Parametric Analysis on the Effect of Measures

This chapter describes parametric analysis methodology and analysis results for Doppler feedback enhancement and burn-up reactivity swing reduction.

Parametric Analysis Methodology

A hypothetical 300 MWe fast reactor core was used for the parametric survey to enhance Doppler feedback and burn-up reactivity swing. Table 15.1 and Fig. 15.2 show the assumed core conditions and RZ geometry for parametric survey, respectively. The calculation methods were as follows. Core burn-up characteristics were analyzed with the burnup calculation code STANBRE [13]. Reactivity coefficients were analyzed using the diffusion calculation code DIF3D [14]. The effective cross sections used in these calculations were obtained by the cell calculation code SLAROM-UF [15], based upon 70 group cross sections from JENDL-4.0 [16] with a self-shielding factor table as a function of background cross section. This method for the production of the effective cross sections is considered to be adequate to take into account the influence of each diluting material upon the self-shielding effect of heavy isotopes for the parametric study. Concerning material compositions, a homogeneous model of fuel, diluent, and spectrum moderator was used.

To begin with, in the survey to improve Doppler feedback, 21 elements to enhance resonance absorption were evaluated as a diluent material for the TRU alloy: Cr, Mn, Fe, Ni, Nb, Mo, Tc, Ru, Rh, Pd, Nd, Sm, Gd, Tb, Dy, Er, Tm, Ta, W, Os, and Au. Moreover, the effect by neutron moderators such as BeO, 7Li2O, 11B4C (100 % enrichment of 11B was assumed), and ZrH2 were investigated to clarify the impact against Doppler feedback by neutron spectrum softening. To compare the Doppler effect enhancement of various diluent materials and neutron spectrum moderators in a simple manner, each material was hypothetically added to TRU-10wt%Zr alloy. The amount of each material added was adjusted case by case to maintain 1.0 of k-effective at the end of cycle.

Next, in the evaluation to decrease the burn-up swing, the effects of the measures taken to increase the fissile amount at the beginning of the cycle were studied. The effects on burn-up reactivity swing were evaluated by reducing the core height, installing B4C shield at core peripheral, and increasing the number of refueling batches, which all lead to increase of the fissile amount at the beginning of the cycle.

Last, reflecting the results obtained by the parameter surveys, an optimal uranium-free TRU metallic fuel core was specified, and its feasibility in light of Doppler feedback and burn-up swing was evaluated by core performance analysis.

Analysis Results for Doppler Feedback Enhancement

The effects of measures taken to enhance Doppler feedback, that is, diluent and spectrum moderator, are evaluated in this section.

As shown in Fig. 15.3, 6 among 21 diluent materials are found to enhance Doppler feedback more than Zr, the typical metallic fuel alloy. Although Nb, Ni, W, Mo, Fe, and Cr have greater potential to enhance Doppler feedback than Zr, there are some deficiencies that cannot be ignored. First, the melting points of Pu-Ni alloy and Pu-Fe alloy are below 500 oC, which is too low for nuclear fuel [17]. Second, the melting point of Pu-W alloy is too high to fabricate fuel by injection casting because the melting temperature of W itself is above 3,000 oC.

15 Development of Uranium-Free TRU Metallic Fuel Fast Reactor Core 161

Fig. 15.3 Doppler coefficients associated with major diluent elements

Third, the allowable contents of Mo and Nb in the metal fuel alloy are too small to enhance the Doppler coefficients, which are 5 wt% and 3 wt%, respectively, under the condition to maintain their melting temperatures below 1,200 oC to prevent Am vaporization during injection casting [18]. Finally, the number of past experiences with Cr, for example, irradiation testing of Pu-Cr alloy, is less than enough to employ it as a diluent material for uranium-free fuel. Consequently, Zr was chosen as the fuel diluent material.

Then, as shown in Fig. 15.4, the absolute value of the negative Doppler coefficient remarkably increased by introducing a spectrum moderator such as BeO, 11B4C, or ZrH2. The adoption of ZrH2, however, may cause dissociation of hydrogen upon accident. Besides, the usage of 11B4C is costly because almost 100 % enrichment of 11B is necessary to enhance Doppler feedback significantly. Therefore, BeO was selected as a moderator material for the uranium-free core.

Analysis Results for Burnup Reactivity Swing Reduction

This section evaluates the effects of measures taken to reduce burnup reactivity swing of the uranium-free TRU metallic fuel core. In the parameter surveys, the operation cycle length, that is, 150 days, the core volume, and the core power density were kept constant to compare the effect of each countermeasure. The average fuel burnup was also kept constant, save for the survey of the number

162 K. Ishii et al.

Fig. 15.4 Doppler coefficients associated with neutron spectrum moderator

Table 15.2 Results of burn-up reactivity swing reduction


Reduction (%)

Core height changed from 93 to 65 cm


Peripheral S/A reflector changed to B4C absorber


Number of refueling batches changed from 5 to 7


of refueling batches. The adjusting parameter to increase the fissile amount was the zirconium content in TRU-Zr alloy fuel to keep k-effective ΒΌ 1.0 at the end of the cycle.

Table 15.2 shows the summary of the analysis results. The reduction of the core

height from 93 cm to 65 cm resulted in a 12 % decrease of burn-up reactivity swing. The introduction of a B4C shield, where natural boron was assumed, at the core periphery region resulted in only about a 5 % decrease in burn-up reactivity swing. On the other hand, the penalty of this countermeasure is the increase of core power peaking because the leakage of neutrons from the core surface increases. Hence, this measure was not adopted in the subsequent core design. Regarding the effect of the number of refueling batches, the larger is the number of refueling batches, the smaller the burn-up reactivity swing becomes. The effect was approximately a 5 % decrease in burnup reactivity swing for a 40 % increase in the number of refueling batches. This measure was not adopted in the subsequent core design because its effect on the burn-up reactivity swing is small and it leads to significant increase of core power peaking because of the increased difference of burn-up between most burnt fuel and fresh fuel.

Table 15.3 Specification of the uranium-free TRU metallic core



Reactor thermal power

714 MW

Operation cycle length

150 days

Fuel type

TRU-Zr alloy

Number of fuel pins per S/A


Fuel pin diameter

0.48 cm

Core diameter

250 cm

Core height

65 cm

Spectrum moderator

BeO pins in Fuel S/A (number of pins, 196)

TRU composition

LWR discharged

10 years cooled

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