Annals of Nuclear Energy 36 (2009) 998–1001

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Annals of Nuclear Energy

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Technical Note

Reactivity feedbacks of a material test research reactor fueled with variouslow enriched uranium dispersion fuels

Farhan Muhammad *, Asad MajidDepartment of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad 45650, Pakistan

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 December 2008Received in revised form 26 February 2009Accepted 1 March 2009Available online 9 April 2009

0306-4549/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.anucene.2009.03.006

* Corresponding author. Tel.: +92 51 2207381; fax:E-mail address: mfarhan_73@yahoo.co.uk (F. Muh

The reactivity feedbacks of a material test research reactor using various low enriched uranium fuels,having same uranium density were calculated. For this purpose, the original aluminide fuel (UAlx–Al)containing 4.40 gU/cm3 of an MTR was replaced with silicide (U3Si–Al and U3Si2–Al) and oxide (U3O8–Al) dispersion fuels having the same uranium density as of the original fuel. Calculations were carriedout to find the fuel temperature reactivity feedback, moderator temperature reactivity feedback, moder-ator density reactivity feedback and moderator void reactivity feedback. Nuclear reactor analysis codesincluding WIMS-D4 and CITATION were employed to carry out these calculations. It was observed thatthe magnitudes all the respective reactivity feedbacks from 38 �C to 50 �C and 100 �C, at the beginningof life, of all the fuels were very close to each other. The fuel temperature reactivity feedback of theU3O8–Al was about 2% more than the original UAlx–Al fuel. The magnitudes of the moderator tempera-ture, moderator density and moderator void reactivity feedbacks of all the fuels, showed very minor vari-ations from the original aluminide fuel.

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1. Introduction

Material test reactor (MTR) technology is one of the oldest reac-tor technologies and is being used for different purposes since lastcentury. In order to improve their performance, safety and security,these reactors have seen many changes in their configurationssince their birth. A large number of research reactors around theworld have been converted to or designed to use low enriched ura-nium (LEU) fuels. A variety of different LEU fuels is available ofvarying densities and composition. The IAEA has discussed fourtypes of LEU dispersion fuels for use in the material test reactorsin its guide book developed for reactor conversion (IAEA-TEC-DOC-643, 1992). These fuels include the aluminide fuel (UAlx–Al),silicide fuels (U3Si–Al and U3Si2–Al) and the oxide fuel (U3O8–Al).

Extensive analysis has been done and reported in the referencedocument (IAEA-TECDOC-643, 1992) for the IAEA benchmark reac-tor (IAEA-TECDOC-233, 1980; IAEA-TECDOC-643, 1992) using theLEU based UAlx–Al fuel having a uranium density of 4.40 gU/cm3.Situation may arise that a reactor may not get supplies of the fuelit has been using, and may have to rely on available fuel of anothertype. While looking on to the absorption and scattering cross sec-tions of the alloying elements (Duderstadt and Hamilton, 1976),namely Al, Si and O, it is seen that there exists a considerable dif-ference between the cross sections. The absorption cross sectionsof O and Si are much lesser than that of Al in the thermal range.

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+92 51 2208070.ammad).

Also, O and Si are better moderators than Al. Due to differencesin the cross sections of the alloying materials, it is expected thatmost of the neutronic parameters, including the reactor excessreactivity, prompt neutron generation time, delayed neutron frac-tion and the reactivity feedbacks will change. Lower absorptioncross sections and better moderating material can result in longercore lives. The work presented in this paper focuses on theevaluation of the fuel temperature feedback reactivity, moderatortemperature feedback reactivity, moderator density feedback reac-tivity and moderator void feedback reactivity of the IAEA 10 MWbenchmark reactor with the original UAlx–Al LEU fuel replaced withLEU silicide and oxide dispersion fuels having the same uraniumdensity of 4.40 gU/cm3. To highlight the variations occurring in dif-ferent reactor performance parameters, only the UAlx–Al LEU fuel isbeing replaced by the other LEU fuels. All other design parametershave been kept constant.

2. Reactor description

The reactor analyzed is the same one utilized for the benchmarkproblem solved in IAEA-TECDOC-233, 1980, with the water in thecentral flux trap replaced with a 7.7 cm � 8.1 cm block of alumi-num containing a square hole 5.0 cm on each side (IAEA-TEC-DOC-643, 1992). Description of the low enriched uranium core ofthe reactor as described in the reference documents (IAEA-TEC-DOC-233, 1980; IAEA-TECDOC-643, 1992) is given in Table 1. Thecore configuration and burn up of fuel elements in percentage ofloss of the number of initial 235U atoms at beginning of life (BOL)

Table 1Data for low enriched uranium core of IAEA 10 MW benchmark reactor.

Active core height 60.0 cmSpace at the grid plate per fuel element 7.7 cm � 8.1 cmFuel element cross section 7.6 cm � 8.05 cm including support plateMeat dimensions 6.3 cm � 0.051 cm � 60.0 cmThickness of support plate 0.475 cmNumber of fuel plates per fuel element 23 Identical plates, each 0.127 cm thickNumber of fuel plates per control element 17 Identical plates, each 0.127 cm thickIdentification of the remaining plate positions ofthe control element

Four plates of aluminum, each 0.127 cm thick in the position of the 1st, the 3rd, the 21st, and the 23rd standard plateposition; water gaps between the two sets of aluminum plates.

Specifications of the LEU (UAlx–Al) fuel (a) Enrichment 20 w/o U-235(b) 390 g U-235 (qU = 4.40 g/cm3) per fuel element (23 plates)(c) 72 w/o of uranium in the UAlx–Al(d) Only U-235 and U-238 in the fresh fuel

Total steady state power 10 MWth

Thermal hydraulic dataWater (coolant) inlet temperature 38 �CPressure at core height 1.7 barXenon-state Homogeneous xenon content corresponding to average-power-density

Graphite Graphite Water

Water25% 5%

Water

45% 45% 25%

45% 5%25%

ControlElement

7.7cm

8.1cm

y

3 fuel element width ofwater reflector = 24.3 cm

Outsideboundarycondition

=0

3 fuel element width ofwater reflector = 23.1 cm

Outside boundary condition Φ=0

Aluminium Block

x

Φ

Fig. 1. IAEA 10 MW benchmark reactor configuration as defined in IAEA-TECDOC-233 and IAEA-TECDOC-643.

0.127

0.219

8.0

6.3

0.4756.640.475

Fig. 2. The cross sectional view of the standard fuel element of IAEA benchmarkreactor (all dimensions in cm).

0.219

0.565

8.00.127

6.3

0.4756.640.475

Fig. 3. The cross sectional view of the control fuel element of IAEA benchmarkreactor (all dimensions in cm).

F. Muhammad, A. Majid / Annals of Nuclear Energy 36 (2009) 998–1001 999

is given in Fig. 1 while the configurations of the standard fuel andcontrol elements are given in Figs. 2 and 3, respectively. Other de-

tails could be found in the reference documents (IAEA-TECDOC-233, 1980; IAEA-TECDOC-643, 1992).

3. Methodology

The CITATION (Fowler et al., 1971) code was used in this studyto calculate the effective multiplication factor keff of the reactor bysimulating the cores in x–y–z geometry. All control rods were as-sumed to be fully withdrawn. The CITATION code needs macro-scopic absorption cross section (Ra), the v-fission cross section(vRf), the diffusion coefficient (D), the scattering matrix (Rs,g ? g0)and the fission spectrum for all groups, as input data. The WIMS-D4 (Halsall, 1980) code was used for computation of these groupconstants for different regions of the core. The original 1981 crosssection library of UK origin was employed. Five energy groups (Ta-ble 2) were used in WIMS-D4 for generation of required data. Uni-form temperature distribution was used in the analysis. Themodeling and calculation procedures have been fully explainedand validated in our earlier work (Muhammad and Majid, 2008).The same procedure and method has been used in this work.

Table 5Reactivity feedback for change of temperature from 38 �C to 100 �C (Dk/k � 10�3).

Feedback coefficient UAlx–Ala Ratio of feedback to UAlx–Al feedback

U3Si–Al U3Si2–Al U3O8–Al

Fuel temperature �1.6081 1.0009 1.0003 1.0202Moderator temperature �4.7834 0.9976 0.9999 0.9963Moderator density �13.5539 1.0051 1.0064 1.0032

a Muhammad and Majid (2008).

Table 2Energy groups used for macroscopic cross section generation by WIMS-D4.

Group no. EU (eV) EL (eV) Group typea Flux typeb

1 10.0 � 106 0.821 � 106 FastFast2 0.821 � 106 5.530 � 103 Resolved resonances

3 5.530 � 103 0.625 Unresolved resonances Epithermal4 0.625 0.14 Thermal

Thermal5 0.14 0 Thermal

a Khan et al. (2000).b IAEA-TECDOC-233 (1980).

Table 4Reactivity feedback for change of temperature from 38 �C to 50 �C (Dk/k � 10�3).

Feedback coefficient UAlx–Ala Ratio of feedback to UAlx–Al feedback

U3Si–Al U3Si2–Al U3O8–Al

Fuel temperature �0.3206 1.0051 1.0021 1.0250Moderator temperature �1.1515 1.0050 1.0050 1.0046Moderator density �2.2550 0.9986 0.9952 0.9968

a Muhammad and Majid (2008).

1000 F. Muhammad, A. Majid / Annals of Nuclear Energy 36 (2009) 998–1001

4. Results and discussion

The original aluminide fuel of the IAEA benchmark reactor wasreplaced with different fuel materials as stated before. The fuelsanalyzed include silicide (U3Si–Al and U3Si2–Al) and oxide(U3O8–Al) dispersion fuels having the same uranium density of4.40 gU/cm3 as the original fuel. All other design parameters ofthe reactor were kept constant.

The porosity of the U3Si2–Al fuel was calculated from the rela-tion (IAEA-TECDOC-643, 1992)

Vp ¼ 0:072VF � 0:275V2F þ 1:32V3

F ð1Þ

where VF is the volume fraction of the fuel, calculated from the rela-tion (IAEA-TECDOC-643, 1992),

VF ¼qU

11:3ð2Þ

The volume fractions for the U3Si–Al and U3O8–Al fuels werecalculated from Eqs. (3) and (4), respectively (IAEA-TECDOC-643,1992), given below

VF ¼qU

14:6ð3Þ

VF ¼qU

7:0ð4Þ

Since no relation is made available in reference (IAEA-TECDOC-643, 1992) for porosity calculations for U3Si–Al and U3O8–Al fuels,same porosity as found for the U3Si2–Al fuel was used since poros-ity is basically meant for accommodating the fission products andthe uranium content for all the fuels is the same. The characteris-tics of the fuels are given in Table 3.

The change in reactivity was calculated as follows (IAEA TEC-DOC-643, 1992):

Dq ¼ k0 � 1k0

� kT � 1kT

ð5Þ

where k0 = keff at 38 �C, kT = keff at a specified temperature orcondition.

Since feedback coefficients in the reference document (IAEA-TECDOC-643, 1992) have been calculated between 38 �C (the cool-ant inlet temperature) and 50 �C, the same temperature range hasbeen analyzed in this work also. The fuel temperature may rise to

Table 3Characteristics of the LEU dispersion fuels IAEA-TECDOC-643 (1992).

Dispersant VFD (%) qU (g/cm3) P (%) VFM (%)

U3Si–Al 30.1 4.40 6.4 63.5U3Si2–Al 38.9 4.40 6.4 54.7U3O8–Al 62.7 4.40 6.4 30.9

VFD: volume fraction of the dispersant in the fuel meat exclusive of dispersantinternal voids.qU: uranium density in the fuel meat.P: porosity in fuel meat.VFM: volume fraction of the aluminum matrix in the fuel meat.

100 �C in certain transients (Muhammad and Majid, 2009), there-fore reactivity feedbacks have been calculated for temperature of100 �C that could be used in the analysis of such transients. The re-sults obtained are given and analyzed below.

4.1. Reactivity feedback due to change in fuel temperature

The reactivity change in a reactor system due to change in fueltemperature is because of the Doppler broadening of the absorp-tion cross section. As seen from Tables 4 and 5, the reactivity feed-backs of silicide fuels are almost the same as that of the aluminidefuel whereas the oxide fuel has reactivity feedback about 2% morethan that of the aluminide fuel.

The differences between the calculated values are very smallmaking it necessary to take into consideration the uncertaintiesof the cross sections. Different values for uncertainties have beenreported in the literature. These range from 3.5% uncertainty in238U resonance capture cross section (Hardy, 1975), 10% uncer-tainty in 235U resonance capture cross section (Aliberti, et al.,2006), and up to 16% uncertainty in total cross sections (Garcia-Herranz et al., 2008). The calculated differences in the reactivityfeedbacks fall well within the uncertainty range. Hence, it can besaid that fuel replacement will not affect the fuel temperaturefeedback to any significant extent.

4.2. Reactivity feedback due to change in water temperature anddensity

Water, in addition to cooling the fuel, also acts as the modera-tor. The moderation decreases as the water temperature increasesor its density decreases. In any case, the neutron spectrum be-comes harder and since the fission cross section is lower at higherneutron energies, the reactivity of the system decreases. As seenfrom the values in Tables 4 and 5, the moderator temperature feed-back coefficients of silicide and oxide fuels show little change overthe aluminide fuel. The moderator density feedback coefficients ofall the fuels are also almost the same. Such small changes in themoderator temperature and density feedback coefficients are wellwithin the uncertainties of the cross sections.

4.3. Reactivity feedback due to moderator voids

Void reactivity feedback was also calculated for all the four fuelsat the saturation temperature of water, i.e. 115.148 �C at 1.7 barwhich is the water pressure at core height (Table 1). The results

Table 6Reactivity feedback due to void formation (Dk/k � 10�3).

Void (%) UAlx–Al Ratio of feedback to UAlx–Al feedback

U3Si–Al U3Si2–Al U3O8–Al

5 �11.6027 0.9993 0.9993 0.996710 �24.4533 0.9985 0.9994 0.9972

F. Muhammad, A. Majid / Annals of Nuclear Energy 36 (2009) 998–1001 1001

for 5% void and 10% void are given in Table 6. As seen from Table 6,these values are almost same for all the fuels, any small variationsare well within the uncertainties of the cross sections.

5. Conclusions

The results show that if the aluminide fuel of an MTR is replacedwith silicide or oxide fuels, then the reactivity feedback coefficientsdo not change to any significant extent. Only the Doppler feedbackcoefficient of the oxide fuel is slightly greater than the others,which also lies well within the uncertainties of the cross sections.So, it can be expected that the oxide fuel might be more sensitiveto changes in fuel temperatures and might give some advantage incertain power excursion cases. However, the reactor response forchanges in moderator temperature, density and void formationwill be almost same for all the fuels.

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