instability analysis on xenon spatial oscillation in a candu-6 reactor with dupic fuel

Instability analysis on xenon spatial oscillationin a CANDU-6 reactor with DUPIC fuel

Chang-Joon Jeong*, Hangbok Choi

Korea Atomic Energy Research Institute, P.O. Box 105, Yusong, Taejon, 305-600, South Korea

Received 29 June 1999; accepted 14 August 1999

Abstract

The instability induced by xenon spatial oscillation of a CANDU-6 reactor with DUPICfuel has been assessed for three important harmonic perturbations: top-to-bottom, side-to-side and front-to-back oscillations. For each oscillation, the instability index of the DUPICfuel core has been calculated and compared with that of the natural uranium core. Parametric

calculations have also been performed to analyze the e�ect of the power level and axial powershape on the xenon oscillation. This study has shown that the instability due to xenon oscil-lation increases for the DUPIC fuel core compared with the natural uranium core. However,

this study has also shown that the current reactivity device system suppresses the xenonoscillation completely for both the natural uranium and the DUPIC fuel cores. # 2000Elsevier Science Ltd. All rights reserved.

1. Introduction

The xenon spatial oscillation is an important factor in the operation of a powerreactor. In general, the susceptibility to xenon oscillation arises from the out-of-phase interaction between the positive and negative reactivity feedback due to thedestruction of 135Xe by neutron capture and its formation by the decay of the ®ssionproduct, 135I. A large power reactor such as a Canada deuterium uranium(CANDU) (Figs. 1 and 2) reactor is especially more susceptible to spatial oscillation.The extent to which a reactor is susceptible to spatial xenon oscillations depends onthe core dimensions, the power level, the shape of the unperturbed ¯ux distribution,

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E-mail address: [email protected] (C.-J. Jeong).

the in¯uence of the reactivity feedback mechanism of the fuel and moderatortemperature, and, to a lesser extent, the spectrum, as it a�ects the xenon cross-section.Recently, the direct use of spent pressurized water reactor (PWR) fuel in CANDU

reactors, called the DUPIC (Choi et al., 1997) fuel cycle, has been studied as analternative to either the once-through or recycling fuel cycles. One of the particularfeatures of DUPIC fuel is a higher ®ssile content (1.45 wt%), which makes it possi-ble to achieve a discharge burnup more than twice that of the natural uranium fuelin a CANDU reactor. However, in order to accommodate such a high reactivityfuel, the fuel management scheme has to change. For example, the DUPIC fuel coreadopts a 2-bundle shift refueling scheme, whereas the 8-bundle shift is typically usedfor the natural uranium core. As the number of shifted fuel bundles is reduced, theaxial power shape becomes ¯atter, and this is liable to weaken the axial coupling ofthe core. It is also known that the high ®ssile content reduces the thermal ¯ux levelin the DUPIC fuel core, which changes the e�ectiveness of the reactivity devices andxenon property. Therefore, it is expected that the xenon induced spatial instability willincrease, which would necessitate an analysis of the reactor controllability in order topreserve the operational ¯exibility of the DUPIC fuel in the CANDU-6 reactor.

Fig. 1. Plan view of reactor showing reactivity devices.

888 C.-J. Jeong, H. Choi / Annals of Nuclear Energy 27 (2000) 887±899

In this study, the instability induced by xenon spatial oscillation in a CANDU-6reactor loaded with DUPIC fuel has been quantitatively assessed through a com-parative study on the standard natural uranium fuel core. A parametric calculationon the instability of the xenon spatial oscillation is included in this study. Inaddition, the performance of zone control units (ZCUs), which are used for bulkand spatial control of the reactor power, is assessed against the xenon inducedspatial oscillation.

2. Xenon oscillation

Under an equilibrium core condition, the concentration of 135Xe in a reactordepends on the local power. The governing equations of the 135Xe concentration atany point in a reactor can be written as:

dI

dt� iFÿ liI �1�

Fig. 2. Face view of reactor showing zone controller compartments.

C.-J. Jeong, H. Choi / Annals of Nuclear Energy 27 (2000) 887±899 889

dX

dt� liI� xFÿ lxXÿ �xX� �2�

where, I and X are the concentrations of 135I and 135Xe, x and i are their ®ssionyields, lx and li are their decay rates, F is the macroscopic ®ssion rate, � is thethermal ¯ux at the point of interest, and �x is the microscopic thermal absorptioncross-section of 135Xe. The time-dependent response of the xenon concentration tochanges in the power level is illustrated in Fig. 3, which shows the negative reactivitydue to changes in the xenon concentration resulting from a reactor shutdown andsubsequent startup.The susceptibility of the core to the spatial xenon oscillation can be analyzed from

the interaction between the xenon concentration and the neutron ¯ux distribution.In this study, space-time di�usion calculations are used for the prediction of thexenon instability. The group constants and xenon properties are obtained fromWIMS-AECL (Donnelly, 1986). The space-time di�usion calculations are per-formed by RFSP (Jenkins et al., 1991), which is used for the CANDU core designand analysis.

2.1. Oscillation type

In this study, three higher harmonic modes are considered for the analysis of thexenon spatial oscillation characteristics: the top-to-bottom, the side-to-side and thefront-to-back oscillations. These three harmonic modes are typical oscillations con-sidered in the CANDU core physics design. The oscillations are initiated by with-drawing and subsequently reinserting the adjuster rods (ADJs) to perturb thesteady-state ¯ux and xenon distribution. For the top-to-bottom oscillation, all ADJs(see Fig. 1) are withdrawn 50% and then reinserted to induce an oscillation. The

Fig. 3. Xenon reactivity variation following shutdown and subsequent startup.


side-to-side oscillation can be induced by fully withdrawing ADJ numbers 5, 6, 7,12, 13, 14, 19, 20 and 21 simultaneously. The axial oscillation is induced by fullywithdrawing ADJ numbers 1, 2, 3, 4, 5, 6 and 7 together.

2.2. Measure of oscillation

The oscillation characteristics can be represented by power tilts, which are de®ned as:

top-to-bottom tilt �%� � �P1;8 � P3;10 � P6;13� ÿ �P2;9 � P5;12 � P7;14�P14i�1

Pi

� 100 �3�

side-to-side tilt �%� � �P1;8 � P2;9� ÿ �P6;13 � P7;14�P14i�1

Pi

� 100 �4�

front-to-back tilt �%� �P7i�1

Pi ÿP14i�8

Pi

P14i�1

Pi

� 100 �5�

where, Pi is the power of zone i and Pi;j is the power of the zone pair �i; j�, which isshown in Fig. 2.

2.3. Results

For the top-to-bottom xenon oscillation, shown in Fig. 4, the maximum tilt of theDUPIC core is 45.4%, and the oscillation time is about 170 h, while the oscillationtime of the natural uranium core is 120 h with a maximum tilt of 44.5%. For theside-to-side xenon oscillation shown in Fig. 5, it can be seen that the oscillation alsocontinues for 170 h with a maximum tilt of 37% at 13 h after the perturbation.Unlike the top-to-bottom oscillation, the behavior of the side-to-side oscillation isvery similar for both the natural uranium and DUPIC fuel cores because of thesymmetric power distribution. The oscillatory behavior is more distinctive for thefront-to-back tilt as shown in Fig. 6. For the DUPIC fuel core, the duration time isabout 60 h with a maximum tilt of 13%. However, there is only a minor axialoscillation for the natural uranium fuel core, which is mostly due to the axial powershape that strongly couples the front and rear zone powers. The e�ect of the axialpower shape on the axial oscillation is investigated in Section 3.3.The comparison of three oscillations has also shown that the top-to-bottom

oscillation is more susceptible than any other oscillations for both the naturaluranium and DUPIC fuel cores.


3. Instability analysis

The instability of the core due to the xenon oscillation has been analyzed using thedamping factor and the threshold power. The damping factor is a measure of the rateof decay of the oscillation and is de®ned as the ratio of the oscillation amplitudeover an oscillation period. The threshold power is de®ned as a speci®c power levelover which the xenon oscillation occurs, which can be estimated through theoscillation calculations for various power levels. In this section, the damping factor

Fig. 4. Comparison of top-to-bottom oscillation.

Fig. 5. Comparison of side-to-side oscillation.


and the threshold power of both the natural uranium and DUPIC fuel cores areestimated in order to compare the inherent stability of both cores. This section alsodescribes the e�ect of power shape on the instability of the xenon oscillation andcontrollability of the current ZCU system against the xenon oscillation.

3.1. Damping factor

The xenon oscillation induced by a perturbation follows an exponential-sinusoidalbehavior (Corcoran et al., 1973), which can be expressed by:

P�t� � A0 � P0e�t sin

2�

Tt� t0

� ��6�

where P�t� is the oscillating power at time t, A0 is the steady-state value of theoscillating variable, P0 is the amplitude of the envelope of the oscillating term attime zero, T is the period of the oscillation, t0 is the phase shift, and � is the dampingfactor. The damping factor of the xenon oscillation can be obtained from theenvelope of the xenon oscillation, which is written as follows:

y � P0e�t �7�

The damping factor is positive for a divergent oscillation and negative for adamped oscillation. The damping factor was determined by least square ®ts of thecalculated oscillating variables in Eqs. (6) and (7).

Fig. 6. Comparison of front-to-back oscillation.


For the DUPIC fuel core, the damping factor for the top-to-bottom oscillation isÿ1.767�10ÿ2 hÿ1, which is 45% smaller in magnitude than that of the natural ura-nium core. The damping factors of the side-to-side and front-to-back oscillations aredecreased by 37 and 79%, respectively, compared to those of the natural uraniumfuel core. Therefore, all damping factors of the DUPIC fuel core are smaller inmagnitude compared to those of natural uranium fuel core, which means that theinstability of the xenon oscillation for the DUPIC fuel core is increased comparedwith that of the natural uranium core. The damping factors and other parametersare compared in Table 1.

3.2. Threshold power

The threshold power of the xenon oscillation was investigated for various powerlevels. The calculations were performed for the top-to-bottom oscillation becausethis is the most unstable oscillation type. As shown in Fig. 7, the threshold power ofthe DUPIC fuel core is about 10% full power, while it is 20% full power (Kim et.al., 1995) for the natural uranium core. The damping factors are summarized in

Table 1

Damping factors for xenon oscillation

Oscillation Damping factor (hÿ1)

DUPIC core Natural uranium core

Top-to-bottom ÿ1.767�10ÿ2 ÿ3.244�10ÿ2Side-to-side ÿ1.594�10ÿ2 ÿ2.635�10ÿ2Front-to-back ÿ2.517�10ÿ2 ÿ1.198�10ÿ1

Fig. 7. Comparison of top-to-bottom oscillation with di�erent power levels (DUPC core).


Table 2

Damping factors of DUPIC fuel core for di�erent power levels (top-to-bottom oscillation)

Power level (%) Damping factor (hÿ1)

100 ÿ1.767�10ÿ280 ÿ2.336�10ÿ260 ÿ3.085�10ÿ240 ÿ4.391�10ÿ220 ÿ1.212�10ÿ210 ÿ

Fig. 8. Axial bundle power pro®le for various refueling scheme (central channel).

Fig. 9. Comparison of front-to-back oscillation with di�erent refueling schemes (DUPIC core).


Table 2 for various power levels. The decreased threshold power means that thexenon oscillation can occur at a lower power level, which is again an increase in theinstability of the xenon oscillation for the DUPIC fuel core.

3.3. E�ect of power ¯attening to axial oscillation

The higher instability of the xenon oscillation in the DUPIC fuel core is related tothe higher degree of power ¯attening. For the DUPIC fuel core, 2-bundle shiftfueling scheme is adopted for on-power refueling. This scheme gives more axialpower ¯attening compared to the natural uranium core, where the 8-bundleshift fueling scheme is used. In order to assess the e�ect of power ¯attening on axialxenon oscillation, the xenon oscillation calculations have been performed for

Table 3

Damping factors of DUPIC fuel core for various refueling schemes

Refueling scheme Axial form factora Damping factor (hÿ1)

2-bundle shift 0.716 ÿ1.767�10ÿ24-bundle shift 0.695 ÿ4.121�10ÿ26-bundle shiftb 0.557 ÿ8-bundle shiftb 0.540 ÿ

a Average bundle power=maximum bundle power��Average channel power=maximum channel power�.

bActually 6- and 8-bundle shift refueling schemes are not practicable for DUPIC core.

Fig. 10. ZCU controllability of top-to-bottom oscillation (DUPIC core).


di�erent fueling schemes. The axial power shapes for various refueling schemes arecompared in Fig. 8, which shows that the axial power shapes become ¯atter as thenumber of shifted fuel bundles is decreased. As shown in Fig. 9, the xenon oscilla-tion decreases rapidly with an increasing number of shifted fuel bundles, andbecomes negligible when the 6-bundle and 8-bundle shift refueling schemes are used.Table 3 compares the damping factor and the corresponding axial form factor,which is a measure of the power ¯attening.

Fig. 11. ZCU controllability of side-to-side oscillation (DUPIC core).

Fig. 12. ZCU controllability of front-to-back oscillation (DUPIC core).


3.4. Spatial controllability

The CANDU-6 reactor has 14 ZCUs in order to maintain the reference powerdistribution. In order to con®rm the stability of the core against the xenon oscilla-tion, the controllability of the current ZCU system was assessed against the powerperturbation associated with the xenon spatial oscillation. The xenon oscillations ofthe DUPIC fuel core, with and without spatial control are compared in Figs. 10±12for the top-to-bottom, side-to-side and axial oscillation, respectively. These simula-tions have clearly shown that the ZCU system immediately compensates for zonepower variations associated with the xenon oscillations.

4. Summary and conclusion

The instability of the xenon spatial oscillation for the CANDU-6 reactor loadedwith DUPIC fuel has been assessed. This study has shown that:

. The xenon spatial oscillation of the DUPIC fuel core is larger than that of thenatural uranium core. However, the xenon oscillations are self-damped in boththe natural uranium and DUPIC fuel cores.

. The top-to-bottom oscillation is more susceptible than the side-to-side andfront-to-back oscillations for both the natural uranium and DUPIC fuel cores.

. The threshold power of the DUPIC fuel core for the xenon oscillation issmaller than that of the natural uranium core, which means that the xenonoscillation of the DUPIC core could be initiated at a lower power levelcompared with the natural uranium core.

. The front-to-back xenon oscillation could be reduced by increasing the numberof fuel bundles shifted per refueling operation.

. Despite the increased instability, the current ZCU system can damp the xenonoscillation completely for the DUPIC fuel core.

In conclusion, the xenon spatial oscillations of the DUPIC fuel core continue for alonger time compared with the natural uranium core. Especially for the front-to-back oscillation, the maximum power tilt of the DUPIC fuel core increases morethan ®ve times compared with that of the natural uranium core, primarily due to thepronounced axial power decoupling. Nonetheless, the current ZCU systemmaintains the damping capability of the xenon oscillation for the DUPIC fuel core.

Acknowledgements

This work has been carried out under the Nuclear Research and DevelopmentProgram of Korea Ministry of Science and Technology. The authors are grateful toP. Chan of Atomic Energy of Canada Limited for valuable comments.


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instability analysis on xenon spatial oscillation in a candu-6 reactor with dupic fuel

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