14.6. Interaction with the Point Kinetics and the Primary Loop Module

14.6.1. Interaction With the Point Kinetics Module

In Section 14.1.2, the calculation in PLUTO2 of the specific power in the fuel and the total power in an original pin node was described. This was also discussed later when the heat source terms in the fuel pin and in the channel were described. The calculation of the reactivity feedbacks for channels in which PLUTO2 is active is based on fuel temperature and mass distributions and coolant voiding distributions calculated in PLUTO2 and passed to subroutine FEEDBK, where the reactivity feedbacks are calculated.

In PLUTO2, the fuel mass in the fuel pin nodes can be relatively easily calculated because the fixed Eulerian grid used for the in-pin fuel motion is part of the grid on which the material worths are defined (see Figure 14.1.4). The calculational grid in the coolant channel has additional cells above and below the pin grid and is therefore indexed differently. However, the axial spacing of the channel grid corresponds to that of the fuel-pin grid. A problem associated with the calculation of the fuel or sodium masses on the channel grid is the existence of partial Lagrangian cells at the edges of the interaction region. Partial Lagrangian cells such as the channel cell IFMIBT in Figure 14.1.4 contain fuel and sodium that extend into the adjacent cell IFMIBT-1. For the purpose of the reactivity calculation this fuel and sodium are included in cell IFMIBT-1 as opposed to the approach in the hydrodynamics.

14.6.2. Coupling with the Primary Loop Module

The coupling between PLUTO2 and the primary loop module is quite simple when the PRIMAR-1 option has been chosen (i.e., input parameter IPRION set to a value not equal to 4). In this case, PLUTO2 uses the constant outlet coolant plenum pressure PX which is input and an inlet coolant plenum pressure which is determined by PRIMAR-1. PRIMAR-1 calculates the steady-state pump head that is multiplied by an input table or function during the transient (see Section 5.9). Moreover, PLUTO2 also uses the table input for the inlet temperature history and the single input value TUPL for the reentry temperature at the outlet. However, PLUTO2 will not feed back any information to the primary loop module if the PRIMAR-1 option has been chosen.

If the PRIMAR-4 option has been chosen (IPRION=4), PLUTO2 will use the time-dependent inlet and outlet pressures which are calculated by PRIMAR-4. This is done in the following way:

(14.6-1)\[ P_{\text{inlet}} \left( t \right) = P_{\text{inlet}} \left( t_{\text{PR1}} \right) \ + \left( t - t_{\text{PR1}} \right) \cdot \frac{\partial \text{P}_{\text{inlet}}}{\partial \text{t}}\]

where

\(P_{\text{inlet}} \left( t_{\text{PR1}} \right)\) is the PRIMAR-4 calculated inlet pressure at the beginning of the current primary loop time step.

\(\frac{\partial \text{P}_{\text{inlet}}}{\partial \text{t}}\) is the PRIMAR-4 calculated rate or inlet pressure change during the current primary loop time step.

The outlet pressure is calculated in the same manner:

(14.6-2)\[ P_{\text{outlet}} \left( t \right) = P_{\text{outlet}} \left( t_{\text{PR1}} \right) \ + \left( t - t_{\text{PR1}} \right) \cdot \frac{\partial \text{P}_{\text{outlet}}}{\partial \text{t}}\]

PLUTO2 also uses the time-dependent inlet and outlet temperatures calculated by PRIMAR4. Since inlet and outlet temperatures change slowly, only the average values over each PRIMAR-4 step are used in PLUTO2.

When the PRIMAR-4 option has been chosen, PLUTO2 provides PRIMAR-4 with total sodium masses ejected into or received from the inlet or outlet plena during a primary loop time step:

(14.6-3)\[ \Delta M_{\text{Na,ic,inlet}} = N_{\text{subas,ic}} \int_{t_{\text{PR1}}}^{t_{\text{PR2}}}{W_{\text{Na,inlet}} \text{dt}}\]

and

(14.6-4)\[ \Delta M_{\text{Na,ic,outlet}} = N_{\text{subas,ic}} \int_{t_{\text{PR1}}}^{t_{\text{PR2}}}{W_{\text{Na,outlet}} \text{dt}}\]

where

\(ic\) = SAS4A channel number.

\(t_{\text{PR1}}\) = time at the beginning of the PRIMAR-4 time step.

\(t_{\text{PR2}}\) = time at the end of the PRIMAR-4 time step.

\(W_{\text{Na}}\) = sodium liquid and/or vapor mass flow rate.

PLUTO2 also provides PRIMAR-4 with the channel mass flow rates at the end of the primary loop time step. As long as pure liquid sodium is ejected into or received from the upper and lower plena, temporal integrals over the sodium mass flow rate times the temperature of the ejected sodium are also provided by PLUTO2. However, when the upper liquid sodium slug has been ejected out of the subassembly outlet, the additional heat added to the outlet plenum by the subsequently ejected two-phase sodium (which condenses in the plenum) and the ejected fuel during a primary loop time step is calculated by PLUTO2 for use in PRIMAR-4 (see Section 5.11.1):

(14.6-5)\[\begin{split} \Delta E_{\text{v,ic}} = \left\lbrack \lambda_{\text{Na}} \cdot x_{\text{Na}} \cdot W_{\text{Na}} + u_{\text{fu}} {\rho'}_{\text{fu}} \cdot \text{AXMX} \cdot \left\{ e_{\text{fu}} - \text{EGFUTE} \left( T_{\text{Na}} \right) \right\} \right\rbrack \\ N_{\text{sibas,ic}} \cdot \left( t_{\text{PR2}} - t_{\text{PR1}} \right)\end{split}\]

where

\(x_{\text{Na}}, \lambda_{\text{Na}}\) is the quality of the two-phase sodium and the enthalpy of evaporation of sodium in the highest coolant node is SAS4A channel \(ic\).

EGFUTE See Eq. (14.4-179).

The quantities \({\rho'}_{\text{fu}}, e_{\text{fu}}, T_{\text{Na}}\) in Eq. (14.6-5) all refer to the highest coolant node HTP. A similar equation is used for the inlet plenum also. Eq. (5.11-2) in Chapter 5, which calculates an estimate of the flow into or out of each SAS4A channel, requires several coefficients for each SAS4 channel. These coefficients are calculated before boiling by the single-phase hydraulics module, then by the boiling module, and, after fuel-pin failure, they are calculated by PLUTO2 or LEVITATE, depending on which module is active in a certain channel.