13.6. Nomenclature¶
Symbol |
Definition |
Units |
|---|---|---|
\(A_{\text{c}}\) |
Moving cladding cross-sectional area |
m2 |
\(\text{AFRV}\) |
Input constant in single-phase friction factor formula, Eq. 13.2-5 |
|
\(A_{\text{f}}\) |
Total area allowed for cladding by the fuel |
m2 |
\(A_{\text{max}}\) |
Available area for molten cladding |
m2 |
\(A_{\text{s}}\) |
Refrozen steel cross-sectional area |
m2 |
\(A_{\text{v}}\) |
Vapor flow area |
m2 |
\(a\) |
Constant in viscosity Eq. 13.2-18a |
K |
\(\text{BFRV}\) |
Input constant, see AFRV |
– |
\(b_{\text{f}}\) |
Molten cladding/pin turbulent friction factor, Eq. 13.2-16b |
– |
\(C\) |
Liquid-steel volumetric coefficient of thermal expansion, Eq. 13.2-39 |
K-1 |
\(C_{\text{a}}\) |
Mass convection term |
kg/m-s |
\(C_{\text{f}}\) |
Terms in the outer-fuel-node energy Eq. 13.3-17 |
W/m |
\(C_{\text{m}}\) |
Momentum convection term |
m/s2 |
\(C_{\text{v}}\) |
Energy convection term, Eq. 13.3-9 |
W/m |
\(C_{1}, C_{2}, C_{3}\) |
Input constants in the correlation of liquid metal heat transfer, |
|
\(c_{\text{f}}\) |
Eq. 13.2-28 |
– |
\(c_{\text{pc}}\) |
Coefficient of friction with fuel pin, Eq. 13.2-15 |
– |
\(c_{\text{pf}}\) |
Molten cladding specific heat capacity |
J/kg-K |
\(c_{\text{ps}}\) |
Fuel specific heat capacity |
J/kg-K |
\(D_{\text{c}}\) |
Solid steel specific heat capacity |
J/kg-K |
\(D_{\text{c}}\) |
Molten cladding hydraulic diameter |
m |
\(D_{\text{h}}\) |
Hydraulic diameter for bare fuel or fuel pin |
m |
\(D_{\text{v}}\) |
Hydraulic diameter for the vapor |
m |
\(e_{\text{c}}\) |
Moving cladding internal energy |
J/kg |
\(e_{\text{c}}^{o}\) |
Constant, Eq. 13.2-42 |
J/kg |
\(e_{\text{s}}\) |
Refrozen steel internal energy |
J/kg |
\(F_{\text{p}}\) |
Pin/molten-cladding friction force per unit volume of molten cladding |
N/m3 |
\(F_{\text{v}}\) |
Cladding/vapor interfacial force per unit volume of channel |
N/m3 |
\(f\) |
Melt fraction |
– |
\(\text{fps}\) |
Full-power seconds from initial cladding motion |
s |
\(\left( \text{fps} \right)_{0}\) |
Constant in incoherence factor on friction, Eq. 13.2-11 |
s |
\(f_{\text{sf}}\) |
Single-phase friction factor for vapor |
– |
\(g\) |
Gravitational constant |
m/s2 |
\(h\) |
Coefficient of heat transfer to the molten cladding from the solid interface |
W/m2-K |
\(I\) |
Incoherence multiplier on friction |
– |
\(j\) |
Index for axial segment |
– |
\(\Delta K\) |
Reactivity change due to cladding relocation |
δk/k |
\(k_{\text{c}}\) |
Molten cladding thermal conductivity |
W/m-K |
\(k_{\text{f}}\) |
Fuel thermal conductivity |
W/m-K |
\(M\) |
Friction multiplier due to flooding (M is also the total steel mass in channel) |
– |
\(m_{\text{j}}\) |
Mass of cladding in segment \(j\) |
kg |
\(m_{\text{j}}^{o}\) |
Initial mass of cladding in segment \(j\) |
kg |
\({\dot{m}}_{\text{c}}\) |
Mass rate of cladding melting per unit length of channel |
kg/m-s |
\({\dot{m}}_{\text{v}}\) |
Rate of vapor generation per unit length of channel |
kg/m-s |
\(n\) |
Index for time step |
– |
\(P_{\text{e}}\) |
Outer perimeter of intact cladding |
m |
\(P_{\text{r}}\) |
Perimeter of the cladding solid/liquid interface |
m |
\(P/D\) |
Pitch-to-diameter ratio for fuel pins |
– |
\(\frac{\partial\text{p}}{\partial\text{z}}\) |
Channel axial pressure gradient |
Pa/m |
\(Q_{\text{j}}\) |
Cumulative pin segment heat loss from beginning of heat transfer time step |
J |
\(Q_{\text{NT}}\) |
Volumetric heat generation in outer fuel segment |
W/m3 |
\(q\) |
Input constant, Eq. 13.2-18b |
– |
\(\text{Re}\) |
Molten cladding Reynolds number, Eq. 13.2-17 |
– |
\(\left( \text{Re} \right)_{\text{break}}\) |
Turbulent transition Reynolds number, Eq. 13.2-16 |
– |
\(\left( \text{Re} \right)_{\text{v}}\) |
Reynolds number for vapor |
– |
\(r\) |
Radius (from fuel pin axis) |
m |
\(r_{\text{NR}}, r_{\text{NT}}\) |
Fuel radii defined in Figure 13.3.1 |
m |
\(\Delta r_{\text{c}}\) |
Half-thickness of molten cladding layer |
m |
\(\Delta r_{\text{i}}\) |
Half-thickness of the intact cladding |
m |
\(\Delta r_{\text{s}}\) |
Half-thickness of the refrozen cladding |
m |
\(\Delta r_{\text{w}}\) |
Half-thickness of the structure |
m |
\(T_{\text{c}}\) |
Moving cladding temperature |
K |
\(T_{\text{f}}\) |
Fuel surface temperature |
K |
\(T_{\text{i}}\) |
Intact cladding temperature |
K |
\(T_{\text{m}}\) |
Cladding melting temperature |
K |
\(T_{\text{ref}}\) |
Reference temperature in density Eq. 13.2-38 |
K |
\(T_{\text{s}}\) |
Refrozen cladding temperature |
K |
\(T_{\text{w}}\) |
Structure temperature |
K |
\(t\) |
Time |
s |
\(t^{*}\) |
Time at beginning of current heat-transfer time step |
s |
\(\Delta t\) |
CLAP (coolant) time step |
s |
\(\Delta t^{*}\) |
Heat-transfer time step |
s |
\(v_{\text{c}}\) |
Moving cladding velocity |
m/s |
\(v_{\text{flood}}\) |
Flooding velocity |
m/s |
\(W_{\text{j}}\) |
Cladding reactivity worth distribution |
∂k/k-kg |
\(w\) |
Vapor mass flowrate |
kg/s |
\(w_{\text{j}}\) |
Segment midpoint mass flow, Eq. 13.3-14 |
kg/s |
\(w_{\text{j}}^{*}\) |
Segment boundary mass flow, Eq. 13.3-10 |
kg/s |
\(w_{\text{m,j}}\) |
Segment mean mass flow, Eq. 13.3-11 |
kg/s |
\(x\) |
Constant in incoherence factor on friction, Eq. 13.2-11a |
– |
\(y_{1}, y_{2}\) |
Constants in linearized pin friction equation |
N/m3 |
\(z\) |
Elevation |
m |
\(z_{\text{j}}\) |
Segment boundary elevation |
m |
\(z_{\text{m,j}}\) |
Nodal elevation, Eq. 13.3-13 |
m |
\(\Delta z_{\text{j}}\) |
Segment length |
m |
\(\alpha\) |
Vapor fraction based on area available for molten steel and vapor |
– |
\(\alpha_{\text{crit}}\) |
Input constant in two-phase multiplier, Eq. 13.2-10 |
– |
\(\beta\) |
Steel (solid) coefficient of linear thermal expansion, Eq. 13.2-38 |
K-1 |
\(\Gamma\) |
Factor in correction of cladding area for overfilled segments |
m3 |
\(\gamma_{\text{c}}\) |
Computer coefficient, Eq. 13.3-22 |
|
\(\gamma_{\text{f}}\) |
Computed coefficient, Eq. 13.3-19 |
|
\(\varepsilon\) |
Input constant in two-phase multiplier, Eq. 13.2-10 |
– |
\(\theta\) |
Multiplier on heat loss to structure (usually = 1) |
– |
\(\lambda\) |
Effective heat-of-fusion, Eq. 13.2-26 |
J/kg |
\(\lambda_{\text{o}}\) |
Thermodynamic heat-of-fusion |
J/kg |
\(\mu_{\text{c}}\) |
Moving cladding viscosity |
Pa-s |
\(\mu_{\text{m}}\) |
Cladding viscosity at the liquidus temperature |
Pa-s |
\(\mu_{\text{s}}\) |
Solid cladding pseudo-viscosity, Eq. 13.2-18c |
Pa-s |
\(\mu_{\text{t}}\) |
Cladding viscosity at the solidus temperature |
Pa-s |
\(\mu_{\text{v}}\) |
Vapor viscosity |
Pa-s |
\(\xi_{\text{f}}, \xi_{\text{w}}\) |
Computed coefficients |
– |
\(\xi_{1}, \xi_{2}, \xi_{3}\) |
Computed coefficients |
– |
\(\rho_{\text{c}}\) |
Molten cladding density |
kg/m3 |
\(\rho_{\text{c}}^{\circ}\) |
Density of cladding at the liquidus temperature |
kg/m3 |
\(\rho_{\text{f}}\) |
Fuel density |
kg/m3 |
\(\rho_{\text{s}}\) |
Refrozen steel density |
kg/m3 |
\(\rho_{\text{s}}^{\circ}\) |
Solid cladding density at the reference temperature |
kg/m3 |
\(\rho_{\text{v}}\) |
Vapor density |
kg/m3 |
\(\phi\) |
Sensible heat flux from refrozen cladding to the molten interface |
W/m2 |
\(\phi_{\text{c}}\) |
Flux of sensible heat into the moving cladding layer |
W/m2 |
\(\phi_{\text{hf}}\) |
Fusion heat flux, Eq. 13.2-24 |
W/m2 |
\(\phi_{\text{r}}\) |
Heat flux at interface of intact and refrozen cladding |
W/m2 |
\(\phi_{\text{trial}}\) |
Trail heat flux, Eq. 13.2-36 |
W/m2 |
\(\phi_{1}\) |
Heat flux, Eq. 13.2-34 |
W/m2 |
\(\phi_{2}\) |
Heat flux, Eq. 13.2-35 |
W/m2 |
\(\overline{\psi}\) |
Mean ratio of thermal-to-momentum eddy diffusivities |
– |