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