Annals of Nuclear Energy 37 (2010) 582–591

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Annals of Nuclear Energy

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Simulation of uncontrolled loss of flow transients of a material test researchreactor fuelled with low and high enriched uranium dispersion fuels

Farhan Muhammad *

Department 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 25 August 2009Received in revised form 16 December 2009Accepted 27 December 2009Available online 27 January 2010

0306-4549/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.anucene.2009.12.019

* Tel.: +92 51 2207381; fax: +92 51 2208070.E-mail address: farhan73@hotmail.com

The effects of using low and high enrichment uranium fuel on the uncontrolled loss of flow transients in amaterial test research reactor were studied. For this purpose, simulations were carried out of an MTRfuelled separately with LEU and HEU fuel, to determine the reactor performance under loss of flow tran-sients with totally failed external control systems. The coolant pump was assumed to loose its perfor-mance and the coolant flow rate reduced according to the relation m(t)/m0 = exp(�t/25) to a newstable level. The new reduced flows m/m0 = 0.2, 0.4, 0.6 and 0.8 were modeled. The nuclear reactor anal-ysis code PARET was employed to carry out these calculations. It was observed that the reactors stabilizedat new power levels which were lower than the original power level, with the power of HEU fuelled reac-tor slightly lesser than that of the LEU fuelled reactor. However, at the start of transient, the LEU fuelledreactor had a lower power level resulting in lower fuel, clad and coolant temperatures than the HEUfuelled reactor.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

There are a large number of research reactors around the worldbeing used for different purposes. Different reactors use differentfuels of varying uranium enrichment and fuel materials. The firstresearch reactors were fuelled with HEU based fuels having ura-nium enrichment of around 90% in 235U isotope. Later, due to pro-liferation concerns, the HEU based fuels were abandoned in favourof LEU based fuels having uranium enrichment of 20% in 235U iso-tope, since 20% fuel enrichment is an isotopic barrier for weaponusability (Glaser, 2005). Almost all new reactors are now being de-signed to use LEU based fuels. The older ones using HEU fuels arebeing converted to use LEU fuels. The IAEA also devised a standardbenchmark MTR (IAEA-TECDOC-233, 1980) in order to facilitatereactor conversion. Many theoretical calculations have been per-formed and reported in different documents (IAEA-TECDOC-233,1980; IAEA-TECDOC-643, 1992) citing the difference in the twocores under different conditions. The reported thermal hydraulicsanalysis includes the steady state analysis, the controlled tran-sients comprising of fast and slow reactivity insertion and loss offlow transients, and uncontrolled reactivity insertion transient.

It can happen that all the external control mechanisms of areactor fail to respond to some transient event, since the all theexternal control mechanisms have a non-zero failure probability(Lamarsh, 1982). In such a situation, the reactor behavior is deter-

ll rights reserved.

mined solely by the reactivity feedbacks of the reactor. This featureof a reactor is also termed as the inherent safety control of thereactor. The pumps may either fail totally or partially resulting inreduced coolant flow.

Loss of flow is an important transient in nuclear reactor tech-nology and no analysis regarding uncontrolled loss of flow of anMTR has been reported in the available literature, although con-trolled LOFA has been reported frequently (Woodruff et al., 1996;Bokhari et al., 1999; Hainoun et al., 2008). Need is therefore feltto have some benchmark calculations and the difference in HEUand LEU based fuels be worked out. The work presented in this pa-per focuses on the transient behavior of the 10 MW IAEA bench-mark reactor (IAEA-TECDOC-643, 1992) using both HEU and LEUfuels separately, after loss of flow and disabled external controlsystems.

2. Reactor description

The reactor analysed is the same one utilized for the benchmarkproblem solved in IAEA-TECDOC-233, with the water in the centralflux trap replaced with a 7.7 cm � 8.1 cm block of aluminum con-taining a square hole 5.0 cm on each side (IAEA-TECDOC-643,1992). Description of the reactor core is given in Table 1 andFig. 1. The outline schematic of an MTR based on the IAEA bench-mark reactor is given in Fig. 2 showing the main coolant pump andthe path of the coolant flow. Other details could be found in the ref-erence documents (IAEA-TECDOC-233, 1980; IAEA-TECDOC-643,1992).

Nomenclature

ANL Argonne National LaboratoryDe equivalent diameterDNBR departure from nucleate boiling ratioHI coolant enthalpy at inletHf enthalpy of saturated liquidHfg enthalpy required to convert saturated liquid to satu-

rated vapourHEU high enriched uraniumkf fuel thermal conductivityq0 0 0 volumetric heat generation rateL channel lengthLEU low enriched uraniumMDNBR minimum departure from nucleate boiling ratioMTR material test reactorP0 initial steady state reactor powerPmax maximum power attained by the reactorm0 normal steady state coolant flow ratem coolant flow rateq heat generation rateq0 0 heat flux rateq0 0 0 volumetric heat generation rateTb coolant bulk temperature

Tclad,max maximum temperature attained by the cladTfuel,max maximum temperature attained by the fuel (centre-line

temperature)Tout outlet temperature of the coolantTout,max maximum outlet temperature attained by the coolantTsat coolant saturation temperatureTB transition boilingbeff effective delayed neutron fractionK prompt neutron generation timeqf density of liquidqg density of vapourqc reactivity from the reactor power control systemqfb reactivity from thermal hydraulic feedbackqi reactivity inserted by the initiating eventqsd shutdown or trip reactivityqU uranium density in fuelqFT;max fuel temperature feedback reactivityqMT;max moderator temperature feedback reactivityqME;max moderator expansion feedback reactivityqTotal;max total feedback reactivityl coolant viscositylw coolant viscosity at wall temperature

F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591 583

3. Analysis procedure

3.1. Simulation methodology and modelling of core in PARET

The PARET code (Obenchain, 1969) was used to carryout thethermal hydraulics and transient analysis. It is basically a coupledneutronics–hydrodynamics-heat transfer code employing pointkinetics, one-dimensional hydrodynamics, and one-dimensionalheat transfer technique. The code was originally developed forpower reactors for the analysis of SPERT-III experiments (Scottet al., 1967) and was later modified (Woodruff, 1983) to includeflow correlations, and a properties library that was consideredmore applicable to the low pressure, temperatures and flow ratesencountered in research reactors.

In this code, a two-channel model was used to analyse the core;one channel representing the hottest plate and flow channel whilethe other ‘‘average” channel representing the remaining fuel platesin volume weighted sense. The axial source distribution was repre-sented by 21 axial regions and a chopped cosine shape which hasan axial power peaking factor of 1.5 for both the ‘‘average” channeland the hot channel. For the hot channel, this axial distribution was

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

Active core height 60.0 cmExtrapolation length 8.0 cm (in 8.0 cm distance from theSpace at the grid plate per fuel element 7.7 cm � 8.1 cmFuel element cross-section 7.6 cm � 8.05 cm including supportMeat 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 tNumber of fuel plates per control element 17 Identical plates, each 0.127 cm tIdentification of the remaining plate positions

of the control elementFour plates of aluminum, each 0.127third standard plate position; water

Specifications of the UAlx–Al fuel Enrichment 90 w/o U-235 in HEU, 272 w/o of uranium in the UAlx–AlOnly U-235 and U-238 in the fresh fuelTotal power 10 MWthXenon-State Homogeneous Xenon content correNominal coolant flow rate (m3/h) 1000Coolant inlet temperature (�C) 38

multiplied by the other specified hot channel factors i.e. 1.4 nuclearand 1.2 engineering (1.4 � 1.2 = 1.68). A linear approximation wasused for all of the reactivity feedback coefficients. The correlationsused in the PARET code to perform the desired calculations wereSeider–Tate correlation for single phase flow, Jens–Lottes correla-tion for two phase flow, original PARET model for transient twophase flow, and original PARET model for DNB calculations (Table2). The PARET code and simulation methodology have been vali-dated and used in our recent publications (Muhammad and Majid,2009a,b).

3.2. Nuclear reactor thermal hydraulics and feedback reactivitygeneration

The simplified dynamic reactor model used in the PARET code isgiven in Fig. 3. There can be two transient initiating events; reactiv-ity insertion transient and loss of flow transient. Since this workdeals with the loss of flow transients, the processes occurring inthe ‘‘core heat transport” module (Fig. 3) are being elaborated below.

Heat generated in the fuel due to fission, is conducted out of fuelthrough clad and taken out of reactor core by the coolant. Heat

core, the cosine-shaped flux goes to zero)

plate

hickhick

cm thick in the position of the first, the third, the twenty-first, and the twenty-gaps between the two sets of aluminum plates0 w/o U-235 in LEU

sponding to average-power-density

Graphite Graphite Water

Water25% 5%

Water45% 45% 25%

45% 5%25%

ControlElement

7.7cm

8.1cm

y

Aluminium Block

x

0.127

0.219

6.3

0.4756.640.475

Fuel plate

Coolant channel

Fig. 1. IAEA 10 MW benchmark reactor configuration and the fuel elementconfiguration showing the coolant channels as defined in IAEA-TECDOC-643 (1992).

Table 2Heat transfer correlations for different heat transfer regimesa.

Flow/heat transferregime

Correlation

Single phase flow Seider–Tate

Nu ¼ 0:023Re0:8Pr1=3 llw

� �0:14

Two phase flow Jens–Lottes

Tb � Tsat ¼ 60 expð�p=900Þ½ � q00=106h i1=4

Transient 2-phaseflow

Original PARET model

q00TB ¼ q00DNB � jTB½Tclad � ðTcladÞDNB�;jTB is a constant

DNBR Original PARET model

q00DNB ¼ ð0:23� 106 þ 0:094mÞ½3:0þ 0:01ðTsat � TbÞ�0:485þ 1:23 exp �0:0093 L

De

� �h i½1:7� 1:4 expð�aÞ�;

a ¼ 0:532 Hf�HI

Hfg

h i3=4 qf

qg

� �

a Obenchain (1969).

584 F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591

flow out of thin plate-type fuel elements as those of an MTR, can betaken as flowing only in x-direction (Lamarsh, 1982; Todreas andKazimi, 1990). For any time n, the temperature difference betweenthe fuel centreline and clad surface is given by

Tnfuel;max � Tn

c ¼ _qn a2kf A

þ bkcA

� �ð1Þ

The heat removed by the coolant from the clad surface is given by

_qn ¼ hA Tnc � Tn

cool

� �ð2Þ

While the heat carried away by the coolant is given by

_qn ¼ _mncp Tncool;out � Tn

cool;in

� �ð3Þ

Since the flow rate is decreasing with time (Table 4), the tem-peratures of all the materials, namely fuel, clad and coolant startto increase. Any change in fuel and coolant temperatures results

Main pump

Holdup and storage tanks

Main reactor pool

Fig. 2. Simplified schematic diagram of the primary co

in reactivity feedbacks (Ott and Neuhold, 1985). For a reactor withnegative reactivity feedback coefficients, a negative reactivity isproduced. Thus, loss of flow transient becomes a reactivity inducedtransient. In reactivity induced accidents, the reactor power, after areactivity insertion, has an exponential behavior given by (Stacey,2004)

PðtÞ ¼ P0 expZ t

0

qðt0Þ þ kqðt0Þb� qðt0Þ dt0

� ð4Þ

Since the induced reactivity due to feedbacks is negative, thereactor power starts to fall. The reactivity q(t) that drives the tran-sient is the net effect of contributions arising from several mecha-nisms (Mirza et al., 1998):

qðtÞ ¼ qiðtÞ þ qfbðtÞ þ qcðtÞ þ qsdðtÞ ð5Þ

Since it has been postulated in this work that the loss in thepump performance goes un-noticed by all the external control sys-tems, no control reactivity or shutdown reactivity is inserted in thereactor. Hence, the reactor power is driven by the feedback reactiv-ity only and Eq. (5) above simply becomes

qðtÞ ¼ qfbðtÞ ð6Þ

Heat exchanger

Coolant flow direction

olant flow of the 10 MW IAEA benchmark reactor.

Σ

[ ρ i(t) ]

Reactor kinetics

Reactivity feedback

Reactor control system

Reactor trip system

[ ρ(t) ]

[ ρ fb(t) ]

[ ρc(t) ]

[ ρsd(t) ]

[ P(t) ]

Core heat transport

.

[ ( ), ( )]wT t m t

( )

( )

( )

f

c

w

T t

T t

T t

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Initiating event (reactivity insertion)

Initiating event (loss of flow)

Feedback signals’ path

Fig. 3. Simplified reactor dynamics model (Obenchain, 1969; Lewis, 1977).

F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591 585

Since the feedback coefficients are negative, the reactivity intro-duced in the reactor is negative which results in reduced reactorpower according to Eq. (4). As the reactor power decreases, thetemperatures of fuel, clad and coolant start to fall reducing themagnitudes of feedback reactivities. Ultimately, a new balance isreached between the coolant flow and reactor power, and the reac-tor power stabilizes at a new level. In this study, since the externalreactivity insertion has been disabled, it will be the internally pro-duced feedback reactivity only that will try to control the reactor.This will also find the effectiveness of the inherent safety of thereactor fuelled with fuels of different enrichment.

Table 4Conditions specified for loss of flow transient.

Condition Value

Initial critical power of reactor 10

4. Results and discussions

A two-channel model was utilized in the PARET code. The hotchannel is the place of highest temperatures in a reactor. All theother channels including the average channel has temperatureslower than that of the hot channel. Therefore, if the hot channelsatisfies the limiting conditions, all the other channels will also sat-isfy them. Therefore, the results compared here are of the hottestchannel only. The values of the reactivity feedback coefficientsfor temperature from 38 �C to 50 �C for LEU were taken fromMuhammad and Majid (2009a) while that for HEU from IAEA-TECDOC-643 (1992), Appendix G-1 were used. They are alsosummarized in Table 3. Other reactor conditions used in thetransient calculations are given in Table 4.

Table 3Reactivity coefficients and parameters used in transient analysis.

Reactivity coefficient/parameter Value

LEU HEUc

beff 0.007185a 0.0076071K (ls) 44.03a 55.96Coolant temperature (�106 Dk/k per �C) �95.9600b �125.2128Void/density (�103 Dk/k per �C) �0.28387b �0.29920Doppler (�106 Dk/k per �C) �26.7200b �0.2739Fuel thermal conductivity (W/m K)c 50.0 158.0Fuel heat capacity (MJ/m3 K)c 2.04600 0.001067T+2.0721Clad thermal conductivity (W/m K)c 180.0 180.0Clad heat capacity (MJ/m3 K)c 2.40840 2.40840

a Muhammad and Majid (2008).b Muhammad and Majid (2009a).c IAEA-TECDOC-643 (1992).

4.1. Steady state

Thermal hydraulic data of the hot channel for reactor operatingat steady state is given in Table 5. As seen from the table, only thefuel maximum temperature of the LEU fuel is more than that of theHEU fuel by 0.9 K due to higher thermal conductivity of the later.All other parameters are same for both the fuels.

4.2. Transient calculations

The coolant pump slow down was modelled by reducing thecoolant flow rate according to relation (7) given below, with thereactor operating at its full power of 10 MW and reactor trip mech-anism disabled.

_mðtÞ ¼ _m0e�t

25 ð7Þ

The relation presented in Eq. (7) has been used to describe slowloss of flow in reference document (IAEA-TECDOC-643, 1992). Fourdata points of 0.2, 0.4, 0.6 and 0.8 for _m= _m0 were used. _m= _m0 valueof 0.2 corresponds to natural cooling flow rate in case of totalpump failure (IAEA-TECDOC-643, 1992).

(MW)Flow reduction rate e�

t25

Reactor scram initiation point Scram disabledHot channel factors (a). Radial � local power peaking

factor = 1.4(b). Axial power peaking factor = 1.5(c). Engineering factor = 1.2

Table 5Steady state thermal hydraulics data.

Parameter HEU LEU a

Power (MW) 10.0 10.0Tfuel,max (�C) 75.5 76.4Tclad,max (�C) 73.8 73.8Tout (�C) 53.2 53.2MDNBR 10.6 10.6

a Muhammad and Majid (2009a).

586 F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591

4.2.1. Reactor powerAs seen from Fig. 4, the power of LEU reactor is slightly lesser than

that of the HEU reactor at the beginning of the transient. Later on, thepower of HEU fuelled reactor becomes lesser than that of the LEUfuelled reactor. This trend continues till the reactor reaches newsteady state power level. The new steady state power levels for_m= _m0 values of 0.2, 0.4, 0.6 and 0.8 for HEU fuels were 1.99 MW,

3.94 MW, 5.90 MW and 7.86 MW respectively, while for LEU fuel,they were 2.17 MW, 4.20 MW, 6.13 MW and 8.08 MW respectively.

Since only the feedback reactivity defines the reactor power inthe absence of any outside interference, these feedbacks are ana-lysed here. Looking on the different feedback reactivities, it is seenthat the fuel temperature (or the Doppler) feedback reactivity(Fig. 5) plays an important and definite role in uncontrolled lossof flow transient. As seen from Fig. 5, the Doppler feedback fromHEU fuel is almost zero, and despite of the fact that the othertwo (moderator temperature (Fig. 6) and moderator expansion(Fig. 7)) feedback reactivities of the HEU fuel are greater than thatof the LEU fuel, the total feedback reactivity (Fig. 8) of the LEU fuelis greater than that of the HEU fuel in the early stages of the tran-sient. This helps in keeping the reactor power low and the maxi-mum fuel, clad and moderator temperatures of the LEU fuelledreactor lower than those of the HEU fuelled reactor. As seen fromTable 6, the maximum values of fuel temperature reactivity feed-back for LEU fuel are �0.05189$, �0.03172$, �0.01766$ and�0.00719$ compared with �0.00054$, �0.00031$, �0.00018$and �0.00007$ of HEU for _m= _m0 values of 0.2, 0.4, 0.6 and 0.8respectively. The maximum values of moderator temperature andmoderator expansion feedback reactivities of HEU fuel are morethan that of the LEU fuel. The maximum values of moderatortemperature reactivity feedback for LEU fuel are �0.09529$,�0.05165$, �0.02748$ and �0.01181$ compared with�0.12396$, �0.06523$, �0.03531$ and �0.01493$ of HEU for_m= _m0 values of 0.2, 0.4, 0.6 and 0.8 respectively. The maximum

0

2

4

6

8

10

Time (s)

Pow

er (M

W)

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e flo

w

0

2

4

6

8

10

Time (s)

Pow

er (M

W)

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e flo

w

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

0/ 0.2. .m m =

0/ 0.6. .

m m =

Fig. 4. Reactor power and relative coolant flow

values of moderator expansion reactivity feedback for LEU fuelare �0.09827$, �0.04983$, �0.02561$ and �0.01061$ comparedwith �0.09827$, �0.04983$, �0.02561$ and �0.01061$ of HEUfor _m= _m0 values of 0.2, 0.4, 0.6 and 0.8, respectively. However,due to large difference in the fuel temperature feedback reactivity,the value of total feedback reactivity is larger for LEU fuel than theHEU fuel. The maximum values of total reactivity feedback for LEUfuel are �0.23295$, �0.12700$, �0.06841$ and �0.02881$ com-pared with �0.22512$, �0.11732$, �0.06110$ and �0.02561$ ofHEU for _m= _m0 values of 0.2, 0.4, 0.6 and 0.8, respectively.

4.2.2. Fuel temperatureThe fuel temperature, in addition to the reactor power, also de-

pends on the fuel thermal conductivity (Eq. (1)) which is differentfor the fuels under consideration. Therefore, the fuel temperaturesof HEU fuel are generally lesser than those of the LEU fuel (Fig. 9).For the higher values of 0.8 and 0.6 of _m= _m0, the maximum tem-peratures of the LEU fuel reached during the transient stage arehigher than those of the HEU fuel due to lower thermal conductiv-ity of LEU fuel. But for lower values 0.4 and 0.2 of _m= _m0, the max-imum fuel temperature of LEU fuel is lower than that of HEU fueldue to lower power of the LEU fuelled reactor (Table 6). However,at the new steady state, the HEU fuel temperature is lower thanthat of the LEU temperature due to higher thermal conductivityand lower power of HEU fuel (Table 7). The new steady state max-imum fuel temperatures for _m= _m0 values of 0.2, 0.4, 0.6 and 0.8 forHEU fuels were 66.4 �C, 69.9 �C, 71.9 �C and 73.5 �C respectively,while for LEU fuel, they were 69.0 �C, 72.2 �C, 73.9 �C and 75.2 �Crespectively.

4.2.3. Clad temperatureThe maximum clad temperature reached during the transient

remained lower for the LEU fuel due to its lower power duringthe transient and the difference was higher for lower values of

0

2

4

6

8

10

Time (s)

Pow

er (M

W)

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e flo

w

0

2

4

6

8

10

Time (s)

Pow

er (M

W)

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e flo

w

0/ 0.4. .

m m =

0/ 0.8. .

m m =

HEU LEU

Rel. Flow

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

during uncontrolled loss of flow accident.

F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591 587

_m= _m0 (Fig. 10). The difference between the maximum clad tem-peratures reached during the transient (Table 6) was 0.2 K,0.6 K, 1.2 K and 2.0 K for _m= _m0 values of 0.8, 0.6, 0.4 and 0.2respectively.

At the new steady state, the maximum clad temperature of theHEU fuel was lesser than that of the LEU fuel (Table 7). The differ-ence between the maximum clad temperatures at the new steady

-0.06

-0.04

-0.02

0.00

0.02

Time (s)

Feed

back

reac

tivity

($)

-0.06

-0.04

-0.02

0.00

0.02

Time (s)

Feed

back

reac

tivity

($)

0/ 0.2. .m m =

0/ 0.6. .m m =

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 5. Fuel temperature feedback reactivity d

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

0/ 0.2. .m m =

0/ 0.6. .m m =

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 6. Moderator temperature feedback reactivit

state was 0.8 K, 1.3 K, 1.8 K and 2.4 K for _m= _m0 values of 0.8, 0.6,0.4 and 0.2 respectively.

4.2.4. Coolant temperatureThe coolant outlet temperature reached during the transient

remained lower for the LEU fuel due to its lower power duringthe transient and the difference increased as the value of

-0.06

-0.04

-0.02

0.00

0.02

Time (s)

Feed

back

reac

tivity

($)

-0.06

-0.04

-0.02

0.00

0.02

Time (s)

Feed

back

reac

tivity

($)

0/ 0.4. .m m =

0/ 0.8. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

uring uncontrolled loss of flow accident.

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

0/ 0.4. .m m =

0/ 0.8. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

y during uncontrolled loss of flow accident.

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

Time (s)

Feed

back

reac

tivity

($)

0/ 0.2. .m m = 0/ 0.4

. .m m =

0/ 0.8. .m m =0/ 0.6

. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 7. Moderator expansion feedback reactivity during uncontrolled loss of flow accident.

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Time (s)

Feed

back

reac

tivity

($)

0/ 0.2. .m m = 0/ 0.4

. .m m =

0/ 0.8. .m m =0/ 0.6

. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900 0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 8. Total feedback reactivity during uncontrolled loss of flow accident.

588 F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591

_m= _m0 decreased (Fig. 11). The difference between the coolantoutlet temperatures reached during the transient (Table 6) was0.0 K, 0.3 K, 0.7 K and 1.3 K for _m= _m0 values of 0.8, 0.6, 0.4and 0.2 respectively.

At the new steady state, the coolant outlet temperature of theHEU fuel was lesser than that of the LEU fuel (Table 7) due to lowerpower of the HEU fuel. The difference between the coolant outlettemperatures at the new steady state (Table 6) was 0.4 K, 0.7 K,

Table 6Thermal hydraulics data during transient phase.

Parameter HEU LEU HEU LEU HEU LEU HEU LEU

_m= _m0 0.2 0.4 0.6 0.8Tfuel,max �C

(s)108.5 (40.436) 107.0 (40.419) 95.2 (23.071) 94.7 (23.043) 86.7 (12.942) 87.0 (12.914) 80.4 (5.786) 81.2 (5.750)

Tclad,max �C(s)

107.7 (40.438) 105.7 (40.424) 93.9 (23.074) 92.7 (23.049) 85.4 (12.944) 84.8 (12.919) 78.9 (5.788) 78.7 (5.753)

Tout,max �C(s)

78.8 (40.842) 77.4 (40.831) 66.7 (23.306) 66.0 (23.284) 60.4 (13.103) 60.1 (13.076) 56.2 (5.903) 56.2 (5.870)

qFT;max $ (s) �0.00054(40.095)

�0.05189(40.368)

�0.00031(21.496)

�0.03172(23.100)

�0.00018(13.606)

�0.01766(12.952)

�0.00007(5.539)

�0.00719(5.800)

qMT;max $(s)

�0.12396(39.100)

�0.09529(39.152)

�0.06523(22.100)

�0.05165(24.395)

�0.03531(13.009)

�0.02748(12.986)

�0.01493(5.829)

�0.01181(5.799)

qME;max $(s)

�0.09827(41.684)

�0.08624(39.209)

�0.04983(24.395)

�0.04362(22.100)

�0.02561(13.016)

�0.02328(12.991)

�0.01061(5.834)

�0.00981(5.810)

qTotal;max $(s)

�0.22512(41.684)

�0.23295(39.196)

�0.11732(24.395)

�0.12700(23.100)

�0.06110(12.970)

�0.06841(12.981)

�0.02561(5.829)

�0.02881(5.801)

Quantity in brackets is the time at which the given quantity occurred.

Table 7Thermal hydraulics data at new steady state.

Parameter HEU LEU HEU LEU HEU LEU HEU LEU

_m= _m0 0.2 0.4 0.6 0.8Power

(MW)1.99 2.17 3.94 4.20 5.90 6.16 7.86 8.08

Tfuel,max

(�C)66.4 69.0 69.9 72.2 71.9 73.9 73.5 75.2

Tclad,max

(�C)66.1 68.5 69.3 71.1 71.0 72.3 72.3 73.1

Tout (�C) 53.1 54.6 53.0 54.0 53.0 53.7 53.0 53.4MDNBR 32.2 29.4 18.9 17.7 14.4 13.7 12.1 11.8

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

0/ 0.2. .m m = 0/ 0.4

. .m m =

0/ 0.8. .m m =0/ 0.6

. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900 0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 9. Maximum fuel temperature during uncontrolled loss of flow accident.

F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591 589

1.0 K and 1.4 K for _m= _m0 values of 0.8, 0.6, 0.4 and 0.2 respectively.No coolant boiling of any type took place for any of the above cases.

4.3. The inherent safety of an MTR

From the above results, it is clear that any undetected loss offlow in an MTR does not pose any threat to the reactor integrity.The reactor is able to control itself due to its inherent safety fea-tures and reduces its power without any outside interference.The new steady state power reached is almost of the order of thereduced flow, i.e. _m= _m0. The reactor is more stable thermal hydrau-lically at new steady state power as seen from the reduced MDNBRvalues given in Table 7. The temperatures of fuel and clad remainwell below their melting points while that of the coolant remainswell below the saturation temperature. Also, no sub-cooled boilingtook place in any of the cases discussed fulfilling an importantsafety requirement for MTR’s (Bokhari et al., 2002). However, theHEU fuel has lesser power at new steady state level than the LEUfuel, resulting in better thermal hydraulic stability.

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

60

70

80

90

100

110

Time (s)

Tem

pera

ture

(°C

)

0/ 0.2. .m m = 0/ 0.4

. .m m =

0/ 0.8. .m m =0/ 0.6

. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900 0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 10. Maximum clad temperature during uncontrolled loss of flow accident.

50

55

60

65

70

75

80

85

Time (s)

Tem

pera

ture

(°C

)

50

55

60

65

70

75

80

85

Time (s)

Tem

pera

ture

(°C

)

50

55

60

65

70

75

80

85

Time (s)

Tem

pera

ture

(°C

)

50

55

60

65

70

75

80

85

3002001000Time (s)

Tem

pera

ture

(°C

)

0/ 0.2. .m m = 0/ 0.4

. .m m =

0/ 0.8. .m m =0/ 0.6

. .m m =

HEU LEU

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Fig. 11. Coolant outlet temperature during uncontrolled loss of flow accident.

590 F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591

4.4. Limitations of the PARET code

PARET has been developed to analyse an MTR in an open loop(Obenchain, 1969). Hence, it is unable to model primary closedloop of a reactor. The results obtained by using this code can beaccurate in case the heat exchanger (Fig. 2) extracts all the heatfrom the coolant that enters it and the coolant temperature enter-ing the core remains constant (38 �C in this case). In case this does

not happed, then the temperatures of all the reactor materials(including fuel, clad and coolant) will be more than calculated inthis work.

5. Conclusions

MTR is an inherently safe reactor as far as loss of flow accidentsare concerned. Both the HEU and LEU fuelled reactors can control

F. Muhammad / Annals of Nuclear Energy 37 (2010) 582–591 591

themselves without any external interference. The LEU has advan-tage of lower power and temperatures during the transient phasedue to its higher Doppler feedback reactivity. However, the newsteady state power of the HEU fuelled reactor is lower than theLEU fuelled reactor.

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