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Progress in Nuclear Energy 53 (2011) 76e79

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Progress in Nuclear Energy

journal homepage: www.elsevier .com/locate/pnucene

Reactivity feedback calculation of a conceptual TRISO fueled compact PWR core

Anwar Hussain*, Cao XinrongCollege of Nuclear Science and Technology, Harbin Engineering University, 145 Nantong Str., Nangang Dist., Harbin, Heilongjiang 150001, PR China

a r t i c l e i n f o

Article history:Received 8 March 2010Received in revised form11 August 2010Accepted 13 August 2010

Keywords:Compact PWRTRISO fuelPu-240Reactivity feedback coefficients

* Corresponding author. Tel.: þ86 451 82519302; faE-mail address: anz_raj@yahoo.com (A. Hussain).

0149-1970/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.pnucene.2010.08.006

a b s t r a c t

Reactivity feedback coefficients have been calculated for a compact sized PWR core that utilizes carboncoated micro fuel particles instead of standard cylindrical fuel pellets with an inventive composition. Asmall amount of Pu-240 with 5 w/o has also been added in tristructural-isotropic (TRISO) fuel in place ofU-238 for the reduction of excess reactivity. The values of fuel, moderator and void reactivity coefficientshave been calculated at the middle of fuel cycle. All the reactivity coefficients were found negative whichmeet the design safety criteria. It was also observed that all reactivity feedback coefficients are inter-linked and their effects are pronounced when coupled together.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The measure of reactivity in a reactor core determines theneutron population and consequently the reactor power at anygiven time (DOE-HDBK-1019/2-93, DOE Fundamentals Handbook,1993). The reactivity can be affected by many factors mainly dueto the fuel depletion, temperature, pressure, or poisons etc.

Reactivity feedback plays a dominant role in the control, safetyand operation of a nuclear reactor which makes the system inher-ently safe. Negative reactivity feedback keeps the reactor steadywhereas positive reactivity feedback makes the reactor inherentlyunstable. Reactivity feedback depends upon properties of nuclearreactor components and its composition that mainly include fueltype, its enrichment, coolant, moderator, type of core lattice, fuelpitch and temperature etc. Temperature is the dominating factor forreactivity feedback phenomenon because any change in tempera-ture results in the change of multiplication factor.

Reactivity coefficients are used to quantify the reactivitychanges that will occur due to the change in a physical propertysuch as the temperature of the moderator or fuel. Reactivity coef-ficients are the amount that the reactivity will change for a givenchange in the parameter.

ax ¼ DrDX

where x represents some variable reactor parameter that affectsreactivity. If the parameter x increases and positive reactivity is

x: þ86 451 82569622.

All rights reserved.

added, then ax is positive. If the parameter x increases and negativereactivity is added, then ax is negative.

In the current research paper temperature coefficients of reac-tivity have been calculated for the conceptual design of a compactsized PWR core that utilizes tristructural-isotropic (TRISO) fuelparticle with an inventive composition. Detailed work in thisresearch area has been presented in our preceding research whichcontributes towards a complete conceptual reactor design (Hussainand Xinrong, 2009; Hussain and Xinrong, 2010).

2. Reactor design

This conceptual compact sized PWR core design utilizes tris-tructural-isotropic (TRISO) fuel particle with an inventivecomposition. The presence of TRISO fuel in PWR technologyimproves integrity of the design due to its fission fragmentsretention ability as this fuel provides first containment boundarywithin fuel itself against the release fission fragments. The TRISOparticles can withstand temperatures of up to 1600 �C for a longtime without breaching their integrity against any release offission products (Morris and Bauer, 2005; PNNL-15134, PacificNorthwest National Laboratory, 2005; Tsiklauri et al., 2002). Thearrangements of fuel rods and fuel assemblies in the core areshown in Fig. 1. The core consists of total 2180 fuel and 45 controlrods with an equivalent diameter of 2.2 m. The height of the fuelrod is 1.5 m and core is also reflected by 8 cm thick berylliumlayers from all the sides. This is a small reactor which has only25 MWth power out put, the main parameters of design are givenin Table 1.

Core equivalent diameter

Fuel assembly with 25 fuel rods

Fuel assembly (5X5)

Fuel assembly with 5 control

rods

Reflector

Fig. 1. Designed core configuration.

1.50

2.50

3.50

4.50

5.50

6.50

200 400 600 800 1000 1200 1400 1600

Fuel temperature Tf (K)

%(

)k/

kΔ

ρ

Fig. 2. Reactivity as a function of fuel temperature.

A. Hussain, C. Xinrong / Progress in Nuclear Energy 53 (2011) 76e79 77

2.1. Main design features

The important feature of the design is novel TRISO fuelcomposition which provides reactivity control technique over theentire fuel cycle. A small amount of Pu-240 with 5.0 w/o has beenadded in TRISO fuel particle composition in the place of U-238which improves the reactivity control. The amount of excess reac-tivity has been reduced significantly by using a small amount ofPu-240 in TRISO fuel. The utilization of inventive TRISO fuel particlecan completely eliminate the use of soluble boron system andrequirement of burnable poison if adequate number of control rodsis used. The Soluble Boron Free (SBF) and Burnable Poison Free(BPF) concepts are more viable in small and medium size reactors(SMRs) because it makes the plant simpler and uniform burnup canbe achieved throughout the core. By excluding the soluble boronsystem, the moderator temperature coefficient of reactivity can bemade negative thought out the fuel cycle.

2.2. Simulation codes

In this study WIMS-D/4 and CITATION computer codes havebeen used for the simulation of a compact nuclear reactor core. TheWinfrith ImprovedMulti-group Scheme version D/4 (WIMS-D/4) isa British origin code which calculates cell averaged macroscopiccross-sections and other lattice parameters for overall spacedependent reactor calculations (Deen and Woodruff, 1995). Thecode has been used for the generation of group constants needed asinput for 3-D computer code CITATION. The computer code CITA-TION solves the finite difference diffusion equation representationsof neutron transport with wide range of geometries. The code

Table 1Main parameters of design.

Parameter Dimension Parameter Dimension

Power out put 25 MWth Fuel type TRISOCore height w1.7 m Fuel enrichment 9%Equivalent core dia w2.2 m Fuel composition UO2

Fuel rod height 150 cm Cladding material ZircaloyFuel rod diameter 2 cm Primary average

pressure6 MPa

Fuel pitch 3 cm Coolant averagetemperature

200 �C

Cladding thickness 1.5 mm Average linearpower density

7.5 kW/m

Number of assemblies 89 Reactor operatingcore life

w2 Years

Number of fuel rods/assembly

25 Inventory of heavymetal

w260 kg

Control rod material Hafnium(Hf)

Reflector Beryllium

Number of control rods 45 Reflector thickness 8 cmCoolant/moderator Light water Lattice type PWR shape

determines the neutron multiplication factor (keff), flux and powerprofiles. The code can also calculate reactivity feedback coefficients,effective delayed neutron fraction and prompt neutron generation(Fowler et al., 1971).

3. Calculation of reactivity coefficients

Although these coefficients are coupled together but in theinitial phase, these coefficients were calculated independently, i.e.only one parameter under consideration was varied and all otherparameters were kept constants. In the second phase of study,these coefficients were calculated by considering the mutualcoupling and interrelated effects. It is needless to say that the rise infuel temperature will also results in rise in moderator temperature,reduction inmoderator density andmay also results in an increasedvoid activity in the reactor core.

3.1. Calculational methodology

The calculational method consists of two main parts, first part isthe generation of group constants and macroscopic cross-sectionsfor various core regions and the second part is generation of keff.Computer codeWIMS-D4was used to generate the group constantsat specific core conditions. Fuel and moderator temperature wasvaried over suitable ranges to generate group constant which wereused later in CITATION code for global calculations. Effectivemultiplication factor (keff) of the core was obtained from CITATIONand then used for the calculation of reactivity. A series of calcula-tions were performed to obtain the reactivity curves by applyingsame procedure.

3.2. Fuel temperature coefficient of reactivity

The fuel temperature coefficient of the core can be calculated byvarying the temperature in the fuel region while keeping thetemperature of the other regions constant. The fuel temperature

Table 2Moderator density profile.

Moderator temperature(K)

Moderator density(g cm�3)

277 1.000293 0.9982311 0.993323 0.988348 0.975373 0.958398 0.9436423 0.9286448 0.9137473 0.8986498 0.8836523 0.86861548 0.8536573 0.8387

4.5

4.7

4.9

5.1

5.3

5.5

5.7

5.9

270 320 370 420 470 520 570

Moderator temperature TM (K)

ρ (%

Δk/k)

Fig. 3. Reactivity as a function of moderator temperature.

Table 3Moderator void profile.

Moderator temperature(K)

Moderator void VM

(%)

300 0340 5380 10420 15460 20500 25540 30580 35

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

-5 0 5 10 15 20 25 30 35 40

Moderator Void (%)

ρ (%

Δ

k/k)

Fig. 4. Reactivity as a function of moderator void.

A. Hussain, C. Xinrong / Progress in Nuclear Energy 53 (2011) 76e7978

coefficient analyses consist of three different ranges of tempera-tures: startup temperature range, intermediate temperature range,and operating temperature range.We have calculated and analyzedthe fuel temperature coefficient of a critical core at the middle offuel cycle for entire temperature range. For calculating the fueltemperature reactivity coefficient, only fuel temperature wasvaried from 300 K to 1500 K in steps of 100 K.

The group constants and cross-sections were generated byWIMS-D/4 and keff by CITATION computer code. The reactivity wascalculated for each value of fuel temperature and then plotted inFig. 2. The reactivity coefficient follows the relationship r¼ 8E�07Tf2� 0.0047Tfþ 7.3801 and value of fuel temperature reactivitycoefficient can be calculated from the gradient of the curve.

3.3. Moderator temperature coefficient of reactivity

In the operating temperature range, the moderator temperaturecoefficient is analyzed by varying themoderator temperaturewhilekeeping the temperature in the fuel and other regions constant. Themoderator temperature coefficient of reactivity was calculated byvarying the temperature of moderator and its density by using

0.00

1.00

2.00

3.00

4.00

5.00

6.00

200 400 600 800

Fuel temp

ρ (%

Δk/k)

Fig. 5. Combined effect of fuel and moderator temperat

density profile inTable 2 (Khan et al., 2007).Moderator temperaturewas varied from 293 K to 573 K in steps of 20 K and correspondingvalues of keff was calculated fromCITATION code. Then the reactivitywas calculated for each value ofmoderator temperature and plottedin Fig. 3. The reactivity coefficient follows the relationshipr¼�8E� 06TM2 þ 0.0017TMþ 6.1273. Its value came out to be lessnegative due to presence of graphite in TRISO fuel.

3.4. Void coefficient of reactivity

For calculating void reactivity coefficient, the void fraction inmoderator was varied from 5% to 35% shown in Table 3. Corre-sponding values of group constants and cross section weregenerated through WIMS-D/4 and keff by CITATION computer code.The reactivity coefficient was calculated by using the value of keffand the results are shown in Fig. 4. It was observed that reactivityfollows the relationship r¼�0.0014VM

2 � 0.0401VMþ 5.9254.

3.5. Combine effect of fuel and moderator coefficients of reactivity

In this analysis fuel temperature was varied from 300 K to1500 K andmoderator temperaturewas varied from 293 K to 573 K.The reactivity was calculated for each value of fuel and moderatortemperature. The coupled fuel and moderator temperature reac-tivity coefficient is plotted as function of fuel temperature in Fig. 5which follows the relationship r¼ 2E� 07Tf2� 0.0045Tfþ 7.3536. Itwas observed that the value of coupled reactivity coefficient islarger than the individual values of fuel and moderator tempera-ture reactivity coefficients.

3.6. Combine effect of fuel, moderator and void coefficients ofreactivity

The combine temperature coefficient is called the system overalltemperature coefficient. To obtain the system overall temperature

1000 1200 1400 1600

erature Tf (K)

ure on reactivity as a function of fuel temperature.

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

200 400 600 800 1000 1200 1400

Fuel temperature Tf (K)

ρ (%

Δk/k)

Fig. 6. System overall reactivity as a function of fuel temperature.

Table 4Reactivity coefficients.

Fuel temperature coefficient �3.34 pcmK�1

Moderator temperature coefficient �4.90 pcmK�1

Void reactivity coefficient �91.00 pcm%VM�1

System overall temperature coefficient �5.80 pcmK�1

A. Hussain, C. Xinrong / Progress in Nuclear Energy 53 (2011) 76e79 79

coefficient, the temperature profiles in Tables 2 and 3 have beenutilized. However somemodern and latest method may be used forthe calculation of these reactivity coefficients.

To account for the mutual coupling and to understand theinterrelated effect, all the coefficients were considered simulta-neously. As it is obvious that the rise in fuel temperature will alsoresults in rise in moderator temperature hence reduction in itsdensity and possible increase in void fraction. In this analysis fuel-temperature was varied from 300 K to 1500 K and moderatortemperature was varied from 293 K to 573 K in steps of 20 K. Themoderator void fractionwas also varied from5% to 35%. The coupledreactivity coefficient is plotted as function of fuel temperature Fig. 6,which follows the relationship r¼�5E� 07Tf2� 0.0049Tfþ 7.4733.It was observed that the value of coupled reactivity coefficient islarger than the individual values of fuel temperature, moderatortemperature moderator void reactivity coefficients.

The values of fuel, moderator and void temperature reactivitycoefficients were calculated from the gradient of reactivity curves

and all found negative which meet the design criteria (IAEA-NS-G-1.12, IAEA, 2005). The values are also listed in Table 4.

4. Conclusions

The aim of this research is to design a compact nuclear reactor byutilizingTRISO fuel inPWRtechnology toget thebenefitsof these twoexisting technologies. The presented study is focused on the calcu-lations of reactivity feedback coefficients. The values of Doppler,moderator, void and overall reactivity coefficients were found�3.34 pcmK�1,�4.90 pcmK�1,�91.00 pcm%VM

�1 and�5.80 pcmK�1

respectivelyat themiddleof fuel cycle.The researchalso revealed thatall reactivity feedback coefficients are coupled together as the rise infuel temperature will also result in the reduction of moderatordensity and formation of voids, consequently the rise in fueltemperature will cause variations in moderator and void reactivitycoefficients other than fuel temperature coefficient of reactivityalone.

References

Deen, J.R., Woodruff, W.L., 1995. WIMS-D 4M USER MANUAL, ANL Report 60439-4841. Argonne National Laboratory, 9700 South Cass Avenue.

DOE Fundamentals Handbook, 1993. Nuclear Physics and Reactor Theory, vol. 2 of 2DOE-HDBK-1019/2-93, Washington, D.C. 20585.

Fowler, T.B., Vondy, D.R., Cunningham, G.W., 1971. Nuclear reactor core analysisCode-CITATION. USAEC Report ORNL-TM-2496, Revision 2. Oak Ridge NationalLaboratory.

Hussain, A., Xinrong, C., 2009. Reactivity control technique for a pressurized waterreactor with an inventive TRISO fuel particle composition. Progress in NuclearEnergy 51 (6e7), 742e745.

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