.. _section-12.nomenclature:
Nomenclature
------------
.. list-table::
:header-rows: 1
:align: center
:widths: 1,3,1
* - Symbol
- Definition
- Units
* - :math:`A_{c}\left(z, t \right)`
- Coolant flow area
- :math:`\text{m}^{3}`
* - :math:`A_{fr}`
- User-input quantity in the friction factor expression
- --
* - :math:`AA_{0}`
- Coefficient in the liquid slug momentum equation
- :math:`\text{Pa}`
* - :math:`b_{fr}`
- User-input quantity in the friction factor expression
- --
* - :math:`BB_{0}`
- Coefficient in the liquid slug momentum equation
- :math:`\text{m}^{-1}-\text{s}^{-1}`
* - :math:`C_{l}`
- Specific heat of liquid sodium
- :math:`\text{J/kg-K}`
* - :math:`D_{h}\left(z, t\right)`
- Hydraulic diameter
- :math:`\text{m}`
* - :math:`E_{i}`
- Heat flow to the vapor through the liquid-vapor Interfaces
- :math:`\text{J}`
* - :math:`E_{t}`
- Total heat energy added to a vapor bubble in a time step
- :math:`\text{J}`
* - :math:`E_{es}`
- Heat flow to the vapor from the cladding and structure
- :math:`\text{J}`
* - :math:`F_{c}\left(z, t\right)`
- Condensation momentum loss term
- :math:`\text{Pa/m}`
* - :math:`f_{v}\left(z, t\right)`
- Friction factor
- --
* - :math:`F_{ce}\left(z, t\right)`
- Condensation momentum loss term to cladding film
- :math:`\text{Pa/m}`
* - :math:`F_{cs}\left(z, t\right)`
- Condensation momentum loss term to structure film
- :math:`\text{Pa/m}`
* - :math:`f_{rwb}, f_{rwt}`
- Liquid film rewetting factors
- --
* - :math:`g`
- Gravitational acceleration
- :math:`\text{m/s}^{2}`
* - :math:`h_{ec}\left(z\right)`
- Heat-transfer coefficient from the cladding surface to the sodium vapor
- :math:`\text{W/m}^{2} K`
* - :math:`h_{sc}\left(z\right)`
- Heat-transfer coefficient from the structure surface to the sodium vapor
- :math:`\text{W/m}^{2} K`
* - :math:`h_{cond}`
- User-supplied condensation heat-transfer coefficient
- :math:`\text{W/m}^{2} K`
* - :math:`I_{1}, I_{2}, I_{3}, I_{4}, I_{5}`
- Coefficients in the liquid slug momentum equation
- --
* - :math:`K`
- Bubble number
- --
* - :math:`K_{vn}`
- Number of bubbles
- --
* - :math:`k_{e}\left(z\right)`
- Cladding thermal conductivity
- :math:`\text{W/m-K}`
* - :math:`k_{l}\left(z\right)`
- Thermal conductivity of liquid sodium at Temperature T(z)
- :math:`\text{W/m-K}`
* - :math:`k_{or}\left(z,t\right)`
- Orifice pressure drop term
- --
* - :math:`p\left(z,t\right)`
- Vapor pressure
- :math:`\text{Pa}`
* - :math:`P_{e}\left(z\right)`
- Perimeter of cladding - :math:`2\pi r_{e}`
- :math:`\text{m}`
* - :math:`Q\left(z,t\right)`
- Total heat flux per unit volume :math:`= Q_{e} + Q_{s}`
- :math:`\text{W/m}^{3}`
* - :math:`\widetilde{Q}\left(t\right)`
- Total heat flow rate into the sodium vapor
- :math:`\text{W}`
* - :math:`q\left(z,t\right)`
- Surface heat flow per unit area
- :math:`\text{W/m}^{2}`
* - :math:`Q_{c}\left(c\right)`
- Volume source due to direct heating by neutrons and gamma rays
- :math:`\text{W/m}^{3}`
* - :math:`Q_{e}\left(z,t\right)`
- Heat flow rate per unit volume through the cladding
- :math:`\text{W/m}^{3}`
* - :math:`q_{e}\left(z,t\right)`
- Cladding-to-vapor heat flux
- :math:`\text{W/m}^{2}`
* - :math:`Q_{s}\left(z, t\right)`
- Heat flow rate per unit volume through the structure
- :math:`\text{W/m}^{3}`
* - :math:`q_{s}\left(z, t\right)`
- Structure-to-vapor heat flux
- :math:`\text{W/m}^{2}`
* - :math:`Q_{es}\left(t\right)`
- Heat flow rate from cladding and structure
- :math:`\text{W}`
* - :math:`r_{e}\left(z\right)`
- Nominal radius of cladding
- :math:`\text{m}`
* - :math:`R_{ec}\left(z, t\right)`
- Thermal resistance between the cladding and the coolant
- :math:`\text{m}^{2}\text{K/W}`
* - :math:`R_{sc}\left(z, t\right)`
- Thermal resistance between the structure and the coolant
- :math:`\text{m}^{2}\text{K/W}`
* - :math:`s`
- Vapor heat transfer surface area
- :math:`\text{m}^{2}`
* - :math:`T\left(z, t\right)`
- Coolant temperature
- :math:`\text{m}`
* - :math:`t`
- Time
- :math:`\text{m}`
* - :math:`T\left(z, t\right)`
- Cladding temperature
- :math:`\text{m}`
* - :math:`T_{l}\left(t\right)`
- Liquid sodium temperature at liquid-vapor interface
- :math:`\text{m}`
* - :math:`T_{s}\left(z, t\right)`
- Structure temperature
- :math:`\text{m}`
* - :math:`T_{v}\left( t\right)`
- Sodium vapor temperature at liquid-vapor interface
- :math:`\text{m}`
* - :math:`v\left(z, t\right)`
- Velocity
- :math:`\text{m/s}`
* - :math:`v_{fe}`
- Velocity of liquid film on the cladding (currently fixed at zero)
- :math:`\text{m/s}`
* - :math:`v_{fs}`
- Velocity of liquid film on the structure (currently fixed at zero)
- :math:`\text{m/s}`
* - :math:`W\left(z, t\right)`
- Mass flow rate
- :math:`\text{kg/s}`
* - :math:`w_{fe}\left(z, t\right)`
- Thickness of liquid film on the cladding
- :math:`\text{m}`
* - :math:`w_{fs}\left(z, t\right)`
- Thickness of liquid film on the structure
- :math:`\text{m}`
* - :math:`z`
- Axial height
- :math:`\text{m}`
* - :math:`z_{i}\left(1, t, K\right)`
- Height of lower liquid-vapor interface in bubble K
- :math:`\text{m}`
* - :math:`z_{i}\left(2, t, K\right)`
- Height of upper liquid-vapor interface in bubble K
- :math:`\text{m}`
* - :math:`\alpha`
- Thermal diffusivity of liquid sodium :math:`= k_{l} \rho_{l} C_{l}`
- :math:`\text{m}^2\text{s}`
* - :math:`\gamma \left(z, t\right)`
- Ratio of cladding surface area to coolant volume
- :math:`\text{m-1}`
* - :math:`\gamma_{2}\left(z, t\right)`
- Ratio of surface area of structure to surface area of cladding
- --
* - :math:`\Delta I_{j}`
- Coefficients in the liquid slug momentum equation
- --
* - :math:`\Delta r_{e}`
- Nominal cladding thickness
- :math:`\text{m}`
* - :math:`\Delta t`
- Time step
- :math:`\text{s}`
* - :math:`\theta_{1}, \theta_{2}`
- Coefficients which set the degree of implicitness of the liquid slug calculation
- --
* - :math:`\lambda\left(z, t\right)`
- Heat of vaporization
- :math:`\text{J}/\text{kg}`
* - :math:`\mu\left(z, t\right)`
- Sodium vapor viscosity
- :math:`\text{Pa}-\text{s}`
* - :math:`\rho_{t}\left(z\right)`
- Density of liquid sodium
- :math:`\text{kg/m}^{3}`
* - :math:`\rho_{v}\left(z\right)`
- Density of sodium vapor
- :math:`\text{kg/m}^{3}`
* - Subscripts and Superscripts
-
-
* - :math:`b`
- Bottom
-
* - :math:`c`
- Coolant
-
* - :math:`e`
- Cladding
-
* - :math:`I`
- Interface quantity
-
* - :math:`J`
- Global node number of the node under consideration
-
* - :math:`J1`
- Global node number of the lower interface of the bubble under consideration
-
* - :math:`J2`
- Global node number of the upper interface of the bubble under consideration
-
* - :math:`l`
- Liquid
-
* - :math:`L`
- Lower interface
-
* - :math:`s`
- Structure
-
* - :math:`t`
- Top
-
* - :math:`u`
- Upper interface
-
* - :math:`v`
- Vapor
-
* - :math:`1,2`
- Beginning and end of current time step
-