.. _ch3nom:

Nomenclature
================================================================================

.. list-table::
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	* - Subscript
	  - Description
	  -
	* - c
	  - Coolant
	  -
	* - e
	  - Cladding
	  -
	* - f
	  - Fuel
	  -
	* - g
	  - Plenum gas
	  -
	* - kz
	  - Reflector zone
	  -
	* - p
	  - Gas plenum region
	  -
	* - si
	  - Structure inner node
	  -
	* - so
	  - Structure outer node
	  -
	* - 1
	  - Beginning of the time step
	  -
	* - 2
	  - End of the time step
	  -

|

.. list-table::
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	* - Symbol
	  - Description
	  - Units
	* - :math:`A_{\text{c}}`
	  - Coolant flow area
	  - m\ :sup:`2`
	* - :math:`A_{\text{ep}}`
	  - Cross sectional area of the clad in the gas plenum region
	  - m\ :sup:`2`
	* - :math:`A_{\text{g}}`
	  - Cross sectional area of the plenum gas
	  - m\ :sup:`2`
	* - :math:`A_{\text{fr}}`, :math:`b_{\text{fr}}`
	  - Coefficients in the friction factor correlation: :math:`f = A_{\text{fr}}\left( \text{Re} \right)^{b_{\text{fr}}}`
	  - --
	* - :math:`c`
	  - Specific heat
	  - J/kg-K
	* - :math:`\overline{c}_{\text{c}}`
	  - Coolant specific heat
	  - J/kg-K
	* - :math:`c_{\text{e}}`
	  - Cladding specific heat
	  - J/kg-K
	* - :math:`\overline{c}_{\text{f}}`
	  - Average fuel specific heat, averaged over a time step
	  - J/kg-K
	* - :math:`c_{\text{m}}`
	  - Modified specific heat in the melting range
	  - J/kg-K
	* - :math:`c_{\text{mix}}`
	  - Coolant specific heat in the mixing zone used for re-entry temperature calculation
	  - J/kg-K
	* - :math:`c_1`, :math:`c_2`, :math:`c_3`
	  - Correlation constants used in coolant heat-transfer coefficients
	  - --
	* - :math:`D`
	  - Right-hand-side terms in the matrix equations for radial temperature profiles
	  - J/m
	* - :math:`D_{\text{h}}`
	  - Hydraulic diameter
	  - m
	* - :math:`d_{\text{sti}}`
	  - Structure inner node thickness
	  - m
	* - :math:`d_{\text{sto}}`
	  - Structure outer node thickness
	  - m
	* - :math:`E_{\text{ec}}`
	  - Heat flux from clad to coolant, integrated over a time step
	  - J/m\ :sup:`2`
	* - :math:`E_{\text{sc}}`
	  - Heat flux form structure to coolant, integrated over a time step
	  - J/m\ :sup:`2`
	* - :math:`f`
	  - Friction factor
	  - --
	* - :math:`f_{\text{i}}`
	  - Fraction of the structure thickness represented by the inner node
	  - --
	* - :math:`f_{\text{o}}`
	  - Fraction of the structure thickness represented by the outer node
	  - --
	* - :math:`g`
	  - Acceleration of gravity
	  - m/s\ :sup:`2`
	* - :math:`h_{\text{b}}`
	  - Bond gap conductance
	  - W/m\ :sup:`2`-K
	* - :math:`h_{\text{c}}`
	  - Coolant-film heat-transfer coefficient
	  - W/m\ :sup:`2`-K
	* - :math:`h_{\text{cond}}`
	  - Condensation heat-transfer coefficient for sodium vapor
	  - W/m\ :sup:`2`-K
	* - :math:`H_{\text{eg}}`
	  - Heat-transfer coefficient form the gas in the gas plenum to the cladding
	  - W/m\ :sup:`2`-K
	* - :math:`H_{\text{erc}}`
	  - Heat-transfer coefficient from the cladding or reflector outer node to the coolant
	  - W/m\ :sup:`2`-K
	* - :math:`h_{\text{r}}`
	  - Equivalent radiation heat-transfer coefficient
	  - W/m\ :sup:`2`-K
	* - :math:`H_{\text{rio}}`
	  - Heat-transfer coefficient from the structure inner node to the reflector outer node
	  - W/m\ :sup:`2`-K
	* - :math:`H_{\text{sic}}`
	  - Heat-transfer coefficient from the structure inner node to the coolant
	  - W/m\ :sup:`2`-K
	* - :math:`H_{\text{stio}}`
	  - Heat-transfer coefficient from the structure inner node to the structure outer node
	  - W/m\ :sup:`2`-K
	* - :math:`i`
	  - Radial node number
	  - --
	* - :math:`ic`
	  - Core channel number
	  - --
	* - :math:`I_1`
	  - Inertial integral in the momentum equation
	  - m\ :sup:`-1`
	* - :math:`I_2`
	  - Acceleration integral in the momentum equation
	  - m/kg
	* - :math:`I_3`
	  - Friction integral in the momentum equation
	  - m/kg
	* - :math:`I_4`
	  - Orifice term in the momentum equation
	  - m/kg
	* - :math:`I_5`
	  - Density integral in the momentum equation
	  - kg/m\ :sup:`2`
	* - :math:`j`
	  - Fuel axial node number
	  - --
	* - :math:`jc`
	  - Coolant axial node number
	  - --
	* - :math:`\text{JC}`
	  - Axial node number
	  - --
	* - :math:`k`
	  - Thermal conductivity
	  - W/m-K
	* - :math:`k_{\text{ep}}`
	  - Cladding thermal conductivity in the gas plenum region
	  - W/m-K
	* - :math:`\overline{k}_{\text{i~j}}`
	  - Weighted average thermal conductivity for heat flow from node i to j
	  - W/m-K
	* - :math:`K_{\text{or}}`
	  - Orifice coefficient
	  - --
	* - :math:`L`
	  - 1 for subassembly inlet, 2 for outlet
	  - --
	* - :math:`\text{MZC}`
	  - Total number of coolant axial nodes
	  - --
	* - :math:`m_{\text{e}}`
	  - Cladding mass
	  - kg
	* - :math:`m_{\text{f}}`
	  - Fuel mass
	  - kg
	* - :math:`M_{\text{mix}}`
	  - Mass of sodium in the mixing volume
	  - kg
	* - :math:`\text{NC}`
	  - Radial node number of the coolant node
	  - --
	* - :math:`\text{NE}`
	  - Radial node number for the cladding mid-point
	  - --
	* - :math:`\text{NE}'`
	  - Radial node number for the cladding outer surface node
	  - --
	* - :math:`\text{NE}''`
	  - Radial node number for the cladding inner surface node
	  - --
	* - :math:`\text{NN}`
	  - NT-1
	  - --
	* - :math:`N_{\text{ps}}`
	  - Number of fuel pins represented by a channel
	  - --
	* - :math:`\text{NR}`
	  - Radial node number for the fuel outer surface radius. (note :math:`\text{NR}=\text{NE}''`)
	  - --
	* - :math:`\text{NSI}`
	  - Radial node number for the inner structure node
	  - --
	* - :math:`\text{NSO}`
	  - Radial node number for the outer structure node
	  - --
	* - :math:`\text{NT}`
	  - Radial node number for the fuel outer surface temperature node
	  - --
	* - :math:`p`
	  - Pressure
	  - Pa
	* - :math:`p_{\text{b}}`
	  - Pressure at the bottom of the subassembly
	  - Pa
	* - :math:`p_{\text{b1}}`, :math:`p_{\text{b2}}`
	  - p\ :sub:`b` at beginning and end of a time step
	  - Pa
	* - :math:`p_{\text{in}}`
	  - Pressure in the coolant inlet plenum
	  - Pa
	* - :math:`\overline{P}_{\text{j}}`
	  - Heat production rate in axial node j
	  - W
	* - :math:`P_{\text{r}}`
	  - Radial power shape, per unit mass
	  - --
	* - :math:`p_{\text{t}}`
	  - Pressure at the top of the subassembly
	  - Pa
	* - :math:`p_{\text{t1}}`, :math:`p_{\text{t2}}`
	  - p\ :sub:`t` at the beginning and end of a time step
	  - Pa
	* - :math:`p_{\text{x}}`
	  - Pressure in the coolant outlet plenum
	  - Pa
	* - :math:`\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{fr}}`
	  - Friction pressure drop
	  - Pa/m
	* - :math:`\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{k}}`
	  - Orifice pressure drop
	  - Pa/m
	* - :math:`Q_{\text{c}}`
	  - Coolant heat source due to direct heating by neutrons and gamma rays
	  - W/m\ :sup:`3`
	* - :math:`Q_{\text{ct}}`
	  - Total steady-state heat source per unit of coolant volume
	  - W/m\ :sup:`3`
	* - :math:`Q_{\text{ec}}`
	  - Heat flow from clad to coolant
	  - W/m\ :sup:`3`
	* - :math:`q_{\text{fe}}`
	  - Fuel-to-cladding heat flux
	  - W/m\ :sup:`2`
	* - :math:`Q_{\text{sc}}`
	  - Heat flow from structure to coolant
	  - W/m\ :sup:`3`
	* - :math:`Q_{\text{sm}} \left( i \right)`
	  - Sum of the heat sources for all radial nodes inside and including node i
	  - W
	* - :math:`Q_{\text{st}}`
	  - Structure heat source due to direct heating by neutrons and gamma rays
	  - W/m\ :sup:`2`
	* - :math:`Q_{\text{v}}`
	  - Heat source per unit volume
	  - W/m\ :sup:`3`
	* - :math:`r`
	  - Radius
	  - m
	* - :math:`r_{\text{brp}}`
	  - Clad inner radius in the gas plenum region
	  - m
	* - :math:`\text{Re}`
	  - Reynolds number
	  - --
	* - :math:`R_{\text{ec}}`
	  - Thermal resistance between clad and coolant
	  - m\ :sup:`2`-K/W
	* - :math:`R_{\text{ehf}}`
	  - Thermal resistance of the outer fourth of the cladding
	  - m\ :sup:`2`-K/W
	* - :math:`r_{\text{erp}}`
	  - Cladding outer radius in the gas plenum region
	  - m
	* - :math:`R_{\text{g}}`
	  - Thermal resistance of the gas in the plenum
	  - m\ :sup:`2`-K/W
	* - :math:`r_{\text{o}} \left( i \right)`
	  - Steady-state radial mesh
	  - m
	* - :math:`S_{\text{er}}`
	  - Perimeter of the cladding or reflector in contact with the coolant
	  - m
	* - :math:`S_{\text{st}}`
	  - Structure perimeter, heat-transfer area per unit height
	  - m
	* - :math:`T`
	  - Temperature
	  - K
	* - :math:`t`
	  - Time
	  - s
	* - :math:`T_{\text{cin}}`
	  - Coolant inlet temperature
	  - K
	* - :math:`T_{\text{cout}}`
	  - Coolant outlet temperature
	  - K
	* - :math:`T_{\text{eex}}`
	  - Extrapolated clad temperature
	  - K
	* - :math:`T_{\text{eq}}`
	  - Equilibrium temperature in the mixing volume
	  - K
	* - :math:`\overline{T}_{\text{exp}}`
	  - Temperature of the sodium expelled from the subassembly into a mixing volume, averaged over a time step
	  - K
	* - :math:`\overline{T}_{\text{f}}`
	  - Average fuel temperature at an axial node, mass-weighted average
	  - K
	* - :math:`T_{\text{g}}`
	  - Plenum gas temperature
	  - K
	* - :math:`T_{\text{liq}}`
	  - Liquidus temperature
	  - K
	* - :math:`T_{\text{out}}`
	  - Bulk temperature in the coolant outlet plenum
	  - K
	* - :math:`t_{\text{p1}}`, :math:`t_{\text{p2}}`
	  - Times at the beginning and end of a PRIMAR time step
	  - s
	* - :math:`T_{\text{ri}}`
	  - Reflector inner node temperature
	  - K
	* - :math:`T_{\text{ro}}`
	  - Reflector outer node temperature
	  - K
	* - :math:`T_{\text{sol}}`
	  - Solidus temperature
	  - K
	* - :math:`T_{\text{o}}`
	  - Temperature at the beginning of a time step
	  - K
	* - :math:`T_1`
	  - Temperature at the beginning of a time step
	  - K
	* - :math:`{T'}_1`
	  - Temperature of the coolant entering an axial node at the end of a time step
	  - K
	* - :math:`T_2`
	  - Temperature at the end of a time step
	  - K
	* - :math:`{T'}_2`
	  - Temperature of the coolant entering an axial node at the end of a time step
	  - K
	* - :math:`U_{\text{melt}}`
	  - Heat of fusion
	  - J/kg
	* - :math:`v`
	  - Velocity
	  - m/s
	* - :math:`w`
	  - Coolant mass flow rate
	  - kg/s
	* - :math:`w_{\text{e}}`
	  - Estimated mass flow rate
	  - kg/s
	* - :math:`w_{\text{fe}}`
	  - Thickness of the liquid-sodium film left on the cladding after voiding occurs
	  - m
	* - :math:`w_{\text{fr}}`
	  - Thickness of the liquid-sodium film left on the reflector after voiding occurs
	  - m
	* - :math:`w_{\text{fst}}`
	  - Thickness of the liquid-sodium film left on the structure after voiding occurs
	  - m
	* - :math:`w_1`, :math:`w_2`
	  - w at beginning and end of a time step
	  - kg/s
	* - :math:`\Delta w`
	  - Change in w during a time step
	  - kg/s
	* - :math:`x`
	  - Distance
	  - m
	* - :math:`x_{\text{I1}} \left( \text{JC} \right)`
	  - Nodal contribution to I\ :sub:`1`
	  - m\ :sup:`-1`
	* - :math:`x_{\text{I2}} \left( \text{JC} \right)`
	  - Nodal contribution to I\ :sub:`2`
	  - m/kg
	* - :math:`x_{\text{I3}} \left( \text{JC} \right)`
	  - Nodal contribution to I\ :sub:`3`
	  -
	* - :math:`x_{\text{I5}} \left( \text{JC} \right)`
	  - Nodal contribution to I\ :sub:`5`
	  - kg/m\ :sup:`2`
	* - :math:`z`
	  - Axial position
	  - m
	* - :math:`z`
	  - Elevation
	  - m
	* - :math:`\Delta z`
	  - Node height
	  - m
	* - :math:`z_{\text{pb}}`
	  - Elevation at the bottom of the gas plenum
	  - m
	* - :math:`z_{\text{pt}}`
	  - Elevation at the top of the gas plenum
	  - m
	* - :math:`z_{\text{pll}}`
	  - Reference elevation of the coolant inlet plenum
	  - m
	* - :math:`z_{\text{plu}}`
	  - Reference elevation of the coolant outlet plenum
	  - m
	* - :math:`\alpha`
	  - Heat capacity terms in the matrix equations for radial temperature profiles
	  - J/m-K
	* - :math:`\alpha_{\text{e}}`
	  - Cladding thermal expansion coefficient
	  - K\ :sup:`-1`
	* - :math:`\alpha_{\text{f}}`
	  - Fuel thermal expansion coefficient
	  - K\ :sup:`-1`
	* - :math:`\beta`
	  - Thermal conductivity terms in the matrix equations for radial temperature profiles
	  - J/m-K
	* - :math:`\gamma_{\text{c}}`
	  - Fraction of the total heat production that goes directly into the coolant
	  - --
	* - :math:`\gamma_{\text{e}}`
	  - Fraction of the total heat production that goes directly into the cladding
	  - --
	* - :math:`\gamma_{\text{s}}`
	  - Fraction of the total heat production that goes directly into the structure
	  - --
	* - :math:`\gamma_2`
	  - Ratio of the structure perimeter to the cladding perimeter
	  - --
	* - :math:`\Delta r`
	  - Radial node size
	  - m
	* - :math:`\Delta r_{\text{i,j}}`
	  - Effective radial distance for heat flow from node I to node j
	  - m
	* - :math:`\Delta t`
	  - Time-step size
	  - s
	* - :math:`\Delta z`
	  - Axial node height
	  - m
	* - :math:`\varepsilon`
	  - Thermal emissivity
	  - --
	* - :math:`\theta_1`, :math:`\theta_2`
	  - Degree of explicitness or implicitness in the solution
	  - --
	* - :math:`\rho`
	  - Density
	  - kg/m\ :sup:`3`
	* - :math:`\rho_{\text{c}}`
	  - Coolant density
	  - kg/m\ :sup:`3`
	* - :math:`\rho_{\text{cin}}`
	  - Coolant density in the inlet plenum
	  - kg/m\ :sup:`3`
	* - :math:`\rho_{\text{cout}}`
	  - Coolant density in the outlet plenum
	  - kg/m\ :sup:`3`
	* - :math:`\left( \rho c_{\text{g}} \right)`
	  - Density times specific heat of the plenum gas
	  - J/m\ :sup:`3`-K
	* - :math:`\left( \rho c_{\text{r}} \right)`
	  - Density times specific heat for the reflector
	  - J/m\ :sup:`3`-K
	* - :math:`\rho_{\text{e}}`
	  - Cladding density
	  - kg/m\ :sup:`3`
	* - :math:`\sigma`
	  - Stefan-Bolzmann constant
	  - W/m\ :sup:`2`-K\ :sup:`4`
	* - :math:`\tau`
	  - Time constant for flow rate changes
	  - s
	* - :math:`\tau_{\text{c}}`
	  - Condensation heat-transfer time constant
	  - s
	* - :math:`\tau_{\text{ro}}`
	  - Time constant for temperature changes in the outer reflector node
	  - s
	* - :math:`\tau_{\text{sti}}`
	  - Time constant for temperature changes in the inner structure node
	  - s
	* - :math:`\mu`
	  - Coolant viscosity
	  - Pa-s
	* - :math:`\overline{\mu}\left( \text{JC} \right)`
	  - Average value of :math:`\mu` for node JC
	  - Pa-s
	* - :math:`\Psi`
	  - Source terms in the matrix equations for radial temperature profiles
	  - --