5.15. Nomenclature
Symbol |
Description |
Units |
|---|---|---|
\(A\) |
Coolant flow area |
m2 |
\(A_{\text{CP}}, A_{\text{CI}}\) |
Primary and intermediate coolant flow areas in the intermediate heat exchanger |
m2 |
\(A_{\text{k}}\) |
Coolant flow area of element \(k\) in a liquid segment |
m2 |
\(A_{\text{w}}\) |
Wall area of a compressible volume |
m2 |
\(A_{\text{inter}}\) |
Area of liquid-gas interface |
m2 |
\(a_{0} (i)\) |
1/m |
|
\(a_{1} (i)\) |
Coefficients for liquid segment \(i\). |
1/m-s |
\(a_{2} (i)\) |
1/m-s |
|
\(a_{3} (i)\) |
1/m |
|
\(a_{1} (j),...,a_{4} (j)\) |
Coefficients in the simultaneous equations for the temperature changes at node \(j\) in the intermediate heat exchanger |
J/m2-K |
\(\Delta a_{0} (k)\) |
1/m |
|
\(\Delta a_{1} (k)\) |
Contributions from element \(k\) in liquid segment \(i\) to the |
1/m-s |
\(\Delta a_{2} (k)\) |
coefficients \(a_{0}\left( i \right)\), …, \(a_{3}(i)\) |
1/m-s |
\(\Delta a_{3} (k)\) |
1/m |
|
\(b_{0} (j)\) |
Coefficients in the pressure change expression for |
Pa |
\(b_{1} (j)\) |
Compressible volume \(j\) |
kg/m-s |
\(b_{2} (j)\) |
kg/m-s-K |
|
\(C_1\), \(C_2\), \(C_3\) |
Coefficients in electrical resisitivity correlation |
Ω/m, Ω/m-K, Ω/m-K2 |
\(C\) |
Electrical resisitivity proportionality constant |
– |
\(c_{\text{c}},c_{\text{l}}\) |
Specific heat of coolant or liquid |
J/kg-K |
\(c_{\text{w}}\) |
Specific heat of compressible volume or pipe wall |
J/kg-K |
\({\overline{c}}_{\text{P}},\ {\overline{c}}_{\text{I}}\) |
Spatially averaged primary and intermediate coolant heat capacities in the intermediate heat exchanger |
J/kg-K |
\(\overline{c}\) |
Spatially averaged coolant heat capacity in the bypass |
J/kg-K |
\(C_{1},C_{2},C_{3}\) |
User-supplied correlation coefficients in film heat-transfer calculation |
– |
\(c_{1} (j),...,c_{6} (j)\) |
Coefficients in the simultaneous equations for the temperature changes at node \(j\) in the intermediate heat exchanger |
J/m-K |
\(C_{0} (L,ic)\) |
Coefficients in the expression for core channel |
kg/s2 |
\(C_{1} (L,ic)\) |
flow estimate in channel \(\text{ic}\) at end \(L\) |
m |
\(C_{2} (L,ic)\) |
\(L\) = 1 for inlet, 2 for outlet |
m |
\(C_{3} (L,ic)\) |
1/kg |
|
\(c_{\text{ij}}\) |
Matrix in cover-gas pressure change equation |
— |
\(c(I,J)\) |
Matrix in compressible volume pressure change equation for liquid flow |
kg |
\(\Delta c(I,J)\) |
Contribution to the matrix \(c(i,j)\) |
kg |
\(D_{1},D_{2},D_{3}\) |
Right side of simultaneous equation solution in the cover gas, intermediate heat exchanger, and bypass channel treatments |
W/m |
\(D,D_{\text{h}}\) |
Hydraulic diameters |
m |
\(\text{DRACS}\) |
Direct reactor auxiliary cooling system |
|
\(d_{\text{A}},d_{\text{B}},d_{\text{D}}\) |
Reflector thicknesses in the bypass channel |
m |
\(d_{\text{SH}},d_{\text{TU}}\) |
Shell and tube thicknesses in the intermediate heat exchanger |
m |
\(d_{1}\) |
Coefficients in coolant-wall temperature |
J/m-K |
\(d_{2}\) |
Calculations |
J/m2-K |
\(d_{5}\) |
m-K/J |
|
\(d_{\text{j}}\) |
Right side of cover-gas pressure change matrix equation |
Pa |
\(d(j)\) |
Right side of liquid flow pressure change matrix equation |
kg2/m-s2 |
\(\Delta d(j)\) |
Contribution to \(d(j)\) |
kg2/m-s2 |
\(E_{\text{src}}\) |
Heat source |
W/m3 |
\(e_{1} (j),...,e_{10} (j)\) |
Coefficients in the simultaneous equations for the temperature changes at node \(j\) in the intermediate heat exchanger |
|
\(e_{0} (L,ic)\) |
Coefficients in the expression for core channel |
kg/s |
\(e_{1} (L,ic)\) |
flow estimate in channel \(\text{ic}\) at end \(L\) |
m-s |
\(e_{2} (L,ic)\) |
m-s |
|
\(F_{\text{ij}}\) |
Cover-gas flow rate from compressible volume i to compressible volume \(j\) |
kg/s |
\(F_{0\text{ij}}\) |
kg/s |
|
\(F_{1\text{ij}}\) |
Coefficients in the expression for \(F_{\text{ij}}\) |
m-s |
\(F_{2\text{ij}}\) |
m-s |
|
\(F_Q\) |
Fraction of pump heat to be modeled |
– |
\(f\) |
Moody friction factor |
– |
power source frequency |
Hz |
|
\(f_{\text{r}}\) |
Fraction of a coolant node at pipe inlet |
– |
\(f_{1} (j),...,f_{8} (j)\) |
Coefficients in the simultaneous equations for the temperature changes at node \(j\) in the intermediate heat exchanger |
|
\(f_{1},f_{2}\) |
Fractions of reactor power |
– |
\(G\) |
Specific flow rate |
kg/m2-s |
\(GH\) |
Gravity head |
m |
\(G_{2}\) |
Pressure drop parameter |
– |
\(g\) |
Acceleration due to gravity |
m/s2 |
\(H\) |
Head |
m |
\(H_{\text{r}}\) |
Pump reference head |
m |
\(H_{\text{SP}},H_{\text{PT}},H_{\text{TI}}\) |
Overall heat-transfer coefficients for the intermediate heat exchanger |
W/m2-K |
\(H_{\text{AB}},H_{\text{BC}},H_{\text{CD}}\) |
Overall heat-transfer coefficients between regions in the bypass channel |
W/m2-K |
\(H_{\text{snk}} A_{\text{snk}}\) |
Heat transfer coefficient times area |
W/K |
\((hA)_{\text{snk}}\) |
Heat transfer coefficient times area |
W/K |
\(H_{\text{D}}\) |
Steam drum total enthalpy |
J |
\(h_{\text{D}}\) |
Specific enthalpy |
J/kg |
\(h_{\text{f}}\) |
Liquid specific enthalpy |
J/kg |
\(h_{\text{g}}\) |
Vapor specific enthalpy |
J/kg |
\(h_{\text{c}},h_{\text{CP}},h_{\text{CI}}\) |
Coolant film coefficients |
W/m2-K |
\(h_{\text{w}},h_{\text{wc}}\) |
Wall and wall-to-coolant heat-transfer coefficients |
W/m2-K |
\(h_{\text{FS}},h_{\text{fFT}}\) |
Fouling factors in the intermediate heat exchanger |
W/m2-K |
\(I\) |
Line-to-line total pump current |
A |
\(I_J\) |
Line-to-line pump current through \(R_J\) |
A |
\(I_D\) |
Line-to-line pump current through \(R_D\) |
A |
\(\text{IHX}\) |
Intermediate heat exchanger |
|
\(K_{\text{cold}}\) |
A cold leg pressure loss coefficient |
s2/m |
\(k_{\text{c}}\) |
Coolant thermal conductivity |
W/m-K |
\(k_{\text{SH}},k_{\text{TU}}\) |
Shell and tube thermal conductivities in the intermediate heat exchanger |
W/m-K |
\(L,L_{\text{i}}\) |
Length |
m |
\(\Delta L(N)\) |
Length-integrated volumetric heat source |
W/m2 |
\(L_{\text{k}}\) |
Length of element k in a liquid flow segment |
m |
\(L_{\text{n}}\) |
Length of a node at pipe inlet |
m |
\(L_{\text{B}} / D_{\text{B}}\) |
Length-to-diameter ratio per bend in an element |
– |
\(L_1\), \(L_2\) |
Inductances in equivalent circuit pump models |
H |
\(M\) |
Mach number for cover gas flow |
– |
\(M_{\text{D}}\) |
Steam drum total mass |
kg |
\(M_{\text{w}}\) |
Pipe wall mass per unit length |
kg/m |
\(\delta_{\text{m}}\) |
Change in liquid mass |
kg |
\(\delta m_{\text{i}}\) |
Change in cover gas mass in compressible volume \(i\) during a sub-interval of time |
kg |
\(\Delta m,\Delta m_{\text{l}}\) |
Change in liquid mass |
kg |
\(\Delta m_{\text{ji}}\) |
Mass of cover gas flowing from compressible volume \(j\) to \(i\) during a sub-interval of time |
kg |
\(m(i)\) |
Cover-gas mass in compressible volume \(i\) |
kg |
\(m\) |
Number of evaporators in parallel |
– |
\(m_{\text{g}}\) |
Gas mass in a compressible volume |
kg |
\(m_{\text{r}}\) |
Liquid mass in a compressible volume at a reference pressure |
kg |
\(\Delta m\) |
Change in liquid mass in a compressible volume during a time sub-interval |
kg |
\(N_{\text{B}}\) |
Number of bends in an element |
– |
\(P,P_{\text{er}},P_{\text{A}},P_{\text{D}},P_{\text{SP}},P_{\text{TI}}\) |
Perimeters |
m |
\(P_{\text{s}}\) |
Power shape for vertical section |
– |
\(p,p_{\text{l}}\) |
Liquid pressure in a compressible volume |
Pa |
\(p_{\text{d}},p_{\text{d}1},p_{\text{d}2}\) |
Pump head coefficients |
|
\(p_{\text{r}}\) |
Reference liquid pressure in a compressible volume |
Pa |
\(\Delta p\) |
Change in liquid pressure in a compressible volume during time sub-interval |
Pa |
\(p(i),p_{\text{g}}\) |
Cover-gas pressure in compressible volume i |
Pa |
\(P_{1},P_{2}\) |
Power shape normalization for Regions 1 and 2 |
|
\(p(\text{JIN}),p(\text{JX})\) |
Inlet and outlet plenum pressures in core flow estimate |
Pa |
\(\Delta p_{\text{i}}\) |
Change in cover-gas pressure in compressible volume i during a sub-interval of time |
Pa |
\(p_{\text{in}} (i),p_{\text{out}} (i)\) |
Pressures at the inlet and outlet of liquid segment i |
Pa |
\(\delta p\) |
Change in liquid pressure |
Pa |
\(\Delta p_{\text{fr}} (i)\) |
Frictional pressure loss in liquid segment i |
Pa |
\(\Delta p_{\text{w}2} (i)\) |
Pressure loss proportional to the square of the flow in liquid segment i |
Pa |
\(\Delta p_{\text{v}} (i)\) |
Valve pressure loss in liquid segment i |
Pa |
\(\Delta p_{\text{gr}} (i)\) |
Gravity head in liquid segment i |
Pa |
\(\Delta p_{\text{p}} (i)\) |
Pump head in liquid segment i |
Pa |
\(P_{\text{TOT}} Q_{\text{MULT}}\) |
Reactor power for a time step |
W |
\(P_{\text{s}} (j)\) |
Power shape by nodes |
– |
\(P1,P3\) |
Power shape normalization factors |
– |
\(Q_{\text{A}},Q_{\text{B}},Q_{\text{D}}\) |
Neutron and decay heating sources in reflectors |
W/m3 |
\(\text{QMULT}\) |
Power multiplication factor |
– |
\(q_{\text{c}}'\) |
Linear heat rate in liquid element fluid |
W/m |
\(q_{\text{w}}'\) |
Linear heat rate in liquid element wall |
W/m |
\(q_{\text{wa}}'\) |
Linear heat rate in liquid element wall \(a\) |
W/m |
\(q_{\text{wb}}'\) |
Linear heat rate in liquid element wall \(b\) |
W/m |
\(q,Q\) |
Heat flow from compressible volume walls |
W/m2 |
Region length-integrated sodium heat source w |
W/m2 |
|
Length-integrated volumetric heat source |
W/m2 |
|
\(Q\) |
Heat removal rate |
– |
Volumetric flow rate |
m3/s |
|
\(R\) |
Universal gas constant |
J/kg-K |
\(R_1\), \(R_D\), \(R_J\), \(R_M\) |
Circuit resistances in equivalent circuit models |
Ω |
\(\text{Re}\) |
Reynolds number |
– |
\(\text{Ri}\) |
Richardson number |
– |
\(S\) |
Slant height ratio of the tube-side in the intermediate heat exchanger |
– |
\(s\) |
Pump speed |
1/s |
Pump slip |
– |
|
\(T\) |
Pump torque |
N-m |
\(T,T_{\text{g}}\) |
Cover-gas temperature |
K |
\(T,T_{\text{l}}\) |
Liquid temperature |
K |
\(T_{\text{c}},T_{\text{w}}\) |
Coolant and wall temperatures |
K |
\(T_{\text{f}}\) |
Friction torque loss |
N-m |
\(T_{\text{m}},T_{\text{p}}\) |
Motor torque, pump torque |
N-m |
\(T_{\text{SH}},T_{\text{TU}}\) |
Shell and tube node temperatures in the intermediate heat exchanger |
K |
\({\overline{T}}_{\text{CP}},{\overline{T}}_{\text{CI}}\) |
Spatially averaged coolant temperatures in the intermediate heat exchange |
K |
\(T(i)\) |
Cover-gas temperature in compressible volume i |
K |
\(T_{\text{in}} (j),T_{\text{out}} (j)\) |
Temperature of the incoming and outgoing fluid at compressible volume j |
K |
\(T_{\text{ji}}\) |
Temperature of the cover-gas flowing from compressible volume j to i |
K |
\(T_{\text{B}}\) |
Temperature of the flow from a bypass channel to the outlet plenum |
K |
\(T_{\text{C}}\) |
Temperature of the flow from a core channel to the outlet plenum |
K |
\(T_{\text{snk}}\) |
Temperature of the heat sink |
K |
\(T_{\text{Na,i}}\) |
Sodium temperature in the i-th region |
K |
\(T_{\text{out}}\) |
Outlet temperature in outlet plenum |
K |
\(T_{\text{out}} (t)\) |
Steam generator outlet temperature |
K |
\(\delta T\) |
Change in liquid temperature |
K |
\(\Delta T\) |
Liquid temperature change during a time sub-interval |
K |
\(\Delta T_{\text{w}}\) |
Wall temperature change during a time sub-interval |
K |
\(\Delta T_{\text{SH}}, \Delta T_{TU}\) |
Shell and tube node temperature changes during a time sub-interval |
K |
\(\Delta T_{\text{CP}},\Delta T_{\text{CI}}\) |
Coolant node temperature changes during a time a sub-interval |
K |
\(\Delta t\) |
Time-step size |
s |
\(\Delta t_{\text{s}},\delta t\) |
Sub-interval of a time step |
s |
\(U\) |
Overall heat transfer coefficient |
W/m2-K |
\(u\) |
Flow velocity |
m/s |
\(V(i),V_{\text{g}}\) |
Cover-gas volume in compressible volume \(i\) |
m3 |
\(V_{\text{D}}\) |
Steam drum volume |
m3 |
\(v_{\text{D}}\) |
Steam drum specific volume |
m3/kg |
\(v_{\text{j}}\) |
Jet velocity at hot-cold interface |
m/s |
\(v\) |
Liquid velocity |
m/s |
\(V,V_{\text{l}}\) |
Liquid volume in a compressible volume |
m3 |
\(V_{\text{r}}\) |
Liquid volume in a compressible volume at a reference pressure |
m3 |
\(V_s\) |
Line-to-line voltage of pump power source |
V |
\(\Delta V_{\text{g}}\) |
Change in cover gas volume |
m3 |
\(\Delta V_{\text{l}}\) |
Change in liquid volume |
m3 |
\(w\) |
Pump flow rate |
kg/s |
\(w(i)\) |
Liquid flow rate in segment \(i\) |
kg/s |
\(\overline{w}(i)\) |
Time-averaged liquid flow rate in segment \(i\) |
kg/s |
\({\overline{w}}_{\text{in}}\left( i \right)\), \({\overline{w}}_{\text{out}}\left( i \right)\) |
Time-averaged liquid flow rate into and out from compressible volume \(j\) |
kg/s |
\({\overline{w}}_{\text{B}}\) |
Average flow rate from a bypass channel into the outlet plenum |
kg/s |
\({\overline{w}}_{\text{C}}\) |
Average flow rate from a core channel into the outlet plenum |
kg/s |
\(w_{\text{c}} (L,ic)\) |
Core flow rate in channel \(\text{ic}\) at end \(L\) at the beginning of the timestep |
kg/s |
\(\Delta w(i)\) |
Change in the liquid flow rate in segment \(i\) during a time sub-interval |
kg/s |
\(X_1\), \(X_2\) |
Reactances in equivalent circuit pump models |
Ω |
\(z,z_{\text{r}},z_{\text{ref}}\) |
Reference elevation |
m |
\(z_{\text{i}},z_{\text{inter}}\) |
Liquid-gas interface elevation |
m |
\(z_{\text{in}},z_{\text{out}}\) |
Height of element inlet and outlet |
m |
\(z_{\text{PLENL}}\) |
Lower plenum elevation |
m |
\(z_{\text{PLENU}}\) |
Upper plenum elevation |
m |
\(z_{\text{IHX}}\) |
Reference height of the thermal center of the intermediate heat exchanger |
m |
\(\Delta z,\Delta z(j)\) |
Height of the \(j\)-th node |
m |
\(\alpha_{\text{P}}\) |
Volume pressure expansion coefficient |
1/Pa |
\(\alpha_{\text{T}}\) |
Volume temperature expansion coefficient |
1/K |
\(\alpha_{1},...,\alpha_{4}\) |
Tri-diagonal matrix coefficients in the cover gas, intermediate heat exchanger, and bypass channel treatments |
W/m-K |
\(\beta_{\text{P}}\) |
Liquid sodium compressibility |
1/Pa |
\(\beta_{\text{T}}\) |
Liquid sodium thermal expansion coefficient |
1/K |
\(\beta_{1},...,\beta_{4}\) |
Tri-diagonal matrix coefficients in the cover gas, intermediate heat exchanger , and bypass channel treatments |
w/m-K |
\(\gamma\) |
Ratio of specific heat at constant pressure to that at constant volume |
– |
\(\gamma_{\text{N}1},\gamma_{\text{N}3}\) |
Fraction of neutron power |
– |
\(\gamma_{\text{D}1},\gamma_{\text{D}3}\) |
Fraction of decay power |
– |
\(\gamma(i)\) |
Factor in the degree of implicitness in liquid segment \(i\) |
– |
\(\gamma_{\text{c}} (L,ic)\) |
Factor in the degree of implicitness in core channel \(\text{ic}\) at end \(L\) |
– |
\(\delta_{\text{ij}}\) |
Kronecker delta symbol |
– |
\(\epsilon\) |
Pump efficiency |
– |
\(\varepsilon ,\varepsilon (k)\) |
Pipe roughness factor |
m |
\(\varepsilon_{\text{i}}\) |
Factor in equation for cover-gas flow in compressible volume \(i\) |
– |
\(\varepsilon_{\text{v}}\) |
Cover-gas volume fraction |
– |
\(\xi\) |
Ratio of shutoff head to design head |
– |
\(\rho,\rho_{\text{l}}\) |
Liquid density |
kg/m3 |
\({\overline{\rho}}_{\text{P}},\ {\overline{\rho}}_{\text{I}}\) |
Spatially averaged primary and intermediate coolant densities in the intermediate heat exchanger |
kg/m3 |
\(\rho_{\text{I}},\rho_{0}\) |
Fluid density at element inlet and outlet |
kg/m3 |
\((\rho c)_{\text{SH}},(\rho c)_{\text{TU}}\) |
Shell and tube densities times specific heats in the intermediate heat exchanger |
J/m3-K |
\((\rho c)_{\text{A}},(\rho c)_{\text{B}},(\rho c)_{\text{D}}\) |
Densities times specific heats in the bypass channel |
J/m3-K |
\(\rho_r\) |
Electrical resisitivity |
Ω |
\(\tau\) |
Cover-gas time constant |
s |
\(\tau_{\text{m}},\tau_{\text{p}}\) |
Motor torque, pump torque |
N-m |
\(\theta_{1} (i), \theta_{2} (i)\) |
Degree of implicitness in the time differencing in liquid segment \(i\) |
– |
\(\theta_{2\text{c}} (L,ic)\) |
Degree of implicitness in the time differencing in core channel \(\text{ic}\) at end \(L\) |
– |
\(\phi\) |
Phase angle between voltage and current |
– |
\(\Psi\) |
circuit total resistance |
Ω |
Subscripts 3 and 4 appended to quantities refer to the values of those quantities at the beginning and at the end, respectively, of a time interval.