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1. NAME AND TITLE**

FRANCO: Finite Element Fuel Rod Analysis Code System.

**2. CONTRIBUTOR**

Penn State University, University Park, Pennsylvania.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; IBM PC, IBM RS/6000 and Sun (P00363/MNYCP/00).

**4. NATURE OF PROBLEM SOLVED**

The FRANCO code is a quasi-static two-dimensional fuel rod analysis code, that calculates the fuel temperature and material deformation as a function of heat generation rate. Both solid and annular fuel configurations are modeled.

**5. METHOD OF SOLUTION**

FRANCO uses two-dimensional finite element theory and applications for mechanical deformation and heat conduction, and determines the temperature distribution from the fuel center to the coolant adjacent to the clad at a position along the fuel rod axis. FRANCO calculates the average temperature of each radial division, the nodal displacement, and strain and stress within the fuel pellet and clad. The principal stresses, which represent maximum and minimum stresses within an element, result from Mohr's circle relationship between normal stresses. FRANCO is capable of predicting the thermo-mechanical behavior in the radial direction of a single fuel rod for both boiling water reactors (BWR's) and pressurized water reactors (PWR's). The cross sectional plane geometry of fuel rod is modeled using three-node constant strain triangular finite elements, and both thermal and mechanical solutions are computed with a same finite element configuration. The local linear heat generation rate is modeled as a uniform heat source in a fuel pellet, and the coolant temperature and heat transfer coefficient are applied as known boundary conditions at the boundary of the cladding surface. The total load to form the global force vector consists of the thermal load that results form thermal expansion of the material and the mechanical load exerted by pressure. FRANCO assumes the fuel-cladding gap region to be conductive material in order to simplify the analysis, and this gap is simulated by either an open gap or a closed gap model. A time-dependent problem can be simulated by FRANCO using quasi-static analysis when time-dependent parameters are provided. FRANCO can treat a steady-state or mild transient condition as a time-independent problem, where time-dependent parameters are input as "snap shots." Consequently, the FRANCO code is able to run faster and easier compared to other industrial codes with comparable results; and hence, FRANCO is useful in analyzing the fuel element performance as a first cut or scoping tool.

**6. RESTRICTIONS OR LIMITATIONS**

FRANCO analyzes only a quarter of fuel rod cross-sectional area because azimuthal symmetric geometry is assumed for fuel pellet, gap, and clad. Fuel densification, swelling, and relocation are not considered in FRANCO, but a fuel relocation model can be considered by making an assumption about the reduced gap size. A smaller gap size rather than as-manufactured gap size were used in some of the FRANCO benchmark problems to account for the effect of fuel relocation. FRANCO models the elastic deformation of fuel and cladding, but not plastic deformation. Gas thermal conductivity is used as a material property input because the gap region is assumed to be a conductive material like the fuel and clad. FRANCO handles steady-state conditions and mild transient power changes.

**7. TYPICAL RUNNING TIME**

The FRANCO code (PFRANCO.EXE for Solid Fuel Analysis, and HFRANCO.EXE for Hollowed Fuel Analysis) is written in the WATFOR77 language for IBM-PC and mainframe executions. Executions of the code sample decks take 3-8 minutes on a 386 25 MHZ environment, and less than 4 minutes on 486 IBM and faster CPUs.

**8. COMPUTER HARDWARE REQUIREMENTS**

FRANCO runs on IBM personal computers and mainframes. It also runs on IBM RS/6000 and Sun workstations.

**9. COMPUTER SOFTWARE REQUIREMENTS**

FRANCO is written in WATFOR77, and the WATCOM compiler was used to build the IBM PC executables included in the package. At RSICC the packaged executables were tested on an IBM PC 486/DX2 66 and on an IBM Pentium under MS-DOS as bundled with Windows 95. FRANCO was also tested using the Lahey LF90 compiler (Version 1.10h) under MS-DOS as bundled with Windows 95 on an IBM PC 486. The Fortran sources were also compiled using the GNU F77 compiler Version 2.7.2 under Slackware Linux 2.0 on an IBM Pentium (60MHz).

**10. REFERENCES**

a. included in the package:

Kwangho Lee, "Evaluation of the Finite Element Fuel Rod Analysis Code (FRANCO)," Penn State University Master Thesis (December 1994).

b. background information:

M. A. Feltus and Kwangho Lee, "Evaluation of the FRANCO Finite Element Fuel Rod
Analysis Code," *Ann. Nucl. Energy 23,* pp 553-565, (1996).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document in (10.a) and one 1.44 DS/HD 3.5-in. diskette written in self-extracting compressed DOS files which include the FRANCO source, PC executables, test cases and documentation.

**12. DATE OF ABSTRACT**

October 1996.

** KEYWORDS:** CYLINDRICAL GEOMETRY; HEAT TRANSFER; MICROCOMPUTER