KENO-5, SCALE-1 Module with Pn Scattering, Supergrouping, Diffusion Albedo Reflection

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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3. DESCRIPTION OF PROBLEM OR FUNCTION

KENO is a multigroup, Monte Carlo criticality code containing a special geometry package which allows easy description of systems composed of cylinders, spheres, and cuboids (rectangular parallelepipeds) arranged in any order with only one restriction. They cannot be rotated or translated. Each geometrical region must be described as completely enclosing all regions interior to it. For systems not describable using this special geometry package, the program can use the generalized geometry package (GEOM) developed for the O5R Monte Carlo code. It allows any system that can be described by a collection of planes and/or quadratic surfaces, arbitrarily oriented and intersecting in arbitrary fashion. The entire problem can be mocked up in generalized geometry, or one generalized geometry unit or box type can be used alone or in combination with standard KENO units or box types. Rectangular arrays of fissile units are allowed with or without external reflector regions. Output from KENO consists of keff for the system plus an estimate of its standard deviation and the leakage, absorption, and fissions for each energy group plus the totals for all groups. Flux as a function of energy group and region and fission densities as a function of region are optional output.

KENO-4: Added features include a neutron balance edit, PICTURE routines to checkthe input geometry, and a random number sequencing subroutine written in FORTRAN-4.

KENO is a multigroup, Monte Carlo criticality code containing a special geometry package which allows easy description of systems composed of cylinders, spheres, and cuboids (rectangular parallelepipeds) arranged in any order with only one restriction. They cannot be rotated or translated. Each geometrical region must be described as completely enclosing all regions interior to it. For systems not describable using this special geometry package, the program can use the generalized geometry package (GEOM) developed for the O5R Monte Carlo code. It allows any system that can be described by a collection of planes and/or quadratic surfaces, arbitrarily oriented and intersecting in arbitrary fashion. The entire problem can be mocked up in generalized geometry, or one generalized geometry unit or box type can be used alone or in combination with standard KENO units or box types. Rectangular arrays of fissile units are allowed with or without external reflector regions. Output from KENO consists of keff for the system plus an estimate of its standard deviation and the leakage, absorption, and fissions for each energy group plus the totals for all groups. Flux as a function of energy group and region and fission densities as a function of region are optional output.

KENO-4: Added features include a neutron balance edit, PICTURE routines to checkthe input geometry, and a random number sequencing subroutine written in FORTRAN-4.

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4. METHOD OF SOLUTION

The scattering treatment used in KENO assumes that the differential neutron scattering cross section can be represented by a P1 Legendre polynomial. Absorption of neutrons in KENO is not allowed. Instead, at each collision point of a neutron tracking history the weight of the neutron is reduced by the absorption probability. When the neutron weight has been reduced below a specified point for the region in which the collision occurs, Russian roulette is played to determine if the neutron's history is to be terminated at that point or if the neutron is to survive with an increased weight. Splitting of high-weight neutrons is allowed in order to minimize the variance in keff for systems with regions of widely varying average weigths.

The scattering treatment used in KENO assumes that the differential neutron scattering cross section can be represented by a P1 Legendre polynomial. Absorption of neutrons in KENO is not allowed. Instead, at each collision point of a neutron tracking history the weight of the neutron is reduced by the absorption probability. When the neutron weight has been reduced below a specified point for the region in which the collision occurs, Russian roulette is played to determine if the neutron's history is to be terminated at that point or if the neutron is to survive with an increased weight. Splitting of high-weight neutrons is allowed in order to minimize the variance in keff for systems with regions of widely varying average weigths.

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6. TYPICAL RUNNING TIME

KENO4 running times are highly problem- dependent. A bare 2x2x2 array of highly-enriched cylindrical units was executed on an IBM360/195. A total of 22,500 neutron histories were run in 0.281 minutes for a deviation of 0.52% in k-effective. A total 30,900 histories were run on an IBM3033 in 0.294 minutes. The same problem was run with a 6-inch paraffin reflector, tracking 18,600 histories for a deviation of 0.69% in keff in 2.249 minutes of 360/195 time. The same problem required 2.981 minutes on an IBM3033 to track 30.900 histories, yielding a deviation of 0.52%. The time required to execute a problem depends on the complexity of the geometry, the number of energy groups, and the type of materials in the problem. On an IBM3033 the sample problems require from 10 CPU seconds to 3 CPU minutes and on an IBM4331 from 2.7 to 60.9 CPU minutes. On a CDC CYBER170/875 and CYBER175 the sample problems require from 15 CP seconds to 5 CP minutes.

KENO4 running times are highly problem- dependent. A bare 2x2x2 array of highly-enriched cylindrical units was executed on an IBM360/195. A total of 22,500 neutron histories were run in 0.281 minutes for a deviation of 0.52% in k-effective. A total 30,900 histories were run on an IBM3033 in 0.294 minutes. The same problem was run with a 6-inch paraffin reflector, tracking 18,600 histories for a deviation of 0.69% in keff in 2.249 minutes of 360/195 time. The same problem required 2.981 minutes on an IBM3033 to track 30.900 histories, yielding a deviation of 0.52%. The time required to execute a problem depends on the complexity of the geometry, the number of energy groups, and the type of materials in the problem. On an IBM3033 the sample problems require from 10 CPU seconds to 3 CPU minutes and on an IBM4331 from 2.7 to 60.9 CPU minutes. On a CDC CYBER170/875 and CYBER175 the sample problems require from 15 CP seconds to 5 CP minutes.

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7. UNUSUAL FEATURES OF THE PROGRAM

KENO4 input is extensively checked for consistency and completeness. The geometry input is simple, easily describes arrays of units, allows the description of several units of different size and shape in the same problem, and uses multigroup cross sections. A restart capability is available, enabling the user to run a long problem in several short passes. A search option is available for altering the unit size or the spacing between units in order to achieve a predetermined value of keff.

KENO4 input is extensively checked for consistency and completeness. The geometry input is simple, easily describes arrays of units, allows the description of several units of different size and shape in the same problem, and uses multigroup cross sections. A restart capability is available, enabling the user to run a long problem in several short passes. A search option is available for altering the unit size or the spacing between units in order to achieve a predetermined value of keff.

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8. RELATED AND AUXILIARY PROGRAMS

Related codes include MORSE and O5R. Auxiliary programs which read the cross section, albedo, and weights library data and create binary files to be read by KENO4/S are included.

KENO4/S is a module of SCALE at ORNL. KENO4/S can read cross sections from an AMPX working format interface library in addition to the standard KENO4 format cross sections and ANISN format cross sections. HANDY is a program to aid in preparing O5R (generalized geometry) input for KENO4; GEOMCHK reads and checks both the standard KENO4 geometry and the generalized geometry (O5R) input available in KENO4. GEOMCHK can also generate two-dimensional printer plots of slices through the geometry. HANDY and GEOMCHK are included with the IBM version only.

Related codes include MORSE and O5R. Auxiliary programs which read the cross section, albedo, and weights library data and create binary files to be read by KENO4/S are included.

KENO4/S is a module of SCALE at ORNL. KENO4/S can read cross sections from an AMPX working format interface library in addition to the standard KENO4 format cross sections and ANISN format cross sections. HANDY is a program to aid in preparing O5R (generalized geometry) input for KENO4; GEOMCHK reads and checks both the standard KENO4 geometry and the generalized geometry (O5R) input available in KENO4. GEOMCHK can also generate two-dimensional printer plots of slices through the geometry. HANDY and GEOMCHK are included with the IBM version only.

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10. REFERENCES

- L.M. Petrie and N.F. Landers

KENO IV/S - An Improved Monte Carlo Criticality Program,

NUREG/CR-0200, Volume 2, Section F5 (ORNL/NUREG/CSD-2/V2), October 1981.

- GEOMCHK, KENO Geometry Checking Routine,

ORNL Note June 22, 1983.

- HANDY, ORNL Note, November 25, 1975, Revised December 6, 1985.

- KENO4/S, NESC No. 450.3033B, KENO4/S IBM Version Tape Description

and Implementation Information,

National Energy Software Center Note 88-84, June 30, 1988.

- KENO4/S, NESC No. 450.7600, KENO4/S CDC Version Tape Description

and Implementation Information,

National Energy Software Center Note 86-63, June 10, 1986.

- G.E. Whitesides and N. F. Cross

KENO - A Multigroup Monte Carlo Criticality Program,

CTC-5, September 10, 1969.

- KENO Data Guide

CTC-5 Errata pp. 21-32, September 1971.

- G.E. Whitesides

Adjoint Biasing in Monte Carlo Criticality Calculations,

Transactions of the American Nuclear Society, Vol. 2, No.1,

June 1968.

- J.R. Knight and L.M. Petrie

16 and 123 group Weighting Functions for KENO,

ORNL-TM-4660, November 1975.

- N.M. Greene, J.L. Lucius, W.E. Ford, III, J.E. White, R.Q. Wright, and L.M. Petrie

AMPX - A Modular Code System for Generating Coupled Multigroup

Neutron-Gamma Libraries from ENDF/B,

ORNL-TM-3706, March 1976.

- D.C. Irving and R.M. Freestone, Jr.

O5R, A General Purpose Monte Carlo Transport Code,

ORNL-3622, February 1965.

- G.R. Handley and J.N. McLeod

A User's Manual for HANDY (A FORTRAN IV Program for Calculating

Numerical Coefficients of the General Second-degree Equation in

Three Variables),

Y-1615, June 1968.

- L.M. Petrie and N.F. Landers

KENO IV/S - An Improved Monte Carlo Criticality Program,

NUREG/CR-0200, Volume 2, Section F5 (ORNL/NUREG/CSD-2/V2), October 1981.

- GEOMCHK, KENO Geometry Checking Routine,

ORNL Note June 22, 1983.

- HANDY, ORNL Note, November 25, 1975, Revised December 6, 1985.

- KENO4/S, NESC No. 450.3033B, KENO4/S IBM Version Tape Description

and Implementation Information,

National Energy Software Center Note 88-84, June 30, 1988.

- KENO4/S, NESC No. 450.7600, KENO4/S CDC Version Tape Description

and Implementation Information,

National Energy Software Center Note 86-63, June 10, 1986.

- G.E. Whitesides and N. F. Cross

KENO - A Multigroup Monte Carlo Criticality Program,

CTC-5, September 10, 1969.

- KENO Data Guide

CTC-5 Errata pp. 21-32, September 1971.

- G.E. Whitesides

Adjoint Biasing in Monte Carlo Criticality Calculations,

Transactions of the American Nuclear Society, Vol. 2, No.1,

June 1968.

- J.R. Knight and L.M. Petrie

16 and 123 group Weighting Functions for KENO,

ORNL-TM-4660, November 1975.

- N.M. Greene, J.L. Lucius, W.E. Ford, III, J.E. White, R.Q. Wright, and L.M. Petrie

AMPX - A Modular Code System for Generating Coupled Multigroup

Neutron-Gamma Libraries from ENDF/B,

ORNL-TM-3706, March 1976.

- D.C. Irving and R.M. Freestone, Jr.

O5R, A General Purpose Monte Carlo Transport Code,

ORNL-3622, February 1965.

- G.R. Handley and J.N. McLeod

A User's Manual for HANDY (A FORTRAN IV Program for Calculating

Numerical Coefficients of the General Second-degree Equation in

Three Variables),

Y-1615, June 1968.

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The cross section, albedo, and weights data are included for the sole purpose of allowing the sample problems to be run for instructional purposes and should not be assumed useful for any other purpose without close examination as to their applicability.

The cross section, albedo, and weights data are included for the sole purpose of allowing the sample problems to be run for instructional purposes and should not be assumed useful for any other purpose without close examination as to their applicability.

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Keywords: Monte Carlo method, adsorption, criticality, fission, lifetime, multigroup, reactivity, statistics, three-dimensional, transport theory, x-y-z.