9.8.8.3. Solution Techniques and Code Implementation

9.8.8.3.1. 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 9.8.16 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.

Table 9.8.16 DEFORM-5 Input Data

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	‑

9.8.8.3.2. Fuel/Cladding Eutectic Alloy Formation

Equation (9.8.2-1) 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. (9.8.2-1). 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. (9.8.2-1) 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.

9.8.8.3.3. Fission Gas

On each time step, the fill and fission gas masses computed on the first time step, Section 9.8.8.3.1, 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.

9.8.8.3.4. Cladding Strain

In the transient, subroutine STRANC computes the incremental cladding strains for each time step from the formulation in Section 9.8.8.2.3. 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.

9.8.8.3.5. 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 9.8.8.2.4. 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.

9.8.8.3.6. 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.