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.