Argonne National Laboratory
Reduced Enrichment for Research and Test Reactors
Nuclear Science and Engineering Division at Argonne
U.S. Department of Energy

RERTR Publications:
Analysis Methods for Thermal Research and Test Reactors



M. M. Bretscher
RERTR Program

Argonne National Laboratory
Argonne, IL 60439-4841 USA

February 1997


Simple diffusion theory cannot be used to evaluate control rod worths in thermal reactors because of steep flux gradients that occur within the absorber material. However, reliable control rod worths can be calculated within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters or if group-dependent current-to-flux ratios are specified on the absorber surface.

For thin slab absorbers the effective diffusion parameters are functions of a pair of blackness coefficients. Methods for calculating these blackness coefficients in the P1, P3 and P5 approximations, with and without scattering, are discussed, and equations for the corresponding mesh-dependent effective diffusion parameters are derived.

For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is presented.

An alternate method for calculating control rod worths isolates the absorber from the diffusion-theory calculation by specifying group-dependent current-to-flux ratios on the absorber surface. Neutron transport calculations are used to determine these current-to-flux ratio internal boundary conditions subject to limits set by radius-dependent black absorber rods.

These methods are illustrated for a number of absorber materials and geometries. Computed control rod worths are compared with detailed Monte Carlo calculations and, where possible, with experimental measurements. In general, control rod worths based on these diffusion-theory methods are found to be consistent with those from Monte Carlo calculations and with measured values.


PDF version available
This document, " Computing Control Rod Worths in Thermal Research Reactors Fuel ", ANL/RERTR/TM-29, February 1997, is available in is available in PDF format.
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Manuel M. Bretscher
Argonne National Laboratory 362
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This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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