16.6. LEVITATE Interaction with Other Modules

16.6.1. Interaction with the Point Kinetics Module

The LEVITATE interface with the point kinetics model has been described briefly in Section 16.1.3.3.3.

The axial mass and temperature distributions needed to calculate the reactivity feedbacks in the point kinetics module are calculated in the LEVITATE driver routine, LEVDRV, at the end of each PRIMAR time step. The changes in reactivity are due to changes in the distribution of sodium, fuel and steel in the active core region, and changes in the fuel temperature. The formulation for these feedbacks is given in Chapter 4, Section 4.5.

16.6.2. Coupling with the Primary Loop Module

As explained briefly in Section 16.1.3.3.1, LEVITATE can be coupled with either PRIMAR-1 or the more advanced PRIMAR-4 module. The PRIMAR-1 model is used whenever the input variable IPRION has a value not equal to 4. In this case, LEVITATE uses the constant outlet plenum pressure PX which is input and an inlet plenum pressure which is determined by PRIMAR-1. This is the only information needed in LEVITATE to calculate the motion of the liquid sodium slugs. A temperature calculation within the sodium slugs is not currently performed in LEVITATE and thus no plenum temperature information is expected. If the PRIMAR-1 option has been chosen, LEVITATE will not return any information to the primary loop module.

When the PRIMAR-4 option is selected (IPRION=4), LEVITATE will use the time-dependent inlet and outlet pressures which are calculated by PRIMAR-4 to determine the dynamics of the liquid sodium slugs. The inlet pressure used in each LEVITATE time step is calculated as follows:

(16.6-1)\[ P_{\text{inlet}}\left( t \right) = P_{\text{inlet}}\left( t_{\text{PR1}} \right) \ + \left( t - t_{\text{PR1}} \right) \cdot \frac{\partial \text{P}_{\text{inlet}}}{\partial \text{t}}\]

where

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

\(\frac{\partial \text{P}_{\text{inlet}}}{\partial \text{t}}\) - is the rate of change of the inlet pressure during the previous primary loop time step, calculated by PRIMAR-4

\(t_{\text{PR1}}\) - is the time at the beginning of the current primary loop time step.

The outlet pressure is calculated in the same manner:

(16.6-2)\[ P_{\text{outlet}} \left( t \right) = P_{\text{outlet}} \left( t_{\text{PR1}} \right) \ + \left( t - t_{\text{PR1}} \right) \cdot \frac{\partial \text{P}_{\text{outlet}}}{\partial \text{t}}\]

When the PRIMAR-4 option is used, LEVITATE provides PRIMAR-4 with the total sodium masses ejected into or received from the plena during a primary loop time step:

(16.6-3)\[ \Delta M_{\text{Na,ic,inlet}} = N_{\text{subas,ic}} \cdot \int_{t_{\text{PR1}}}^{t_{\text{PR2}}}{W_{\text{Na,inlet}} \cdot \text{dt}}\]

and

(16.6-4)\[ \Delta M_{\text{Na,ic,outlet}} = N_{\text{subas,ic}} \cdot \int_{\text{t}_{\text{PR1}}}^{t_{\text{PR2}}}{W_{\text{Na,outlet}} \cdot \text{dt}}\]

where

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

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

\(W_{\text{Na}}\) - is the sodium mass flow rate in kg/s

LEVITATE also provides PRIMAR-4 with the channel mass flow rates at the end of the primary loop time step. As long as single phase liquid sodium is ejected into the upper or lower plena, temporal integrals of the product (sodium flow rate ⨉ temperature) are also provided by LEVITATE. However, when the upper liquid sodium slug has been ejected out of the subassembly, LEVITATE calculates the total enthalpy of the two-phase mixture ejected during a primary loop time step:

(16.6-5)\[\begin{split} \Delta h_{\text{ic}} = \left\lbrack \left( 1 - X_{\text{Na,IITP-1}} \right) \cdot h_{\text{N} l} + X_{\text{Na,IITP-1}} \cdot h_{\text{Nv}} \right\rbrack \\ \cdot W_{\text{Na}} \cdot N_{\text{subs,ic}} \cdot \left( t_{\text{PR2}} - t_{\text{PR1}} \right)\end{split}\]

where

\(X_{\text{Na,IITP-1}}\) - is the sodium quality in the axial node \(\text{IITP-1}\), the highest full node in the subassembly.

\(h_{\text{N1}}\), \(h_{\text{Nv}}\) - are the enthalpies of the liquid sodium and sodium vapor, respectively, in the axial node \(\text{IITP-1}\).