12.15. Nomenclature

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