.. _section-9.8.3: Solution Techniques and Code Implementation ------------------------------------------- .. _section-9.8.3.1: Initialization ~~~~~~~~~~~~~~ The DEFORM‑5 calculation is specified by setting ISSFUE = 0, ISSFU2 = 1, and IMETAL > 0 in the SAS4A/SASSYS‑1 input deck. (See :numref:`table-9.8.3-1` 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 :sasinp:`FLTPOW` and :sasinp:`FPDAYS`. If input variable :sasinp:`BURNFU` has been specified, then its numerical value is taken to be the cladding fluence in units of 10\ :sup:`22` neutrons/cm\ :sup:`2`; 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 :sasinp:`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 :sasinp:`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 :sasinp:`PLENL` and :sasinp:`RBRPL`), the fuel geometry (See :sasinp:`AXHI` and :sasinp:`ROUTFP`), the fuel porosity (See :sasinp:`PRSTY`), an assumed fill pressure of 10\ :sup:`5` Pa, an input initial pressure (See :sasinp:`P0GAS`) at the reference temperature (See :sasinp:`TR`), the ideal gas constant (See :sasinp:`RGASSI`) and the molecular weights of the fission and fill gases (See :sasinp:`FGMM` and :sasinp:`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-9.8.3-1: .. list-table:: DEFORM-5 Input Data :header-rows: 1 :align: center :widths: auto * - 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 - ‑ .. _section-9.8.3.2: Fuel/Cladding Eutectic Alloy Formation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Equation (:ref:`9.8.2-1`) is used to calculate the cladding penetration rate on the inner cladding surface, independent of the input-specified values of :sasinp:`IMETAL` and :sasinp:`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 :sasinp:`IRAPEN`; otherwise the rate is given by the exponential form in Eq. (:ref:`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, :sasinp:`TFSOL`\ (:sasinp:`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. (:ref:`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. .. _section-9.8.3.3: Fission Gas ~~~~~~~~~~~ On each time step, the fill and fission gas masses computed on the first time step, :numref:`section-9.8.3.1`, are used with the transient temperatures to set the time-dependent internal-cladding and internal-fuel pressures. If input variable :sasinp:`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 :sasinp:`IPORFG`, to estimate the impact of fuel density changes on porosity volume as the fuel changes temperature. These calculations are performed in subroutine FAILUR. .. _section-9.8.3.4: Cladding Strain ~~~~~~~~~~~~~~~ In the transient, subroutine STRANC computes the incremental cladding strains for each time step from the formulation in :numref:`section-9.8.2.3`. If input variable :sasinp:`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. .. _section-9.8.3.5: 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 :numref:`section-9.8.2.4`. The computed life fractions will be printed, but will not trigger cladding failure, and subsequent post‑failure model execution, unless the input value of :sasinp:`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 :sasinp:`FIRLIM`, :sasinp:`SECLIM`, :sasinp:`THRLIM`, :sasinp:`DTFAL1`, :sasinp:`DTFAL2`, :sasinp:`DTFAL3` and :sasinp:`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 :numref:`Chapter %s`). For :sasinp:`IGASRL` > 0, input variable :sasinp:`FRUPT`\ (1) contains the cladding life fraction for failure of all the pins in the channel. This failure computation is independent of MFAIL. .. _section-9.8.3.6: Printed Output ~~~~~~~~~~~~~~ DEFORM‑5 printed output is produced from subroutine OUTPT5 on a main time step frequency set by input variables :sasinp:`IPO` and :sasinp:`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.