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 |