.. _section-9.4:

Solution Algorithm and Flow Charts
----------------------------------

:numref:`figure-9.4-1` and :numref:`figure-9.4-2` show the MFUEL solution algorithm for
pre-transient and transient analyses. MFUEL assumes the fuel pin can
be modeled using a 1.5-dimensional approximation, therefore axial and
radial loops are not explicitly shown in the algorithms. In each
calculation step, MFUEL loops over each axial node independently and
solves for the radial solution using a first-order approximation.

Pre-transient analysis is performed on a channel-by-channel basis
during the SAS steady-state calculation. Based on user input, MFUEL
solves for the changes to a fuel pin from the as-fabricated
conditions to the start of the SAS transient simulation. As shown in
:numref:`figure-9.4-1`, the MFUEL pre-transient analysis loops over the
user-defined irradiation history using substeps, as appropriate, to
characterize the changes in the fuel pin. At the end of pre-transient
characterization, MFUEL advances the fuel pin state to the match the
user-defined SAS steady-state power and flow. With the new state,
MFUEL updates the SAS axial and radial channel mesh and prints the
steady-state solution.

For each substep of the pre-transient analysis, an average value for
the user-provided power and flow is determined. The average power and
flow is passed to the SAS thermal-hydraulic solver to determine fuel
pin temperatures using the fuel pin composition and geometry at the
start of the substep. Using the average power, the fuel pin burnup is
incremented, along with the neutron fluence and dose to the cladding.
Given the fuel temperature, redistribution of the fuel constituents
is determined. If contact between the fuel and cladding has been
predicted, iron and lanthanide migration is included. The coolant
temperature is used to determine the clad and sodium corrosion
interaction, which in addition to the iron and lanthanide migration,
is used to determine the thickness of compromised, or wasted,
cladding at the inner and outer surfaces. Fission gas production,
migration, and release is simulated to determine the impact on fuel
swelling. Given the state of swelling and the fuel pin temperatures,
mechanical analysis is performed to determine the radial and axial
elongation of the fuel pin and cladding. With the state of the fuel
pin now known, the Cumulative Damage Fraction (CDF) and Mechanistic
Clad Failure (MCF) of the clad are evaluated to determine the failure
probability. The CDF and MCF value, along with the clad dose and
wastage thickness are then checked to determine if warning or error
messages need to be printed, providing users with an indication that
a parameter has exceeded its validated range or clad failure has been
predicted. Finally, the plenum pressure is updated based on the
expansion of the fuel and cladding, the amount of fission gas
released, and the relocation of in-pin sodium.

.. _figure-9.4-1:
.. figure:: media/Fig5.png
   :align: center
   :figclass: align-center
   :width: 6.25in
   :height: 7.90625in

   MFUEL Pre-transient Solution Algorithm

Similar to the MFUEL pre-transient analysis, the MFUEL transient
analysis is performed on a channel-by-channel basis. For channels
that utilize the MFUEL model, fuel pin conditions are updated at the
end of each SAS heat transfer time step. The MFUEL transient analysis
advances the state of the fuel pin using substeps, as shown in
:numref:`figure-9.4-2`. At the end of each main time step, MFUEL determines the
reactivity contribution of the channel due to fuel and clad axial
expansion.

For each sub-step of the transient analysis, the temperature and
power of the fuel pin at the end of the main time step are used. SAS
determines the temperature and power using the fuel pin geometry at
the end of pre-transient and fuel pin composition at the start of
main time step. Using the power, fuel pin burnup is incremented along
with the neutron fluence and dose of the cladding. Given the fuel
temperature, redistribution of the fuel constituents is determined.
In the case of contact, lanthanide and iron migration are solved for.
If the surface temperature of the fuel pin is high enough for
eutectic formation to occur, iron migration is bypassed, and in its
place the migration of the eutectic is determined. Corrosion due to
sodium is tracked on the outside of the cladding. This internal and
external wastage is used to determine the remaining thickness of the
cladding for mechanical analyses. Fission gas production, migration,
and release is simulated to determine the impact on fuel swelling.
Given the state of swelling and the fuel pin temperature, mechanical
analysis is performed to determine the radial and axial elongation of
the fuel and cladding. With the state of the fuel pin now known, the
CDF and MCF of the clad are evaluated to determine the failure
probability. The CDF and MCF values, along with the clad dose and
wastage thickness, are then checked to determine if warning or error
messages need to be printed, providing users with an indication that
a parameter has exceeded its validated range or clad failure has been
predicted. Finally, the plenum pressure is updated based on the
expansion of the fuel and cladding, the amount of fission gas
released, and the relocation of in-pin sodium.

.. _figure-9.4-2:
.. figure:: media/Fig6.png
   :align: center
   :figclass: align-center
   :width: 5.56944in
   :height: 5.93056in

   MFUEL Transient Solution Algorithm