\ :sup:`-1` * - :math:`\Delta t` - Time-step length - s * - :math:`\delta` - Mean surface roughness - m * - :math:`\varepsilon` - Strain or emissivity - * - :math:`\eta` - Outer radius of solid fuel annulus - m * - :math:`\rho` - Inner radius of solid fuel annulus or density - m kg m\ :sup:`-3` * - :math:`\rho s,j` - Density of sodium in fuel-cladding gap in axial segment j - kg m\ :sup:`-3` * - :math:`\rho sp` - Density of sodium in the plenum - kg m\ :sup:`-3` * - :math:`v` - Poisson's ratio - * - :math:`\phi` - Neutron flux - n m\ :sup:`-2`\ s\ :sup:`-1` * - :math:`\sigma` - Stress, Pa, or Stefan-Boltzmann constant - J s\ :sup:`-1`\ m\ :sup:`-2`\ k\ :sup:`-4` * - :math:`Y` - Time constant, s\ :sup:`-1`, or incubation parameter - n/m\ :sup:`2` * - :math:`\Sigma` - Negative fractional density change in the cladding - | .. list-table:: :header-rows: 0 :align: center :widths: auto * - **Superscripts** - - * - :math:`f` - Force component - * - :math:`th` - Thermal component - * - :math:`p` - Plenum - * - :math:`v` - Central fuel void - | .. list-table:: :header-rows: 0 :align: center :widths: auto * - **Subscripts** - - * - :math:`r` - Radial or reference - * - :math:`\theta` - Circumferential - * - :math:`z` - Axial - * - :math:`f` - Force or fuel - * - :math:`th` - Thermal - * - :math:`\rho` - Inner radius of the solid fuel annulus - * - :math:`\eta` - Outer radius of the solid fuel annulus - * - :math:`g` - Plenum gas or fuel-cladding gap - * - :math:`FC` - Fuel-cladding interface - * - :math:`c` - Cladding - * - :math:`m` - Maximum - * - :math:`k` - Iteration counter - * - :math:`i` - Time step or radial node - * - :math:`j` - Axial node - * - :math:`B` - Bubble - * - :math:`fg` - Fission gas - * - :math:`s` - Swelling - * - :math:`v` - Central fuel void - * - :math:`p` - Plenum or pore - * - :math:`He` - Helium - * - :math:`T` - Total - * - :math:`R` - Reference - * - :math:`cav` - Molten cavity - * - :math:`mc` - Melting of cladding -