.. _section-12.nomenclature: Nomenclature ------------ .. list-table:: :header-rows: 1 :align: center :widths: auto * - 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 -