NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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PHENIX | NESC0454/01 | Tested | 01-AUG-1979 |

Machines used:

Package ID | Orig. computer | Test computer |
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NESC0454/01 | CDC 7600 | CDC 7600 |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

PHENIX is a two-dimensional, multigroup, diffusion-burnup-refueling code for use with fast reactors. The code is designed primarily for fuel-cycle analysis of fast reactors and can be used to calculate the detailed burnup and refueling history of fast breeder reactor concepts having any generalized fractional batch reloading scheme. Either ordinary keff calculations or searches on material concentration or region dimensions can be performed at any time during the burnup history. The complete fuel cycle history can be calculated in one run, or the individual burnup intervals can be treated separately. The refueling option of the code accounts for the spatial flux shifts over the reactor lifetime in the calculation of fuel discharge.

PHENIX is a two-dimensional, multigroup, diffusion-burnup-refueling code for use with fast reactors. The code is designed primarily for fuel-cycle analysis of fast reactors and can be used to calculate the detailed burnup and refueling history of fast breeder reactor concepts having any generalized fractional batch reloading scheme. Either ordinary keff calculations or searches on material concentration or region dimensions can be performed at any time during the burnup history. The complete fuel cycle history can be calculated in one run, or the individual burnup intervals can be treated separately. The refueling option of the code accounts for the spatial flux shifts over the reactor lifetime in the calculation of fuel discharge.

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4. METHOD OF SOLUTION

Eigenvalues are computed by standard source- iteration techniques, with group rebalancing, successive line overrelaxation, and fission-source overrelaxation used to accelerate convergence. These methods are used in the two-dimensional diffusion theory code 2DB (NESC Abstract 325) and are incorporated in PHENIX. However, several basic differences exist between the 2DB methods and those used in PHENIX. In PHENIX, a sinusoidal initial flux guess can be used in which the code generates the appropriate values for the flux at each mesh point for any combination of reflective and vacuum boundary conditions. Additionally in PHENIX, the line inversion can be performed by rows (radial), columns (axial), or by alternating the direction from one mesh sweep to the next. Based on experiments with different core geometries and different combinations of boundary conditions, the code will determine the best direction by considering the boundary conditions together with the average axial and radial mesh spacing. The concentration search calculation has also been changed to include the simultaneous addition or removal of any combination of materials in any combination of reactor zones. The performance of convergence tests and calculation of new eigenvalues in search problems are based on techniques used in the Los Alamos SN codes DTF4 (NESC Abstract 209) and 2DF (NESC Abstract 173).

Burnup is performed by PHENIX using zone-averaged total fluxes and zone- and group-averaged cross sections as in 2DB. Each input burnup time-step is arbitrarily divided into 10 smaller time-steps and the burnup equation is then solved as a march-out problem using the smaller time-steps. A constant total power constraint is used to adjust the magnitude of the fluxes at the end of each subdivided time-step.

With the fractional batch refueling scheme used in PHENIX, the fuel fraction with the greatest burnup is discharged. This discharge is calculated by actually burning initially clean fuel over its period of residence in the reactor using the appropriate zone- averaged total fluxes and zone-group-averaged cross sections from previous burnup intervals. Refueling is then accomplished by subtracting the discharge-atom density from the homogenized-region atom density and adding the appropriate clean-fuel atom density. The principal advantage of this refueling technique is the requirement to explicitly tag each fuel isotope only once per region.

Eigenvalues are computed by standard source- iteration techniques, with group rebalancing, successive line overrelaxation, and fission-source overrelaxation used to accelerate convergence. These methods are used in the two-dimensional diffusion theory code 2DB (NESC Abstract 325) and are incorporated in PHENIX. However, several basic differences exist between the 2DB methods and those used in PHENIX. In PHENIX, a sinusoidal initial flux guess can be used in which the code generates the appropriate values for the flux at each mesh point for any combination of reflective and vacuum boundary conditions. Additionally in PHENIX, the line inversion can be performed by rows (radial), columns (axial), or by alternating the direction from one mesh sweep to the next. Based on experiments with different core geometries and different combinations of boundary conditions, the code will determine the best direction by considering the boundary conditions together with the average axial and radial mesh spacing. The concentration search calculation has also been changed to include the simultaneous addition or removal of any combination of materials in any combination of reactor zones. The performance of convergence tests and calculation of new eigenvalues in search problems are based on techniques used in the Los Alamos SN codes DTF4 (NESC Abstract 209) and 2DF (NESC Abstract 173).

Burnup is performed by PHENIX using zone-averaged total fluxes and zone- and group-averaged cross sections as in 2DB. Each input burnup time-step is arbitrarily divided into 10 smaller time-steps and the burnup equation is then solved as a march-out problem using the smaller time-steps. A constant total power constraint is used to adjust the magnitude of the fluxes at the end of each subdivided time-step.

With the fractional batch refueling scheme used in PHENIX, the fuel fraction with the greatest burnup is discharged. This discharge is calculated by actually burning initially clean fuel over its period of residence in the reactor using the appropriate zone- averaged total fluxes and zone-group-averaged cross sections from previous burnup intervals. Refueling is then accomplished by subtracting the discharge-atom density from the homogenized-region atom density and adding the appropriate clean-fuel atom density. The principal advantage of this refueling technique is the requirement to explicitly tag each fuel isotope only once per region.

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6. TYPICAL RUNNING TIME

A straight keff calculation in r-z geometry with 8 energy groups and 900 mesh points requires 40 seconds. If the same problem is carried out over the complete cycle of the code, for the first burnup interval (clean reactor, sinusoidal flux guess), running time is about 75 seconds. Each subsequent burnup interval requires 60 to 65 seconds for the same calculational sequence. The number of burnup intervals required to reach equilibrium is a direct function of the particular fractional batch refueling scheme. Thus, if the reactor requires 5 burnup intervals to reach equilibrium from the clean configuration, the total running time is between 5 and 6 minutes.

A straight keff calculation in r-z geometry with 8 energy groups and 900 mesh points requires 40 seconds. If the same problem is carried out over the complete cycle of the code, for the first burnup interval (clean reactor, sinusoidal flux guess), running time is about 75 seconds. Each subsequent burnup interval requires 60 to 65 seconds for the same calculational sequence. The number of burnup intervals required to reach equilibrium is a direct function of the particular fractional batch refueling scheme. Thus, if the reactor requires 5 burnup intervals to reach equilibrium from the clean configuration, the total running time is between 5 and 6 minutes.

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10. REFERENCES

R. Douglas O'Dell, Thomas J. Hirons, PHENIX, A Two-

dimensional Diffusion-Burnup-Refueling Code, LA-4231, April 3,

1970, and Supplement.

Thomas J. Hirons and R. Douglas O'Dell, Calculational

Modeling Effects on Fast Breeder Fuel-cycle Analysis, LA-4187,

April 1969.

Thomas J. Hirons and R. Douglas O'Dell, Calculational

Models for Fast Reactor Fuel-Cycle Analysis, Nuclear Applications

and Technology, Vol. 9, p. 93, July 1970.

W. W. Little, Jr. and R. W. Hardie, 2DB User's

Manual, BNWL-831, Rev. 1, February 1969.

K. D. Lathrop, DTF-IV, A FORTRAN-IV Program for

Solving the Multigroup Transport Equation with Anisotropic

Scattering, LA-3373, July 15, 1965.

W. H. Hannum and B. M. Carmichael, DPC, A Two-

dimensional Data Preparation Code, LA-3427-MS, February 3, 1965.

B. J. Toppel, A. L. Rago, and D. M. O'Shea, MC**2, A

Code to Calculate Multigroup Cross Sections, ANL-7318, June 1967.

R. Douglas O'Dell, Thomas J. Hirons, PHENIX, A Two-

dimensional Diffusion-Burnup-Refueling Code, LA-4231, April 3,

1970, and Supplement.

Thomas J. Hirons and R. Douglas O'Dell, Calculational

Modeling Effects on Fast Breeder Fuel-cycle Analysis, LA-4187,

April 1969.

Thomas J. Hirons and R. Douglas O'Dell, Calculational

Models for Fast Reactor Fuel-Cycle Analysis, Nuclear Applications

and Technology, Vol. 9, p. 93, July 1970.

W. W. Little, Jr. and R. W. Hardie, 2DB User's

Manual, BNWL-831, Rev. 1, February 1969.

K. D. Lathrop, DTF-IV, A FORTRAN-IV Program for

Solving the Multigroup Transport Equation with Anisotropic

Scattering, LA-3373, July 15, 1965.

W. H. Hannum and B. M. Carmichael, DPC, A Two-

dimensional Data Preparation Code, LA-3427-MS, February 3, 1965.

B. J. Toppel, A. L. Rago, and D. M. O'Shea, MC**2, A

Code to Calculate Multigroup Cross Sections, ANL-7318, June 1967.

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11. MACHINE REQUIREMENTS

65K memory, 1 random-access storage device (disk), and 2 magnetic tape units. If cross sections are input from cards, only one tape unit is required. The other tape unit is used for flux guesses or dumps (if desired), and to store burnup data needed for the refueling portion of the program.

65K memory, 1 random-access storage device (disk), and 2 magnetic tape units. If cross sections are input from cards, only one tape unit is required. The other tape unit is used for flux guesses or dumps (if desired), and to store burnup data needed for the refueling portion of the program.

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NESC0454/01

File name | File description | Records |
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NESC0454_01.001 | SAMPLE PROGRAM (F4,EBCDIC) | 3518 |

NESC0454_01.002 | SAMPLE INPUT DATA | 103 |

NESC0454_01.003 | SAMPLE OUTPUT | 1552 |

Keywords: depletion, diffusion, fast reactors, fuel cycle, multigroup, two-dimensional.