.. _section-14.6:

Interaction with the Point Kinetics and the Primary Loop Module
---------------------------------------------------------------

.. _section-14.6.1:

Interaction With the Point Kinetics Module
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In :numref:`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
:numref:`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 :numref:`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.

.. _section-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 :numref:`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:

.. math::
    :label: 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

:math:`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.

:math:`\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:

.. math::
    :label: 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:

.. math::
    :label: 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

.. math::
    :label: 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

:math:`ic` = SAS4A channel number.

:math:`t_{\text{PR1}}` = time at the beginning of the PRIMAR-4 time
step.

:math:`t_{\text{PR2}}` = time at the end of the PRIMAR-4 time step.

:math:`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 :numref:`section-5.11.1`):

.. math::
    :label: 14.6-5

	\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)

where

:math:`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 :math:`ic`.

**EGFUTE** See :eq:`14.4-150`.

The quantities
:math:`{\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:`eq-5.11-2` in :numref:`Chapter %s<section-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.