.. _section-11.4:
Integration of FPIN2 into SASSYS/SAS4A and Usage of Integrated Model
--------------------------------------------------------------------
A general purpose SAS-FPIN2 interface has been designed and most of the
communication between the two codes is established at this interface
minimizing the impacts of coupling on both codes. This coupling strategy
allows for maintaining the stand-alone capability of the two codes while
assuring that any future improvements to FPIN2 are automatically
reflected in SASSYS/SAS4A.
.. _section-11.4.1:
SAS-FPIN2 Coupling Methodology
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Two modes of SAS-FPIN2 coupled operations are provided. In the
stand-alone mode, FPIN2 reads its own input deck and executes without
linking to SASSYS/SAS4A. This mode is provided primarily for
verification/debugging purposes, to allow independent development of
FPIN2, and to allow it to continue its role as a tool for
thermo-mechanical analysis of individual fuel pins.
In the interfaced mode, FPIN2 replaces the SASSYS/SAS4A metal fuel
element mechanics module DEFORM-5 and calculates the updated dimensions,
stresses, and strains at the end of each time step. These FPIN2 results
are then made available for use in the analysis of accident energetics
by providing estimates of axial expansion of fuel, time and location of
cladding failure, and the condition of the fuel element at the time of
the failure (although the communication between FPIN2 and the SAS4A
in-pin and ex-pin fuel relocation modules, PINACLE and LEVITATE, is not
yet established). In the interfaced mode, some of the input necessary to
run FPIN2 is included in the SASSYS/SAS4A input deck, and the remaining
is interpreted from corresponding SASSYS/SAS4A variables.
.. _section-11.4.1.1:
Stand-alone FPIN2 Calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In the stand-alone mode, FPIN2 is run by a call to main FPIN2 driver
routine, FPMAIN. In this mode, FPIN2 performs complete
thermal-mechanical calculations for a single fuel element. When the heat
transfer option to calculate the coolant and structure temperatures is
invoked, the fuel element is assumed to be surrounded by a circular
coolant channel and an outer wall in pin-in-a-pipe geometry. The code
also provides an option in which the cladding outer surface temperature
may be specified as a function of time to drop the coolant channel and
structure calculations. This mode is mainly provided for direct
verification and code debugging purposes.
In the stand-alone mode, FPIN2 input is appended at the end of
SASSYS/SAS4A input deck after the ENDJOB record. The stand-alone FPIN2
input deck consists of the following records entered in free format:
1. Title,
1. Integer data (including integer debug data),
2. -1/ End of Integers,
3. Decimal data (including decimal debug data),
4. -1/ End of Decimals.
Integer and decimal input data are entered in a form similar to the
SASSYS/SAS4A input data. Each of the FPIN2 input variables has an
assigned location number. The first entry in a line of input data is the
location number of the first member of the set of input data values. The
second entry is the number of data values that follow. Integer and
decimal input data fields are initialized to zero before reading in the
data; therefore, a variable does not have to be read in if it has the
value of zero. A line of data may continue over several records;
however, the maximum number of data values in a line is limited with
2000. The primary unit system for stand-alone FPIN2 input and output is
CGS with exception of pressure which is specified in Bar. Temperature is
specified in Kelvin. The full list of FPIN2 input variable for
stand-alone calculation along with a brief description for each variable
is provided in :numref:`section-A11.2`.
.. _section-11.4.1.2:
Interfaced SAS-FPIN2 Calculation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The SAS-FPIN2 interface consists mainly of the steady-state and
transient FPIN2 driver routines. The steady-state driver, FPINIT,
performs setup of FPIN2 for the interfaced calculation and initializes
FPIN2 input from SASSYS/SAS4A data. This routine is executed only once
prior to the transient calculations. The transient FPIN2 driver routine,
FPDRIV, incorporates the time-advancement scheme and interfaces dynamic
variables between the two codes.
During the initialization of FPIN2 from SASSYS/SAS4A input, interface
routine FPINIT looks for inconsistencies in fuel element modeling,
prints diagnostic messages, and terminates the execution if necessary.
The main inconsistencies that a user should be aware of are summarized
below:
1. A gas plenum below the fuel column is not allowed in FPIN2;
therefore, the execution is terminated if SASSYS/SAS4A input variable
:sasinp:`IPLUP` is non-zero.
2. If the fuel element contains axial blankets, i.e., :sasinp:`MZUB` and/or :sasinp:`MZLB`
are non-zero, a warning
message is printed since FPIN2 mechanics calculation is not normally
performed for the axial segments containing blanket fuel. [#7]_
3. An error message is printed and execution is terminated if the number
of axial segments in fuel exceeds FPIN2's limit (20),
4. An error message is printed if SASSYS/SAS4A input variable :sasinp:`IPOWRZ`
is non-zero (applicable only when :sasinp:`IHTFLG`\ ≠0).
5. Cross-checking of the input data for abnormalities are also performed
(such as zero pin pressure) and diagnostic messages are printed.
Since FPIN2 has been primarily developed for the transient analysis of
fuel elements, it lacks models to describe pre-transient irradiation
features such as fuel restructuring, fission gas retention and
fuel-cladding gap narrowing. These pre-transient conditions are to be
provided as input for the metallic fuels as discussed in :numref:`section-11.4.3`.
The as-irradiated geometry, fuel elongation, fission product and
porosity distributions, and the effect of fast neutron fluence on
cladding are typically obtained from the relevant in-reactor fuel
performance database at a desired burnup, or from steady-state fuel
performance codes such as LIFE-METAL [11-18] and STARS [11-6]. FPIN2 has
the capability to interpret its input from the LIFE-METAL output. This
capability is also extended to the integrated SAS-FPIN2 model.
Normally, FPIN2 heat transfer is by-passed in the interfaced mode and
the fuel element temperatures are lined with SASSY/SAS4A calculated
fuel, cladding, plenum, and cavity temperatures. To accomplish this
by-pass, the FPIN2 mechanics/thermal-hydraulics boundary is identified,
and routines that are used in heat transfer calculation are isolated.
All the common block variables that are used in the mechanics
calculation (but altered in one of these heat-transfer routines) are
linked with their SASSYS/SAS4A counterparts. The FPIN2 results for
stresses and displacements are in turn made available to SAS4A for the
estimates of axial expansion of fuel and associated reactivity effects,
time and location of cladding failure, and the condition of the fuel at
the time of failure.
In the interfaced mode, setting the input flag, IHTFLG, may also turn on
FPIN2's own heat transfer model. The option for including FPIN2 heat
transfer model is mainly provided for debugging and code verification
purposes. It requires additional data to be interfaced regarding fuel
pin heat generation rate and cladding outer surface temperature for each
axial segment at each time step as the dynamic boundary condition. When
this option is set, FPIN2 uses its own built-in metallic fuel thermal
property routines.
In order to establish consistency between SASSYS/SAS4A and FPIN2
calculations in the interfaced mode, some modifications to the FPIN2
code were necessary. Major changes to FPIN2 for this integration are
summarized below:
1. Generic precision conversions are performed by combining all type
declaration statements in a file and replacing them in each
subprogram with an INCLUDE statement referencing this file.
2. Along the same line, type specific intrinsic functions are converted
to their generic equivalents.
3. Various table interpolations for time-dependent boundary conditions
(pin power and cladding outer surface temperature when IHTFLG=1) are
bypassed and these variables are linked with their SASSYS/SAS4A
calculated counterparts.
4. Various calls to built-in FPIN2 material thermal property subprograms
are also bypassed and the thermal properties that are needed in FPIN2
mechanics calculation are substituted with their SASSYS/SAS4A
calculated equivalents.
5. Steady-state and transient pin plenum gas temperature is interfaced
with the corresponding SASSYS/SAS4A variable.
6. Constant liquid eutectic alloy melting temperature is converted to a
variable and listed as an integrated SAS-FPIN2 model input, XEUTHR.
7. Initial cladding effective inner surface wastage is described as a
new integrated SAS-FPIN2 model input variable and incorporated into
FPIN2 by defining it as part of the variable for cladding wall
thinning due to eutectic penetration.
8. The constant coolant channel pressure is converted to a dynamic array
variable and interfaced with its axially varying time-dependent
SASSYS/SAS4A counterpart.
All these changes are implemented in such a way that they do not affect
the stand-alone performance of FPIN2.
The radial mesh structure for SASSYS/SAS4A, stand-alone FPIN2, and
interface SAS-FPIN2 calculations are shown in :numref:`figure-11.4-1`. As presented
in :numref:`Chapter %s<section-3>`, the radial mesh structure in SASSYS/SAS4A for fuel
elements at a given axial segment can be set up based on either equal
radial difference or equal mass principle. In either case, the boundary
nodes are the half sixe as shown in :numref:`figure-11.4-1`. In FPIN2, on the other
hand, finite elements are initially defined in a mesh based on an equal
radial difference principle with all elements having the same thickness
as shown in :numref:`figure-11.4-1`. In order to avoid extensive remapping of the
thermal and mechanical variables between two meshes during the
interfaced calculations, the consistency between the initial mesh
structures is accomplished by pulling SASSYS/SAS4A-calculated mesh
information into FPIN2 common blocks, and forcing FPIN2 to use the same
mesh structure in the fuel and cladding (:numref:`figure-11.4-1`). When FPIN2 heat
transfer is by-passed, however, this procedure requires substitution of
mesh-centered temperatures for boundary nodes, namely
:math:`T_{\text{f}1}`, :math:`T_{\text{fNDRF}}`, :math:`T_{\text{c}1}`, and
:math:`T_{\text{c}3}` (locations marked with a "\*" in :numref:`figure-11.4-1`),
that are not calculated in SASSYS/SAS4A. In the interfaced mode, these
temperatures are approximated with a linear interpolation between the
temperatures of the neighboring nodes.
.. _figure-11.4-1:
.. figure:: media/image6.png
:align: center
:figclass: align-center
Radial Mesh Structure and Temperature for an Axial Segment in (a) FPIN2 Code, (b) SASSYS/SAS4A, and (c) Integrated SAS-FPIN2 Model.
Although the fuel element mechanics model of FPIN2 uses an implicit
solution scheme, the interaction between the SASSYS/SAS4A
thermal-hydraulics and FPIN2 mechanics calculations is explicit. In the
SASSYS/SAS4A code system, a multi-level time-step hierarchy is used in
which a main time step is divided into one or more primary-loop, heat
transfer, and coolant dynamics time steps as described in :numref:`Chapter %s<section-2>`. The
control over the length of a computational time step is performed using
a variety of internal and user-specified restrictions. The FPIN2
mechanics calculation is performed at the each heat transfer time step
using newly calculated temperatures. Limitations imposed by stability
and accuracy requirements assure that heat-transfer time steps are small
enough to avoid the problem of unstable results between the thermal and
mechanical calculations due to explicit coupling. The implicit treatment
in FPIN2 is somewhat inconsistent with the explicit nature of the
SASSYS/SAS4A code system and it often results in a notable increase in
computation time. However, the capabilities gained by this coupling are
often well worth this additional computational cost.
.. _section-11.4.1.3:
Subroutine Descriptions and Flow-charts
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The list of SAS-FPIN2 interface routines is presented in :numref:`table-11.4-1`.
In the stand-alone mode, the FPIN2 main program is called form the
SASSYS/SAS4A steady-state driver routine SSTHRM and FPIN2 is executed
without interfacing to SASSYS/SAS4A. In the interfaced mode, FPIN2 is
coupled to the rest of the SASSYS/SAS4A calculations through two main
driver subroutines, FPINIT and FPDRIV. First the steady-state FPIN2
driver routine FPINIT is called from SSTHRM for initialization of FPIN2
for interfaced calculations. A flowchart for the FPINIT subroutine is
shown in :numref:`figure-11.4-2`. Then, during the transient calculations,
SASSYS-SAS4A thermal-hydraulic manager TSTHRM calls for the transient
interface routine FPDRIV that acts as the FPIN2 transient driver.
.. _table-11.4-1:
.. list-table:: SAS-FPIN2 Interface Subroutines
:header-rows: 1
:align: center
:widths: auto
* - Subroutine Name
- Description
* - FPMAIN
- In the stand-alone mode, FPIN2 driver (main program)
* - FPINIT
- In the interfaced mode, steady-state FPIN2 initialization routine
* - FPDRIV
- In the interfaced mode, FPIN2 transient driver routine
* - SASTMP
- In the interfaced mode, SAS-FPIN2 thermal-hydraulics interface (when FPIN2 heat transfer module is by-passed)
* - FPNOUT
- In the interfaced mode, output of the FPIN2 results
.. _figure-11.4-2:
.. figure:: media/image7.png
:align: center
:figclass: align-center
FPINIT Subroutine Flow Diagram
Subroutine FPDRIV basically includes the section of FPMAIN that is used
for the time advancement scheme. This time advancement scheme is
preceded by an upper interface routine, SASTMP that pulls SASSYS/SAS4A
calculated temperatures into FPIN2 common blocks, and is followed by a
lower interface section that takes FPIN2 updated axial and radial mesh
information and puts it back into SASSYS/SAS4A common locations. SASTMP
is also used by steady-state interface routine FPINIT to extract the
initial temperature distribution from SASSYS/SAS4A. A flowchart for the
subroutine FPDRIV is presented in :numref:`figure-11.4-3`.
.. _section-11.4.2:
Input Description for Interfaced SAS-FPIN2 Calculation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Two groups of input variables are identified for interfaced SAS-FPIN2
calculations. Integrated model variables that describe the mode of the
interfaced calculation and FPIN2 variables that are not readily provided
by SASSYS/SAS4A are included in SASSYS/SAS4A common blocks INPCHN (for
integer variables) and PMATCH (for real variables). The list of these
"new" variables is provided in :numref:`table-11.4-2`.
Another category includes input variables that are provided by
SASSYS/SAS4A calculations and/or are translated from SASSYS/SAS4A input.
The list of these variables along with SASSYS/SAS4A counterparts is
presented in :numref:`table-11.4-3`. The variables in :numref:`table-11.4-2` and :numref:`table-11.4-3` constitute the full list of input parameters necessary to run
FPIN2 in the interfaced mode. Further information on some of the input
parameters related to pre-transient fuel element characterization is
given in the following section. When interpreting FPIN2 input from
SASSYS/SAS4A data, dimensional conversions are necessary since the
principal unit systems for SASSYS/SAS4A and FPIN2 and SI and CGS,
respectively.
.. _figure-11.4-3:
.. figure:: media/image8.png
:align: center
:figclass: align-center
FPDRIV Subroutine Flow Diagram
.. _table-11.4-2:
.. list-table:: Input Variables for Integrated SAS-FPIN2 Model
:header-rows: 1
:align: center
:widths: auto
* - BLOCK 51 \* INPCHN
-
-
-
* - Location
- Symbol
- Value
- Definition/Comments
* - 285
- IFPIN2
- =0
- Do not use FPIN2 metal fuel model
* -
-
- =1
- Use FPIN2
* - (Note: No other data required when IFPIN2=0)
-
-
-
* - 286
- IFPI01
- =0
- Use FPIN2 in interfaced mode
* -
-
- =1
- Use FPIN2 in standalone mode
* - (Note: No other data required when IFPI01=1)
-
-
-
* - 287
- IHTFLG
- =0
- Bypass FPIN2 heat transfer calculation
* -
-
- =1
- Include FPIN2 heat transfer calculation
* - 288
- LHTOPT
- =0
- Perform heat transfer calculation including coolant and wall
* -
-
- =1
- Perform heat transfer calculation with input value of cladding outer surface temperatures
* - 289
- LCRACK
- =0
- No fuel cracking
* -
-
- =1
- Radial fuel cracks included
* - 290
- LFPLAS
- =0
- Allow creep-plastic strains in fuel
* -
-
- =1
- Suppress creep-plastic strains in fuel
* - 291
- LCPLAS
- =0
- Allow creep-plastic strains in clad
* -
-
- =1
- Suppress creep-plastic strains in clad
* - 292
- LFSWEL
- =0
- Allow swelling-hotpressing strains in fuel
* -
-
- =1
- Suppress swelling-hotpressing strains in fuel
* - 293
- LCSWEL
- =0
- Allow swelling strains in clad
* -
-
- =1
- Suppress swelling strains in clad
* - 294
- LLRGST
- =0
- Large strain analysis
* -
-
- =1
- Small perturbation analysis
* - 295
- LFCSLP
- =0
- Fuel-clad locked when gap is closed
* -
-
- =1
- Independent fuel-clad axial displacement
* - 296
- LOUTSW
- =0
- No detailed printing of results - summary only
* -
-
- =1
- Normal detailed printout under LFREQA, MFREQA, and LFREQB control
* - 297
- LFREQA
-
- Initial print frequency, number of time steps between normal detailed printout
* - 298
- MFREQA
-
- Total number of time steps under LFREQA control
* - 299
- LFREQB
-
- Final print frequency
* - 300
- LGRAPH
- =0
- Do not write graphics file
* -
-
- =1
- Write a graphics data file
* - 301
- LDBOUT
- =0
- Do debug output
* -
-
- =1
- Add debug output to regular LOUTSW=2 output
* - 302
- LDBSTP
- =0
- Program stops when molten cavity freezes
* -
-
- =1
- Ignore this program stop
* - 303
- LDBFPL
- =0
- Use recommended fuel flow stress (Eq. :ref:`11.3-16<eq-11.3-16>`)
* -
-
- =1
- Use simple power law fuel creep:\ :math:`\dot{\varepsilon} = C_{0}\sigma_{e}^{C_{1}}`
(Note: XFPLC0 and XFPLC1 are required)
* - 304
- LDBFDV
- =0
- Use recommended fuel swelling-hotpressing (Eq. :ref:`11.3-30<eq-11.3-30>`)
* -
-
- =1
- Use equilibrium swelling model (ANL-IFR-6 and -23)
* -
-
- =2
- Use simple power law fuel swelling: :math:`\dot{\varepsilon} = C_{0}\sigma_{m}^{C_{1}}`
(Note: XFDVC0 and XFDVC1 are required)
* - 305
- LDBCPL
- =0
- Use recommended clad flow stress
* -
-
- =1
- Ideal plastic flow for clad: :math:`\sigma_{y} = C_{0} + C_{1}{\overline{\varepsilon}}^{p}`
(Note: XCIPL0 and XCIPL1 are required)
* -
-
- =2
- Use high-temperature power-law creep
* -
-
- =3
- Use simple power law clad creep: :math:`\dot{\varepsilon} = C_{0}\sigma_{e}^{C_{1}}`
(Note: XCIPL0 and XCIPL1 are required)
* - 306
- LGPRES
-
- (Not currently used)
* - 307
- LGAPCL
- =0
- Use fuel-clad opening/closure model
* -
-
- =1
- Fuel-clad gap always closed
* - 308
- LCPROP
- =0
- Use material property correlations (when IHTFLG=1)
* -
-
- =1
- Use temperature independent material properties (when IHTFLG=1)
* - 309
- LSKIPM
- =0
- Perform mechanical calculations
* -
-
- =1
- Bypass mechanical calculations, heat transfer only (when IHTFLG=1)
* - 310
- LGCLOS
- =0
- Use gap closure routine at 100% fuel melting
* -
-
- =1
- Do not close gap (if open) at 100% fuel melting
* - 311-334
- LDBOTA(J)
-
- Axial debug print vector (0=no-print, 1=print)
* - 355-345
- LDBOTF(I)
-
- Fuel radial debug print vector (0=no-print, 1=print)
* - 346-348
- LDBOTC (IC)
-
- Clad radial debug print vector (0=no-print, 1=print)
|
.. list-table::
:header-rows: 1
:align: center
:widths: auto
* - BLOCK 63 \* PMATCH
-
-
* - Location
- Symbol
- Definition/Comments
* - 105
- XEUTHR
- Liquid eutectic threshold temperature (K) (Default=988.) (See :sasinp:`FSPEC` for consistent input)
* - 106
- XGBFRA
- (Not currently used)
* - 107-130
- XCLDHR(J)
- Pre-transient hardness parameter used in clad flow stress calculation. (Default value is 0.223, the value appropriate for 20% CW unirradiated stainless steel.)
* - 131
- XFPLC0
- Fuel power law creep constant C\ :sub:`0` (when LDBFPL=1)
* - 132
- XFDVC1
- Fuel power law creep constant C\ :sub:`1` (when LDBFPL=1)
* - 133
- XFDVC0
- Fuel power law swelling constant C\ :sub:`0` (when LDBFDV=2)
* - 134
- XFDVC1
- Fuel power law swelling constant C\ :sub:`1` (when LDBFDV=2)
* - 135
- XCIPL0
- Clad idealized flow stress constant C\ :sub:`0` (when LDBCPL=1 or 3)
* - 136
- XCIPL1
- Clad idealized flow stress constant C\ :sub:`0` (when LDBCPL=1 or 3)
* - 137
- XHTERR
- Relative convergence criterion for heat transfer calculation (when IHTFLG=1) (Default=0.0005)
* - 138
- XEPSCA
- Relative convergence criterion for cavity pressure (Default=0.001)
* - 139
- XEPSFE
- Relative convergence criterion for finite element analysis (Default=0.0005)
* - 140
- XEPTES
- Relative convergence criterion for plastic-creep strains (Default=0.0005)
* - 141
- XEVTES
- Relative convergence criterion for swelling strains (Default=0.0005)
|
.. _table-11.4-3:
.. list-table:: FPIN2 Input Variables that are Provided by SASSYS/SAS4A Calculations and/or Interpreted from SASSYS/SAS4A Input.
:header-rows: 1
:align: center
:widths: auto
* - Description
- FPIN2
Variable
- SASSYS/SAS4A
Counterpart
* - Metal fuel type (U-Fs, binary, or ternary)
- IFTYPE
- IMETAL
* - Cladding type (Type 316, D9, or HT9)
- ICTYPE
- ICTYPE
* - Number of axial segments in fuel column
- NDZ
- MZ
* - Number of radial elements in fuel
- NDRF
- NT
* - Number of radial elements in cladding
- NDRC
- 3
* - Transient initiation time (s)
- TZERO
- 0.
* - Computation time step size (s)
- DTIME
- DTP
* - Initial height of axial segments
- DZ(J)
- AXHI(J)
* - Initial length of plenum (cm)
- ZPLENM
- PLENL
* - Initial length of bond sodium in plenum (cm)
- ZPLNA
- BONDNA, pin geometry
* - Gas constant for plenum gases
(Bar-cm\ :sup:`3`/gm-K)
- PLGASR
- RGASSI, HEMM, FGMM, P0GAS, FGFI
* - Gas constant for central cavity gases
(Bar-cm\ :sup:`3`/gm-K)
- GASCON
- RGASSI, HEMM, FGMM
* - Initial pin pressure (Bar)
- PINT
- P0GAS
* - Reference temperature at which PINT is specified (K)
- PLTREF
- TR
* - External (channel) pressure (Bar)
- PEXT
- PCOOL2(J)
* - Plenum gas temperature (K)
- PGASTM
- TGASP2
* - Description
- FPIN2
Variable
- SASSYS/SAS4A
Counterpart
* - Peak fuel burnup (at.%)
- BURNUP
- BURNFU
* - Fuel radial mesh array (cm)
- RADF(I,J)
- R(I,J)
* - Clad radial mesh array (cm)
- RADC(I,J)
- R(NE,J), R(NEP,J)
* - Distribution of fission gas in closed porosity or in solution (gm/cm\ :sup:`3`)
- FISGAS(I,J)
- ROGSPI, BURNFU, FIFNGB
* - Fraction of FISGAS on grain boundaries (Default=0.10)
- GBFRAC
- FIFNGB
* - Distribution of total fuel porosity
- PORES(I,J)
- PRSTY2(I,J)
(based on PRSTY(IFUELV))
* - Axial profile of cladding fluence (10\ :sup:`22` n/cm\ :sup:`2`)
- CLDFLU(J)
- BURNFU, FPDAYS, PBAR(J), FLTPOW, AXHI(J)
* - Effective cladding inner surface wastage thickness (cm)
- WASTE
- TWASTI, TWASTO
* - Mass of fuel elements (gm)
- FMASS(I,J)
- FUELMS(I,J)
* - Mass of cladding elements (gm)
- CMASS(I,J)
- DENSS, cladding geometry.
* - Distribution of Pu in ternary fuel
- FRACPU(I,J)
- FUPUMS(I,J), FUELMS(I,J) (based on PUZRTP(IFUELV))
* - Distribution of Zr in ternary fuel
- FRACZR(I,J)
- FUZRMS(I,J), FUELMS(I,J)
(based on PUZRTP(IFUELV))
* - Fuel solidus temperature (node-by-node) (K)
- FTSOL(I,J)
- TSOLIJ(I,J)
* - Fuel liquidus temperature (node-by-node) (K)
- FTLIQ(I,J)
- TLIQIJ(I,J)
* - Normalized time dependent reactor power (when IHTFLG=1)
- POWNEW
- QMULT
* - Pin power coupling factor (when IHTFLG=1)
- QCONST
- 1.
* - Axial profile of energy generation rate (normalized) (when IHTFLG=1)
- QAX(J)
- PSHAPE(J)
* - Radial profile of energy generation rate (W/gm) (when IHTFLG=1)
- QR(I,J)
- RADPRS(I,J), POW, GAMTNE, GAMTNC, GAMSS, FUELMS
* - Cladding outer surface temperature (K) (when IHTFLG=1 and IHTOPT=1)
- TCSURF(J)
- T2(NEP,J)
.. _section-11.4.3:
Pre-transient Fuel Element Characterization
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The steady-state fuel element characterization forms the initial
conditions from which the transient calculations begin. The FPIN2
mechanics calculation is initiated from a stress-free state for hot and
irradiated (swollen) fuel elements. Prior irradiation of fast reactor
fuel elements influences their thermal and mechanical response during
accident transients significantly. The pre-transient features that are
more important for metallic fuels are fuel geometry, fission product,
alloy, and porosity distributions, fuel elongation, and the effects of
fast neutron fluence on transient cladding properties. These initial
conditions can be obtained from the in-reactor fuel performance database
or from a fuel performance computer code. In this section, the methods
that are suggested to determine the fuel element pre-transient
characterization are outlined.
.. _section-11.4.3.1:
Zone Formation
^^^^^^^^^^^^^^
Post-irradiation destructive examinations of ternary fuel pins
irradiated in EBR-II reveal significant migration of plutonium and
zirconium. This redistribution produces distinct zones that are
associated with different metallurgical phases. Micrographs from
irradiated ternary fuel pins typically show a three-ring structure that
could be separated physically for examination [11-19]. Analysis of these
rings reveals that the intermediate zone is depleted in zirconium while
the inner and outer zones are enriched in zirconium. The weight fraction
of plutonium, on the other hand, remains nearly uniform. The Zr
deficient central zone generally consist of the high temperature γ phase
in which all constituents are mutually soluble in the solid sate as
described in :numref:`section-11.3.4`. The primary influence of alloy
redistribution and zone formation on transient fuel response is through
the changes in fuel material properties with alloy content. The most
dramatic change is in the fuel solidus temperature where zirconium
depletion may lead to initial fuel melting at a radial location other
than the hotter axial centerline.
SASSYS/SAS4A provides capabilities to model this fuel composition
variation by zone in metallic fuels (:sasinp:`IMETAL`\ =2)
as discussed in :numref:`section-10.3.5`. This multiple radial fuel zone option is
invoked by setting :sasinp:`IFUELC`\ =1. The distributions
are determined by fixing the zone boundaries and the alloy content of
the each zone (see input variables :sasinp:`IZNC`,
:sasinp:`IZNM`, and :sasinp:`MFTZN`). The representative alloy distributions that are chosen to
characterize ternary fuel to be analyzed are specified in the input as
weight fractions for each fuel type (:sasinp:`PUZRTP`). These distributions are used in the fuel material property
routines to determine variations in properties with alloy content.
SASSYS/SAS4A converts this zone information to internal arrays that
describe metal fuel composition and composition-dependent quantities on
a node-by-node basis. In the integrated SAS-FPIN2 model, FPIN2
interfaces with these internal SASSYS/SAS4A arrays to initialize
variable FRACPU(I,J), FRACZR(I,J), FTSOL(I,J), FTLIQ(I,J) and
FMASS(I,J).
.. _section-11.4.3.2:
Fission Gas Distribution
^^^^^^^^^^^^^^^^^^^^^^^^
Fission gas plays an important role in transient fuel element response.
The gas that is retained in the fuel during steady-state irradiation
provides a source for expansion of both solid and liquid fuel during
overheating. The quantity of fission gas in the plenum is also important
since the plenum pressure is a major contributor to cladding loading.
The distribution of fission gas retained in the fuel matrix is specified
as input in FPIN2 (FISGAS(I,J)). Part of this gas is assigned to grain
boundary bubbles (GBFRAC) and the remainder of the gas is assumed to be
in solution or in small bubbles within the fuel grains. A number of
models that address the various aspects of fission gas behavior are
available. One of these, the STARS code gives a detailed self-consistent
picture of the distribution of the gas between the fuel matrix, grain
boundaries, edge tunnels, large pores, and the plenum [11-6].
The fraction of the retained gas on the grain boundaries increases with
burnup as more gas is released and as the plenum pressure becomes
significant compared to surface tension constraint on the grain boundary
bubbles. In the integrated model, the distribution of fission gas in
fuel closed porosity and in solution is calculated from SASSYS/SAS4A
input variables according to following formula
(11.4‑1)
.. _eq-11.4-1:
.. math::
\text{FISGAS} \left( \text{I,J} \right) = \text{ROGSPI} \cdot \text{BURNFU} \cdot \left( 1 - \text{FIFNGB} \right) \cdot 1 \cdot 10^{- 3}
where the fraction of fission gas on grain boundaries is simply
(11.4‑2)
.. _eq-11.4-2:
.. math::
\text{GNFRAC} = \text{FIFNGB}
The unit of FISGAS(I,J) in Eq. :ref:`11.4-1<eq-11.4-1>` is gm/cm\ :sup:`3`. The default
value of GBFRAC is 0.10.
The two other relevant input information required by FPIN2 are the
plenum and cavity gas constants, PLGASR and GASCON, in
Bar-cm\ :sup:`3`/gm-K. For fresh fuel pins (BURNFU=0) these constants
are simply calculated from
(11.4‑3)
.. _eq-11.4-3:
.. math::
\text{GASCON} = \text{PLGASR} = \frac{\text{RGASSI}}{\text{HEMM}} 1 \cdot 10^{1}
For irradiated pins (BURNFU≠0) the following formulas are used
(11.4‑4)
.. _eq-11.4-4:
.. math::
\text{GASCON} = \frac{\text{RGASSI}}{\text{FGMM}} 1 \cdot 10^{1}
(11.4‑5)
.. _eq-11.4-5:
.. math::
\text{PLGASR} = \frac{\text{RGASSI} \cdot \text{POGAS} \cdot 1 \cdot 10^{1}}{\text{POGAS} \cdot \text{FGMM} - \left( 1 - \text{FGFI} \right) \cdot 1.0133 \cdot 10^{5} \cdot \left( \text{FGMM} - \text{HEMM} \right)}
.. _section-11.4.3.3:
Porosity Distribution
^^^^^^^^^^^^^^^^^^^^^
The porosity distribution is also input into FPIN2 (through PORES(I,J)
variable). As given in the input description in :numref:`table-11.4-3`, these
values are the total porosity of the nodes, exclusive of the volume of
any macroscopic cracks (crack volumes are specified separately as
input). The difference between the total porosity and the grain boundary
bubble porosity is equal to the porosity of the large pores that are
free of surface tension restraint. These large pores may be
interconnected (open) or closed. In FPIN2, however, all large pores are
assumed to be open and fission gas residing in the open porosity after
steady-state irradiation is calculated from the local open pore volume
and temperature assuming that the pore pressure is in equilibrium with
the plenum pressure. This gas is assumed to be trapped in the fuel
during transient heating.
Few measurements of porosity distributions are available for the
metallic fuels. Therefore, the fractional porosity is generally
determined from the fuel geometry, the fuel mass, and the fuel and
fission product densities assuming a uniform distribution. In
SASSYS/SAS4A, porosity distribution is specified on a zone-by-zone basis
using the porosity values for eight fuel types (:sasinp:`PRSTY`) as described in :numref:`section-11.4.3.1`. Integrated model
interfaces with an internal SASSYS/SAS4A array variable (PRSTY2(I,J) to
get final distribution on a node-by-node basis.
The magnitude and distribution of the total porosity do not play a large
role in mechanics calculation as long as there is sufficient volume to
accommodate the grain boundary bubbles so that the resultant open
porosity is greater than zero. The FPIN2 models assume that the open
porosity does not contribute to solid fuel swelling or to hot pressing
because.
1. Sodium logging may partially fill the pores,
1. Driving pressures for swelling are small since the voids are
connected to the plenum,
2. Most of the voids are probably large enough so that the time
constants for their growth are long compared to the span of the
accident transient [11-14].
The distribution of open porosity does not significantly influence the
mechanics results either. Although fission gas in the open pores is
trapped at the time of fuel melting, its pressure is in equilibrium with
the plenum pressure so that this gas contributes little to molten fuel
expansion. Most of the expansion comes from the grain boundary gas or
the gas in solution in the fuel matrix that has significant swelling
potential when it collects into large bubbles following fuel melting.
Coalescence of small bubbles into large bubbles is very rapid in liquid
fuel [11-20] and is assumed to occur instantaneously in the FPIN2
calcualtion of molten fuel extrusion.
.. _section-11.4.3.4:
Cladding Fluence
^^^^^^^^^^^^^^^^
The axial distribution of the cladding fluence is needed in life
fraction correlation evaluations. In the integrated SAS-FPIN2 model,
this variable is determined from the following formula
(11.4‑6)
.. _eq-11.4-6:
.. math::
\text{CLDFLU}\left( J \right) = 8.64 \cdot 10^{- 22} \frac{\text{FPDAYS} \cdot \text{FLTPOW} \cdot \text{PBAR} \left( J \right)}{\text{AXHI}\left( J \right)}
Were FPDAYS, FLTPOW, and AXHI(J) are SASSYS/SAS4A input variables, and
PBAR(J) is an internal SASSYS/SAS4A array variable. The unit of
CLDFLU(J) in this equation is 10\ :sup:`22` neutrons/cm\ :sup:`2`. For
applications where fast-flux to linear-power ratio (:sasinp:`FLTPOW`)
is not available, cladding fluence is approximately set
equal to the burnup in at.% (i.e., :sasinp:`BURNFU`). [#8]_
.. _section-11.4.3.5:
Length of Sodium in Plenum
^^^^^^^^^^^^^^^^^^^^^^^^^^
The initial length of sodium in the pin plenum is expected to be
specified for hot and irradiated conditions in FPIN2. In the integrated
model, this value is calculated internally using SASSYS/SAS4A subroutine
NABOND. This subroutine evaluates the gap thickness for each axial
segment and determines the amount sodium in the plenum from initial mass
of sodium added to produce the fuel-cladding bound (:sasinp:`BONDNA`). The length in sodium in the plenum then is calculated from
plenum geometry consistent with the steady-state temperature
distribution.
.. _section-11.4.3.6:
Effective Cladding Inner Surface Wastage
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The integrated SAS-FPIN2 model provides an extended capability to
include the effects of cladding wastage on fuel element mechanics that
is not an original part of the FPIN2 code. The SAS-FPIN2 interface has
been modified to include two SASSYS/SAS4A input variables describing
initial wastage thicknesses on the cladding inner and outer surfaces
(:sasinp:`TWASTI` and :sasinp:`TWASTO`, respectively.)
Cladding wastage is typically considered in design-basis safety
assessments. The bases of the wastage in metallic fuel elements are the
scratches on the cladding surfaces, diffusion of fuel constituents and
fission products into the cladding, and the eutectic formation at the
fuel cladding interface. Diffusion of fuel and fission products creates
a lanthanide rich FCCI zone that has distinctly different microstructure
with cracks and it is assumed to be strengthless. In addition, a
separate carbon depleted band with decreased hardness is often
identified next to the FCCI zone in HT9 cladding. Although this region
exhibits only a moderate decrease in strength, it can conservatively be
considered as part of the wastage for the safety cases.
In the integrated SAS-FPIN2 model, effective inner surface wastage is
defined as the sum of inner and outer surface wastages and it is
incorporated into the mechanics calculation by defining them as part of
an FPIN2 variable describing the cladding eutectic penetration. This
allows consideration of the wastage bands as part of the cladding for
heat transfer while the stress field is determined considering only the
thickness of unaffected cladding that is available to carry the load.
.. _section-11.4.4:
Output Description and Graphics File Usage
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A brief description of the output generated by FPIN2 in the interfaced
mode is as follows. A sample of the regular output for fuel/cladding
summary information and plenum/molten cavity results is shown in :numref:`figure-11.4-4`. In the first part of the output, FPIN2 mechanics results are
printed for each axial segment separately. The descriptions of the
variables printed in this category are presented in :numref:`table-11.4-4`. FPIN2
regular output for each axial segment is followed by a summary of
plenum/molten cavity results as shown in the bottom portion of :numref:`figure-11.4-4`. The description of the variables printed in this category is
presented in :numref:`table-11.4-5`.
In addition to regular FPIN2 output described above, a series of
diagnostic messages are also printed as part of SASSYS/SAS4A output as
the integrated model calculations progress. These diagnostic messages
can be categorized as follows:
1. Messages regarding the execution of the FPIN2 such as non-convergent
iterations and maximum iteration warnings in various parts of the
program, and occurrence of non-positive definite matrix,
2. Messages regarding the non-physical phenomena such as negative gas
pressure, inconsistent input for constitutive equation options, or
negative open porosity,
3. Information messages regarding the cladding failure in a particular
axial segment, fuel-cladding gap mixup, complete cladding melting,
and cavity solidification stop.
A summary of these messages is also printed at the end of the transient
calculations.
The FPIN2 detailed output option can be invoked by setting the input
flag :sasinp:`LOUTSW`\ =1. This option generates a huge
printout for the details of FPIN2 calculations and it is used for
debugging purposes only. The information printed under this option is
generally self-explanatory; therefore, it is not discussed separately
here. The print frequency of the regular and detailed FPIN2 output
discussed above is controlled by the same SASSYS/SAS4A input parameters
that control DEFORM5 output.
For graphics use, some of the variables printed in regular output are
stored in binary form in a graphics file at every time step by invoking
the option :sasinp:`LGRAPH`\ =1. The logical unit number
assigned for FPIN2 graphics file is 23. The list of variables printed in
the graphics file is presented in :numref:`table-11.4-6`.
.. _figure-11.4-4:
.. figure:: media/image9.png
:align: center
:figclass: align-center
FPIN2 Regular Output for Fuel Element Mechanics Summary
.. _table-11.4-4:
.. list-table:: Description of the variables in FPIN2 Regular Output for Fuel Element Mechanics Summary
:header-rows: 1
:align: center
:widths: auto
* - Variable
- Unit
- Description
* - PCAV
- Pa
- Molten fuel cavity pressure
* - VGCAV
- cm\ :sup:`3`
- Volume of gas in molten fuel cavity
* - RCAV
- cm
- Outer radius of the molten fuel cavity
* - WFUEL
- mm
- Axial displacement of fuel column segment
* - FCGAP
- mm
- Fuel-cladding gap thickness
* - PFC
- Pa
- Contact pressure between the fuel and cladding
(plenum pressure if gap is open)
* - RCMELT
- cm
- Radius of cladding melting
* - TCMID
- K
- Temperature of cladding at radial midpoint
* - SIGAV
- Pa
- Average hoop stress in cladding
* - EPSPTMID
-
- Plastic hoop strain in cladding at radial midpoint
* - WCLAD
- mm
- Axial displacement of cladding segment
* - CLIFE
-
- Cladding life fraction
* - CLDPR
- %
- Eutectic penetration of the cladding
|
.. _table-11.4-5:
.. list-table:: Description of the Variable in FPIN2 Regular Output for Plenum/Multen Cavity Results
:header-rows: 1
:align: center
:widths: auto
* - Variable
- Unit
- Description
* - CVGAST
- K
- Molten fuel average temperature
* - VOLCV
- cm\ :sup:`3`
- Total molten cavity volume
* - VFSOL
- cm\ :sup:`3`
- Volume of fuel in molten cavity between solidus and liquidus
* - VFLIQ
- cm\ :sup:`3`
- Volume of fuel in molten cavity above liquidus
* - CVGASV
- cm\ :sup:`3`
- Volume of fuel vapor in molten cavity
* - PPLEN
- Pa
- Pin plenum pressure
* - PLGAST
- K
- Pin plenum average temperature
* - PLGASV
- cm\ :sup:`3`
- Volume in pin plenum available to gas
* - PLNAV
- cm\ :sup:`3`
- Volume of sodium in plenum
* - EXTRUS
- cm\ :sup:`3`
- Volume of molten fuel extruded into the plenum
* - WFTOT
- cm
- Total axial displacement of fuel
* - WCTOT
- cm
- Total axial displacement of cladding
* - F-TAVE
- K
- Average temperature of entire fuel column
* - C-TAVE
- K
- Average temperature of cladding tube containing fuel
|
.. _table-11.4-6:
.. list-table:: Description of the Variables Stored in FPIN2 Binary Graphics File (Logical Unit #23)
:header-rows: 1
:align: center
:widths: auto
* - *Order*
- *Variable*
- *Unit*
- *Description*
* - 1
- TIME
- s
- Current time at which values of the variables are reported
* - 2
- PCAVTY
- Pa
- Molten fuel cavity pressure
* - 3
- CVGAST
- K
- Molten fuel cavity temperature
* - 4
- AMELTF(NDZ)
- %
- Areal (radial) melt fraction for the top axial segment
* - 5
- PPLEN
- Pa
- Pin plenum pressure
* - 6
- PLGAST
- K
- Pin plenum temperature
* - 7
- PFC(NDZ)
- Pa
- Fuel-cladding contact pressure at top axial segment
* - 8
- SIGCM(NDZ)
- Pa
- Cladding average hoop stress in top axial segment
* - 9
- EPSPTM(NDZ)
-
- Cladding average plastic hoop strain in top axial segment
* - 10
- FRCPEN(NDZ)
- %
- Cladding eutectic penetration at top axial segment
* - 11
- XLIFEF(NDZ)
-
- Cladding life fraction for top axial segment
* - 12
- WCTOT
- cm
- Total cladding axial displacement
* - 13
- WFTOT
- cm
- Total fuel axial displacement
* - 14
- EXTRUL
- cm
- Length of molten fuel extruded into plenum
* - 15
- FUELTL
- cm
- Total fuel elongation
* - 16
- TCLADM(NDZ)
- K
- Average cladding temperature in top axial segment
.. rubric:: Footnotes
.. [#7]
FPIN2 mechanical analysis can be performed for axial blankets by
describing them as a type of fuel with known material mechanical
properties.
.. [#8]
EBR-II specific, may not be valid for other reactors.