================================================================================
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<eq-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<eq-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<eq-13.2-16b>`
- --
* - :math:`C`
- Liquid-steel volumetric coefficient of thermal expansion, Eq. :ref:`13.2-39<eq-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<eq-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<eq-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<eq-13.2-28>`
- --
* - :math:`c_{\text{pc}}`
- Coefficient of friction with fuel pin, Eq. :ref:`13.2-15<eq-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<eq-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<eq-13.2-11a>`
- 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<eq-13.2-18b>`
- --
* - :math:`\text{Re}`
- Molten cladding Reynolds number, Eq. :ref:`13.2-17<eq-13.2-17>`
- --
* - :math:`\left( \text{Re} \right)_{\text{break}}`
- Turbulent transition Reynolds number, Eq. :ref:`13.2-16<eq-13.2-16a>`
- --
* - :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<eq-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<eq-13.3-14>`
- kg/s
* - :math:`w_{\text{j}}^{*}`
- Segment boundary mass flow, Eq. :ref:`13.3-10<eq-13.3-10>`
- kg/s
* - :math:`w_{\text{m,j}}`
- Segment mean mass flow, Eq. :ref:`13.3-11<eq-13.3-11>`
- kg/s
* - :math:`x`
- Constant in incoherence factor on friction, Eq. :ref:`13.2-11a<eq-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<eq-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<eq-13.2-10a>`
- --
* - :math:`\beta`
- Steel (solid) coefficient of linear thermal expansion, Eq. :ref:`13.2-38<eq-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<eq-13.3-22>`
-
* - :math:`\gamma_{\text{f}}`
- Computed coefficient, Eq. :ref:`13.3-19<eq-13.3-19>`
-
* - :math:`\varepsilon`
- Input constant in two-phase multiplier, Eq. :ref:`13.2-10<eq-13.2-10a>`
- --
* - :math:`\theta`
- Multiplier on heat loss to structure (usually = 1)
- --
* - :math:`\lambda`
- Effective heat-of-fusion, Eq. :ref:`13.2-26<eq-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<eq-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<eq-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<eq-13.2-36>`
- W/m\ :sup:`2`
* - :math:`\phi_{1}`
- Heat flux, Eq. :ref:`13.2-34<eq-13.2-34>`
- W/m\ :sup:`2`
* - :math:`\phi_{2}`
- Heat flux, Eq. :ref:`13.2-35<eq-13.2-35>`
- W/m\ :sup:`2`
* - :math:`\overline{\psi}`
- Mean ratio of thermal-to-momentum eddy diffusivities
- --