Hot duct break transient with two- and three-loop ALLEGRO models

ALLEGRO is a concept of a small nuclear reactor with the primary aim to demonstrate the viability of the Generation IV (GFR) Gas cooled Fast Reactor technology and to ensure the experimental and qualification background for its new refractory fuel.

Available online 5 November 2020

0029-5493/© 2020 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Hot duct break transient with two- and three-loop ALLEGRO models

Guszt´av Mayer

Centre for Energy Research (EK), 1525 Budapest 114, P.O Box 49, Budapest, Hungary

A R T I C L E I N F O

Keywords:

Gas cooled fast reactor

Three-loop ALLEGRO

Hot duct break

CATHARE

Bypass transient

A B S T R A C T ALLEGRO is a concept of a small nuclear reactor with the primary aim to demonstrate the viability of the Generation IV (GFR) Gas cooled Fast Reactor technology and to ensure the experimental and qualification background for its new refractory fuel In the GFR development the so-called bypass transients represent a pivotal role during safety analysis Since the hot duct is located inside the cold duct there is no loss of coolant during the transient, nevertheless a huge core bypass may develop, which threatens the cladding integrity The current ALLEGRO design consists of two primary cooling loops but a three-loop version is also investigated In this paper the hot duct break transient is studied with a two- and three-loop ALLEGRO model by using the French CATHARE thermal hydraulics code The preliminary analysis showed that the three-loop model has a better cooling performance

1 Introduction

The development of ALLEGRO traces back to the beginning of the

2000′s when the GEN IV International Forum (GIF) selected the Gas

cooled Fast Reactor (GFR) technology as a future development direction

aiming at the closing of the fuel cycle, ensuring proliferation resistance,

sustainability, reliability and high thermal efficiency (Stainsby et al.,

2011) The development started by the collaboration of European

research institutes, universities and companies

As part of the European gas cooled fast reactor development, two

basic designs were developed parallel Both of them have helium

pri-mary coolant at a pressure of 7.0 MPa, circulated by the pripri-mary

blowers The first design is the GFR, which is the large-scale prototype of

the gas fast reactor technology with a thermal power of 2400 MW

(GFR2400) The second is the ALLEGRO, which is the demonstrator of

the GFR2400 and which has an envisaged thermal power of not higher

than 75 MW

The CEA 2009 ALLEGRO design has two secondary circuits with

pressurized water coolant at a pressure of 6.5 MPa The tertiary circuit of

ALLEGRO is an air cooler, which delivers the heat to the ambient air

There is no electricity production envisaged with ALLEGRO Since the

core outlet coolant temperature for these reactors is proposed to be at

about 800 ◦C, a new refractory carbide fuel is aimed to be developed,

which withstands this high temperature and the fast neutron spectrum

The primary aim of ALLEGRO is to qualify the new refractory carbide

fuel in fast neutron spectrum and in high temperature helium

environ-ment This newly tested and qualified fuel will be used later in the GFR-

2400 reactors Other important role of ALLEGRO as a demonstrator reactor is to show the viability of the helium cooled technology for the GFR-2400 reactors

Significant part of the current nuclear developments focuses on SMRs (small modular reactors) (Karol et al., 2015), which have the benefit of being manufactured at a plant and bringing to a site to be assembled Due to its relatively low thermal power ALLEGRO may also serve as an SMR The modularity, the less on-site construction may significantly decrease the costs, which makes the design favorable on the energy market Nevertheless, ALLEGRO being a fast spectrum reactor, the closure of the fuel cycle would also be beneficiary on the long term energy production

The predecessor of ALLEGRO was called ETDR (Experimental Technology Demonstration Reactor) (Morin et al., 2009) Later, the concept was redesigned and it was renamed to ALLEGRO (Poette et al., 2009b, 2009a) The new reactor concept, ALLEGRO featured a higher thermal power of 75 MW and two coolant loops in comparison to the earlier reactor concept of 50 MW and a single coolant loop The concept was investigated within several European and national projects Recently, the ALLEGRO reactor has been developed by a consortium named V4G4 Centre of Excellence (Gad´o, 2014), associating several research organizations and companies from Czech Republic, France, Hungary, Poland and Slovakia (V´acha et al., 2019)

Since there is still no experimental reference for the new carbide fuel

in fast neutron spectrum, ALLEGRO cannot directly be started with this fuel For that reason, a three-step methodology is planned to be used In the first step, the ALLEGRO core will contain MOX or UOX fuel with

E-mail address: gusztav.mayer@energia.mta.hu

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

https://doi.org/10.1016/j.nucengdes.2020.110911

Received 28 August 2020; Received in revised form 16 October 2020; Accepted 16 October 2020

which consists of stainless steel cladding, will have lower, 520 C outlet

temperature The different outlet temperatures will be reached by

adjusting some gagging at the inlet of each fuel sub-assembly Finally, in

the third core-configuration the already tested carbide fuel will be

loaded into the core Because of the good refractory properties of the

ceramic cladding the outlet temperature will be 800 ◦C for all the

subassemblies

The development of ALLEGRO is an iterative process A study (Mayer

and Bentivoglio, 2015), performed for the CEA 2009 ALLEGRO MOX

core by using the CATHARE thermal hydraulics code, pointed out that

the two-loop version of ALLEGRO satisfies the defined peak cladding

temperature (PCT) values for loss of flow accident (LOFA), loss of off-site

power (LOSP), loss of heat sink (LOHS), loss of coolant accident (LOCA

up to 10 in.) A new nitrogen injection strategy was proposed in order to

handle 1 in LOCA + blackout, 10 in LOCA + guard vessel failure, total

hot and cold duct break Nevertheless, another study (Mayer and

Ben-tivoglio, 2014) pointed out that the hot duct break transient aggravated

by the loss of the second loop may lead to higher PCT values than the

required limit in a conservative case Investigating this topic further, the

idea of using three primary loops instead of two has arisen to improve

the design The hypothesis is that in case of a three-loop design a single

failure has less effect on the PCT values, because there is one additional

loop - which is intact - for the heat removal Accordingly, this study

focuses on the differences between the cooling capabilities of the two-

and three-loop ALLEGRO models in case of hot duct break

This study does not contain uncertainty analysis of the hot duct break

transient, because the primary goal is to show the difference between the

cooling capabilities of the two- and three-loop models Of course, the

final safety analysis of ALLEGRO should definitely be supported by

uncertainty analysis

The novelty of this paper is that it compares the cooling performance

of the two- and the three-loop ALLEGRO models for the hot duct break

initiating event, which is aggravated by the failure of one of the two

primary blowers The newly developed three-loop ALLEGRO input deck

is available for future studies with wide range of scenarios like LOCA,

LOFA, etc and it supports the designers to make decision in the two- or

three-loop question

2 The CEA 2009 ALLEGRO design

Fig 1 shows the main cooling loops of CEA 2009 ALLEGRO design It

consists of two primary and three decay heat removal (DHR) loops The

two main loops are used parallel and the DHR loops are closed in normal

operation The core is cooled by helium at pressure of 7 MPa The

blowers are driven by the main motors with electrical power of 418 kW

and a smaller power pony motor is mounted to the same shaft in order to

ensure cooling in case of scram The successful scram signal switches off

the main motors and starts the pony motors to maintain the blower

primary system to secondary system leakage accident (PRISE) The water coolant is circulated by the secondary pumps Since the electricity production is not envisaged in ALLEGRO, the heat is removed from the secondary circuit by an air cooler, the ultimate heat sink is the ambient air

When the heat removal from the core by using the two primary loops

is not sufficient, the primary valves close, the DHR valves open and the DHR blowers start parallel The secondary circuit of the DHR loops contains pressurized water at 1.0 MPa and there is no active element in

it Since the flow is driven by natural circulation, the heat exchangers are located highly above the core The tertiary circuit of the DHR loop is a pool, which ensures cooling capacity for 24 h by the vaporization of its water content It is sized to dissipate the decay heat by purely natural convection, if the system is pressurized Since the hot duct break tran-sient belongs to the Category 4 trantran-sients (see later at fuel acceptance criteria), the DHR loops do not play any role in this study The heat is removed by the use of the main heat exchangers and the main blowers are driven by their pony (auxiliary) motors

The three-loop model has the same structure (Fig 2), the only dif-ference is that it has a third primary cooling loop The power of the core

is the same in both the two- and three-loop models One important advantage of the three-loop model against the two-loop model is that it

is more resistant to single failure For instance, in case of a hot duct break in the first loop and a blower failure in the second loop, there is still a third cooling loop available in the three-loop model In the two- loop model only the first blower is supposed to run, even though it is located in the broken loop In case of the three-loop model both the first blower in the broken loop and the third blower in the intact loop are supposed to operate According to this, in case of the three-loop model only the 1/3 of the total blower capacity is lost instead of the ½

3 Representation of hot duct guillotine break

In the current ALLEGRO design the hot duct (hot leg) is located in-side the cold duct (cold leg) as it can be seen in Fig 3a In this concentric pipe arrangement a thermal insulation is necessary between the hot and the cold ducts (Fig 3b) to decrease the heat exchange In this arrange-ment three kinds of breaks can be imagined In the first only the hot duct and its insulation are broken and the cold duct remains intact In the second case the cold duct is broken and the hot duct remains intact In the third both the hot and cold ducts are broken In the first case there is

no depressurization of the system, because the break is inside the cold duct, which is the outer boundary of the primary circuit Nevertheless, there is a huge core bypass (see Fig 3a) In the second case, when the cold duct is broken, there is a LOCA transient in which there is a depressurization of the primary circuit In order to keep necessary backup pressure for this scenario a so-called guard vessel is used, which encompasses the whole primary circuit and can maintain maximum

Fig 1 The cooling loops of CEA 2009 ALLEGRO design

10–13 bar backup pressure In the third case there is a LOCA transient

and a core bypass transient at the same time This research focuses on

the first case, in which the hot duct is broken and the cold duct remains

intact and there is no depressurization of the system and no LOCA

Until the cold duct remains intact, the classical 200% size break –

which is usually supposed in most of the pressurized water reactor

(PWR) analyses – can geometrically be excluded because of the lack of

sufficient space in the cold duct The two new hot duct parts (as a result

of the guillotine break) have a large diameter each and they have no

sufficient place to move in perpendicular directions generating two fully

opened pipes On the other hand, the shrinking of the hot duct in axial

direction is possible due to the fast and high temperature change of the

pipe wall The axial displacement of the hot duct (Fig 4) is also possible

due to the flexible supports in the heat exchangers, which are designed

to ease the thermomechanical stresses caused by the elongation of the

pipe In this study the hot duct break size was selected between 20% (~127 mm = 5 in.) and 100% (600 mm = 23.6 in.) of the inner hot duct diameter without supposing any other objects (debris of insulation, liner, etc.) in the flow path

In case of hot duct break, the pressure loss between the hot and the cold ducts plays a major role during the transient The lower is the pressure loss coefficient the higher core bypass may develop In a pre-vious study this value was selected to be 0.549 (Mayer and Bentivoglio,

2014) In a recent paper by using the computational fluid dynamics (CFD) technique (Farkas et al., 2019) the pressure loss coefficient was found to be around the value of 1.0 Keeping in mind that the CFD codes use turbulence models, which may bring some uncertainty into the calculations, and to stay conservative, the smaller value of 0.549 was selected for all of these calculations in the present study

4 The CATHARE code

The French proprietary CATHARE 2 V2.5_3 code with its graphical user interface GUITHARE is developed by CEA, EDF, FRAMATOME and IRSN Originally it was elaborated for thermal hydraulic simulation of pressurized and boiling water reactors, but later its validity was extended for gas cooled reactors The code was validated against exist-ing system loops with gas coolant (Bentivoglio and Tauveron, 2006, 2008; Bentivoglio and Messi´e, 2008; Polidori et al., 2013) and was used for transient analysis of GFR2400MW (Mayer and Bentivoglio, 2015), and code-to-code benchmarks of ALLEGRO (Bubelis et al., 2008; Kvizda

et al., 2019) Recently, the application of the code was extended for gases where the ideal gas equation of state is not valid (Mauger et al.,

2019)

5 Hot duct break model

The simulation of the ALLEGRO hot duct break with a one- dimensional code like CATHARE is limited Since the hot duct is in-side the cold duct, in case of hot duct break the hot and the cold ducts are connected to with a simple pipe element There is a valve in this pipe, which is closed during normal operation When the break is initialized this valve is opened Fig 5 shows the bypass which is formed due to the opening of the valve

Fig 2 The cooling loops of the three-loop ALLEGRO design

Fig 3a Representation of ALLEGRO hot duct break For the sake of simplicity

only the broken loop is depicted Dashed arrows show decreased coolant mass

flow rate through the core due to the huge core bypass There is no LOCA, since

the outer boundary of the primary circuit remains intact

Fig 3b The cross section of ALLEGRO ducts The hot duct is located inside the

cold duct

Fig 4 Representation of the hot duct guillotine break of ALLEGRO There is a

gap between the two hot duct parts, which causes a core bypass

6 The new three-loop ALLEGRO input deck

In the European VINCO project, a code-to-code benchmark was

performed by the members of the V4G4 consortium (Kvizda et al., 2019)

using the CATHARE2, RELAP5-3D and MELCOR codes In that work

each participant developed an own input deck, which were based on an

earlier CEA input and on a new ALLEGRO database and benchmark

specification In this work the VINCO input deck is used for the two-loop

modeling On the other hand, for the three-loop calculations the

development of a new ALLEGRO input was necessary In this study,

using the two-loop VINCO ALLEGRO CATHARE input deck, a new three-

loop model was developed to simulate the hot duct break scenario In the

followings the modifications between the two models are described

6.1 Core

Since this study focuses primarily on the thermal hydraulic processes

in ALLEGRO, the reactor core and its neutronic parameters were kept

identical in both the two- and three-loop models In this way, it is easy to

compare the cooling capabilities of the two models

In the VINCO benchmark (Kvizda et al., 2019) a new thermal

hy-draulics core model was used, in which the thermal inertias of the

reflector and shielding materials were modeled As a result, the

calcu-lated maximum cladding temperatures were significantly lower

compared to the case when the thermal inertia of the inner elements

were neglected Nevertheless, those calculations may contain large

un-certainties concerning the heat exchange coefficients, because the lack

of the current experimental support In order to stay conservative, in this

paper the inner coupling between the heat structures in the core (as it

was modeled in the VINCO project) are neglected for both the two- and

three-loop models

6.2 Main heat exchangers

The CEA 2009 ALLEGRO model contains two main heat exchangers

(MHX), which remove 37.5 MW thermal power individually In order to

remove the same thermal power with three loops (25 MW/MHX), the

following modifications were carried out The heating perimeter of the

heat exchangers and the flow areas were decreased to the 2/3 of the two-

loop model on both the primary and secondary side of the MHXs This

ensures similar velocity distribution in the two- and three-loop models in

the MHXs

6.3 Air cooler

In the three-loop model, similarly to the MHXs, the air cooler was

modeled by decreasing the number of heat exchanger pipes to the 2/3 of

the original number of the two-loop model This was achieved by

modifying the heat exchange perimeter The flow area at the tertiary

side was also decreased by the same factor in order to get similar ve-locity distribution in the air cooler

6.4 DHR blowers

The DHR loops and blowers do not play any role in the hot duct break transient, since the DHR valves are closed during the whole procedure For this reason, there were no modifications in the new input deck regarding the DHR loops

6.5 Main blowers

The main primary blower characteristic is described with a nondi-mensional head and torque map in the original VINCO model In this study the same map is used for the two-loop calculations, but the reference values of the blower were modified Since the total mass flow rate of the three-loop ALLEGRO core remained unchanged, its nominal value in each loop was set to the 2/3 of the two-loop version This modification influenced the nominal torque of the blowers The nominal head of the blowers remained unchanged

6.6 Piping

The length and diameter of the primary hot and cold ducts were not modified in the three-loop ALLEGRO model The pressure loss co-efficients along the loops were identical in the two- and the three-loop models

7 Nodalization scheme

The input deck developed in the earlier projects was the starting point of this study Its simplified nodalization scheme is shown in Fig 6

On the left hand side there is the core The upper and the lower plenums are represented by CATHARE VOLUME elements There are four chan-nels that represent the inner part of the core: two bypasses, one average and one hot channel They are modeled by using the so-called AXIAL elements The reflector and shielding is also taken into account at the bottom and at the upper part of these channels Between the hot and the cold ducts there is an AXIAL element which connects them This is the representation of the internal break used in the simulations For the sake

of simplicity, only one secondary and one tertiary circuit is shown on the right hand side of Fig 6 The main heat exchanger (MHX) is represented

by using two axial elements, one on the primary and a second in the secondary circuit The pressure of the secondary circuit is maintained by the pressurizer The tertiary circuit consists of only one axial element and two boundary conditions The three DHR loops, the guard vessel, the nitrogen injection lines are not depicted since they do not play any role in the hot duct break scenario

Fig 5 Representation of the hot duct break modeling in the two-loop ALLEGRO model The red arrow represents the break flow After the closure of the second

valve (Main valve 2) the second loop has no effect The three DHR loops are closed during the transient (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

8 Acceptance criteria for fuel

Acceptance criteria for the ALLEGRO MOX cladding can be found in

(Kvizda et al., 2019) In case of design extension condition (DEC) the

proposed limit is 1300 ◦C, which is the melting temperature of the

cladding If the PCT remains below this limit the cladding integrity is

ensured For categories 3 and 4 the 850 ◦C temperature maximum is

proposed On the one hand, it is the limit of cladding burst at high (100

bar or higher) pressure difference On the other hand, it is the maximum

temperature of strong pellet cladding mechanical interaction (PCMI)

with the irradiated, brittle cladding For categories 1 and 2 the limit of

620 ◦C for the cladding temperature is proposed Since the break of the

total hot duct belongs to the category 4 transients, the corresponding

temperature limit for the fuel cladding is 850 ◦C

9 Results

9.1 The role of blower inertia

The hot duct break transient starts with the opening of the break

between the hot and the cold ducts in the first loop This is accomplished

by the opening of the valve between the hot and the cold ducts as it was

described previously At the same time - as a single failure criterion - the

blower and its pony motor in the second loop are supposed to be out of

operation Since the opening of the break causes a large core bypass, the

“power to mass flow rate” signal activates the scram, which stops the reactor and results in the decreasing of core power according to Fig 7 The sequence of events of the investigated transients can be found in

Table 1 The scram signal lets the absorbers fall into the core and at the same time it also switches the main blowers off This action is needed to avoid the fast overcooling of the fuel and its cladding in most of the scram cases, because of the low thermal inertia of the ALLEGRO core As the main blower rotational speed in the first loop (Fig 8) decreases to 20%

of its nominal value, a pony motor – which is mounted to the same shaft -

is activated and it maintains the 20% rotational speed of the main blower during the whole transient

Four hot duct break transients were investigated with a break size of 23.6 in., which is the inner diameter of the hot duct In the first case, the two-loop input deck of ALLEGRO with a blower inertia of 10 kg*m*m was used The remaining three simulations were carried out by using the new three-loop model with blower inertias of 6.7, 10 and 20 kg*m*m The 6.7 kg*m*m value in the three-loop model corresponds to the same

Fig 6 Representation of the ALLEGRO CATHARE nodalization scheme The internal break is modeled by using an axial element, which connects the hot and cold

the ducts Only one primary loop is depicted The three DHR loops are not presented

Fig 7 Reactor power on logarithmic scale

Table 1

Sequence of events and maximum peak cladding temperatures

Simulation id

Number of primary

Moment of scram 3.4E− 04 3.4E− 04 3.4E− 04 6.9E− 04 s Stop of 1st main

motor 6.8E− 04 6.8E− 04 6.8E− 04 1.4E− 03 s Stop of 2nd main

motor 6.8E− 04 6.8E− 04 6.8E− 04 1.4E− 03 s Stop of 3rd main

Start of 2nd pony

Closure of main

Partial closure of

Peak cladding

total primary rotational inertia of the two-loop model (6.667*3 = 10*2)

It can be seen in Fig 8 that if the blower inertias are 10 kg*m*m in both

models, then the first blower reaches the 20% rotational speed about 5 s

earlier in the two-loop model than in the three-loop model If the 6.67

kg*m*m value for the blower inertia is set for the three-loop model then

the rotational speeds of the 1st blower are almost identical in the two-

and in the three-loop model It is not surprising because the total inertia

of the blowers in the primary circuit is the same for both models in this

case When the 20 kg*m*m blower inertia is selected for the three-loop

model (total of 60 kg*m*m for the three blowers), the rotational speed of

the first blower reaches the 20% of its nominal value significantly later,

at about 33 s It will soon be clear, that this ensures better cooling

performance and lower peak cladding temperature at the beginning of

the transient

The pony in the second loop is supposed not to operate because of the

single failure criterion, and as a result of this the main blower finally

stops Fig 9 shows the second blower rotational speed for all of the

previously mentioned four cases It can be seen that as the blower inertia

is higher, the time instance of the stop of the blower is also higher It

should be noted that the value of the blower friction was the same in all

models

In the third loop the blower rotational speed decreases up to the 20%

of its nominal value, where the pony is activated which maintains the

flow during the rest of the transient (Fig 10) Of course, in the two-loop

model there is no third loop and there is no third blower

Shortly after the pony motors in the first and third loops are activated

and maintain the 20% rotational speed of the nominal value of the main

blowers, the mass flow rate in the second loop becomes negative, which

may damage the second blower In order to avoid this issue, the blower

protection signal partially closes (stem position of the valve is 5%) the

main valve in the second loop when the rotational speed ratio compared

to the two other blowers becomes lower than 80% This is depicted in

Fig 11 When the second blower rotational speed reaches the 5% of its nominal value, the valve in the second loop closes fully (stem position is 0%) It can be seen in Fig 11 that similarly to the previous examples the blower inertia influences the partial and the full closure time instants of the second valve The larger blower inertia results in more delayed valve closure actuation If the total inertias of the blowers are equal, the time instances of the actuation in the two- and three-loop models are very close to each other There are no primary valve actuations in the first and

in the third loop during the transient, the stem positions are kept con-stant Of course, in steady state conditions the stem positions are controlled values to ensure the desired mass flow rates in the loops

Fig 12 depicts the core mass flow rate, which is mainly influenced by the pressure rise of the blowers and the pressure losses throughout the system including the hot duct break (The core pressure loss in nominal conditions is roughly 0.8 bar and in the heat exchanger 0.2.) It can be seen that at the first 100 s of the transient the core mass flow rates are very similar in the two- and three-loop models - when the total blower inertias are the same - but after that point the mass flow rate in the two- loop model becomes higher Other outcome for the three-loop model is that the core mass flow rates are higher for the larger blower inertias until the startup of ponies Later, the mass flow rates become very similar in the three-loop calculations

Fig 13 shows that the steady mass flow rate through the break be-tween the cold and the hot ducts is one order higher compared to the core mass flow rate (Fig 12) During the first minute of the transient the blower inertia has a large effect on the break mass flow rate It is mainly driven by the rotational speed of the blowers Obviously, the blowers with higher inertia generate higher break mass flow rates After reaching the 20% pony speed, the break mass flow rates of the different models become very similar In the two-loop model the final break mass flow rate is slightly smaller than in the three-loop model

Fig 8 Rotational speed of the main blower in the first loop for

different models

Fig 9 Rotational speed of the main blower in the second loop for

different models

Fig 10 Rotational speed of the main blower in the third loop with different

blower inertias

Fig 11 Valve positions in the second loop

The peak cladding temperature has a limit of 850 ◦C for the

ALLE-GRO MOX core in Category 4 transients Fig 14 shows the time

evolu-tion of maximum cladding temperature The break size is 23.6 in for

each simulation It can be seen that the peak cladding temperature for

the two-loop model is the highest amongst all cases, even if the 6.7

kg*m*m blower inertia is used in the three-loop model The temperature

difference is 31 ◦C It can also be seen that if the blower inertia in the

three-loop model is 20, then the peak cladding temperature is below the

850 ◦C limit, even if the break size is the largest

9.2 The effect of break size

In the previous example a guillotine break was envisaged at the hot

duct near the reactor downcomer with the conservative assumption of a

24.6 in (100%) break size In ALLEGRO cross duct geometry the

classical 200% hot duct break is not possible because of geometrical reasons, without the break of the cold duct (total cross duct – break of both the hot and the cold ducts) Nevertheless, in case of a small break at the hot duct, the steel material of the pipe in the vicinity of the break may dramatically be overcooled in a relatively short time, which may result in high thermal stresses and increased crack propagation In the roughly 10 m long DHR ducts the 100% break size is theoretically imaginable, if conservative considerations are taken into account by supposing the shrinking of the hot duct caused by the fast and sudden temperature drop

In Figs 15 and 16 the maximum cladding temperatures can be seen for different break sizes for the two- and three-loop models, respectively Considering smaller break sizes, the peak cladding temperature is decreasing In order to show more comparative results between the two- and the three-loop ALLEGRO versions, we suppose that the total blower inertia is the same for both models

According to Fig 15 the PCTs fall below the 850 ◦C criterion in case

of the 15 in or smaller break sizes When the three-loop model is used (Fig 16) the PCT criterion fulfils for break sizes up to 20 in., even if the

decreased 20/3 ≈ 6.7 kg*m*m inertia is used for each blower 9.3 Two loops versus three loops

Selecting the 23.6 in break size and comparing the two- and three- loop models with the 10 kg*m*m and the 6.6667 kg*m*m inertia, respectively, the whole picture may seem contradictory, because the PCT in the three-loop model is lower by 31 ◦C compared to the two-loop model, despite the fact that the results show very similar core mass flow rates for both models during the first two minutes of the transients It can

be explained by Fig 17, which shows the lower plenum temperatures Since the coolant flows from the lower plenum to the core, its temper-ature influences the cladding tempertemper-ature It can be seen that there is a lower inlet core temperature in case of the three-loop model than in the two-loop model The difference is 31 ◦C This explains the better per-formance of the three-loop model It should be noted that in the three- loop model the third primary circuit is operating during the transient, because the single failure criterion was used only for the second blower The upper plenum temperature (Fig 18) reveals more difference between the models in case of 23.6-inch hot duct break In the three-loop model the upper plenum temperature is significantly lower than in the two-loop model Closer analysis of the data showed that in case of the three-loop model the operating third blower changes the main flow di-rections according to Fig 19 A relevant portion of the third loop coolant does not flow into the core but into the break in the first loop It changes the flow direction towards the upper plenum in the first loop As a result

of that the cold helium coolant flows directly to the upper plenum, which causes low temperature The mass flow rates from the upper plenum towards the first loop hot duct inlet can be seen in Fig 20 The

Fig 12 Core mass flow rate

Fig 13 Break mass flow rate

Fig 14 Maximum cladding temperature Fig 15 Maximum cladding temperatures for the two-loop model for different break sizes The inertia of both blowers is 10 kg*m*m

figure shows that as the primary valves in the second loops are closed,

the mass flow rate in the first loop of the two-loop model becomes

positive, opposed to the three-loop model in which it stays negative The

cold helium flows to the upper plenum directly This explains the low

upper plenum temperature in the three-loop model in Fig 18

10 Conclusion

The difference between the cooling performances of the two- and

three-loop ALLEGRO models were investigated in case of hot duct break

develops

The core model was the same in both the two- and three-loop ver-sions In the three-loop model the heat exchange surfaces and loop mass flow rates were decreased to the 2/3 of the two-loop model The total blower inertia was kept constant in one of the three-loop examples for easy comparison

The results showed that the peak cladding temperature was lower by

31 ◦C in case of the three-loop model than in the two-loop model, if the total blower inertias (20 kg*m*m for all the systems, i.e 2*10 for the two-loop system and 3*6.667 for the three-loop system) were identical The main reason of this is that the lower plenum temperature is also lower in the three-loop simulation The calculations showed larger,

65 ◦C difference in PCTs between the two- and three-loop models, when the inertia of each blower was the same (10 kg*m*m for each) The increased blower inertia led to significantly lower PCT values From cooling point of view, increasing the blower inertia seems a promising tool in case of hot duct break Nevertheless, the fast over-cooling of the cladding should be avoided in case of other initiating events, when the scram is actuated and the core cooling is good, for instance in loss of flow accident (LOFA) This suggests that the blower inertia should have a carefully selected trade-off value in ALLEGRO The effect of the hot duct break size was studied by varying the diameter of the pipe, which represents the hot duct break This pipe connects the hot and the cold ducts in this break model The results showed that the break size plays a major role in the final peak cladding temperatures For this reason, it is important to elaborate an ALLEGRO design in which the hot duct break with large break sizes is practically eliminated or at least the probability of the accident is low

To sum up the results, three main conclusions for the ALLEGRO developers can be drawn Firstly, the gain coming from the additional (third) loop is not very significant compared to the two-loop version in case of hot duct break transient It is not necessarily worth the extra cost which occurs due to the construction of the third primary loop Never-theless, it has to be emphasized that in these calculations the hot and the cold duct diameters were the same for both the two- and three-loop models For this reason, further studies would be beneficial in which the diameter of the three-loop hot and cold duct is proportionally decreased This decreased diameter may increase the benefit of the three-loop model against the two-loop model in the sense of PCT In addition, further future studies are necessary to assess the effect of bypass transients at different break locations of ALLEGRO Such a study may reveal larger gain in PCT between the two- and three-loop models Additionally, in this study the break was supposed not to have any debris

in the cooling path, which may significantly influence the cooling capability of the loops Since the debris in the cooling path increases the risk of blower failure, the three-loop model may have more benefit Secondly, increasing the blower rotational inertia, instead of using three loops, may help a lot in the sense of peak cladding temperature, which design modification may result in a much lower building cost Thirdly, the relevance of the three cooling loops may be more sig-nificant for other initiating events such as total cross duct break which needs to be further investigated The question of using two or three primary loops in ALLEGRO is still under consideration and it should be supported by probabilistic safety assessment (PSA) studies too

CRediT authorship contribution statement Guszt´av Mayer: Conceptualization, Methodology, Software,

Vali-dation, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization, Project administration, Funding acquisition

Fig 16 Maximum cladding temperatures for the three-loop model for different

break sizes The inertia of each blower is 6.67 kg*m*m

Fig 17 Lower plenum temperatures

Fig 18 Upper plenum temperatures

Declaration of Competing Interest

The authors declare that they have no known competing financial

interests or personal relationships that could have appeared to influence

the work reported in this paper

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Fig 19 Representation of the hot duct break modeling in the three-loop ALLEGRO model after the closure of the second loop valve The red arrows represent the

break flow and the direction changes compared to the two-loop model (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig 20 The evolution of mass flow rates coming from the upper plenum to the

inlet of the hot ducts in the first (broken) loop