Dr. John R. White
Chemical and Nuclear Engineering Department
University of Massachusetts Lowell
May 28, 1999

Much of the work on this project during May 1999 was focussed on the identification of a new reference LEU core configuration that retains the regulating rod in its current D9 location. Several candidate core configurations were studied last month -- see the April 1999 Progress Report. In particular, a 21-element core with 19 full fuel elements and 2 partial fuel assemblies was identified as the best configuration addressed to date. This configuration, which was referred to as leu212p5, has a full fuel element in D8 and a graphite reflector in the C8 and E8 positions. In addition, it has partial fuel elements in the B4 and F4 grid locations. A 2-D version of this core configuration has a computed excess reactivity of about 3.2% and a regulating rod worth of about 0.44. Both these values satisfy the design criteria that puts an upper limit on k-excess of between 4.5% and 5.0% and a lower limit of 0.35 for the worth of the regulating blade.

However, a major uncertainty in any 2-D computation is the choice of the buckling approximation used to estimate the neutron leakage in the direction not explicitly treated in the 2-D model. The computed k_eff is a direct function of the buckling approximation, and it can easily vary several percent depending upon the value of transverse buckling used in the VENTURE computations. In all the computation to date, a B² value of 0.0021 cm^-2 has been used. This value was obtained from the early HEU to LEU conversion studies documented in Ref. 1, and it comes from simple bare homogeneous reactor theory with a correction for the water reflector at the top and bottom of the core. In particular, the transverse buckling is computed from

where H is the active fuel height and is an estimate of the reflector savings. For the LEU fuel, the active fuel height is 59.69 cm (23.5 in) and Ref. 1 used an effective reflector savings of 4.5 cm. The value of computed using a simple correlation in Ref. 2 gives about 8 cm. However, this assumes a pure water reflector, and this value was reduced to account for the structural components in the upper and lower axial reflectors and to account for the control blades that are parked in the upper reflector. The relatively large reduction from 8.0 cm to 4.5 cm was justified by comparison to a 3-D Monte Carlo model discussed in Ref. 1.

As discussed in the last Progress Report, the difference between the computed k_eff values for the 2-D and 3-D VENTURE models from the current work is quite large (about 1.8), which suggests that the buckling approximation in the 2-D models should probably be adjusted. To facilitate a new series of computations, the leu212p5 configuration was renamed leu213. In addition, a 3-D model called leu313 was also developed that has the same fuel element layout as the leu213 2-D model. The multiplication factors for these 2-D and 3-D calculations were compared and the transverse buckling in the 2-D model was adjusted to bring the computed k_eff values closer together. After a few iterations, a new effective reflector savings of 7.0 cm was chosen since it gives a better comparison between the 2-D and 3-D models, yet it still accounts for the non-ideal conditions in the actual system. This reflector savings gives a transverse buckling of about 0.00182 cm^-2. This value of B² will be used for all subsequent LEU 2-D XY VENTURE computations.

A summary of the 2-D and 3-D k_eff results from the above study is given in Table I. The new B² of 0.00182 cm^-2 has clearly reduced the observed difference, but it has not eliminated the 2-D versus 3-D bias -- since a reflector savings much greater than 7.0 cm could not be justified. Although the B² change has reduced the bias, it clearly has not reduced the uncertainty in the 2-D calculations -- it has only re-normalized the computed k_eff to be more consistent with the 3-D result. We do expect, however, that this is a better approximation, and that the new 2-D estimate of k-excess will be much closer to reality.

However, a direct consequence of the 2-D buckling readjustment and the 3-D calculation in Table I is that the current 21-element leu213/leu313 configuration no longer represents a viable initial core because of the relatively large predicted k-excess. Thus, using the new buckling approximation, a series of 2-D computations was made that varied the location of the two partial fuel assemblies within the 21-element configuration. The worth of the regulating blade was calculated in the configurations with relatively low k-excess. In addition, a few 3-D computations were also performed for the more promising configurations.

The data from this latest sensitivity study are presented in Table II. The movement of the partial elements within rows B and F (outside the control blades) have little effect, and a similar observation is valid for partial fuel placed in column 3 -- thus, configurations leu213, leu213a, and leu213b are all too reactive. However, moving the partial elements into the core center region around the central flux trap in location D5 gives a sizable reduction in the computed k-excess. Thus, the leu213c, leu213d, and leu213e configurations appear quite feasible from both the beginning-of-life (BOL) excess reactivity requirement and the minimum regulating blade worth criterion.

From Table II, it appears that the leu213d/leu313d layout may be the best configuration for the BOL LEU core. This configuration should have an initial excess reactivity of between 3.2% and 3.7%. Although all three configurations (leu213c, leu213d, and leu213e) are well within the k-excess limit, the leu213d/leu313d core allows operation of the facility with the control blades nearer the top of the core. This tends to reduce blade shadowing of the experimental facilities and gives less flux tilting towards the bottom of the core (due to less blade insertion). Thus, this configuration appears to be the best candidate for the reference BOL LEU core. A 2-D midplane material map showing the arrangement of full and partial fuel elements and other components within the 9x7 grid is given below in Fig. 1. It is recommended that this arrangement become the new proposed reference LEU core with the regulating rod in the D9 position. This core arrangement will be studied in detail over the next few months in preparation for initial loading of the LEU fuel in early Fall 1999.

*NOTE: During review of these results, a minor error in the 3-D model was detected; a radiation basket is located in grid position G5 instead of a graphite reflector. This error is consistent among all the 3-D models, and it should lead to a slight decrease in the computed k_eff value relative to the desired configuration. Thus, all the values listed here should increase slightly when the fix is made.

1. R. S. Freeman, "Neutronic Analysis for the Conversion of the ULR from High Enriched Uranium to Low Enriched Uranium Fuel," MS Thesis, Nuclear Engineering, University of Massachusetts Lowell (1991).
2. J. R. Lamarsh, Introduction to Nuclear Engineering, 2^nd Edition, Addison-Wesley Publishing Company, Inc., Reading MA (1983).

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