**1. NAME AND TITLE**

TRD-3: Two-Dimensional Removal-Diffusion Neutron Shielding Code System.

TRD-1 calculated only neutron flux in two-dimensional rectangular coordinates (X-Y). The second version, TRD-2, was developed in cylindrical coordinates (R-Z) for calculating the neutron flux around nuclear power reactors. TRD-3 adds the function of gamma-ray flux calculation to TRD-2.

**2. CONTRIBUTOR**

Energy Research Laboratory, Hitachi, Ltd., Hitachi-shi, Ibaraki-ken, Japan.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 3033.

**4. NATURE OF PROBLEM SOLVED**

TRD-3 calculates neutron and gamma-ray flux distributions in and/or out of the reactor core.

**5. METHOD OF SOLUTION**

The neutron flux is calculated by the removal-diffusion method which divides the neutron flux into a removal flux and a diffusion flux. The removal portion is designated as the unscattered contribution of neutrons which come from the fission source. The neutrons scattered in the materials are removed from the removal flux and taken into the source of the diffusion equation for neutron balances. Gamma-ray transport is computed with use of buildup factors. Gamma-ray sources include fission and neutron capture.

The point kernel method is used to calculate the removal flux and Gaussian integration is adopted to calculate the total contribution from each source point in the source region. This integral method can calculate accurate flux outside the source region but not in the source region where the calculation is significantly affected by Gaussian mesh numbers. For this reason, a new method equivalent sphere integration was developed. Using this new method, each source element is considered to be a sphere with the same volume of original source element, and this allows the contributions from spheres to be calculated using an analytical function.

In order to obtain the diffusion neutron flux, a finite difference equation is solved by the ADI method.

**6. RESTRICTIONS OR LIMITATIONS**

The maximum values of each item are as follows:

a) elements: 18

b) materials: 20

c) mesh points: 60 x 60

d) regions: 10 x 10

**7. TYPICAL RUNNING TIME**

Computing time has varied from less than 1 minute to 1 hour on the IBM 3033, depending upon calculation mesh points and integral mesh points. In the case of 2091 calculation mesh points and 621 integral mesh points, computing time is 18.4 minutes of CPU time.

The estimated running time for the 5 sample problems on the IBM 3033 is 96 seconds.

**8. COMPUTER HARDWARE REQUIREMENTS**

TRD-3 is operable on the IBM 3033. It requires a minimum of 85 K words and uses two tape or disc auxiliary storage units.

A plotter is used as auxiliary equipment. If a plotter is not available, set the IIMAP = O in input data.

The clock is sampled.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required. Standard operation is used. Overlay is required.

**10. REFERENCES**

**a. Included in package:**

Energy Research Laboratory, Hitachi Ltd., Hitachi-shi, Ibaraki, Japan, "TRD-3, Two-Dimensional Removal Diffusion Code for Shielding Calculations."

NEA Data Bank, "Program TRD-3, Note from the NEA Data Bank, The Subroutine 'INPUT1' Reads the Library Data From Unit 5 Before the Input Data" (March 1982).

**b. Background information:**

S. Uchida et al., "Experimental Investigation of Neutrons Penetrating through Two-Dimensional
Heterogeneous Structure Consisting of Graphite and Aluminum," *J. Nucl. Sci. Tech.*, 15, 222-229
(1978).

S. Uchida et al., "Experimental Investigation of Neutrons Streaming through the Grid-Plate Shield
of Liquid Metal Fast Breeder Reactors," *Nucl. Sci. Eng.*, 65, 155-159 (1978).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains the source codes and sample problem input and output.

**12. DATE OF ABSTRACT**

January 1982; reviewed June 1983.

**KEYWORDS: ** TWO-DIMENSIONS; NEUTRON; GAMMA-RAY; REMOVAL-DIFFUSION;
MULTIGROUP