3.18. Nomenclature
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 |
Symbol |
Description |
Units |
|---|---|---|
\(A_{\text{c}}\) |
Coolant flow area |
m2 |
\(A_{\text{ep}}\) |
Cross sectional area of the clad in the gas plenum region |
m2 |
\(A_{\text{g}}\) |
Cross sectional area of the plenum gas |
m2 |
\(A_{\text{fr}}\), \(b_{\text{fr}}\) |
Coefficients in the friction factor correlation: \(f = A_{\text{fr}}\left( \text{Re} \right)^{b_{\text{fr}}}\) |
– |
\(c\) |
Specific heat |
J/kg-K |
\(\overline{c}_{\text{c}}\) |
Coolant specific heat |
J/kg-K |
\(c_{\text{e}}\) |
Cladding specific heat |
J/kg-K |
\(\overline{c}_{\text{f}}\) |
Average fuel specific heat, averaged over a time step |
J/kg-K |
\(c_{\text{m}}\) |
Modified specific heat in the melting range |
J/kg-K |
\(c_{\text{mix}}\) |
Coolant specific heat in the mixing zone used for re-entry temperature calculation |
J/kg-K |
\(c_1\), \(c_2\), \(c_3\) |
Correlation constants used in coolant heat-transfer coefficients |
– |
\(D\) |
Right-hand-side terms in the matrix equations for radial temperature profiles |
J/m |
\(D_{\text{h}}\) |
Hydraulic diameter |
m |
\(d_{\text{sti}}\) |
Structure inner node thickness |
m |
\(d_{\text{sto}}\) |
Structure outer node thickness |
m |
\(E_{\text{ec}}\) |
Heat flux from clad to coolant, integrated over a time step |
J/m2 |
\(E_{\text{sc}}\) |
Heat flux form structure to coolant, integrated over a time step |
J/m2 |
\(f\) |
Friction factor |
– |
\(f_{\text{i}}\) |
Fraction of the structure thickness represented by the inner node |
– |
\(f_{\text{o}}\) |
Fraction of the structure thickness represented by the outer node |
– |
\(g\) |
Acceleration of gravity |
m/s2 |
\(h_{\text{b}}\) |
Bond gap conductance |
W/m2-K |
\(h_{\text{c}}\) |
Coolant-film heat-transfer coefficient |
W/m2-K |
\(h_{\text{cond}}\) |
Condensation heat-transfer coefficient for sodium vapor |
W/m2-K |
\(H_{\text{eg}}\) |
Heat-transfer coefficient form the gas in the gas plenum to the cladding |
W/m2-K |
\(H_{\text{erc}}\) |
Heat-transfer coefficient from the cladding or reflector outer node to the coolant |
W/m2-K |
\(h_{\text{r}}\) |
Equivalent radiation heat-transfer coefficient |
W/m2-K |
\(H_{\text{rio}}\) |
Heat-transfer coefficient from the structure inner node to the reflector outer node |
W/m2-K |
\(H_{\text{sic}}\) |
Heat-transfer coefficient from the structure inner node to the coolant |
W/m2-K |
\(H_{\text{stio}}\) |
Heat-transfer coefficient from the structure inner node to the structure outer node |
W/m2-K |
\(i\) |
Radial node number |
– |
\(ic\) |
Core channel number |
– |
\(I_1\) |
Inertial integral in the momentum equation |
m-1 |
\(I_2\) |
Acceleration integral in the momentum equation |
m/kg |
\(I_3\) |
Friction integral in the momentum equation |
m/kg |
\(I_4\) |
Orifice term in the momentum equation |
m/kg |
\(I_5\) |
Density integral in the momentum equation |
kg/m2 |
\(j\) |
Fuel axial node number |
– |
\(jc\) |
Coolant axial node number |
– |
\(\text{JC}\) |
Axial node number |
– |
\(k\) |
Thermal conductivity |
W/m-K |
\(k_{\text{ep}}\) |
Cladding thermal conductivity in the gas plenum region |
W/m-K |
\(\overline{k}_{\text{i~j}}\) |
Weighted average thermal conductivity for heat flow from node i to j |
W/m-K |
\(K_{\text{or}}\) |
Orifice coefficient |
– |
\(L\) |
1 for subassembly inlet, 2 for outlet |
– |
\(\text{MZC}\) |
Total number of coolant axial nodes |
– |
\(m_{\text{e}}\) |
Cladding mass |
kg |
\(m_{\text{f}}\) |
Fuel mass |
kg |
\(M_{\text{mix}}\) |
Mass of sodium in the mixing volume |
kg |
\(\text{NC}\) |
Radial node number of the coolant node |
– |
\(\text{NE}\) |
Radial node number for the cladding mid-point |
– |
\(\text{NE}'\) |
Radial node number for the cladding outer surface node |
– |
\(\text{NE}''\) |
Radial node number for the cladding inner surface node |
– |
\(\text{NN}\) |
NT-1 |
– |
\(N_{\text{ps}}\) |
Number of fuel pins represented by a channel |
– |
\(\text{NR}\) |
Radial node number for the fuel outer surface radius. (note \(\text{NR}=\text{NE}''\)) |
– |
\(\text{NSI}\) |
Radial node number for the inner structure node |
– |
\(\text{NSO}\) |
Radial node number for the outer structure node |
– |
\(\text{NT}\) |
Radial node number for the fuel outer surface temperature node |
– |
\(p\) |
Pressure |
Pa |
\(p_{\text{b}}\) |
Pressure at the bottom of the subassembly |
Pa |
\(p_{\text{b1}}\), \(p_{\text{b2}}\) |
pb at beginning and end of a time step |
Pa |
\(p_{\text{in}}\) |
Pressure in the coolant inlet plenum |
Pa |
\(\overline{P}_{\text{j}}\) |
Heat production rate in axial node j |
W |
\(P_{\text{r}}\) |
Radial power shape, per unit mass |
– |
\(p_{\text{t}}\) |
Pressure at the top of the subassembly |
Pa |
\(p_{\text{t1}}\), \(p_{\text{t2}}\) |
pt at the beginning and end of a time step |
Pa |
\(p_{\text{x}}\) |
Pressure in the coolant outlet plenum |
Pa |
\(\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{fr}}\) |
Friction pressure drop |
Pa/m |
\(\left( \frac{\partial \text{p}}{\partial \text{z}} \right)_{\text{k}}\) |
Orifice pressure drop |
Pa/m |
\(Q_{\text{c}}\) |
Coolant heat source due to direct heating by neutrons and gamma rays |
W/m3 |
\(Q_{\text{ct}}\) |
Total steady-state heat source per unit of coolant volume |
W/m3 |
\(Q_{\text{ec}}\) |
Heat flow from clad to coolant |
W/m3 |
\(q_{\text{fe}}\) |
Fuel-to-cladding heat flux |
W/m2 |
\(Q_{\text{sc}}\) |
Heat flow from structure to coolant |
W/m3 |
\(Q_{\text{sm}} \left( i \right)\) |
Sum of the heat sources for all radial nodes inside and including node i |
W |
\(Q_{\text{st}}\) |
Structure heat source due to direct heating by neutrons and gamma rays |
W/m2 |
\(Q_{\text{v}}\) |
Heat source per unit volume |
W/m3 |
\(r\) |
Radius |
m |
\(r_{\text{brp}}\) |
Clad inner radius in the gas plenum region |
m |
\(\text{Re}\) |
Reynolds number |
– |
\(R_{\text{ec}}\) |
Thermal resistance between clad and coolant |
m2-K/W |
\(R_{\text{ehf}}\) |
Thermal resistance of the outer fourth of the cladding |
m2-K/W |
\(r_{\text{erp}}\) |
Cladding outer radius in the gas plenum region |
m |
\(R_{\text{g}}\) |
Thermal resistance of the gas in the plenum |
m2-K/W |
\(r_{\text{o}} \left( i \right)\) |
Steady-state radial mesh |
m |
\(S_{\text{er}}\) |
Perimeter of the cladding or reflector in contact with the coolant |
m |
\(S_{\text{st}}\) |
Structure perimeter, heat-transfer area per unit height |
m |
\(T\) |
Temperature |
K |
\(t\) |
Time |
s |
\(T_{\text{cin}}\) |
Coolant inlet temperature |
K |
\(T_{\text{cout}}\) |
Coolant outlet temperature |
K |
\(T_{\text{eex}}\) |
Extrapolated clad temperature |
K |
\(T_{\text{eq}}\) |
Equilibrium temperature in the mixing volume |
K |
\(\overline{T}_{\text{exp}}\) |
Temperature of the sodium expelled from the subassembly into a mixing volume, averaged over a time step |
K |
\(\overline{T}_{\text{f}}\) |
Average fuel temperature at an axial node, mass-weighted average |
K |
\(T_{\text{g}}\) |
Plenum gas temperature |
K |
\(T_{\text{liq}}\) |
Liquidus temperature |
K |
\(T_{\text{out}}\) |
Bulk temperature in the coolant outlet plenum |
K |
\(t_{\text{p1}}\), \(t_{\text{p2}}\) |
Times at the beginning and end of a PRIMAR time step |
s |
\(T_{\text{ri}}\) |
Reflector inner node temperature |
K |
\(T_{\text{ro}}\) |
Reflector outer node temperature |
K |
\(T_{\text{sol}}\) |
Solidus temperature |
K |
\(T_{\text{o}}\) |
Temperature at the beginning of a time step |
K |
\(T_1\) |
Temperature at the beginning of a time step |
K |
\({T'}_1\) |
Temperature of the coolant entering an axial node at the end of a time step |
K |
\(T_2\) |
Temperature at the end of a time step |
K |
\({T'}_2\) |
Temperature of the coolant entering an axial node at the end of a time step |
K |
\(U_{\text{melt}}\) |
Heat of fusion |
J/kg |
\(v\) |
Velocity |
m/s |
\(w\) |
Coolant mass flow rate |
kg/s |
\(w_{\text{e}}\) |
Estimated mass flow rate |
kg/s |
\(w_{\text{fe}}\) |
Thickness of the liquid-sodium film left on the cladding after voiding occurs |
m |
\(w_{\text{fr}}\) |
Thickness of the liquid-sodium film left on the reflector after voiding occurs |
m |
\(w_{\text{fst}}\) |
Thickness of the liquid-sodium film left on the structure after voiding occurs |
m |
\(w_1\), \(w_2\) |
w at beginning and end of a time step |
kg/s |
\(\Delta w\) |
Change in w during a time step |
kg/s |
\(x\) |
Distance |
m |
\(x_{\text{I1}} \left( \text{JC} \right)\) |
Nodal contribution to I1 |
m-1 |
\(x_{\text{I2}} \left( \text{JC} \right)\) |
Nodal contribution to I2 |
m/kg |
\(x_{\text{I3}} \left( \text{JC} \right)\) |
Nodal contribution to I3 |
|
\(x_{\text{I5}} \left( \text{JC} \right)\) |
Nodal contribution to I5 |
kg/m2 |
\(z\) |
Axial position |
m |
\(z\) |
Elevation |
m |
\(\Delta z\) |
Node height |
m |
\(z_{\text{pb}}\) |
Elevation at the bottom of the gas plenum |
m |
\(z_{\text{pt}}\) |
Elevation at the top of the gas plenum |
m |
\(z_{\text{pll}}\) |
Reference elevation of the coolant inlet plenum |
m |
\(z_{\text{plu}}\) |
Reference elevation of the coolant outlet plenum |
m |
\(\alpha\) |
Heat capacity terms in the matrix equations for radial temperature profiles |
J/m-K |
\(\alpha_{\text{e}}\) |
Cladding thermal expansion coefficient |
K-1 |
\(\alpha_{\text{f}}\) |
Fuel thermal expansion coefficient |
K-1 |
\(\beta\) |
Thermal conductivity terms in the matrix equations for radial temperature profiles |
J/m-K |
\(\gamma_{\text{c}}\) |
Fraction of the total heat production that goes directly into the coolant |
– |
\(\gamma_{\text{e}}\) |
Fraction of the total heat production that goes directly into the cladding |
– |
\(\gamma_{\text{s}}\) |
Fraction of the total heat production that goes directly into the structure |
– |
\(\gamma_2\) |
Ratio of the structure perimeter to the cladding perimeter |
– |
\(\Delta r\) |
Radial node size |
m |
\(\Delta r_{\text{i,j}}\) |
Effective radial distance for heat flow from node I to node j |
m |
\(\Delta t\) |
Time-step size |
s |
\(\Delta z\) |
Axial node height |
m |
\(\varepsilon\) |
Thermal emissivity |
– |
\(\theta_1\), \(\theta_2\) |
Degree of explicitness or implicitness in the solution |
– |
\(\rho\) |
Density |
kg/m3 |
\(\rho_{\text{c}}\) |
Coolant density |
kg/m3 |
\(\rho_{\text{cin}}\) |
Coolant density in the inlet plenum |
kg/m3 |
\(\rho_{\text{cout}}\) |
Coolant density in the outlet plenum |
kg/m3 |
\(\left( \rho c_{\text{g}} \right)\) |
Density times specific heat of the plenum gas |
J/m3-K |
\(\left( \rho c_{\text{r}} \right)\) |
Density times specific heat for the reflector |
J/m3-K |
\(\rho_{\text{e}}\) |
Cladding density |
kg/m3 |
\(\sigma\) |
Stefan-Bolzmann constant |
W/m2-K4 |
\(\tau\) |
Time constant for flow rate changes |
s |
\(\tau_{\text{c}}\) |
Condensation heat-transfer time constant |
s |
\(\tau_{\text{ro}}\) |
Time constant for temperature changes in the outer reflector node |
s |
\(\tau_{\text{sti}}\) |
Time constant for temperature changes in the inner structure node |
s |
\(\mu\) |
Coolant viscosity |
Pa-s |
\(\overline{\mu}\left( \text{JC} \right)\) |
Average value of \(\mu\) for node JC |
Pa-s |
\(\Psi\) |
Source terms in the matrix equations for radial temperature profiles |
– |