A review of existing SuperCritical Water reactor concepts, safety analysis codes and safety characteristics

SuperCritical Water Reactor(SCWR) applies water beyond the thermodynamic critical point as the coolant, which aims to achieve high efficiency around 45% compared to 33% for existing commercial light water reactors.

Available online 22 September 2022

0149-1970/© 2022 The Authors Published by Elsevier Ltd This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Review

A review of existing SuperCritical Water reactor concepts, safety analysis

codes and safety characteristics

Pan Wua,*, Yanhao Rena, Min Fenga, Jianqiang Shana,b, Yanping Huangc, Wen Yangc

aSchool of Nuclear Science and Technology, Xi’an Jiaotong University, No 28 Xianning West Road, Xi’an, Shaanxi, China

bThe State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

cNuclear Power Institute of China, Cheng Du, 610000, China

A R T I C L E I N F O

Keywords:

Supercritical water reactor

Safety performance

System code development

A B S T R A C T SuperCritical Water Reactor(SCWR) applies water beyond the thermodynamic critical point as the coolant, which aims to achieve high efficiency around 45% compared to 33% for existing commercial light water reactors In order to raise the reactor operating temperature and reactor criticality, the existing SCWR core designs are quite different from those of boiling water reactors or pressurized water reactors, which further effect their safety performance and safety system design A comprehensive review on existing developed SCWR reactor concepts of different countries, including pressure-vessel type and pressure-tube type SCWRs, as well as thermal, fast and mixed spectrum SCWRs, is carried out to deeply explain the core design features of SCWR The development methods of safety analysis tool for SCWR are also summarized to shed a light on the key scientific difficulties and how these problems are solved up to now All the special techniques applied to enable trans-critical simulations are still unphysical and lack of validation Moreover, the safety characteristics of existing SCWR concepts are discussed Based on these review work and discussions, the research status of SCWR concepts, safety analysis tool development and safety characteristics are clearly presented Safety analysis tool validations and more comprehensive accident evaluations should be further carried out to better illustrate the safety performance of these SCWR concepts

1 Introduction

SuperCritical water-cooled reactor,abbreviated as SCWR, owns

unique core design using water above the critical point as coolant, which

is quite different from other Generation-IV reactor concepts (

Schulen-berg et al., 2011) A large amount of research interests arose from

nu-clear industry and academic community for its huge advantages in high

thermal efficiency, simple system configuration as well as good

tech-nical inheritance from existing commercial power plants SCWR reactor

system operates under pressure of 25 MPa(374 ◦C, 22.1 MPa is the water

critical point) and applies water as the coolant and moderator Coolant

heated by the reactor fuels is directly led to turbine to produce power,

which makes SCWR own a similar system configuration as Boiling Water

Reactor(BWR) At the same time, successful operation of supercritical

and ultra-supercritical thermal power plant (Buongiorno et al., 2003)

facilitates application of supercritical water as heat transfer medium

Though SCWR has so many advantages, it also has some

shortcom-ings to overcome Because of demand of large coolant enthalpy rise

through the core, the ratio of mass flowrate over thermal power of SCWR

is much lower than those of pressurized water reactor (PWR) as well as boiling water reactor (BWR) The ratio of mass flowrate over thermal power of SCWR is around 1/12 of that of PWR and around 1/10 of that

of BWR, which indicates that SCWR has higher fuel temperature rise when loss of flow accident(LOFA) happens and has a quicker depressurizing process when loss of coolant accident(LOCA) happens Meanwhile, the specific heat of overheated SCW in upper core region is quite low When accidents happen to SCWR, the coolant and the fuel material will encounter a huge temperature rise, which is negative for the reactor safety Many researchers have worked on how to improve SCWR safety performance under normal operation and accidents through unique core designs and innovative safety system designs In

2019, IAEA-TECDOC-1869 (IAEA, 2019) summarized the research sta-tus of supercritical water reactor, which focused on the contents related

to reactor design, including the existing reactor type, thermal hydraulics and material and chemistry while little information on the system code development and SCWR safety performance is included

In this paper, reactor core and safety system designs developed by

* Corresponding author

E-mail address: wupan2015@mail.xjtu.edu.cn (P Wu)

Contents lists available at ScienceDirect Progress in Nuclear Energy

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

https://doi.org/10.1016/j.pnucene.2022.104409

Received 6 May 2022; Received in revised form 23 August 2022; Accepted 8 September 2022

different countries and institutions are extensively reviewed At the

same time, the safety analysis tool development methodologies and

safety performances of different types of SCWR concepts are also deeply

reviewed to provide some insights for further SCWR development

2 Existing rector concept development

From the aspect of core structure, SCWR concepts can be divided into

pressure tube type and pressure vessel type Canadian SCWR(Yetisir

et al., 2016) applies pressure tube to contain the high-pressure coolant

and fuel in the reactor core while SCWR concepts developed by other

countries apply pressure vessel to contain the coolant and fuels From

the aspect of neutron energy level, SCWR concepts could be divided into

fast spectrum type(Oka et al., 2010a), thermal spectrum type(Wu et al.,

2014)(Oka et al., 2010a; Ishiwatari and Oka et al., 2010b; Novog et al.,

2012) and mixed spectrum type SCWR(Xu et al., 2011; Liu et al., 2013)

In this section, SCWR concepts from different countries will be

exten-sively reviewed

2.1 Chinese SCWR concepts

There are two main types of theoretically mature Chinese SCWR

concepts, which are CSR1000 which is named as Chinese supercritical

water-cooled reactor and the SCWR-M which is named as mixed

spec-trum supercritical water-cooled reactor Thermal specspec-trum is used for

CSR1000, whereas mixed neutron spectrum is used for SCWR-M (Zhu

et al., 2012; Liu et al., 2013; Wu and Geffraye et al., 2011)

2.1.1 CSR1000

In 2014, Nuclear Power Institute of China (NPIC) proposed CSR1000

which is a pressure-vessel SCWR (Wu et al., 2014) CSR1000 applies

thermal spectrum while supercritical water is assumed to cool the core

and moderate the neutrons Coolant and moderator will be strongly

mixed in the lower plenum The thermal power and electrical power of

CSR1000 are 2300 MW and 1000 MW respectively The temperature at

the entrance of the core is 280 ◦C whereas the temperature at the exit of

the core is 500 ◦C, as a result, the thermal efficiency of CSR1000 can

reach 45% In order to have a more even distribution of axial power,

CSR1000 applies a two-pass core design, which is shown in Fig 1(a) The

difference in coolant temperature in different flow channels are shown

in Fig 1(b)

There are 177 fuel assemblies in CSR1000 reactor core The first and

second-pass cores consist 57 assemblies and 120 assemblies, respec-tively The distribution of two pass fuel assemblies is shown in Fig 2

Fig 3 shows the cross section of fuel assembly, consisting of 4 sub- assemblies and 4 water rods Water flowing through these two paths acts as moderator and coolant simultaneously Additionally, for better

Abbreviations

ACR Advanced Candu Reactor

ADS Automatic Depressurization System

AECL Atomic Energy of Canada Limited

AFS Auxiliary Feedwater System

ATWS Anticipated Transient Without Scram

BWR Boiling Water Reactor

CANDU Canadian Deuterium Uranium Reactor

CANFLEX CANdu Flexible

CGNPC China Guangdong Nuclear Power Corporation

CR Control Rood

CSR1000 Chinese Supercritical Water-Cooled Reactor

ESBWR Economic Simplified Boiling Water Reactor

GDCS Gravity Driven Core Cooling System

HEC High Efficiency Fuel Channel

HPLWR High Performance Light Water Reactor

ICS Isolation Condenser System

LOCA Loss Of Coolant Accident

LOECC Loss Of Emergency Core Cooling

LOFA Loss Of Flow Accident LPCI Low Pressure Core Injection System MCST Maximum Cladding Surface Temperature MOX Mixed Oxide Fuel

MSIV Main Steam Isolation Valve NPIC Nuclear Power Institute of China PCCS Passive Containment Cooling System

PT Pressure-Tube

PV Pressure-Vessel PWR Pressurized Water Reactor R&D Research And Design RMT Reactor Make-Up Tank RPV Reactor Pressure Vessel SCP Supercritical Parameters of Water Coolant SCWR Supercritical Water-Cooled Reactor SCWR-M Mixed Spectrum Supercritical Water-Cooled Reactor SRV Safety Release Valve

SUPER FR Supercritical Fast Reactor SUPER LWR Supercritical Light Water-Cooled Reactor VVER Water-Water Energetic Reactor

Fig 1 The flow scheme in CSR1000 and corresponding coolant temperature

variation(Wu et al., 2014)

control of reactivity, cross-shaped control rods are used

2.1.2 SCWR-M

Unlike CSR1000, in order to avoid serious problems that may be

encountered in mechanical design and safety analysis (Zhu et al., 2012),

proposed a mixed core design scheme in which the fuel assemblies are

divided into multiple layers, and this design scheme can simultaneously

achieve high core exit temperatures (Zhu et al., 2012; Liu et al., 2013)

The Chinese mixed spectrum reactor(SCWR-M) core is made up of

thermal spectrum core and fast spectrum core Fig 4 shows the

distribution of fuel assemblies in SCWR-M The core of SCWR-M is made

up of 284 fuel assemblies while 164 fuel assemblies locates in the outer zone reacting with thermal spectrum neutrons and 120 fuel assemblies locates in the inner zone reacting with fast spectrum neutrons (Liu et al.,

2013) For the zone with thermal spectrum, as shown in Fig 5(a), there are three layers of fuel assemblies with varying fuel enrichment at different heights The fast zone is designed to be short in order to in-crease neutron leakage so that SCWR-M can obtain a negative void reactivity feedback, which is shown in Fig 5(b)

The flow path is shown in Fig 6 Low-temperature water enters the pressure vessel and flows upward into the upper chamber, after which it flows into both the coolant and the moderator channels, with the 25 percent of coolant flowing into the moderator channel in the zone of thermal Then coolant flows out of the zone of thermal spectrum into the lower chamber, and from the lower chamber it flows into the fast zone The temperatures at the entrance and the exit of reactor core are 280 ◦C and 510 ◦C respectively

The average line power of the core is 18 kW/m The active heights of the thermal zone and the fast zone are 4.5m and 2.0m respectively

2.2 Japanese SCWR concepts

Japan carried out researches and design works for fast and moder-ated SCWR concepts simultaneously Water is used as a moderator and works in Super LWR in form of water rods Water rod is a space in the core filled with light water Its presence ensures negative void reactivity and provide additional emergency core cooling injection during acci-dents Meanwhile a fast neutron spectrum SCWR named Super FR, is also under development In order to ensure a negative void coef-ficientZirconium hydride layers are used for Super FR Both of these different concepts will be introduced to compare respective behaviors (Oka et al., 2010a)

2.2.1 Super LWR

The University of Tokyo proposed Super LWR for the first time which includes a once-through coolant cycle without recirculation line, as shown in Fig 7 Some of the plant parameters are also included in Fig 7 After design updates, the feed water temperature of Super LWR is

Fig 2 Fuel assembly distribution of CSR1000(Wu et al., 2014)

Fig 3 Cross section of CSR1000 fuel assembly(Wu et al., 2014)

Fig 4 Fuel assemblies distribution in SCWR-M(Xu et al., 2011) Fig 5 Struture of fuel assembly of SCWR-M

updated to be 290 ◦C and the reactor exit temperature is 510 ◦C The thermal and electric powers are 4039 MW and 1725 MW respectively As shown in Fig 8, Super LWR applies a two-pass core, in which the fuel assemblies located at the outer region of reactor core are cooled firstly

by the downward flowing coolant The coolant flows upward through the fuel assemblies located at the inner side of the core after mixing in the lower chamber The arrangement of fuel assembly in the core is shown in Fig 9, with 372 fuel assemblies being divided into three-batch fueling()

The fuel design of Super LWR uses UO2 for fuel pellets, which is the same as that of LWRs The material of the fuel cladding is stainless steel and nickel-based alloy The design of fuel assembly, which is the same as that of LWR, is shown in Fig 10

2.2.2 Super-fast reactor

Super FR’s flow circulation is the same as that of the Super LWR which has already been shown in Fig 7 Since fast reactors do not require moderators, the power density of fast reactors is much higher than that of thermal reactors, which further result in better economy The operating conditions of Super FR and Super LWR are totally the same The pressure of reactor when it’s normally operated is 25 MPa, while the temperatures of reactor core’s inlet and outlet are 280 ◦C and

508 ◦C respectively

The principle of mixed-oxide fuel(MOX) design of the Super FR needs

to accommate high Pu content, except which the principle is the same as that of the Super LWR A zirconium hydride layer is placed in the blanket fuel assemblies to make the reactor has a negative coolant void reac-tivity, which is shown in Fig 11 The arrangement of the reactor core is shown in Fig 12(Oka et al., 2010a)

Super FR also applies two-pass flow, as shown in Fig 13 (Oka et al., 2010a) The coolant flows downward through the blanket assemblies and part of the seed assemblies The coolant gathered in the lower plenum flows through the rest part of seed assemblies Two-pass flow core is helpful to increase the reactor operating temperature while satisfy the cladding temperature design limits

2.3 Canadian SCWR

Canadian SCWR is only pressure-tube type SCWR concept It was updated from the mature CANDU in several aspects The main features

of CANDU have been preserved, such as modular fuel channels

Fig 6 Flow paths in the core(Xu et al., 2011)

Fig 7 Flow circulation of coolant cycle for Super LWR(Oka et al., 2010a)

Fig 8 Schematic diagram of coolant flow inside core(Oka et al., 2010a) Fig 9 The fuel assembly distribution of the core(Oka et al., 2010a)

configuration and selecting heavy water as the moderator Canadian

SCWR’s operating pressure is 25 MPa, while the temperatures of core’s

inlet and outlet are 350 ◦C and 625 ◦C respectively The thermal power

and the electric power are 2540 MW and 1200 MW with a thermal

ef-ficiency of 48%(Novog et al., 2012)

‘No-core-melt’ concept is proposed for Canadian SCWR The

radia-tion heat exchange between fuel rods inside the pressure tube and the

low temperature heavy water moderator outside the pressure tube can

carry away the decay heat of the fuel under extreme operating

condi-tions, which greatly reduces the probability of core meltdown in the

reactor

There are 336 fuel channels in the core of Canadian SCWR The

average channel power is 7.5 MW(t) The schematic map of the design of

Canadian SCWR is shown in Fig 14 Coolant entering each pressure tube

flows into the center channel downward first and then flows upward to carry away heat.(Khartabil, 2008)

The design of the fuel assembly has experienced a series of upgrades,

as shown in Fig 15 Each channel includes a single fuel assembly while a stainless-steel fuel cladding remains in direct contact with the fuel pellets

2.4 European SCWR-HPLWR

SCWR developed by the European Union is a pressure vessel type reactor, which is called High Performance Light Water Reactor (HPLWR) The operating pressure of HPLWR is 25 MPa and the tem-perature of core exit is 500 ◦C The thermal power and the electric powers are 2300 MW and 1000 MW respectively The structure of pressure vessel of HPLWR is shown in Fig 16(Allison et al., 2016) The unique feature of HPLWR core design is that it applies a three- path flow scheme, which is shown in Fig 17(a) Since there are three processes of coolant flow, the heating process of coolant is also divided into 3 stages Meanwhile, the core of HPLWR is separated into three parts, which is shown in Fig 17(b)

Each fuel assembly has an assembly box which has 9 sub-assemblies with total 40 fuel rods in it and an additional moderator box in the

Fig 10 Design of fuel assembly for Super LWR

Fig 11 Fuel assemblies of Super FR(Oka et al., 2010a)

Fig 12 Fuel assembly distribution of the core for Super FR(Oka et al., 2010a)

Fig 13 Two-pass flow core of Super FR

Fig 14 Schematic map of conceptual Canadian SCWR core design

center Cross section of HPLWR fuel assembly is shown in Fig 18

(Starflinger et al., 2010)

2.5 Russian SCWR concept-VVER-SCP

The Russian SCWR concept(VVER-SCP) is developed with reference

to VVER, PWR and BWR reactors The fuel material for VVER-SCP could

be uranium dioxide, MOX fuel, and other kinds of fuel The temperatures

of the core’s inlet and outlet are 280 ◦C and 540 ◦C respectively The efficiency of VVER-SCP increases from 40% to 44–45% Unusually, VVER-SCP applies single-pass coolant flow scheme The coolant flow scheme of single-pass core is shown in Fig 19 Compared with the

Fig 15 The fuel assembly design of the Canadian SCWR

Fig 16 The structure of pressure vessel of HPLWR(Allison et al., 2016)

multiple-pass flow scheme applied by other SCWR core designs, single-

pass core has advantages in system simplification while it may also lead

to non-uniform power distribution along the axial direction with large

hot channel factor(Kalyakin and Kirillov et al., 2014)

2.6 Korean SCWR concept -SCWR-R

A 1400MWe SCWR concept named SCWR-R, is developed by Korea Atomic Energy Research Institute Different from other thermal type SCWR concepts, SCWR-R applies cruciform-type solid moderator(U/ ZrH2), instead of water or heavy water, to provide additional modera-tion and simplify the core structure, which is helpful for decreasing the power peak The design of fuel assembly is shown in Fig 20 There are

300 fuel rods in each fuel assembly, whereas 25 cruciform-type solid moderator pins, and 16 single solid moderator pins The core of SCWR-R includes 193 fuel assemblies using a typical four-batch fuel-loading pattern Meanwhile, there are jet pumps installed in the downcomer to enable coolant recirculation, as shown in Fig 21, which is helpful to decrease the rise of enthalpy in the core The core flowrate of SCWR-R is

6441 kg/s and the flowrate and temperature of the feedwater is around

2518 kg/s and 280 ◦C Internal circulation results in the increase of core inlet temperature from 280 to 350 ◦C(Bae et al., 2008), which is beyond the pseudo critical temperature High core inlet temperature helps avoid

Fig 17 Design of thermal care

Fig 18 Design of HPLWR fuel assembly (Allison et al., 2016)

Fig 19 Coolant flow scheme of single-pass core(Kalyakin and Kirillov

et al., 2014)

Fig 20 Fuel assembly design

risks of flow instability and heat transfer deterioration inside the core

(Bae et al., 2007)

3 Discussion

The basic operating parameters of supercritical water reactors in

various countries are summarized in Table 1 As can be seen from the

table, SCWR can achieve high cycle efficiency because of its higher

outlet temperature SCWR concepts can be designed as thermal, fast or

mixed neutron spectrum type Most of SCWR designers apply multiple

passes to make up the core, which aims to reduce the coolant outlet

temperature of each pass-through coolant pre-mixing in the lower

plenum or upper plenum This is because that SCWR has a very large

coolant enthalpy rise between core inlet and outlet, which is eight times

of that of existing PWR reactors Thus, a hot channel factor of 2 would

result in coolant outlet temperature of 1200 ◦C in single-pass core

configuration, which exceed the coolant temperature limit by a large

degree(Schulenberg et al., 2011) Another method to decrease the

enthalpy rise inside the core is achieved through adding an internal

circulation, which is adopted by Korean designers

On the aspects of SCWR applied moderator, most of the SCWR

concepts applied water as moderator, which also act as coolant as well Some SCWR concepts don’t need moderator, such as VVER-SCP Cana-dian SCWR applies heavy water as moderators while Korean SCWR-R applies cruciform-type solid moderator pin

Beyond these key differences, the above design concepts have many similar challenges which provides the possibility for existing SCWR re-searchers to collaborate with each other, for example, materials selec-tion for fuel cladding and reactor internal components, water chemistry study applicable for all SCWR concepts As well as thermal-hydraulics and safety analysis For the aspect of thermal-hydraulics and safety, there are huge gaps in SCWR’s heat transfer and critical flow database for SCWR concept development Data from the SCWR prototype pile are needed The unique thermohydraulic behavior and sharp property changes with water around the critical point needs to be investigated more deeply A test reactor needs to be designed and built to provide verification and reference for the reactor design and fuel design

4 Safety analysis tool development for SCWR

Safety analysis code is an essential analysis tool for SCWR safety evaluation and safety system design As SCWR apply water as coolant, its safety analysis code has many similarities with those used for PWR or BWR Many researchers take advantage of mature PWR commercial safety analysis codes’ predicting ability under subcritical pressure and expand these codes’ application range to supercritical pressure Through this method, a large amount of pressurized accidents and depressurized accidents with slow depressurization rate can be evaluated However, there are still problems when coolant system pressure decreases quickly

to subcritical pressure, which is a typical process in loss of coolant ac-cident(LOCA) scenario Water passing through critical point experiences sharp property change, which makes system codes hard to converge Three basic methods are developed to overcome this problem

4.1 Separate code applied for simulation under supercritical and subcritical pressure

Researchers from Japan apply a series of codes, named SPRAT, to carry out safety analysis for their SCWR concepts(Super LWR and Super FR) Code SPRAT applies homogenous model and fully implicit nu-merical method to solve conservation equations Code SPRAT-DOWN is developed based on SPRAT, which could only simulate transients under supercritical pressure(Yuki Ishiwatari, 2005) A separate code named SPRAT-DOWN-DP is developed to simulate quickly depressurization process for SCWR When the coolant system depressurizes to equilib-rium pressure between coolant system and containment, another spe-cific code SCRELA is applied to simulate the core reflood process (Ishiwatari et al., 2006) Code SCRELA has detailed constitutive models

to evaluate reflood process and it’s the only code focusing on validating

Fig 21 SCWR-R design concept

Table 1

Key parameters of SCWR

Federation Korea

its code prediction ability on reflood process for tight lattice bundles of

SCWR Comprehensive safety analyses for super LWR require the above

codes to cooperate together to finish simulating accident like LOCA

4.2 Pseudo two-phase region development under supercritical pressure

region

For researchers who try to upgrade mature safety analysis code for

PWR or BWR based on two-fluid model to supercritical pressure,

developing pseudo two-phase region for supercritical pressure condition

is a solution Pseudo two-phase region development for supercritical

water tries to regard supercritical water as subcooled supercritical

water, overheated supercritical water and two-phase supercritical

water, which is consistent with phase state definition for water under

subcritical pressure In this way, water blowing down from supercritical

pressure to subcritical pressure will experience a continuous phase

change, which is helpful for code numerical convergence Many codes

for SCWR apply this method, such as APROS(H¨anninen and Kurki,

2008), ATHLET(Zhou et al., 2012), CATHARE(Geffraye et al., 2011;

IAEA, 2014) and so on

4.2.1 APROS

For the upgrated APROS, the latent heat of condensation or

vapor-ization at supercritical pressure is assumed to be constant The pseudo

saturation enthalpies are achieved through the following equations

(H¨anninen and Ylijoki, 2008):

h 1,sat(p) = hpc(p) − Lpe

2

h g,sat(p) = hpc(p) +Lpe

2 Besides the pseudo two phase region development for physical

property calculation, the empirical correlations for interfacial heat

transfer under supercritical pressure should also be implemented into

APROS code A very large interfacial heat transfer coefficient is assumed

at pseudo two phase region at supercritical pressure, which could make

the void fraction vary almost instantly when coolant go through the

pseudo two phase region

Under subcritical pressure, the heat transfer calculation regimes of

APROS(H¨anninen and Kurki, 2008; Kurk, 2008) are represented by

wetted wall regime,dry wall regime and a transition regime Critical

heat flux (CHF), minimum film boiling temperature(MFB), wall

tem-perature as well as coolant temtem-perature are used to define different heat

transfer regimes However, critical heat flux, minimum film boiling

temperature don’t exist under supercritical pressure Upgrated APROS

code applies Jackson correlation to evaluate the heat transfer

co-efficients under supercritical pressure(Hall et al., 1967) Different values

for variable n in the following equation are defined by comparing wall

temperature with coolant temperature and pseudo critical temperature

Surface tension is assumed to 0 under supercritical pressure Under supercritical pressure, velocities of pseudo gas and liquid are assumed to be the same Thus, a very large number is assigned to the interfacial friction under supercritical pressure

Additionally, correlation of Kirillov is applied(Pioro et al., 2004) to calculate the wall friction under supercritical pressure:

(1.82 log10(Reb) − 1.64)2

(

ρw

ρb

)0.4

4.2.2 ATHLET-SC

Pseudo two phase region is set for ATHLET-SC where pressure is over 22.05 MPa, instead of critical pressure(22.1 MPa) The latent heat at 22.05 MPa is set as the latent heat over all supercritical pressure region,

as shown in Fig 22 The effects of width of the pseudo two phase zone are studied in order to avoid convergence problem of the modified code and large deviation from reality Bishop et al.(Bishop et al., 1964)、 Krasnoshchekov and Protopopov(Krasnoshchekov and Protopopov,

1966) and Yamagata et al.(Yamagata et al., 1972), Jackson(Jackson,

2009), Cheng et al.(Cheng et al., 2009) are incorporated into the code to simulate the heat transfer under supercritical pressure

The velocities of pseudo gas and liquid under supercritical pressure are assumed to be the same Interfacial heat transfer is mainly made up

of heat conduction The flow type is assumed to be annular flow(under unheated condition) or inverted annular flow(under heated condition) Thus, the interfacial heat transfer and interfacial area can be calculated

by following equations(Zhou et al., 2012):

Fig 22 Pseudo two phase method applied in ATHLET-SC

Nub=0.0183Re 0.82

b Pr0.5

b

(

ρw

ρb

)0.3(

c p

c p,b

)n

n =

⎧

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎩

0.4, if Tb< Tw< Tpc or 1.2Tpc< Tb< Tw

0.4 + 0.2

(

Tw

Tpc

− 1

)

0.4 + 0.2

(

Tw

Tpc

− 1

)(

1 − 5

(

Tb

Tpc

− 1 ))

, if Tpc< Tb< 1.2Tpcand Tb< Tw

α L= ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅2λ L

(1 − x)D2

√

α V= 2λ̅̅̅̅̅̅̅̅V

xD2

√

A i,annual flow=π

̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅

(1 − x)D2

√

⋅l

A i,inverted annual flow=π

̅̅̅̅̅̅̅̅

xD2

√

⋅l

λ, thermal conductivity; D h , hydraulic diameter; A i , interface area; l,

length of volume; x, void fraction; α, interphase heat transfer coefficient

Subscript L denotes the liquid phase while V denotes the vapor phase

4.2.3 CATHARE

Unlike APROS and ATHLET-SC, there is only pseudo liquid or vapor

region while no pseudo two phase region exists under supercritical

pressure for CATHARE, as shown in Fig 23 The void fraction of

su-percritical water is 0 if bulk temperature is smaller than corresponding

pseudo critical temperature and is 1 if bulk temperature is larger than

corresponding pseudo critical temperature No buffer zone exists

be-tween pseudo liquid and vapor region CATHARE version for SCWR is

reported to be numerically robust to carry out fast trans-critical pressure

simulation according to (Geffraye et al., 2011) However, it’s a pity the

author doesn’t find any paper describes how CATHARE code make it

since sudden void fraction change when bulk temperature moves cross

the pseudo critical temperature is apt to cause non-convergence during

numerical calculation

4.3 Physical property modification around critical point

Another method applied by SCWR system codes is to process the

physical property around critical point unphysically to avoid sharp

property change These codes include SCTRAN(Wu et al., 2015),

CATHENA(Beuthe et al., 2020), RELAP5/MOD4(Allison et al., 2016;

Lou, 2016) or RELAP5-3D(Riemke et al., 2003)

4.3.1 SCTRAN

SCTRAN is developed by Xi’an Jiaotong University (Wu et al., 2015)

to provide a safety analysis tool for SCWR, which applies homogenous

model to predict the flow characteristics of coolant Homogenous model

is suitable for supercritical water as there is no phase change and the

fluid can be treated as single phase What should be done to enable

SCTRAN to simulate trans-critical process is that the physical properties

under supercritical pressure and near critical pressure should be

continuous and their derivatives near the critical point should be

decreased artificially Through calculation of fluid temperature, specific

volume, specific heat and saturated enthalpy through fitted property

correlations, physical properties could change smoothly through critical

pressure SCTRAN code has been used to carry out safety evaluations for

accidents including LOCA and non-LOCA type for pressure vessel type

SCWR, such as CGNPC SCWR(Wu et al., 2015), CSR1000(Wu et al.,

2014), and pressure tube type SCWR, such as Canadian SCWR(Wu et al.,

2013)

4.3.2 CATHENA

CATHENA is a safety analysis code developed by Atomic Energy of Canada Limited(AECL) for CANDU reactors It applies one-dimensional two-fluid model to simulate water flowing in pipes In order to apply CATHENA to carry out safety analysis for Canadian SCWR (Beuthe et al.,

2020), implements a novel method to enable CATHENA simulating ac-cidents and startup transients for SCWR Instead of introducing pseudo two phase regime (Beuthe et al., 2020), treats the supercritical regime as

a single uninterrupted phase, whose void fraction is always 0 Thus, there is only transition from supercritical fluid at high temperature to sub-critical steam because of sudden void fraction variation from 0 to 1,

as shown in Fig 24 A special strategy is developed to split the super-critical phase into vapor and liquid phases under subsuper-critical pressures and an initial value of void fraction is estimated when trans-critical process from supercritical to subcritical pressure occurs Additionally, the sharp physical property change near the vicinity of the critical point

is manually mitigate to avoid convergence problem of numerical simu-lation Supercritical blowdown process is simulated by modified CATHENA to verify its ability to simulate trans-critical process

4.3.3 RELAP5 series codes

Several modifications have been made for RELAP5-3D to enable its ability to simulate slow and fast blowdown process from supercritical to sub-critical pressure(Rassame et al., 2017) Different versions of RELAP5

Fig 23 Regions of liquid and vapor for CATHARE (IAEA (2014))

Fig 24 Strategy for supercritical/subcritical transitions in CATHENA(Beuthe

et al., 2020)

Fig 25 Trans-critical transition mechanisms in RELAP5/MOD4