**1. NAME AND TITLE**

KDLIBE: Kernel-Diffusion Shielding Analysis System.

AUXILIARY ROUTINES

QADRD: Kernel Integration - Uncollided Flux Calculation.

SURF: Conical and Plane Surface Scattering Calculation.

RAMP: Multigroup Source Term Data Generator.

GAMMIX: Microscopic Gamma Production Cross Section Generator.

ZIP III: Generalized Nuclear Analysis.

REORG: Secondary Gamma Source Data Generator.

QADRR: Kernel Integration Dose Rate Calculation.

UPDONC: Cross Section Update.

GEORGE: Multigroup One-Dimensional Diffusion Calculation (Linkage of C-VII, Multigroup Constant Generator, and F-N, Multigroup, Multiregion One-Dimension Neutron Diffusion Calculation).

DATA LIBRARIES

Neutron Cross Sections.

Gamma-Ray Cross Sections.

**2. CONTRIBUTOR**

Nuclear Systems Programs, Space Systems, Missile and Space Division, General Electric Company, Cincinnati, Ohio.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; IBM 360/91/75.

**4. NATURE OF PROBLEM SOLVED**

KDLIBE is an automated kernel-diffusion analysis sequence, with associated nuclear data, which was developed for shield nuclear analysis. The method is suitable for many preliminary and parametric shielding calculations. The sequence and data have been applied to the analysis of titanium hydride, and lithium hydride-Hevimet shields for space nuclear power reactors and lead-water shields for undersea nuclear reactors.

**5. METHOD OF SOLUTION**

KDLIBE is a kernel-diffusion code system composed of 9 separate routines, each of which may be run independently. Six of these may be run as a removal-diffusion sequence with certain data passed to the succeeding routine by tape or disc. This sequence may be broken at any time and restarted on output card option. SURF, ZIP III, and UPDONC are independent; QADRD, RAMP, GEORGE, GAMMIX, REORG, and QADRR make up the removal-diffusion sequence.

The basic idea of the removal-diffusion sequence is as follows. A reasonably accurate flux calculation can be made by using the transport kernel to calculate the uncollided flux due to the primary source and diffusion theory to calculate the collided flux, where the source for the diffusion theory calculation is obtained from the uncollided flux and the zeroeth moment scatter-transfer matrix in each material.

QADRD combines the point-to-point attenuation function with summation over source regions. It is derived from QAD-P5 (CCC-48) by replacing all optional material attenuation functions by a simple exponential function having an energy-dependent neutron removal cross section. Uncollided (removal) neutron fluxes are computed and stored on tape or disc for use in RAMP's multigroup external source calculation to get input for GEORGE and for combination with GEORGE diffusion fluxes in REORG.

RAMP combines the uncollided multigroup flux from QADRD with multigroup scatter transfer cross sections to produce multigroup (external) source terms for input to GEORGE multigroup diffusion calculation.

GEORGE is a linkage of 2 routines, each of which may be run independently. C-VII performs a normal mode (space-independent buckling), continuous slowing down calculation using 19 non-thermal group cross sections and one thermal group. Multigroup cross sections in 1 to 19 groups for each of several reactor regions are produced for use in the F-N part of GEORGE, which solves the 1-dimensional multigroup diffusion equation with transverse buckling to account for leakage perpendicular to the direction of computation. Output includes reactivity, flux, and power distributions. C-VII employs an analytical solution.

GAMMIX processes input microscopic gamma production cross sections into macroscopic (mixed) composition cross sections for input to REORG. Up to 20 incident neutron flux groups and 30 gamma source groups are allowed, and a total of 20 microscopic cross sections may be computed. The mixed data is weighted by atom densities and g-factors.

REORG combines the collided (diffusion) fluxes from GEORGE with the uncollided fluxes from QADRD and uses these total fluxes (in the diffusion energy group structure) to compute secondary gamma sources for use in QADRD. Compatibility of lattice points and group structure between the collided and uncollided is achieved through interpolation/extrapolation and collapsing.

QADRR was developed from QAD-P5 (CCC-48), incorporating the material attenuation functions from 14-O (CCC-1) for the calculation of neutron and gamma-ray dose and energy absorption rates. The point kernel method combines the use of point-to-point attenuation functions with summation over source regions.

SURF calculates neutron and gamma-ray dose rates and flux distribution in energy at unshielded receiver points due to direct beam and once-scattered radiation from angularly anisotropic point sources.

ZIP III contains most of the same algorithms in GEORGE and uses the same data library, and is specially designed for cylindrical calculations limited to 2 or 3 diffusion groups. Its principal use is for reactor survey and parametric calculations and for determining the bare-equivalent transverse dimensions for more detailed 1-dimensional cylindrical calculations using GEORGE or multigroup transport. Output includes matched savings, reactivity, and radial and axial power distributions.

UPDONC prepares, duplicates, updates by correction, addition or deletion, punches, graphs, and edits the nuclear data tape (NDT) used by GEORGE and ZIP III.

**6. RESTRICTIONS OR LIMITATIONS**

Limits implied by core storage and code dimensions are outlined in the description of the input of each part of the code system.

**7. TYPICAL RUNNING TIME**

Estimated running time in seconds of the packaged sample problems and core storage required (IBM 360/91) are: UPDONC, .60 sec., 118K; QADRD, .80 sec., 128K; RAMP, 2.2 sec., 192K; GAMMIX, .37 sec., 130K; GEORGE, 2.73 sec., 260K run as an overlay; REORG, 2.18 sec., 206K; QADRR, 12.8 sec., 172K; SURF, 6.56 sec., 162K; and ZIP III, 15.16 sec., 236K.

**8. COMPUTER HARDWARE REQUIREMENTS**

The system was originally designed for the GE 635 and made operable on the IBM 360. Maximum number of tape units or direct access devices: 3 plus input-output.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The packaged codes were run on the IBM 360/75/91 Operating System using OS-360 FORTRAN H compiler. GEORGE requires the overlay feature. UPDONC requires special cross sections which are included in the package.

**10. REFERENCES**

W. B. Henderson and W. E. Edwards, "NSP Kernel-Diffusion Library, KDLIBE, NS0910 (User's Manual)," GESP-226 (1970).

P. G. Fischer, F. D. Wenstrup, and R. A. Pastore, "Program C5 - Direct and Adjoint Bare Reactor Program - Multigroup Constant Generator," XDC-59-6-220 (May 1959).

P. G. Fischer, "Multi-group, Multi-region, One Space Dimension Neutron Diffusion Theory Calculation - Program F-N (ANP 308)," XDC-60-3-68 (January 1960).

J. E. MacDonald, "Conical and Plane Surface Scattering Program - SURF," GEMP-582 (February 1968).

M. R. Edwards, "The UPDONC Code," GEMP-456 (December 1966).

W. E. Edwards, "Shield Kernel-Diffusion Analysis," GEMP-599 (March 1968).

J. R. Lilley, "Computer Code HFN - Multigroup, Multiregion Neutron Diffusion Theory in One Space Dimension," HW-71545 (November 1961).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source codes, data libraries and sample problem input and output.

**12. DATE OF ABSTRACT**

August 1971; revised December 1984.

**KEYWORDS:** KERNEL; SPINNEY METHOD; ALBERT-WELTON; TWO-COMPONENT;
SINGLE SCATTERING; NEUTRON; GAMMA-RAY; REMOVAL DIFFUSION