.. _section-16.1:
Overview
--------
.. _section-16.1.1:
Historical Background and Physical Description of the LEVITATE Model
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In an unprotected loss-of-flow (LOF) accident in an LMFBR, the boiling
and voiding of the coolant sodium in the high-power subassemblies will
lead to an overpower situation if the sodium void worth of the reactor
considered is moderately positive. A high-power level causes the
subsequent events in the voided channels such as cladding motion,
fuel-pin breakup, and fuel motion to occur nearly simultaneously. A
positive reactivity contribution from these effects could lead to a
potentially energetic LOF-driven-TOP accident, whereas a negative
contribution would most likely lead the accident into a transition phase
much like that predicted as the likely outcome of a LOF accident in a
low-void-worth LMFBR.
The LEVITATE model [16-1] has been designed to treat both the high-power
and the near-nominal power conditions in voided assemblies. This means
that cladding and fuel motion can be treated in a combined or sequential
fashion. The earlier CLAZAS [16-2] and SLUMPY [16-3] models in SAS3A
[16-4] were designed only to treat these phenomena in a sequential
fashion. The new LEVITATE model also treats several relevant phenomena
not considered in the earlier models. The most important of these are
several pin-disruption modes, continuous fuel-steel flow regimes and
fuel-steel crust and plug formation, and a tight coupling with the
sodium dynamics. LEVITATE has also been designed to incorporate a
fuel-chunk model, describing the motion of the solid fuel chunks present
in the coolant channel. This model has become operational in the
developmental version of LEVITATE and was not available in the initial
release version of SAS4A. Since two-phase sodium which is generated by
the chugging of the lower sodium slug may penetrate the disrupted
region, fuel may be pushed upwards or "levitated," prompting the name of
this model.
The LEVITATE development used the PLUTO2 code [16-5] as a starting point
and still shares some features with that code. PLUTO2 and LEVITATE are
complementary models with some degree of overlap. PLUTO2 can treat
overpower situations in sodium-filled channels, i.e., fuel-coolant
interactions and fuel sweepout, but not the later cladding motion,
fuel-steel mixing, and pin disintegration.
.. _section-16.1.2:
Physical Description of the LEVITATE Model
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
LEVITATE models the fuel subassembly in a one-dimensional geometry,
assuming that all pins in the subassembly behave coherently. Three basic
thermal-hydraulic models are used for each subassembly:
1. The hydrodynamic model describing the cavities inside the fuel pins,
which initially contain liquid fuel and fission gas.
2. The hydrodynamic model describing the coolant channel, bounded by the
outside cladding surface and the hexcan wall. This channel contains
initially liquid sodium and sodium vapor.
3. The heat-transfer and melting/freezing model, describing the solid
fuel-pin stubs, which separate the outer channel from the inner
cavity.
A typical LEVITATE configuration illustrating some of the recently
introduced models is presented in :numref:`figure-16.1-1`. Other features presented
in this figure are introduced below.
.. _section-16.1.2.1:
Fuel-pin Disruption and In-pin Fuel Motion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
As the loss-of-flow accident proceeds, the inside of the fuel pin begins
to melt, leading to the formation of an internal cavity. This cavity is
filled with a mixture of molten fuel and fission gas, and expands
continuously, both radially and axially, due to fuel melting. The
fuel-gas mixture in the cavity is pressurized due to the presence of
fission gas and fuel vapor. As the cavity walls continue to melt and the
cladding temperature approaches the melting point, this continued
pressurization of the cavity leads to fuel-pin failure, as illustrated
in :numref:`figure-16.1-2`. Based on the mechanism of fuel-pin failure, two
disruption modes are currently modeled in LEVITATE.
1. *Total disruption of the fuel pin at a certain axial location.* When
a large fraction of the pin has become molten at a certain axial
location and the cladding is no longer effective in restricting
radial motion, the fuel pin is totally disrupted. In this case, the
area previously occupied by pins becomes part of the coolant channel
and only the two fuel-pin stubs remain, as shown in :numref:`figure-16.1-1`. The
flow of molten fuel and fission gas inside the stubs continues to be
described by a hydrodynamic model. As exemplified in :numref:`figure-16.1-1`,
this mode of disruption leads to significant area changes in the
coolant channel. This situation has made necessary an accurate
treatment of abrupt area changes in the hydrodynamic modeling.
2. *Mechanical cladding failures at a certain axial location.* If a
large fraction of the fuel is still in a solid state, the initial
geometry of the fuel pin remains intact. However, due to low cladding
resistance and a higher pressure inside the pin than in the coolant
channel, molten fuel and fission gas from the pin cavity are ejected
into the coolant channel through a cladding rupture.
Due to the fuel-pin failure, the inner cavity is connected to the
coolant channel which is at a significantly lower pressure, and the
molten fuel inside the pin is accelerated rapidly toward the pin failure
location. This motion is modeled by the in-pin hydrodynamic model. An
ejection model transfers molten fuel and fission gas from the pin cavity
to the coolant channel, thus connecting the two main hydrodynamic
models.
.. _figure-16.1-1:
.. figure:: media/image2.png
:align: center
:figclass: align-center
Typical LEVITATE Configurations Fuel-pin Cavity Formation
.. _figure-16.1-2:
.. figure:: media/image3.png
:align: center
:figclass: align-center
Fuel Pin Cavity Formation
.. _section-16.1.2.2:
Hydrodynamics of the Coolant Channel
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Before the molten fuel-fission gas mixture is ejected from the pin
cavities, the coolant channel contains only sodium and perhaps molten
steel; but as the fuel and fission gas begin to interact with these
original components, a very complex situation develops, involving a
large number of components that have to be tracked separately. The
moving components in the channel are solid and liquid fuel, solid and
liquid steel, fission gas, and vapors of fuel, steel and sodium. The
material motion is described by a multi-component, multi-phase,
nonequilibrium hydrodynamic model. The region described by this model is
bounded axially by the liquid sodium slugs, and is generally referred to
as "the interaction region". This region can increase or decrease,
depending on the dynamics of the liquid slugs which are described by a
simple incompressible model. The dependent variables in the interaction
region are the density, velocity and enthalpy. A separate mass and
energy equation is solved for each component, but only three coupled
momentum equations for three velocity fields are solved. The components
treated together in the velocity fields are: (a) liquid fuel and liquid
steel, (b) fission gas, fuel vapor, steel vapor and two-phase sodium and
(c) solid fuel chunks and solid steel chunks.
The interaction between the different components present in the channel,
i.e., mass, energy, and momentum transfer, is largely determined by the
local configuration which, in turn, is determined by the flow regime
used. Earlier codes such as SLUMPY used only particulate fuel flow
regimes, which may lead to unrealistically rapid fuel dispersal. The
assumption underlying these models was that the molten fuel contained in
a disrupted pin cell ejected from the pins breaks up into droplets upon
entering the coolant channels. Tentner et al. [16-6] have argued,
however, that such a particulate flow cannot be justified in
sodium-voided regions which develop soon after pin failure. First, there
is no apparent reason why molten fuel which contacts little or no liquid
sodium should fragment. Second, most of the frozen fuel found in TREAT
tests appeared to be in continuous form, rather than in the form of
rounded frozen droplets. The continuous flow regimes modeled in LEVITATE
are: a bubbly fuel flow regime, a partial annular fuel flow regime, an
annular steel flow regime and a bubbly steel flow regime. These flow
regimes will be described later in considerable detail.
.. _section-16.1.2.3:
The Freezing/Melting Models Describing the Solid Fuel-pin Stubs
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
At the axial locations where solid fuel pins are still present, the
coolant channel is separated from the pin cavity by the cladding and the
remaining solid fuel. The temperature field in the cladding and fuel is
calculated by a transient heat-transfer model, using the temperatures in
the channel and cavity as boundary conditions. Continuous melting occurs
at the fuel pin cavity boundary, leading to an increase in cavity
diameter and addition of molten fuel and fission gas to the moving
components in the cavity. The situation is more complicated at the
channel boundary. It has been previously argued that, in the
sodium-voided regions which develop during a loss-of-flow situation,
continuous fuel flow regimes are likely to exist. Under these
conditions, the molten-fuel/cladding interface temperature usually falls
between the freezing temperatures of these substances, resulting in
solidification of the initially molten ceramic fuel and melting of the
initially solid steel. The assumption which was generally made in the
modeling of the simultaneous fuel freezing steel melting phenomena was
that the frozen fuel crust is mechanically stable and does not break up
under the influence of fluid frictional shear or buoyancy forces [16-7].
However, experiments conducted by Spencer et al. [16-8] indicate that
this is not the case for the flow of molten fuel in pin bundles. In
these experiments, significant steel ablation and fuel-steel mixing were
observed that could not have occurred in the presence of a stable crust
[16-9].
The fuel-freezing model used in LEVITATE allows for the formation of a
partial fuel crust when the temperature of the fuel in the channel drops
below an input freezing temperature. This input temperature is always
between the liquidus and solidus temperatures.
When the dominant component in the channel is molten steel, steel
freezing can occur, leading to the formation of steel plugs.
The temperature of the fuel crust, at any given location, is calculated
by the heat-transfer model. Depending on its temperature and other local
conditions, which will be described in detail later, the fuel crust can
continue to grow, can start to remelt or can break up when the
underlying cladding begins to melt.
.. _section-16.1.2.4:
Geometry Description and Interaction among LEVITATE Models
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The geometry modeled in LEVITATE is illustrated schematically in :numref:`figure-16.1-3`, which will also be used to describe the interaction of the
physical models described previously.
LEVITATE calculates all the thermal hydraulic events that occur in a pin
subassembly. The subassembly is bounded axially by the lower and upper
plena. Although only one pin is shown in :numref:`figure-16.1-3`, LEVITATE will
account for the appropriate number of pins per subassembly, as specified
in the input description. The hydrodynamic in-pin calculations are
performed on a mesh grid using the subscript K, having the origin at the
bottom of the lower blanket. The top node of the upper blanket is
indicated by the variable MZ. The active fuel core extends from KCORE1
to KCORE2. The fuel pin cavity, which increases gradually both radially
and axially, cannot extend beyond the active core boundaries. The
disrupted pin region extends from KDISBT to KDISTP. The hydrodynamic
coolant channel calculations as well as the freezing and melting
calculations are performed on a mesh-grid using the subscript I, with
the origin at the bottom of the fuel pins. The integer IDIFF indicates
the offset between the I and K grids, i.e.,
(16.1-1)
.. _eq-16.1-1:
.. math::
I = K + \text{IDIFF}
.. _figure-16.1-3:
.. figure:: media/image4.png
:align: center
:figclass: align-center
Geometry Modeled by LEVITATE
The top node in the subassembly and in the LEVITATE domain is indicated
by the variable IITP. The hydrodynamic and melting/freezing models,
however, operate only in the interaction region, which extends from
IFMIBT to IFMITP. This region is bounded axially by the lower and upper
sodium slugs and can expand or contract depending on the dynamics of the
slugs. The slug motion is determined by the pressure difference acting
on them, e.g., the lower slug motion is determined by the pressure
difference between the cell IFMIBT and the lower plenum. The slug motion
is calculated by an incompressible model to be described later. Each
material component is restricted to its own region, with moving
boundaries which are tracked continuously. The procedure reduces
significantly the undesirable numerical diffusion effects. :numref:`figure-16.1-3`
illustrates only the liquid fuel region, which extends from the cell
IFFUBT to IFFUTP. The pin disrupted region extends from the cell IDISBT
to IDISTP, corresponding to the integers KDISBT and KDISTP on the K
grid. The cladding rupture extends from IFRIBT to IDISBT-1 and from
IDISTP+1 to IFRITP. If no pin disruption is present, the cladding
rupture extends from IFRIBT to IFRITP. It is noted that IFRIBT and
IFRITP are the lowermost and uppermost cells with a cladding rupture but
that it is not necessary that all the intermediate cells exhibit a
cladding rupture, although this is generally the case. The in-pin
hydrodynamic model is connected to the coolant channel hydrodynamic
model via the ejection process. Fuel and fission gas can be ejected from
the cavity into the channel either via the cladding rupture or, when the
pins have been disrupted, via the open ends of the remaining pin stubs.
These ejection processes are described by appropriate physical models.
.. _section-16.1.3:
Interaction of LEVITATE with Other Models within the SAS4A System
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. _section-16.1.3.1:
LEVITATE Initiation
^^^^^^^^^^^^^^^^^^^
LEVITATE can be initiated by only two routines of the SAS4A code, i.e.,
FUINIT and PLUTO2.
The initiation of fuel motion is decided, for any given channel, in the
routine FAILUR, called from TSTHRM. If FAILUR predicts the onset of fuel
motion, the module FUINIT is called to prepare the transition to the
fuel motion modules, LEVITATE or PLUTO2, and to decide which of these
two models should be used (:numref:`figure-14.7-1` in :numref:`Chapter %s<section-14>`). Several
conditions characteristic of LOF situations have to be met for the
initiation of LEVITATE:
- Pin failure must occur after sodium boiling has occurred.
- Only one large sodium vapor bubble must be present in the coolant
channel. The bubble must extend over at least four axial cells.
- The pin failure should be located within the vapor bubble.
The objective of these constraints is to insure that the pin failure
occurs in a largely voided region, where the LEVITATE models are valid.
If, however, the pin failure occurs in a region containing significant
amounts of liquid sodium, PLUTO2 should be initiated. In such a case,
the molten fuel is likely to fragment into droplets upon contact with
the sodium, leading to the more rapid fuel sweepout characteristic of
TOP situations. This type of event is modeled in PLUTO2, but not in
LEVITATE. If any of the above conditions are not met, the PLUTO2 fuel
motion model will be initiated by FUINIT. One particular case must be
noted. If two or more bubbles are present, a check is made for the
presence of a dominant voided region. If such a region is found (length
of voided region/length of boiling region >0.7), a flag is set (ILEPLI =
1), which will then be used in PLUTO2, as described below. Control is
still transferred to PLUT02, whether or not a dominant bubble has been
found.
When LEVITATE is initiated in FUINIT, an interface routine, LESAIN, is
called to prepare all variables characteristic for LEVITATE. If the
steel motion module, CLAP, was operational prior to LEVITATE initiation,
an additional interface routine, LECLIN, is called from FUINIT. LECLIN
is used to translate the CLAP steel-related variables to LEVITATE
variables. Then two initialization routines, common for LEVITATE and
PLUTO2, are called: PLINPT and PLSET. At the same time the flag ICALC
used in TSTHRM is set to 2 [ICALC(ICH)=2] the value reserved for
LEVITATE. Control is then returned to TSTHRM, which checks on ICALC(ICH)
to decide which model has to be used in channel ICH.
The other path for LEVITATE initiation is via PLUTO2. Although some
accident sequences can begin as TOP situations in any given channel,
eventually the presence of the molten fuel in the coolant channel leads
to a disrupted geometry, requiring the use of LEVITATE. The PLUTO2
module checks at the end of each primary time step whether or not
control should be transferred to LEVITATE. Control should be transferred
to LEVITATE whenever the original bundle geometry has to be changed due
to steel ablation or possible pin disruption. Control is also
transferred to LEVITATE whenever the fuel vapor pressure in the channel
becomes significant. PLUTO2 does not model geometry changes due to
ablation or pin disruption, and the fuel vapor is not currently included
in the PLUTO2 channel hydrodynamic model.
The criteria for the transfer are as follows:
- Three or more axial cladding cells (see the input variable NCPLEV)
are completely molten, indicating that steel ablation and fuel-steel
mixing should occur, or
- The temperature of the molten fuel is above 4000 K, indicating the
presence of a significant fuel vapor pressure, or
- The flag ILEPLI is found to have the value 1, indicating the presence
of an initial large voided region.
When any of these criteria is satisfied, the flag ICALC(ICH) is set to
2, and a number of LEVITATE variables not used in PLUTO2 are set by
executing LEPLIN. Control is then returned from PLUTO2 to TSTHRM, which
will transfer control to LEVITATE. The relationship between LEVITATE and
other SAS4A modules is illustrated schematically in :numref:`figure-16.1-4`.
.. _figure-16.1-4:
.. figure:: media/image5.png
:align: center
:figclass: align-center
Relationship between LEVITATE and Other SAS4A Modules
.. _section-16.1.3.2:
LEVITATE Calculations
^^^^^^^^^^^^^^^^^^^^^
Once the LEVITATE initialization routines have been executed and the
flag ICALC (ICH) has been set to 2, the SAS4A transient driver TSTHRM
will transfer control to the LEVITATE driver routine LEVDRV. LEVDRV will
retain control and advance the solution in the channel ICH until the end
of the primary loop time step is reached. It should be noted that once
LEVITATE is initiated, the coolant time step is set equal to the
primary-loop time step and these two steps can be used interchangeably.
The flow chart in :numref:`figure-16.1-5` shows the logic of the LEVITATE driver.
First LEVDRV will execute LESET2. This subroutine initializes all
temporary integers and arrays. These are values that can be calculated
using the permanent quantities. They are kept only as long as LEVDRV
retains control in the channel ICH. The solution is then advanced in the
channel ICH by calling a sequence of subroutines from LEIF through
LEDISR. The solution for the hydrodynamic in-pin model and the ejection
of material from the pin cavities into the coolant channel are obtained
in the routines LElPIN and LE2PIN. All the other routines in the
sequence mentioned above are used to model the thermal and hydrodynamic
processes which occur in the coolant channel.
Next, the LEVITATE driver routine determines the maximum time step
acceptable for the coolant channel calculation in the next cycle. This
value is compared with the maximum time step calculated for the in-pin
model in LE2PIN, and the smaller of the two will be the LEVITATE time
step for the next calculational cycle. It is noted that the LEVITATE
time step is not allowed to exceed the time remaining until the end of
the heat-transfer time step. If this happens, the LEVITATE time step
will be cut back, so that the end of the next LEVITATE time step will
coincide with the end of the heat-transfer time step. The next task of
LEVDRV is to calculate the data for the fuel, steel and sodium
reactivities. These calculations are described in more detail in the
next section on LEVITATE interaction with the FEEDBK routine.
If the end of the LEVITATE time step coincides with the end of a
heat-transfer time step the PLHTR routine is called. This routine
calculates the new temperatures in the solid fuel pin and in the
cladding outside the interaction region at the end of the current heat
transfer time step. Then a new heat transfer time step is calculated.
If it is time to produce output, LEVDRV will print the output described
in :numref:`section-16.9`. Then if the end of the LEVITATE time step does not
coincide with the end of the primary loop time step, a new computational
cycle begins. Otherwise LEVDRV returns control to TSTHRM.
.. _section-16.1.3.3:
LEVITATE Interfaces
^^^^^^^^^^^^^^^^^^^
During the time period when LEVITATE performs calculations in a given
channel, it interacts with the PRIMAR hydrodynamic model, the PLHTR heat
transfer model, and the FEEDBK reactivity model (:numref:`figure-16.1-4`).
.. _figure-16.1-5:
.. figure:: media/image6.png
:align: center
:figclass: align-center
LEVITATE Driver Flowchart
.. _section-16.1.3.3.1:
LEVITATE Interface with the PRIMAR Hydrodynamic Model
'''''''''''''''''''''''''''''''''''''''''''''''''''''
PRIMAR calculates the hydrodynamic behavior of the sodium loop outside
the reactor vessel. Two options are now available, PRIMAR-1 and
PRIMAR-4. PRIMAR-1, which can be selected by setting the input IPRION
not equal to 4, calculates the inlet and outlet sodium pressures, using the
pump flow decay curve, without accounting for the pressure events
occurring in the LEVITATE region. Thus, no feedback is returned from
LEVITATE to PRIMAR-1. LEVITATE uses the pressures calculated by
PRIMAR-1, together with the pressures in the voided region to model the
motion of the liquid sodium slugs which bound the voided region. The
quantities PREX and PRIN, which in LEVITATE designate the upper and
lower plenum pressures, respectively, are set in LEVDRV, using the
pressures PX and PIN received from PRIMAR-1. PRIMAR-4 is a more
sophisticated model, which accounts for the events calculated by
LEVITATE. LEVITATE receives the inlet and outlet pressures from
PRIMAR-4, as well as the time derivatives of these pressures. This
information is used to determine the behavior of the sodium slugs. It
also integrates the mass flow rates for the two slugs over the PRIMAR-4
time step and returns this information to PRIMAR-4. These calculations
are performed in the LEVITATE routine LEMOCO, after solving the momentum
conservation equations. The PRIMAR-4 model can be selected by setting
the input variable IPRION equal to 4.
.. _section-16.1.3.3.2:
LEVITATE Interface with the PLHTR Heat-Transfer Module
''''''''''''''''''''''''''''''''''''''''''''''''''''''
PLHTR calculates the temperature transients in the fuel pin. As such, it
interfaces with LEVITATE at the pin cavity surface and at the outer
fuel-pin surface.
A heat flux, based on the temperature difference between the temperature
of the pin inner node and the cavity temperature and an appropriate
heat-transfer coefficient is calculated in the routine LElPIN. This flux
is then used in LEVITATE as a boundary condition to calculate the fuel
temperature in the pin cavity. The same flux is integrated over the
heat-transfer time step and the resulting energy HFCAWA is then made
available to the PLHTR module, for use as the boundary condition on the
cavity side in the transient pin temperature calculation.
A similar heat flux, based on the temperature difference between the
fuel-pin outer node and the inner node of the cladding is calculated in
the LEMISC routine. The heat-transfer coefficient used is generally
based on the gap conductance. A more complex situation exists when the
cladding has been completely ablated at a certain axial location. In
this case, the fuel is in direct contact with the materials in the
channel, and the heat-transfer coefficient and temperature difference
used are dependent on the local configuration. The heat flux calculated
is then used as a boundary condition in LEVITATE for the calculation of
the transient cladding temperature, or, when the cladding has been
ablated, for the calculation of the temperatures in the channel. This
heat flux is also integrated over the heat-transfer time step, and the
resulting energy, HFPICL is then returned to the PLHTR module, where it
is used as the outer-pin boundary condition in the transient pin
temperature calculation.
.. _section-16.1.3.3.3:
LEVITATE Interface with the FEEDBK Reactivity Model
'''''''''''''''''''''''''''''''''''''''''''''''''''
FEEDBK calculates the net reactivity changes for the whole reactor
during a time step and transfers this information to the neutronic model
which calculates the changes in the reactor power. LEVITATE calculates
the sodium, fuel and steel axial mass distributions for the SAS4A
channel under its control at the end of each time step. In other
channels, these masses can be updated by other modules, e.g., PLUTO2,
which have control at the given time. The transient axial mass
distributions are used in subroutine FEEDBK to calculate the coolant
void, cladding motion, and fuel motion reactivity feedbacks. When all
channels have been calculated, the material relocation reactivities are
used in FEEDBK, together with the Doppler reactivity, to determine the
total reactivity of the core. Using this information, the neutronic
model determines the new power level which is used by LEVITATE in the
following time step. The power level at the end of each LEVITATE time
step is determined in LEVDRV, using an exponential fit of the power-time
history supplied by the neutronic model. This fit is based on the power
level at the beginning of the previous main time step, the power level
at the beginning of the current main time step and the precalculated
power level at the end of the current main time step. By using this
calculated power level and the axial input power distribution, the
specific power for each axial cell is calculated.
.. _section-16.1.3.4:
LEVITATE Termination
^^^^^^^^^^^^^^^^^^^^
At the present time, LEVITATE is the last phenomenological module called
by SAS4A. Thus the decision to terminate a SAS4A run will generally be
made in LEVITATE. This decision is made in the routine LEABLA, where the
number of completely molten hexcan wall cells are counted. If this
number N\ :sub:`sr,melt` is greater or equal to an input specified
number, NSLEEX, LEVITATE will print an explanatory message and will
terminate the calculations. The reason behind this is that once the
hexcan walls have been totally molten at a certain axial location it is
likely that inter-channel lateral material exchanges will be initiated,
i.e., a transition-phase domain is being entered that is not modeled in
SAS4A.
Other possibilities to terminate the SAS4A calculations, which are not
necessarily specific to LEVITATE are: (a) exceeding the maximum number
of main time steps in the transient calculation MAXSTP; (b) exceeding
the maximum problem time TIMAX; and (c) decreasing the fuel motion
reactivity below the input value NFUELD.
.. _section-16.1.4:
Improvements and New Models Relevant to the LEVITATE Module in SAS4A Version 1.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This section describes the differences between the LEVITATE module
present in the SAS4A Release 1.1 version and that used in the SAS4A
Release 1.0.
The most important enhancement to the LEVITATE Release 1.1 is the
availability of the chunk model, which describes the formation and
relocation of solid fuel and/or steel chunks. Although the chunk model
was described in the documentation to Release 1.0, the actual code did
not incorporate this capability which was still being tested at the time
of release. The chunk modeling capability has been fully integrated in
the Release 1.1 LEVITATE module. However, the user should be aware that
this model has not yet been validated by experiment analysis and its
results should be used cautiously at this time.
The chunk model can be switched on by setting the input variable
:sasinp:`ICHUNK`\ =1. If ICHUNK is set to zero, the chunk model is
completely disabled and the code will work in the same manner as in
Release 1.0, i.e., will homogenize the moving solid fuel with the liquid
fuel in the channel. The new input variables relevant for the chunk
model are :sasinp:`ICHUNK`, :sasinp:`ILUBLK`, :sasinp:`ASRALU`,
:sasinp:`RALUDI`, and :sasinp:`RALUFZ`. These variables are
described in :numref:`table-16.8-1`.
Another feature added to the current LEVITATE version is the presence of
a partial annular steel flow regime. This flow regime is described in
:numref:`section-16.4.1.4`. The partial annual steel flow regime is used only when
the chunk model is used, i.e., ICHUNK=1. If ICHUNK=0 the full annular
flow regime is still used. It should be noted here that the annular
steel flow regime becomes more important when the chunk model is used,
because the frozen fuel can separate from the molten fuel-steel field,
leading to the presence of more cells characterized by the steel annular
flow regime.
A mechanistic model describing the ejection of the molten fuel from the
pin cavity into the coolant channel has also been added to the LEVITATE
module. This model is optional and can be used by setting the input
variable :math:`\text{INRAEJ=1}`. The velocity of the ejected fuel is calculated using
a radial momentum conservation equation. The radial momentum can also be
convected axially, in axial cells where the cladding failure has
occurred.
A complete calculation of the sodium and structure temperatures in the
sodium slug region has also been added and the corresponding temperature
map is now part of the LEVITATE regular output.