================================================================================ Nomenclature ================================================================================ .. list-table:: :header-rows: 1 :align: center :widths: auto * - Symbol - Definition - Units * - :math:`A_{\text{c}}` - Moving cladding cross-sectional area - m\ :sup:`2` * - :math:`\text{AFRV}` - Input constant in single-phase friction factor formula, Eq. :ref:`13.2-5` - * - :math:`A_{\text{f}}` - Total area allowed for cladding by the fuel - m\ :sup:`2` * - :math:`A_{\text{max}}` - Available area for molten cladding - m\ :sup:`2` * - :math:`A_{\text{s}}` - Refrozen steel cross-sectional area - m\ :sup:`2` * - :math:`A_{\text{v}}` - Vapor flow area - m\ :sup:`2` * - :math:`a` - Constant in viscosity Eq. :ref:`13.2-18a` - K * - :math:`\text{BFRV}` - Input constant, see AFRV - -- * - :math:`b_{\text{f}}` - Molten cladding/pin turbulent friction factor, Eq. :ref:`13.2-16b` - -- * - :math:`C` - Liquid-steel volumetric coefficient of thermal expansion, Eq. :ref:`13.2-39` - K\ :sup:`-1` * - :math:`C_{\text{a}}` - Mass convection term - kg/m-s * - :math:`C_{\text{f}}` - Terms in the outer-fuel-node energy Eq. :ref:`13.3-17` - W/m * - :math:`C_{\text{m}}` - Momentum convection term - m/s\ :sup:`2` * - :math:`C_{\text{v}}` - Energy convection term, Eq. :ref:`13.3-9` - W/m * - :math:`C_{1}, C_{2}, C_{3}` - Input constants in the correlation of liquid metal heat transfer, - * - :math:`c_{\text{f}}` - Eq. :ref:`13.2-28` - -- * - :math:`c_{\text{pc}}` - Coefficient of friction with fuel pin, Eq. :ref:`13.2-15` - -- * - :math:`c_{\text{pf}}` - Molten cladding specific heat capacity - J/kg-K * - :math:`c_{\text{ps}}` - Fuel specific heat capacity - J/kg-K * - :math:`D_{\text{c}}` - Solid steel specific heat capacity - J/kg-K * - :math:`D_{\text{c}}` - Molten cladding hydraulic diameter - m * - :math:`D_{\text{h}}` - Hydraulic diameter for bare fuel or fuel pin - m * - :math:`D_{\text{v}}` - Hydraulic diameter for the vapor - m * - :math:`e_{\text{c}}` - Moving cladding internal energy - J/kg * - :math:`e_{\text{c}}^{o}` - Constant, Eq. :ref:`13.2-42` - J/kg * - :math:`e_{\text{s}}` - Refrozen steel internal energy - J/kg * - :math:`F_{\text{p}}` - Pin/molten-cladding friction force per unit volume of molten cladding - N/m\ :sup:`3` * - :math:`F_{\text{v}}` - Cladding/vapor interfacial force per unit volume of channel - N/m\ :sup:`3` * - :math:`f` - Melt fraction - -- * - :math:`\text{fps}` - Full-power seconds from initial cladding motion - s * - :math:`\left( \text{fps} \right)_{0}` - Constant in incoherence factor on friction, Eq. :ref:`13.2-11` - s * - :math:`f_{\text{sf}}` - Single-phase friction factor for vapor - -- * - :math:`g` - Gravitational constant - m/s\ :sup:`2` * - :math:`h` - Coefficient of heat transfer to the molten cladding from the solid interface - W/m\ :sup:`2`-K * - :math:`I` - Incoherence multiplier on friction - -- * - :math:`j` - Index for axial segment - -- * - :math:`\Delta K` - Reactivity change due to cladding relocation - δk/k * - :math:`k_{\text{c}}` - Molten cladding thermal conductivity - W/m-K * - :math:`k_{\text{f}}` - Fuel thermal conductivity - W/m-K * - :math:`M` - Friction multiplier due to flooding (M is also the total steel mass in channel) - -- * - :math:`m_{\text{j}}` - Mass of cladding in segment :math:`j` - kg * - :math:`m_{\text{j}}^{o}` - Initial mass of cladding in segment :math:`j` - kg * - :math:`{\dot{m}}_{\text{c}}` - Mass rate of cladding melting per unit length of channel - kg/m-s * - :math:`{\dot{m}}_{\text{v}}` - Rate of vapor generation per unit length of channel - kg/m-s * - :math:`n` - Index for time step - -- * - :math:`P_{\text{e}}` - Outer perimeter of intact cladding - m * - :math:`P_{\text{r}}` - Perimeter of the cladding solid/liquid interface - m * - :math:`P/D` - Pitch-to-diameter ratio for fuel pins - -- * - :math:`\frac{\partial\text{p}}{\partial\text{z}}` - Channel axial pressure gradient - Pa/m * - :math:`Q_{\text{j}}` - Cumulative pin segment heat loss from beginning of heat transfer time step - J * - :math:`Q_{\text{NT}}` - Volumetric heat generation in outer fuel segment - W/m\ :sup:`3` * - :math:`q` - Input constant, Eq. :ref:`13.2-18b` - -- * - :math:`\text{Re}` - Molten cladding Reynolds number, Eq. :ref:`13.2-17` - -- * - :math:`\left( \text{Re} \right)_{\text{break}}` - Turbulent transition Reynolds number, Eq. :ref:`13.2-16` - -- * - :math:`\left( \text{Re} \right)_{\text{v}}` - Reynolds number for vapor - -- * - :math:`r` - Radius (from fuel pin axis) - m * - :math:`r_{\text{NR}}, r_{\text{NT}}` - Fuel radii defined in :numref:`figure-13.3-1` - m * - :math:`\Delta r_{\text{c}}` - Half-thickness of molten cladding layer - m * - :math:`\Delta r_{\text{i}}` - Half-thickness of the intact cladding - m * - :math:`\Delta r_{\text{s}}` - Half-thickness of the refrozen cladding - m * - :math:`\Delta r_{\text{w}}` - Half-thickness of the structure - m * - :math:`T_{\text{c}}` - Moving cladding temperature - K * - :math:`T_{\text{f}}` - Fuel surface temperature - K * - :math:`T_{\text{i}}` - Intact cladding temperature - K * - :math:`T_{\text{m}}` - Cladding melting temperature - K * - :math:`T_{\text{ref}}` - Reference temperature in density Eq. :ref:`13.2-38` - K * - :math:`T_{\text{s}}` - Refrozen cladding temperature - K * - :math:`T_{\text{w}}` - Structure temperature - K * - :math:`t` - Time - s * - :math:`t^{*}` - Time at beginning of current heat-transfer time step - s * - :math:`\Delta t` - CLAP (coolant) time step - s * - :math:`\Delta t^{*}` - Heat-transfer time step - s * - :math:`v_{\text{c}}` - Moving cladding velocity - m/s * - :math:`v_{\text{flood}}` - Flooding velocity - m/s * - :math:`W_{\text{j}}` - Cladding reactivity worth distribution - ∂k/k-kg * - :math:`w` - Vapor mass flowrate - kg/s * - :math:`w_{\text{j}}` - Segment midpoint mass flow, Eq. :ref:`13.3-14` - kg/s * - :math:`w_{\text{j}}^{*}` - Segment boundary mass flow, Eq. :ref:`13.3-10` - kg/s * - :math:`w_{\text{m,j}}` - Segment mean mass flow, Eq. :ref:`13.3-11` - kg/s * - :math:`x` - Constant in incoherence factor on friction, Eq. :ref:`13.2-11a` - -- * - :math:`y_{1}, y_{2}` - Constants in linearized pin friction equation - N/m\ :sup:`3` * - :math:`z` - Elevation - m * - :math:`z_{\text{j}}` - Segment boundary elevation - m * - :math:`z_{\text{m,j}}` - Nodal elevation, Eq. :ref:`13.3-13` - m * - :math:`\Delta z_{\text{j}}` - Segment length - m * - :math:`\alpha` - Vapor fraction based on area available for molten steel and vapor - -- * - :math:`\alpha_{\text{crit}}` - Input constant in two-phase multiplier, Eq. :ref:`13.2-10` - -- * - :math:`\beta` - Steel (solid) coefficient of linear thermal expansion, Eq. :ref:`13.2-38` - K\ :sup:`-1` * - :math:`\Gamma` - Factor in correction of cladding area for overfilled segments - m\ :sup:`3` * - :math:`\gamma_{\text{c}}` - Computer coefficient, Eq. :ref:`13.3-22` - * - :math:`\gamma_{\text{f}}` - Computed coefficient, Eq. :ref:`13.3-19` - * - :math:`\varepsilon` - Input constant in two-phase multiplier, Eq. :ref:`13.2-10` - -- * - :math:`\theta` - Multiplier on heat loss to structure (usually = 1) - -- * - :math:`\lambda` - Effective heat-of-fusion, Eq. :ref:`13.2-26` - J/kg * - :math:`\lambda_{\text{o}}` - Thermodynamic heat-of-fusion - J/kg * - :math:`\mu_{\text{c}}` - Moving cladding viscosity - Pa-s * - :math:`\mu_{\text{m}}` - Cladding viscosity at the liquidus temperature - Pa-s * - :math:`\mu_{\text{s}}` - Solid cladding pseudo-viscosity, Eq. :ref:`13.2-18c` - Pa-s * - :math:`\mu_{\text{t}}` - Cladding viscosity at the solidus temperature - Pa-s * - :math:`\mu_{\text{v}}` - Vapor viscosity - Pa-s * - :math:`\xi_{\text{f}}, \xi_{\text{w}}` - Computed coefficients - -- * - :math:`\xi_{1}, \xi_{2}, \xi_{3}` - Computed coefficients - -- * - :math:`\rho_{\text{c}}` - Molten cladding density - kg/m\ :sup:`3` * - :math:`\rho_{\text{c}}^{\circ}` - Density of cladding at the liquidus temperature - kg/m\ :sup:`3` * - :math:`\rho_{\text{f}}` - Fuel density - kg/m\ :sup:`3` * - :math:`\rho_{\text{s}}` - Refrozen steel density - kg/m\ :sup:`3` * - :math:`\rho_{\text{s}}^{\circ}` - Solid cladding density at the reference temperature - kg/m\ :sup:`3` * - :math:`\rho_{\text{v}}` - Vapor density - kg/m\ :sup:`3` * - :math:`\phi` - Sensible heat flux from refrozen cladding to the molten interface - W/m\ :sup:`2` * - :math:`\phi_{\text{c}}` - Flux of sensible heat into the moving cladding layer - W/m\ :sup:`2` * - :math:`\phi_{\text{hf}}` - Fusion heat flux, Eq. :ref:`13.2-24` - W/m\ :sup:`2` * - :math:`\phi_{\text{r}}` - Heat flux at interface of intact and refrozen cladding - W/m\ :sup:`2` * - :math:`\phi_{\text{trial}}` - Trail heat flux, Eq. :ref:`13.2-36` - W/m\ :sup:`2` * - :math:`\phi_{1}` - Heat flux, Eq. :ref:`13.2-34` - W/m\ :sup:`2` * - :math:`\phi_{2}` - Heat flux, Eq. :ref:`13.2-35` - W/m\ :sup:`2` * - :math:`\overline{\psi}` - Mean ratio of thermal-to-momentum eddy diffusivities - --