9.3. Solution Techniques and Code Implementation¶
9.3.1. Initialization¶
The DEFORM‑5 calculation is specified by setting ISSFUE = 0, ISSFU2 = 1,
and IMETAL > 0 in the SAS4A/SASSYS‑1 input deck. (See Table 9.3.1 for a
listing of DEFORM‑5‑related input data). On the first transient time
step, DEFORM‑5 sets constants used in the strain rate and transient
damage correlations and the eutectic penetration rate correlation,
initializes integral program variables, and calculates the local
cladding fluence as a function of the input‑specified local linear power
rating and input data FLTPOW and FPDAYS.
If input variable BURNFU has
been specified, then its numerical value is taken to be the cladding
fluence in units of 1022 neutrons/cm2; this is an
approximation often used for EBR‑II‑irradiated fuel elements. If a
steady‑state irradiation temperature for use in cladding damage
calculations is specified in input variable TIRRFU,
it is stored on the first time step for future use. All of the
first‑time‑step initialization is performed on entry to subroutine
D5INIT.
If input variable IPINFG has the value 0, then
on the first time step, the initial fuel element fill and fission gas
masses for the DEFORM‑5 fission gas model are calculated in subroutine
FAILUR. Using the fission gas plenum geometry (See PLENL and RBRPL),
the fuel geometry (See AXHI and ROUTFP),
the fuel porosity (See PRSTY), an assumed fill pressure of 105 Pa, an input
initial pressure (See P0GAS) at the reference
temperature (See TR), the ideal gas constant
(See RGASSI) and the molecular weights of the
fission and fill gases (See FGMM and HEMM),
the masses of fill gas and fission gas are computed from the
ideal gas law.
On time steps following the first, entry D5INI2 is executed to save cladding temperatures, fission gas pressures, coolant pressures, and to calculate the time derivative of the cladding temperature at the beginning of the transient DEFORM‑5 calculation.
Equation Symbol |
Equation Number |
SAS4A/SASSYS‑1 Input |
Suggested Value |
||
|---|---|---|---|---|---|
Name |
Block |
Location |
|||
‑ |
‑ |
IPO |
1 |
12 |
>0 |
‑ |
‑ |
IPOBOI |
1 |
13 |
>0 |
‑ |
‑ |
TR |
13 |
419 |
27 |
‑ |
‑ |
FGMM |
13 |
600 |
131 |
‑ |
‑ |
TFSOL |
13 |
786 |
‑ |
‑ |
‑ |
PRSTY |
13 |
1073 |
‑ |
‑ |
‑ |
RGASSI |
13 |
1086 |
8.31434 |
‑ |
‑ |
HEMM |
13 |
1225 |
4 |
‑ |
‑ |
FIRLIM |
13 |
1266 |
‑ |
‑ |
‑ |
SECLIM |
13 |
1267 |
‑ |
‑ |
‑ |
THRLIM |
13 |
1268 |
‑ |
‑ |
‑ |
DTFAL1 |
13 |
1269 |
‑ |
‑ |
‑ |
DTFAL2 |
13 |
1270 |
‑ |
‑ |
‑ |
DTFAL3 |
13 |
1271 |
‑ |
‑ |
‑ |
FGFI |
13 |
1275 |
‑ |
‑ |
‑ |
IFUELV |
51 |
15 |
0 |
‑ |
‑ |
ISSFUE |
51 |
32 |
0 |
‑ |
‑ |
MFAIL |
51 |
86 |
‑ |
‑ |
‑ |
ISSFU2 |
51 |
122 |
1 |
‑ |
‑ |
IMETAL |
51 |
189 |
>0 |
‑ |
‑ |
IFUELC |
51 |
193 |
0 or 1 |
‑ |
‑ |
ICTYPE |
51 |
225 |
0 |
‑ |
‑ |
IGASRL |
51 |
278 |
‑ |
‑ |
‑ |
IRAPEN |
51 |
280 |
0 or 1 |
‑ |
‑ |
IGSPRS |
51 |
282 |
0 or 1 |
‑ |
‑ |
IFPIN2 |
51 |
285 |
0 |
‑ |
‑ |
IPINFG |
51 |
486 |
0 |
‑ |
‑ |
IPORFG |
51 |
488 |
‑ |
‑ |
‑ |
AXHI |
61 |
8 |
‑ |
‑ |
‑ |
PLENL |
61 |
53 |
‑ |
‑ |
‑ |
RBRPL |
61 |
102 |
‑ |
‑ |
‑ |
ROUTFP |
61 |
128 |
‑ |
‑ |
‑ |
FPDAYS |
62 |
1 |
‑ |
‑ |
‑ |
FLTPOW |
62 |
61 |
‑ |
‑ |
‑ |
P0GAS |
63 |
27 |
>0 |
‑ |
‑ |
FRUPT |
64 |
81 |
‑ |
‑ |
‑ |
FMELTM |
65 |
2 |
‑ |
‑ |
‑ |
BURNFU |
65 |
54 |
‑ |
‑ |
‑ |
TIRRFU |
65 |
200 |
‑ |
9.3.2. Fuel/Cladding Eutectic Alloy Formation¶
Equation (9.2-1) is used to calculate the cladding penetration rate on
the inner cladding surface, independent of the input-specified values of
IMETAL and ICTYPE, in subroutine
EUTPEN. The rapid penetration rate in the range from 1353 K to 1506 K is
specified with a positive value of input variable IRAPEN;
otherwise the rate is given by the exponential form in
Eq. (9.2-1). In order for the rapid penetration rate to be effective,
the local fuel surface temperature must be above the input fuel solidus
temperature, TFSOL(IFUELV).
To accommodate large temperature changes on a heat transfer time step in fast transients, the temperature change across the time step is assumed to be linear and Eq. (9.2-1) is numerically integrated over the time step to avoid loss of accuracy. On each heat transfer time step, a new value of the cladding inner radius and the cladding thickness are calculated for use in subsequent cladding damage and strain rate calculations.
9.3.3. Fission Gas¶
On each time step, the fill and fission gas masses computed on the first
time step, Section 9.3.1, are used with the transient temperatures to
set the time-dependent internal-cladding and internal-fuel pressures. If
input variable IGSPRS is set to 0, the pressure
in the fuel porosity and the fission gas plenum is equilibrated in the
transient to simulate rapid fission gas transport through the fuel, an
option for long, slow accident sequences. Otherwise (IGSPRS > 0),
steady‑state gas in the fuel porosity remains in place and is heated
with the fuel temperatures. In the transient, the volume of the fuel
porosity is adjusted according to the input value of IPORFG,
to estimate the impact of fuel density changes on porosity volume
as the fuel changes temperature. These calculations are performed in
subroutine FAILUR.
9.3.4. Cladding Strain¶
In the transient, subroutine STRANC computes the incremental cladding
strains for each time step from the formulation in Section 9.2.3. If
input variable ICTYPE has the value 1 or 2,
then the parameters for 316 stainless steel are used. If ICTYPE has the
value 3, then the parameters for HT‑9 are used. The cladding inner radii
and thicknesses at all axial locations are adjusted to reflect the
transient cladding strains.
9.3.5. Cladding Failure¶
In the transient, subroutine FALMAR computes the cladding rupture time
and the corresponding life fraction at all axial locations using the
formulation in Section 9.2.4. The computed life fractions will be
printed, but will not trigger cladding failure, and subsequent
post‑failure model execution, unless the input value of MFAIL
has been set to 8 on input. In order to initiate LEVITATE
or PLUTO2 with this failure criterion, it is also necessary to specify
FIRLIM, SECLIM, THRLIM, DTFAL1, DTFAL2, DTFAL3
and FMELTM.
In addition, the local coolant margin to boiling, expressed as the ratio of the absolute coolant temperature to the absolute saturation temperature, is also computed in FALMAR for subsequent printing.
Subroutine DFORM5 computes cladding failures to initiate plenum fission
gas release in the coolant boiling model (See Chapter 12). For IGASRL >
0, input variable FRUPT(1)
contains the cladding life fraction for failure of all the
pins in the channel. This failure computation is independent of MFAIL.
9.3.6. Printed Output¶
DEFORM‑5 printed output is produced from subroutine OUTPT5 on a main
time step frequency set by input variables IPO and IPOBOI.
When called, subroutine OUTPT5 prints the
following quantities for all axial location: inner and outer cladding
radii, cladding thickness, internal pin pressure, coolant channel
pressure, cladding hoop stress and strain, incremental cladding strain
and strain rate on the last step, cladding life fraction, coolant
boiling fraction, time to rupture, time for cladding penetration, and
the amount of penetration of the cladding.