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Development of a LOCA analysis code for the supercritical-pressure light water cooled reactors
Pergamon
Ann. Nucl. Energy, Vol. 25, No. 16, pp. 1341-1361, 1998 © 1998 Elsevier Science Ltd. All fights reserved P I h 80306-4549(97)00084-4 Printed in Great Britain 0306-4549/98 $19.00 + 0.00
D E V E L O P M E N T OF A LOCA ANALYSIS C O D E FOR THE S U P E R C R I T I C A L - P R E S S U R E LIGHT WATER C O O L E D REACTORS JONG HO LEE,* SEIICHI KOSHIZUKA and YOSHIAKI OKA Nuclear Engineering Research Laboratory, The University of Tokyo, 2-22 Shirane, Shirakata, Tokai-mura, Naka-gun, lbaraki, 319-11 Japan (Received 8 July 1997) A~traet--The supercritical-pressure light water cooled reactors aim at cost reduction by system simplification and higher thermal efficiency, and have flexibility for the fuel cycle due to technical feasibility for various neutron spectrum reactors. Since loss-of-coolant accident (LOCA) behavior at supercritical pressure conditions cannot be analyzed with the existing codes for the current light water reactors, a LOCA analysis code for the supercritical-pressure light water cooled reactor is developed in this study. This code, which is named SCRELA, is composed of two parts: the blowdown and reflood analysis modules. The blowdown analysis module is designed based on the homogeneous equilibrium model. The reflood analysis module is modeled by the thermal equilibrium relative velocity model. SCRELA is validated by the REFLA-TRAC code, which is developed in the Japan Atomic Energy Research Institute based on TRAC-PF1. A large break LOCA of the thermal neutron spectrum reactor (SCLWR) is analyzed by SCRELA. The result shows that the peak clad temperature (PCT) is nearly 980°C about 60 s after the break and the PCT position is quenched at 170 s This means that PCT is sufficiently lower than the safety limit of 1260°C. In conclusion, the developed code shows the safety of SCLWR under the large break LOCA, and is expected to be applied to LOCA analysis of other types of the supercritical-pressure light water cooled reactors. © 1998 Elsevier Science Ltd. All rights reserved
NOMENCLATURE Symbols A cp Cv D F
Cross section Specific heat under constant pressure Specific heat under constant volume Diameter Friction factor
*Author for correspondence. 1341
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J.H. Lee et al. G h k K L P T V
Vol
W Z
Mass flux Heat transfer coefficient Thermal conductivity Form loss coefficient Length or distance Pressure Temperature Velocity Volume Mass flowrate Height
Greek Letters:
t~ y p
Void fraction Thickness of cladding Ratio of specific heat coefficients Density
Subscripts: ads
b c cr cv
d g 1 L lp
n o qf R sat sub up
w
Automatic depressurization system Bulk Core Critical flow condition Containment vessel Downcomer Gas Liquid Leidenfrost temperature Lower plenum Nozzle Stagnation condition Quench front Radiation Saturation Subcooled Upper plenum Wall
1. INTRODUCTION Supercritical-pressure light water cooled reactors have been conceptually designed for improving light water reactor technology by simplifying the plant system and enhancing thermal efficiency. Supercritical water at a pressure of 25 MPa is employed as the reactor coolant. The coolant temperature increases continuously in the core without abrupt
Development of a LOCA analysis code
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change of density. The high energy core outlet coolant, which corresponds to superheated steam of subcritical water, is directly fed to the turbine. Several types of neutron spectrum reactors, such as a thermal reactor, a fast breeder and a fast converter, can be designed with the same cooling system. The expected economical merits and technical feasibility were presented in the previous papers (Oka and Koshizuka, 1993; Jevremovic et al., 1994; Oka et al., 1995). If a loss-of-coolant accident (LOCA) occurs in the supercritical-pressure light water cooled reactor, the blowdown phase begins at supercritical pressure. Behavior of supercritical water cannot be analyzed with the existing codes for pressurized water reactors (PWRs) and boiling water reactors (BWRs). Also, though the reactor pressure vessel (RPV) is similar to that of PWR, the reflooding behavior is different from that of PWR. Figure 1 represents the general plant system of the direct cycle supercritical-pressure light water cooled reactor. After LOCA, the normal cooling system is not available due to containment isolation and the emergency cooling flow path is established by the actuation of the automatic depressurization system (ADS) and the low pressure coolant injection system (LPCI). The emergency cooling flow path is from the lower plenum through the ADS line to the suppression chamber pool, while a longer flow path through the steam generator to the break appears in PWR. In this paper a new LOCA analysis code is developed for the supercritical-pressure light water cooled reactors. The developed code is composed of two parts, which are the blowdown and reflood analysis modules. The code is applied to a large break LOCA of a thermal neutron spectrum reactor (SCLWR) of 1145 MWe output (Koshizuka et al., 1994). The principal parameters and RPV features of SCLWR are depicted in Table 1.
2. CODE DEVELOPMENT 2.1. Blowdown analysis module 2.1.1. Thermal-hydraulic calculation model In order to estimate the behavior of the blowdown phase, the system model consists of the reactor vessel, hot legs from the reactor vessel outlets to the isolation valves, and an Reaclro r Vessel
I~
)
ADSValve
Turbine
S upres sionChamber
Pool
Mainf ~ a ~ rpump
i
Condenser
Fig. 1. General plant system of supercritical-pressure light water cooled reactor.
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Table 1. Principal parameters of SCLWR Core diameter/height Core inlet/outlet temperature Core inlet/outlet density Fuel rod/pellet diameter Cladding/thickness Lattice pitch/rod diameter, P/D Maximum power density Presssure Coolant flowrate Number of coolant loops Inlet/outlet pipe diameter Reactor vessel height/diameter Thermal power Thermal efficiency Electrical power
267/570 cm 310/416°C 0.725/0.137 gcm -2 0.8/0.694 cm SS/0.046 cm 1.4 (triangular) 363.6 MW/m -2 25 MPa 2032 kg s-1 2 34/53 cm 15.5/3.67m 2780 MW 41.2% 1145 MW
Break
Hot Leg
Cold L F [ Valve ~ [ SafetyInjection~ :
Core Node-N
Valve
De wr
A 3S Line
COl he1
Core Node- 3
Break
Core Node-2
Core Node-1 [iii Chamber Pool il :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Fig. 2. System noding for blowdown analysis. ADS line. Figure 2 shows the system node diagram for the blowdown analysis. The number of calculation nodes at the core, the downcomer, the lower plenum and the upper plenum can be changed. Plant parameters are given as the boundary conditions; for example, the coolant inlet flowrate from an intact line is calculated from the pump characteristic curve and the coolant outlet flowrate is proportional to the core pressure. Since the transient in the blowdown phase is under high flowrate and high pressure
Development of a LOCA analysis code
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conditions, the homogenous equilibrium model (HEM) is selected as the thermalhydraulics. As the pressure drop in the reactor vessel is relatively smaller than that at the break, the pressure in the reactor vessel is assumed as constant. The pressure decrease rate in the blowdown phase is governed by the flowrate at the break. Three correlations of the break flowrate are prepared for different pressure regions. In the superheated steam region, isentropic ideal gas is assumed. Thus, the mass flux and pressure at the critical flow condition are calculated as shown in the following equations:
l
Mass flux: Gcr = 19
2cpToLkPo]
Critical pressure: ecr =
\Po]
p /" 2 "~×/(×-') o~ - ~ - ~ ]
(1)
(2)
where × = ce/cv.
Two-phase critical flow is calculated based on Moody's homogeneous equilibrium model. In the subcooled region, Zaloudeck's correlation is used as Gcr = 0.95ff2gcp(Po - esat).
(3)
Critical flow in the supercritical pressure region is not known. However, the pressure at the break is subcritical even if the stagnation pressure is supercritical. Accordingly, the same correlations in the subcritical regions are also used in the supercritical pressure regions. As long as the stagnation temperature is below or equal to the pseudo-critical temperature, the critical flow is treated as in the subcooled region. When the temperature is higher than the pseudo-critical temperature, the superheated steam region is assumed. Figure 3 shows the critical mass fluxes in the various pressure regions. The core power is evaluated from the point kinetic equations including six groups of delayed neutrons and decay heat of ANS + 20%. The density coefficient of reactivity is only considered for the core power calculation. The radial distribution of temperature in the fuel is assumed uniform. In order to evaluate heat transfer to the coolant in various conditions, the following heat transfer correlations are employed. Dittus-Boelter's correlation is used in the supercritical, subcooled and superheated regions. The radiation heat transfer is involved in the superheated region. Dougal-Rhosenow's correlation is used in the film boiling region. It is also conservatively used in the nucleate boiling region because this region appears for a very short period of the large break LOCA analyzed here. The gap conductance in the fuel rod is assumed uniform. Heat capacities of the reactor vessel and other structures are neglected. 2.1.2. Calculation procedure
Figure 4 presents the calculation flow chart of the blowdown analysis. At first, the break flowrate is calculated by using the values of the previous time step. Subsequently, the flowrate of each node is calculated from the mass and energy conservation equations
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J.H. Lee et al. 1.6e+5
,
•
5.0 MPa 7.5 MPa ,10.0 MPa 12.5 MPa 15.0 MPa
\ .-. 1.2e+5
~!q \
~'~ 8.0e+4
i,,,, , 20.0 MPa ,~o ~ =Joo
,,.,
-
-
25.0
MPa
= tl.. cO
== 4.0e+4 ~ .
O.Oe+O . 1.2e+6
~,
.
~. ~.._
. . 1.8e+6
.
~__.
•
. 2.4e+6
3.0e+6
Stagnation Enthalpy (J/kg) Fig. 3. Critical mass flux as a function o f stagnation enthalpy and pressure.
at an assumed pressure. Heat transfer from the fuel to the coolant is evaluated from the temperature difference in the previous time step. Finally, the system pressure is determined to satisfy the flow balance by an iteration calculation. The flow balance is judged from flowrates at the boundaries: the break point and the core inlet and outlet of an intact line. The flowrates, masses and enthalpies in the nodes at the present time step are determined when the system pressure converges. This procedure is continued until the blowdown is ended; the system pressure is the same with that in the containment vessel. 2.1.3. Code validation
The developed code is named SCRELA, which is an abbreviation of supercriticalpressure light water reactor LOCA analysis code. The blowdown analysis module in SCRELA is validated by comparing with the REFLA-TRAC code, which was developed in the Japan Atomic Energy Research Institute (JAERI) based on TRAC-PF1. An SCLWR analyzed by Koshizuka et al., 1994 is used for the validation calculation. The blowdown calculation starts at a core pressure of 17.0 MPa in the REFLA-TRAC code, since this code is not able to treat the supercritical-pressure conditions. Figures 5 and 6 show the pressure trends of 100% cold-leg and 100% hot-leg break LOCAs, respectively. Figures 7 and 8 represent the break flowrates at the cold-leg and the hot-leg breaks. The blowdown phase ends at 41 and 29 s in the cold-leg and hot-leg break LOCAs, respectively, in the SCRELA calculations. In the initial stage of blowdown, the decrease rate of pressure in the hot-leg break LOCA is higher than that in the cold-leg break LOCA. This is because the break flow is in a superheated steam condition at the hot-leg break, while it is in a subcooled liquid condition at the cold-leg break. After the initial high
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[Stead~' State Value Calculation1 I Start BlowdownCalculation] ,..J re [Calculationof Break FlowI [ APAssumption ] ,...1
I Mass and EnergyConserv.~..~Core Heat Equ. in theEach Nodes I-I Transfer !
I
No ~
ITemperaturel
t+l ~1Descisionof State Values [Timestep change[[ at the Time Step [ t~
N
o
~
~lation
~
Fig. 4. Calculation flow chart of blowdown phase. 28
21
7
o
0
10
20 30 TimeOm¢)
40
50
Fig. 5. Pressure trend in 100% cold-leg break LOCA. depressurization, the decrease rate of pressure is slowed down in both cases because the break flow conditions are changed to two-phase flow. As shown in the figures, the results calculated by the SCRELA and REFLA-TRAC codes are nearly the same. Consequently, the blowdown analysis module developed with HEM is validated.
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25 20 A
REFLA-TRAC SCRELA
15
g 10 ~t
i
¢k
5 0
0
10
20
30
40
50
Timo(sec)
Fig. 6. Pressure trend in 100% hot-leg break LOCA.
1.0e+4 I
7.5e+3 1
" REFLA-TRAC
5.0e+3~
0
i
10
20
30
40
50
Time(sec)
Fig. 7. Break flowrate in 100% cold-leg break LOCA.
7.5e+3
REFLA-TRAC[ SCRELA
6.0e+3 4.5e+3
.¢ 3.0e+3 n-. 1.5e+3 0.0e+OI 0
10
20 30 Time(see)
40
50
Fig. 8. Break flowrate in 100% hot-leg break LOCA.
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2.2. Reflood Analysis Module 2.2.1. System behavior in the reflood phase In the case of cold-leg break LOCA, ECCS coolant flow has two paths by the ADS actuation as shown in Fig. 9(a). One is from the lower plenum through the core, upper plenum, hot-leg pipe and the ADS line in turn. The other is formed directly to the break line. The flow path through the ADS line is shorter than that through the S/G loop in PWRs. The double-ended break like PWRs does not appear in SCLWR. In this reactor, the flow path through the ADS line is utilized as the cooling path in the low pressure condition. In the case of hot-leg break LOCA, since the cold-leg lines are isolated, only upward flow is established in the core from the lower plenum to the break line or the ADS line as shown in Fig. 9(b). Therefore, the cold-leg break LOCA is considered as severer than the hot-leg break LOCA. In this paper, the reflood phase of the 100% cold-leg break LOCA, the severer case, is analyzed.
2.2.2. Thermal-hydraulic (T/H) model The T/H model is based on a system momentum calculation and a core mass and energy calculation:
( a) System momentum calculation model The system momentum calculation is modeled by coupling a reactor vessel part and an ADS line part (Fig. 10). The reactor vessel part is represented by momentum balance between the downcomer and the core water levels. The equation is described in terms of acceleration, pressure difference between the downcomer and the core water levels, static pressure head due to the water level difference, and inertia:
Bmal~Une
_~ c<~} l ".l Break
LPCIWater Inlet
i
Reacl~r Vess el
UI
~T'i c~" ~
LPClWaler Inlet
Supr ess ion Chamber
(a) Cold-leg break
ReacIm Vessel (b) Hot-leg break
Fig. 9. Refloodphenomena.
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J.H. Lee et al. i
Reactor Vessel Module hsi
', A D S <
Loop Module
•i ~ ~
.........
d$
suppressionChamber
Reactor Vessel
Fig. 10. Modeling for momentum calculation.
, r_~
v°,~l
P,-p~+ g~(zd
z~) (4)
-galVdl. akA, -- ~ 1 \ ~ 2K¢,1
(5)
The pumping head of LPCI and the friction loss are neglected. The boundary conditions are water levels in the downcomer and the core, and pressures at these levels. As described in equation (5), the pressure at the core water level is obtained as the addition of the pressure in the upper plenum and the friction loss from the core water level to the upper plenum. The core water level is calculated from a detail core model presented in the following section. The system pressure, which is the same with the upper plenum pressure, is evaluated by adding the pressure loss in the ADS line to the pressure in the containment vessel (CV). The pressure loss in the ADS line is calculated by assuming steady state flow as represented in equation (6):
APads = \Aad,./
"Lkp-
P.p] +Fads.~.2/Sads
÷
~-p -j.l
(6)
The flowrate and enthalpy at the core top are calculated from the following core model.
Development of a LOCA analysis code
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(b) Core T/H calculation model In the core a thermal equilibrium relative velocity model is used in the two-phase region. This means that the relative velocity between water and void is represented by a correlation. Physical properties in the core are obtained by using the pressure at the core water level. The boundary conditions are the flowrate and enthalpy at the core bottom, and the pressure at the core water level. The quench front is calculated by using a quench front velocity correlation. The core is normally divided into 60 nodes. To prevent the numerical instability caused by the abrupt change of the heat transfer coefficient, the neighboring nodes of the quench front are more finely divided into the 1/100 thickness of the normal node as shown in Fig. 11. The heat transfer coefficient sharply changes by about 2 orders of magnitude in the vicinity of a quench front.
(c) T/H correlations Quenchfront velocity correlation For the calculation of the quench front, Yamanouchi's correlation is used:
( ~__ff__~{(:£~ - ~)½(Tw -/i) ~
(7)
The quench front velocity, Vqf, represents the propagation speed of the quench front toward the core top (Duffey and Porthouse, 1973). The heat transfer coefficient at the quench front region, hqf, is a constant value of 5 x l 0 n w m - 2 K -l proposed by Yamanouchi (Jones Jr, 1981). Core Top 6-I(: 2-: ;---'-''--'-''-'-"26-8 :.'-~-'--Z:S-"::.'[:=:-"
6-9 6-7
6-67----_-_--:::-:::_.7::
6-5
6-26-4~::::::::;:::::.::=
6-3 6-1
3-1 ................. 3-8 .................. 3-6 ................. 3-4 . : : 2 2 : : : : : : 2 : : : : : : 3-2 :::::::::::::::::: 2-1( ..................
2-8 ::::~::~::~i~ ~ 2-6 2..4,
i!~i~!~.~i~ ~2~
~~~ ~
" ' . ~ : ~
:::::.:::::..::~::::;::~:::::9:.:: ::::::::::::::::::::::::::::::::::::::: 1-8
~:~ ~
%
~
1-6
~i~i~i ,i;~i~ ~ i ~ i ~ i ~ !
z-2
~!~~::~i~i~ Core
A.Normal Calculation Nodes
B.Fine Calculalion Nodes
Fine Node Width -- Normal Node Wkllh / 100
Fig. 11. Core noding near the quench front.
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Heat transfer coefficient The flow regimes assumed in the reflood analysis code are described in Fig. 12. They are single-phase liquid, saturated two-phase, transient, dispersed and superheated steam flow regimes. The various heat transfer correlations are prepared according to the flow regime. Table 2 summarizes the heat transfer correlations in these flow regimes. In the film boiling and transient boiling flow regimes, Murao and Sugimoto's correlation used in the REFLA-TRAC code is employed (Akimoto and Murao, 1992). In the dispersed flow regime, the compensated value of Murao and Sugimoto's correlation is applied so that the heat transfer coefficient is continuous between the neighboring regimes. Tom's correlation is used in the single-phase liquid, subcooled nucleate boiling and saturated two phase flow regimes. Dittus-Boelter's correlation is adopted in the superheated steam flow regime. Relative velocity correlation In order to describe the relative velocity in two-phase flow, a set of correlations in Mistubishi's LOCA analysis code are used (Mistubishi Heavy Industries Ltd., 1988). The relative velocity correlations in nucleate boiling, film boiling and dispersed flow regimes are prepared. In the transient flow regime, the average value weighted by the void fraction between the film boiling and dispersed flow regimes is used. The flow where the void fraction is above 0.99 is treated as the dispersed flow regime. 2.2.3. Calculation procedure The calculation procedure is described in Fig. 13. When the ECCS water level reaches the core bottom, the reflood calculation is started with the output data from the previous
ated rl
Tb>T
sat
)n
Quench-. Front
~1
Saturation Point
i
Type A
Type B
Fig. 12. Heat transfer regime in core during reflood phase.
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Table 2. Flow regimes and heat transfer correlations Position Below quench front level
Heat transfer regime
Heat transfer correlation
(1) Single liquid phase/subcooled nucleate boiling flow (2) Saturated two-phase flow (3) Subcooled film boiling flow
-Tom's correlation q" = exp(2P/8,7)(Tw- Ts.t)2/22.72 -the same as case (1) -Murao and Sugimoto's correlation h = hsub + hR
hs,b = hs,,,[1.0 + 0.025(T~,t- Tt)] h R = EE(TI~ 4 - Tsar4)~( T w - Tsar)
(4) Film boiling/transient boiling flow
-Murao and Sugimoto's correlation
(5) Dispersed flow
-Compensated Murao and Sugimoto's correlation
h = hsat + hR h~at = O.94[~.g3pgplhfgg/ Lql,zg( Tw - Tsat)] 1/4 h R = Ee( Tw4 - Tsat4) /( T w - T~at)(1 -or) 0"5
Above quench front level
h = hsat,comp Jr"h R hsat ,corn~P = FcP × hsat, Fop" compensation factor
hR = E e ( T w 4 - Tsat4)/(Tw-Tsat)(1-000.5 -Dittus-Boelter's correlation h = 0.023 (k/Dh)Re°'SPr °'4
(6) Superheated steam flow
I
[
- Refill Output Data - Calculation Cond., etc -r I Downcomer Water Level I Quench Front Level ]
I Momentum Conservation Equ. I in Reactor vessel Mass and Energy ConservL.lCore Heat Equ. in the Core Nodes [ 7 Transfer I
I
k+l
I Flowrate and Enthalpy I I Fuel Clad I [ I Temperature I
Icha ~e of] I at the Core Top I'nm, Step] k~ '
[S)~stemMomentum Equation I [- :system(Upper Plenum) Pressure [
t, [ Pressure at Cote Water Level [
Fig. 13. Calculation flow chart of reflood phase.
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J.H. Lee et al.
blowdown and refill calculation. At first, the downcomer and the core water levels are estimated from the ECCS injection flow and the quench front velocity in the previous time step. The water velocity in the downcomer is calculated using equation (4). Next, the water velocity in the core bottom is obtained using the mass conservation equation. After the velocity and enthalpy in the core bottom are known, the flowrate and enthalpy of each node in the core are calculated by the core T/H calculation model. Based on the calculated temperature distribution in the core, the heat transfer from the fuel rod to the coolant is evaluated. Temperatures of the cladding and the pellet are also calculated. These values are used for the core T/H calculation in the next time step. The pressure loss in the ADS line is calculated by substituting the velocity and enthalpy in the upper plenum into equation (6). Then, the pressure in the upper plenum is evaluated by adding the pressure loss in the ADS line to the pressure in the containment vessel. Finally, the pressure at the core water level is calculated by using equation (5). 2.2.4. Code validation
The developed reflood analysis module is also validated by comparing with the REFLA-TRAC code. The validation calculation starts from the output data of the blowdown calculation by Koshizuka et al., 1994. The calculation result is compared with the reference in Fig. 14. The peak clad temperature (PCT) of 1021°C appears at 54 s after the break in the SCRELA analysis, while PCT is 1006°C at 47 s in the REFLA-TRAC analysis. SCRELA analysis presents a conservative result about 15°C. After PCT, the cladding temperature continuously decreases to the quench point. The core bottom is quenched at 65 and 72 s in two codes, respectively. Figure 15 presents the void fractions at the core middle in the SCRELA and the REFLA-TRAC analyses. The flow condition at the core middle changes to the liquid phase at about 55 s in the SCRELA analysis, while it is settled to the liquid phase at about 75 s after large fluctuation in the REFLA-TRAC analysis. We can see the first change to the liquid phase at nearly the same time of about 55 s. Different behavior after 55 s is originated from the difference of the calculation model
12°°t
12
I [] E A- RAcl
t _ 5 ~X CoreTop 200[- C°reB°tt°m ~_~1t 0
30
-
~
]
D
60 Time(see) 90
I L '
~
120
Fig. 14. Fuel cladding temperature in the reflood phase of validation calculation.
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1.0 m 0.8
OR
SCRELA
0.6
I
REFLA-TRAC
O
I,I. 0.4 "O
>o OR
0.2
•- L
0.0 40
I I I i I . . . . 70 Time($ec) 100
130
Fig. 15. Void fraction in the core middle during the reflood phase of the validation calculation.
of the upper plenum. In the SCRELA code, the physical properties in the upper plenum node are assumed unchanged. Namely, the flow velocity and enthalpy in the upper plenum are the same as those of the core top. In spite of this model difference, both trends of the cladding temperature exhibit good agreement.
3. ANALYSIS O F SCLWR LOCA
3.1. Blowdown analysis 3.1.1. Calculation condition Isolation of the intact lines is assumed to start from 1.8 s and to be completed at 3 s after the break by considering the BWR plant data. Coolant flow of the intact lines is taken into account before the isolation. For the sensitivity study, the case of no intact line flow is also calculated. ADS and LPCI systems are considered as ECCS for the mitigation of LOCA. Table 3 shows the parameters of the ECCS design for the large break LOCA. Time delay of LPCI actuation is assumed 30 s due to the starting of the emergency diesel generators. LPCI is conservatively assumed to start at a pressure of 0.8 MPa which is less than the designed value. Actuation of ADS is not considered in the blowdown phase. The refill phase is also successively calculated. It continues until the lower plenum is full of Table 3. ECCS design for large break LOCA Low pressure coolant injection system(LPCI)
Number of units: Capacity: Time delay: Design pressure:
Automatic depressurization system (ADS)
Location: Flow area: Time delay:
4 805 kg s-1 30 s 1.0 MPa Hot-leg 0.22 m 2
30 s
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ECCS water. Heat transfer from the fuel rods to the coolant is neglected during the refill phase. 3.1.2. Calculation results
The pressure trend during the blowdown phase of the 100 % cold-leg break LOCA is exhibited in Fig. 16. The cladding temperature is shown in Fig. 17. The blowdown phase is completed at 41 s after the break and the refill phase is completed at 44 s. The LPCI system is actuated at 33 s. The cladding temperature at the core middle sharply increases to about 800°C in the initial stage due to the degradation of cooling capability and power redistribution, and thereafter, the increase speed of the temperature is slower. The intact line flow drives upward flow, while the break flow does downward flow in the core. Figure 18 shows the flowrates at various positions in the core and the intact line. Consequently, flow stagnation appears in the core. If the flow in the intact line is not considered, the core coolability is better because the downward flow to the break is prevailing. 30
!
With Intact Line Flow I
m
20
No Intact Line Flow
a.
2- i
I
10
2
a.
L
0
10
20 30 Time(sec)
40
50
Fig. 16. Pressure trend in 100% cold-leg break LOCA (blowdown analysis). 1050 .Core Middle(with Intact Line Flow)
--
,.j
~
~
Core Middle(No Intact Line Flow)
550
I~
"~'~""'~'qr~ 300
,
0
co re Bottom I
I
I
15 Time(sec) 30
,
I
45
Fig. 17. Fuel cladding temperature in 100% cold-leg break LOCA (blowdown analysis).
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2OOO lOO0 A|
A
!
i -1000 ,-;- -2000 -3000 0
Core Top Hot-leg(Intact) Cold-Leg (Intact) Core Bottom I
I
10
20
Time(sec)
Fig. 18. Flowrates in 100% cold-leg break LOCA (with intact line flow). In the case of 100 % hot-leg break LOCA, the pressure and the cladding temperature are depicted in Figs 19 and 20, respectively. The blowdown phase ends at 33 s after the break and the refill phase is completed at 40 s. The LPCI system is actuated at 30 s. The cladding temperature at the core middle sharply increases at the beginning due to the redistribution of stored energy in the fuel and a power spike caused by a positive reactivity. Figure 21 shows the reactor thermal power in the cold-leg and hot-leg break LOCAs. The reactor power shows a peak at 0.2 s in the hot-leg break because the core flow is accerelated. The positive reactivity is inserted by increasing the coolant density in the core. On the other hand, the power peak does not appear in the cold-leg break LOCA since the core flow is decelerated. However, the peak temperature is 550°C, which is much lower than the case of cold-leg break LOCA. The cladding temperature decreases after the peak due to the high coolability in the core. This is because the core is cooled by the upward flow by using the coolant inventory in the downcomer and the lower plenum. In the case of hot-leg break, effect of the intact line flow is not large as shown in Fig. 20 since the directions of the intact line flow is the same as the break flow.
2s[ [ 2O
With Intact Line Flow J
15
.}
I
lo
|
0 0
10
20 30 Time(sec)
40
50
Fig. 19. Pressure trend in 100% hot-leg break LOCA (blowdown analysis).
J.H. Lee et al.
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500
i
400
I--
Core Bottom , ! ,
200 0
10
~ i
--"--'-'-'Core ToPl
20 Time(sec)
,
i 40
30
,2o
Fig. 20. Fuel cladding temperature in 100% hot-leg break LOCA (blowdown analysis).
m
Cold-Leg I Hot-Leg
o ~L
"6 40 @
t
rr
0 ~
0.0
2.5
5.0 • Time(sec)
7.5
10.0
Fig. 21. Reactor thermal power in the blowdown phase.
3.2. Reflood analysis 3.2.1. Calculation condition Two out of four LPCI systems are assumed to be available. Therefore, the total available flowrate of ECCS during the reflood is 1610 kg -1 sec. The length of the ADS line is assumed 13 m. The static head in the suppression chamber pool is not considered in the calculation of the pressure loss of the ADS line. The reflood analysis is only carried out in the case of 100% cold-leg break LOCA because this leads to a severer result than the hotleg break LOCA. The calculation starts from the output data from the blowdown analysis with the intact line flow.
3.2.2. Calculation results The reflood phase starts from 44 s after the break. Figure 22 represents the cladding temperatures at the core bottom, middle and top. PCT is 980°C which appears at the core
Development of a LOCA analysis code
1000~
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~ Core Bottom Gore Middle Top
750
Gore
i
~. 250 0
50
100
150
Time(sec)
20O
Fig. 22. Fuel cladding temperature after the break. middle at 56 s. This is sufficiently lower than the limit temperature of stainless steel cladding, 1260°C (Coffman Jr, 1976). The core middle is quenched at 170s. The cladding temperature at the core bottom rapidly drops at 74 s due to the quench. The cladding temperature at the core top exhibits a peak value at about 64 s, and gradually decreases to the quench point. Since the quench front level proceeds from the core bottom to the top in the present calculation using the quench front velocity correlation, the core top is to be quenched later than the core middle as depicted in Fig. 23. Figure 24 describes the history of the heat transfer coefficient at the PCT position, 3.3 m elevation of the core. The flow regime is changed to the subcooled film boiling at about 70 s and finally reaches the subcooled nucleate boiling due to the quench at about 180 s. This means that the saturation liquid level is higher than the quench front level, which is the flow pattern of type B in Fig. 12. This behavior of SCLWR is different from that in PWR. The general trend of the reflood phase in PWR shows that the core above the quench front level is cooled by the 15
10 QuenchFront I DowncomerLevel
s
0 ~
0
70
Time($ec)
140
210
Fig. 23. Quench front and downcomer water levels in the reflood phase.
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J.H. Lee et al. 10 5
i '°litf 1
r 0
0
0 70
' Time(sec)
~ 140
210
Fig. 24. Heat transfer coefficientat the PCT position. two-phase flow regime (Okubo and Murao, 1985; Akimoto and Murao, 1992) which is type A in Fig. 12. The heat transfer coefficient is smaller in the two-phase flow regime than the subcooled film boiling flow regime. This difference is attributed to the friction loss from the upper plenum to the break. Steam generated in the core is release through the ADS line in SCLWR, while it goes through S/G to the break in PWR.
4. CONCLUSIONS In this study, a LOCA analysis code, named SCRELA, is developed for the supercritical-pressure light water cooled reactors. The code consists of the blowdown and the reflood analysis modules, both of which are validated in comparison with the REFLATRAC code. The analysis of the 100% cold-leg break LOCA of SCLWR shows that PCT is 980°C, which is sufficiently lower than the limit of the stainless steel cladding, 1260°C. In addition, the following information is obtained for the SCLWR LOCA. Isolation of the intact line leads to higher core coolability during the blowdown phase because the coolant stagnation is avoided in the core. Actuation of ADS helps the reflooding by releasing steam generated in the core. SCRELA is expected to be applied to the LOCA analyses of other types of supercritical-pressure light water cooled reactors which cannot be analyzed by the existing codes.
REFERENCES
Akimoto, H. and Murao, Y. (1992) Development of reflood model for two fluid model code based on physical models used in REFLA code, J. Nucl. Sci. Technol. 29, 642. Coffman Jr, F. D. (1976) LOCA Temperature Criterion for Stainless Steel Clad Fuel. NUREG-0065. Duffey, R. B. and Porthouse, D. T. C. (1973) The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Des. 25, 379.
Development of a LOCA analysis code
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Jevremovic, T., Oka, Y and Koshizuka, S. (1994) Core design of direct-cycle, supercritical-water cooled fast breeder reactor, Nucl. Technol. 108, 24. Koshizuka, S., Shimamura, K. and Oka, Y. (1994) Large-break loss-of-coolant accident analysis of a direct-cycle supercritical-pressure light water reactor, Ann. Nucl. Energy 21, 177. Mistubishi Heavy Industries Ltd (1988) The Methodology of the ECCS Analysis for the Mistubishi's PWR (Large LOCA). MAPI-1035. Oka, Y. and Koshizuka, S. (1993) Conceptual design of a supercritical-pressure, directcycle light water reactor, Nucl. Technol. 103, 295. Oka, Y., Koshizuka, S., Jevremovic, T. and Okano, Y. (1995), Systems design of directcycle supercritical-water cooled fast reactors, Nucl. Technol., 109, 1. Okubo, T. and Murao, Y. (1985) Assessment of core thermo-hydrodynamic models of REFLA-1D code with CCTF data for reflood phase of PWR-LOCA, J. ofNucl. Sci. Technol. 22, 987. Jones Jr, O. C. (1981) Nuclear reactor safety heat transfer, Hemisphere, 403.
Ann. Nucl. Energy, Vol. 25, No. 16, pp. 1341-1361, 1998 © 1998 Elsevier Science Ltd. All fights reserved P I h 80306-4549(97)00084-4 Printed in Great Britain 0306-4549/98 $19.00 + 0.00
D E V E L O P M E N T OF A LOCA ANALYSIS C O D E FOR THE S U P E R C R I T I C A L - P R E S S U R E LIGHT WATER C O O L E D REACTORS JONG HO LEE,* SEIICHI KOSHIZUKA and YOSHIAKI OKA Nuclear Engineering Research Laboratory, The University of Tokyo, 2-22 Shirane, Shirakata, Tokai-mura, Naka-gun, lbaraki, 319-11 Japan (Received 8 July 1997) A~traet--The supercritical-pressure light water cooled reactors aim at cost reduction by system simplification and higher thermal efficiency, and have flexibility for the fuel cycle due to technical feasibility for various neutron spectrum reactors. Since loss-of-coolant accident (LOCA) behavior at supercritical pressure conditions cannot be analyzed with the existing codes for the current light water reactors, a LOCA analysis code for the supercritical-pressure light water cooled reactor is developed in this study. This code, which is named SCRELA, is composed of two parts: the blowdown and reflood analysis modules. The blowdown analysis module is designed based on the homogeneous equilibrium model. The reflood analysis module is modeled by the thermal equilibrium relative velocity model. SCRELA is validated by the REFLA-TRAC code, which is developed in the Japan Atomic Energy Research Institute based on TRAC-PF1. A large break LOCA of the thermal neutron spectrum reactor (SCLWR) is analyzed by SCRELA. The result shows that the peak clad temperature (PCT) is nearly 980°C about 60 s after the break and the PCT position is quenched at 170 s This means that PCT is sufficiently lower than the safety limit of 1260°C. In conclusion, the developed code shows the safety of SCLWR under the large break LOCA, and is expected to be applied to LOCA analysis of other types of the supercritical-pressure light water cooled reactors. © 1998 Elsevier Science Ltd. All rights reserved
NOMENCLATURE Symbols A cp Cv D F
Cross section Specific heat under constant pressure Specific heat under constant volume Diameter Friction factor
*Author for correspondence. 1341
1342
J.H. Lee et al. G h k K L P T V
Vol
W Z
Mass flux Heat transfer coefficient Thermal conductivity Form loss coefficient Length or distance Pressure Temperature Velocity Volume Mass flowrate Height
Greek Letters:
t~ y p
Void fraction Thickness of cladding Ratio of specific heat coefficients Density
Subscripts: ads
b c cr cv
d g 1 L lp
n o qf R sat sub up
w
Automatic depressurization system Bulk Core Critical flow condition Containment vessel Downcomer Gas Liquid Leidenfrost temperature Lower plenum Nozzle Stagnation condition Quench front Radiation Saturation Subcooled Upper plenum Wall
1. INTRODUCTION Supercritical-pressure light water cooled reactors have been conceptually designed for improving light water reactor technology by simplifying the plant system and enhancing thermal efficiency. Supercritical water at a pressure of 25 MPa is employed as the reactor coolant. The coolant temperature increases continuously in the core without abrupt
Development of a LOCA analysis code
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change of density. The high energy core outlet coolant, which corresponds to superheated steam of subcritical water, is directly fed to the turbine. Several types of neutron spectrum reactors, such as a thermal reactor, a fast breeder and a fast converter, can be designed with the same cooling system. The expected economical merits and technical feasibility were presented in the previous papers (Oka and Koshizuka, 1993; Jevremovic et al., 1994; Oka et al., 1995). If a loss-of-coolant accident (LOCA) occurs in the supercritical-pressure light water cooled reactor, the blowdown phase begins at supercritical pressure. Behavior of supercritical water cannot be analyzed with the existing codes for pressurized water reactors (PWRs) and boiling water reactors (BWRs). Also, though the reactor pressure vessel (RPV) is similar to that of PWR, the reflooding behavior is different from that of PWR. Figure 1 represents the general plant system of the direct cycle supercritical-pressure light water cooled reactor. After LOCA, the normal cooling system is not available due to containment isolation and the emergency cooling flow path is established by the actuation of the automatic depressurization system (ADS) and the low pressure coolant injection system (LPCI). The emergency cooling flow path is from the lower plenum through the ADS line to the suppression chamber pool, while a longer flow path through the steam generator to the break appears in PWR. In this paper a new LOCA analysis code is developed for the supercritical-pressure light water cooled reactors. The developed code is composed of two parts, which are the blowdown and reflood analysis modules. The code is applied to a large break LOCA of a thermal neutron spectrum reactor (SCLWR) of 1145 MWe output (Koshizuka et al., 1994). The principal parameters and RPV features of SCLWR are depicted in Table 1.
2. CODE DEVELOPMENT 2.1. Blowdown analysis module 2.1.1. Thermal-hydraulic calculation model In order to estimate the behavior of the blowdown phase, the system model consists of the reactor vessel, hot legs from the reactor vessel outlets to the isolation valves, and an Reaclro r Vessel
I~
)
ADSValve
Turbine
S upres sionChamber
Pool
Mainf ~ a ~ rpump
i
Condenser
Fig. 1. General plant system of supercritical-pressure light water cooled reactor.
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al.
Table 1. Principal parameters of SCLWR Core diameter/height Core inlet/outlet temperature Core inlet/outlet density Fuel rod/pellet diameter Cladding/thickness Lattice pitch/rod diameter, P/D Maximum power density Presssure Coolant flowrate Number of coolant loops Inlet/outlet pipe diameter Reactor vessel height/diameter Thermal power Thermal efficiency Electrical power
267/570 cm 310/416°C 0.725/0.137 gcm -2 0.8/0.694 cm SS/0.046 cm 1.4 (triangular) 363.6 MW/m -2 25 MPa 2032 kg s-1 2 34/53 cm 15.5/3.67m 2780 MW 41.2% 1145 MW
Break
Hot Leg
Cold L F [ Valve ~ [ SafetyInjection~ :
Core Node-N
Valve
De wr
A 3S Line
COl he1
Core Node- 3
Break
Core Node-2
Core Node-1 [iii Chamber Pool il :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Fig. 2. System noding for blowdown analysis. ADS line. Figure 2 shows the system node diagram for the blowdown analysis. The number of calculation nodes at the core, the downcomer, the lower plenum and the upper plenum can be changed. Plant parameters are given as the boundary conditions; for example, the coolant inlet flowrate from an intact line is calculated from the pump characteristic curve and the coolant outlet flowrate is proportional to the core pressure. Since the transient in the blowdown phase is under high flowrate and high pressure
Development of a LOCA analysis code
1345
conditions, the homogenous equilibrium model (HEM) is selected as the thermalhydraulics. As the pressure drop in the reactor vessel is relatively smaller than that at the break, the pressure in the reactor vessel is assumed as constant. The pressure decrease rate in the blowdown phase is governed by the flowrate at the break. Three correlations of the break flowrate are prepared for different pressure regions. In the superheated steam region, isentropic ideal gas is assumed. Thus, the mass flux and pressure at the critical flow condition are calculated as shown in the following equations:
l
Mass flux: Gcr = 19
2cpToLkPo]
Critical pressure: ecr =
\Po]
p /" 2 "~×/(×-') o~ - ~ - ~ ]
(1)
(2)
where × = ce/cv.
Two-phase critical flow is calculated based on Moody's homogeneous equilibrium model. In the subcooled region, Zaloudeck's correlation is used as Gcr = 0.95ff2gcp(Po - esat).
(3)
Critical flow in the supercritical pressure region is not known. However, the pressure at the break is subcritical even if the stagnation pressure is supercritical. Accordingly, the same correlations in the subcritical regions are also used in the supercritical pressure regions. As long as the stagnation temperature is below or equal to the pseudo-critical temperature, the critical flow is treated as in the subcooled region. When the temperature is higher than the pseudo-critical temperature, the superheated steam region is assumed. Figure 3 shows the critical mass fluxes in the various pressure regions. The core power is evaluated from the point kinetic equations including six groups of delayed neutrons and decay heat of ANS + 20%. The density coefficient of reactivity is only considered for the core power calculation. The radial distribution of temperature in the fuel is assumed uniform. In order to evaluate heat transfer to the coolant in various conditions, the following heat transfer correlations are employed. Dittus-Boelter's correlation is used in the supercritical, subcooled and superheated regions. The radiation heat transfer is involved in the superheated region. Dougal-Rhosenow's correlation is used in the film boiling region. It is also conservatively used in the nucleate boiling region because this region appears for a very short period of the large break LOCA analyzed here. The gap conductance in the fuel rod is assumed uniform. Heat capacities of the reactor vessel and other structures are neglected. 2.1.2. Calculation procedure
Figure 4 presents the calculation flow chart of the blowdown analysis. At first, the break flowrate is calculated by using the values of the previous time step. Subsequently, the flowrate of each node is calculated from the mass and energy conservation equations
1346
J.H. Lee et al. 1.6e+5
,
•
5.0 MPa 7.5 MPa ,10.0 MPa 12.5 MPa 15.0 MPa
\ .-. 1.2e+5
~!q \
~'~ 8.0e+4
i,,,, , 20.0 MPa ,~o ~ =Joo
,,.,
-
-
25.0
MPa
= tl.. cO
== 4.0e+4 ~ .
O.Oe+O . 1.2e+6
~,
.
~. ~.._
. . 1.8e+6
.
~__.
•
. 2.4e+6
3.0e+6
Stagnation Enthalpy (J/kg) Fig. 3. Critical mass flux as a function o f stagnation enthalpy and pressure.
at an assumed pressure. Heat transfer from the fuel to the coolant is evaluated from the temperature difference in the previous time step. Finally, the system pressure is determined to satisfy the flow balance by an iteration calculation. The flow balance is judged from flowrates at the boundaries: the break point and the core inlet and outlet of an intact line. The flowrates, masses and enthalpies in the nodes at the present time step are determined when the system pressure converges. This procedure is continued until the blowdown is ended; the system pressure is the same with that in the containment vessel. 2.1.3. Code validation
The developed code is named SCRELA, which is an abbreviation of supercriticalpressure light water reactor LOCA analysis code. The blowdown analysis module in SCRELA is validated by comparing with the REFLA-TRAC code, which was developed in the Japan Atomic Energy Research Institute (JAERI) based on TRAC-PF1. An SCLWR analyzed by Koshizuka et al., 1994 is used for the validation calculation. The blowdown calculation starts at a core pressure of 17.0 MPa in the REFLA-TRAC code, since this code is not able to treat the supercritical-pressure conditions. Figures 5 and 6 show the pressure trends of 100% cold-leg and 100% hot-leg break LOCAs, respectively. Figures 7 and 8 represent the break flowrates at the cold-leg and the hot-leg breaks. The blowdown phase ends at 41 and 29 s in the cold-leg and hot-leg break LOCAs, respectively, in the SCRELA calculations. In the initial stage of blowdown, the decrease rate of pressure in the hot-leg break LOCA is higher than that in the cold-leg break LOCA. This is because the break flow is in a superheated steam condition at the hot-leg break, while it is in a subcooled liquid condition at the cold-leg break. After the initial high
Development of a LOCA analysis code
1347
[Stead~' State Value Calculation1 I Start BlowdownCalculation] ,..J re [Calculationof Break FlowI [ APAssumption ] ,...1
I Mass and EnergyConserv.~..~Core Heat Equ. in theEach Nodes I-I Transfer !
I
No ~
ITemperaturel
t+l ~1Descisionof State Values [Timestep change[[ at the Time Step [ t~
N
o
~
~lation
~
Fig. 4. Calculation flow chart of blowdown phase. 28
21
7
o
0
10
20 30 TimeOm¢)
40
50
Fig. 5. Pressure trend in 100% cold-leg break LOCA. depressurization, the decrease rate of pressure is slowed down in both cases because the break flow conditions are changed to two-phase flow. As shown in the figures, the results calculated by the SCRELA and REFLA-TRAC codes are nearly the same. Consequently, the blowdown analysis module developed with HEM is validated.
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al.
25 20 A
REFLA-TRAC SCRELA
15
g 10 ~t
i
¢k
5 0
0
10
20
30
40
50
Timo(sec)
Fig. 6. Pressure trend in 100% hot-leg break LOCA.
1.0e+4 I
7.5e+3 1
" REFLA-TRAC
5.0e+3~
0
i
10
20
30
40
50
Time(sec)
Fig. 7. Break flowrate in 100% cold-leg break LOCA.
7.5e+3
REFLA-TRAC[ SCRELA
6.0e+3 4.5e+3
.¢ 3.0e+3 n-. 1.5e+3 0.0e+OI 0
10
20 30 Time(see)
40
50
Fig. 8. Break flowrate in 100% hot-leg break LOCA.
Development of a LOCA analysis code
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2.2. Reflood Analysis Module 2.2.1. System behavior in the reflood phase In the case of cold-leg break LOCA, ECCS coolant flow has two paths by the ADS actuation as shown in Fig. 9(a). One is from the lower plenum through the core, upper plenum, hot-leg pipe and the ADS line in turn. The other is formed directly to the break line. The flow path through the ADS line is shorter than that through the S/G loop in PWRs. The double-ended break like PWRs does not appear in SCLWR. In this reactor, the flow path through the ADS line is utilized as the cooling path in the low pressure condition. In the case of hot-leg break LOCA, since the cold-leg lines are isolated, only upward flow is established in the core from the lower plenum to the break line or the ADS line as shown in Fig. 9(b). Therefore, the cold-leg break LOCA is considered as severer than the hot-leg break LOCA. In this paper, the reflood phase of the 100% cold-leg break LOCA, the severer case, is analyzed.
2.2.2. Thermal-hydraulic (T/H) model The T/H model is based on a system momentum calculation and a core mass and energy calculation:
( a) System momentum calculation model The system momentum calculation is modeled by coupling a reactor vessel part and an ADS line part (Fig. 10). The reactor vessel part is represented by momentum balance between the downcomer and the core water levels. The equation is described in terms of acceleration, pressure difference between the downcomer and the core water levels, static pressure head due to the water level difference, and inertia:
Bmal~Une
_~ c<~} l ".l Break
LPCIWater Inlet
i
Reacl~r Vess el
UI
~T'i c~" ~
LPClWaler Inlet
Supr ess ion Chamber
(a) Cold-leg break
ReacIm Vessel (b) Hot-leg break
Fig. 9. Refloodphenomena.
1350
J.H. Lee et al. i
Reactor Vessel Module hsi
', A D S <
Loop Module
•i ~ ~
.........
d$
suppressionChamber
Reactor Vessel
Fig. 10. Modeling for momentum calculation.
, r_~
v°,~l
P,-p~+ g~(zd
z~) (4)
-galVdl. akA, -- ~ 1 \ ~ 2K¢,1
(5)
The pumping head of LPCI and the friction loss are neglected. The boundary conditions are water levels in the downcomer and the core, and pressures at these levels. As described in equation (5), the pressure at the core water level is obtained as the addition of the pressure in the upper plenum and the friction loss from the core water level to the upper plenum. The core water level is calculated from a detail core model presented in the following section. The system pressure, which is the same with the upper plenum pressure, is evaluated by adding the pressure loss in the ADS line to the pressure in the containment vessel (CV). The pressure loss in the ADS line is calculated by assuming steady state flow as represented in equation (6):
APads = \Aad,./
"Lkp-
P.p] +Fads.~.2/Sads
÷
~-p -j.l
(6)
The flowrate and enthalpy at the core top are calculated from the following core model.
Development of a LOCA analysis code
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(b) Core T/H calculation model In the core a thermal equilibrium relative velocity model is used in the two-phase region. This means that the relative velocity between water and void is represented by a correlation. Physical properties in the core are obtained by using the pressure at the core water level. The boundary conditions are the flowrate and enthalpy at the core bottom, and the pressure at the core water level. The quench front is calculated by using a quench front velocity correlation. The core is normally divided into 60 nodes. To prevent the numerical instability caused by the abrupt change of the heat transfer coefficient, the neighboring nodes of the quench front are more finely divided into the 1/100 thickness of the normal node as shown in Fig. 11. The heat transfer coefficient sharply changes by about 2 orders of magnitude in the vicinity of a quench front.
(c) T/H correlations Quenchfront velocity correlation For the calculation of the quench front, Yamanouchi's correlation is used:
( ~__ff__~{(:£~ - ~)½(Tw -/i) ~
(7)
The quench front velocity, Vqf, represents the propagation speed of the quench front toward the core top (Duffey and Porthouse, 1973). The heat transfer coefficient at the quench front region, hqf, is a constant value of 5 x l 0 n w m - 2 K -l proposed by Yamanouchi (Jones Jr, 1981). Core Top 6-I(: 2-: ;---'-''--'-''-'-"26-8 :.'-~-'--Z:S-"::.'[:=:-"
6-9 6-7
6-67----_-_--:::-:::_.7::
6-5
6-26-4~::::::::;:::::.::=
6-3 6-1
3-1 ................. 3-8 .................. 3-6 ................. 3-4 . : : 2 2 : : : : : : 2 : : : : : : 3-2 :::::::::::::::::: 2-1( ..................
2-8 ::::~::~::~i~ ~ 2-6 2..4,
i!~i~!~.~i~ ~2~
~~~ ~
" ' . ~ : ~
:::::.:::::..::~::::;::~:::::9:.:: ::::::::::::::::::::::::::::::::::::::: 1-8
~:~ ~
%
~
1-6
~i~i~i ,i;~i~ ~ i ~ i ~ i ~ !
z-2
~!~~::~i~i~ Core
A.Normal Calculation Nodes
B.Fine Calculalion Nodes
Fine Node Width -- Normal Node Wkllh / 100
Fig. 11. Core noding near the quench front.
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Heat transfer coefficient The flow regimes assumed in the reflood analysis code are described in Fig. 12. They are single-phase liquid, saturated two-phase, transient, dispersed and superheated steam flow regimes. The various heat transfer correlations are prepared according to the flow regime. Table 2 summarizes the heat transfer correlations in these flow regimes. In the film boiling and transient boiling flow regimes, Murao and Sugimoto's correlation used in the REFLA-TRAC code is employed (Akimoto and Murao, 1992). In the dispersed flow regime, the compensated value of Murao and Sugimoto's correlation is applied so that the heat transfer coefficient is continuous between the neighboring regimes. Tom's correlation is used in the single-phase liquid, subcooled nucleate boiling and saturated two phase flow regimes. Dittus-Boelter's correlation is adopted in the superheated steam flow regime. Relative velocity correlation In order to describe the relative velocity in two-phase flow, a set of correlations in Mistubishi's LOCA analysis code are used (Mistubishi Heavy Industries Ltd., 1988). The relative velocity correlations in nucleate boiling, film boiling and dispersed flow regimes are prepared. In the transient flow regime, the average value weighted by the void fraction between the film boiling and dispersed flow regimes is used. The flow where the void fraction is above 0.99 is treated as the dispersed flow regime. 2.2.3. Calculation procedure The calculation procedure is described in Fig. 13. When the ECCS water level reaches the core bottom, the reflood calculation is started with the output data from the previous
ated rl
Tb>T
sat
)n
Quench-. Front
~1
Saturation Point
i
Type A
Type B
Fig. 12. Heat transfer regime in core during reflood phase.
Development of a LOCA analysis code
1353
Table 2. Flow regimes and heat transfer correlations Position Below quench front level
Heat transfer regime
Heat transfer correlation
(1) Single liquid phase/subcooled nucleate boiling flow (2) Saturated two-phase flow (3) Subcooled film boiling flow
-Tom's correlation q" = exp(2P/8,7)(Tw- Ts.t)2/22.72 -the same as case (1) -Murao and Sugimoto's correlation h = hsub + hR
hs,b = hs,,,[1.0 + 0.025(T~,t- Tt)] h R = EE(TI~ 4 - Tsar4)~( T w - Tsar)
(4) Film boiling/transient boiling flow
-Murao and Sugimoto's correlation
(5) Dispersed flow
-Compensated Murao and Sugimoto's correlation
h = hsat + hR h~at = O.94[~.g3pgplhfgg/ Lql,zg( Tw - Tsat)] 1/4 h R = Ee( Tw4 - Tsat4) /( T w - T~at)(1 -or) 0"5
Above quench front level
h = hsat,comp Jr"h R hsat ,corn~P = FcP × hsat, Fop" compensation factor
hR = E e ( T w 4 - Tsat4)/(Tw-Tsat)(1-000.5 -Dittus-Boelter's correlation h = 0.023 (k/Dh)Re°'SPr °'4
(6) Superheated steam flow
I
[
- Refill Output Data - Calculation Cond., etc -r I Downcomer Water Level I Quench Front Level ]
I Momentum Conservation Equ. I in Reactor vessel Mass and Energy ConservL.lCore Heat Equ. in the Core Nodes [ 7 Transfer I
I
k+l
I Flowrate and Enthalpy I I Fuel Clad I [ I Temperature I
Icha ~e of] I at the Core Top I'nm, Step] k~ '
[S)~stemMomentum Equation I [- :system(Upper Plenum) Pressure [
t, [ Pressure at Cote Water Level [
Fig. 13. Calculation flow chart of reflood phase.
1354
J.H. Lee et al.
blowdown and refill calculation. At first, the downcomer and the core water levels are estimated from the ECCS injection flow and the quench front velocity in the previous time step. The water velocity in the downcomer is calculated using equation (4). Next, the water velocity in the core bottom is obtained using the mass conservation equation. After the velocity and enthalpy in the core bottom are known, the flowrate and enthalpy of each node in the core are calculated by the core T/H calculation model. Based on the calculated temperature distribution in the core, the heat transfer from the fuel rod to the coolant is evaluated. Temperatures of the cladding and the pellet are also calculated. These values are used for the core T/H calculation in the next time step. The pressure loss in the ADS line is calculated by substituting the velocity and enthalpy in the upper plenum into equation (6). Then, the pressure in the upper plenum is evaluated by adding the pressure loss in the ADS line to the pressure in the containment vessel. Finally, the pressure at the core water level is calculated by using equation (5). 2.2.4. Code validation
The developed reflood analysis module is also validated by comparing with the REFLA-TRAC code. The validation calculation starts from the output data of the blowdown calculation by Koshizuka et al., 1994. The calculation result is compared with the reference in Fig. 14. The peak clad temperature (PCT) of 1021°C appears at 54 s after the break in the SCRELA analysis, while PCT is 1006°C at 47 s in the REFLA-TRAC analysis. SCRELA analysis presents a conservative result about 15°C. After PCT, the cladding temperature continuously decreases to the quench point. The core bottom is quenched at 65 and 72 s in two codes, respectively. Figure 15 presents the void fractions at the core middle in the SCRELA and the REFLA-TRAC analyses. The flow condition at the core middle changes to the liquid phase at about 55 s in the SCRELA analysis, while it is settled to the liquid phase at about 75 s after large fluctuation in the REFLA-TRAC analysis. We can see the first change to the liquid phase at nearly the same time of about 55 s. Different behavior after 55 s is originated from the difference of the calculation model
12°°t
12
I [] E A- RAcl
t _ 5 ~X CoreTop 200[- C°reB°tt°m ~_~1t 0
30
-
~
]
D
60 Time(see) 90
I L '
~
120
Fig. 14. Fuel cladding temperature in the reflood phase of validation calculation.
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1.0 m 0.8
OR
SCRELA
0.6
I
REFLA-TRAC
O
I,I. 0.4 "O
>o OR
0.2
•- L
0.0 40
I I I i I . . . . 70 Time($ec) 100
130
Fig. 15. Void fraction in the core middle during the reflood phase of the validation calculation.
of the upper plenum. In the SCRELA code, the physical properties in the upper plenum node are assumed unchanged. Namely, the flow velocity and enthalpy in the upper plenum are the same as those of the core top. In spite of this model difference, both trends of the cladding temperature exhibit good agreement.
3. ANALYSIS O F SCLWR LOCA
3.1. Blowdown analysis 3.1.1. Calculation condition Isolation of the intact lines is assumed to start from 1.8 s and to be completed at 3 s after the break by considering the BWR plant data. Coolant flow of the intact lines is taken into account before the isolation. For the sensitivity study, the case of no intact line flow is also calculated. ADS and LPCI systems are considered as ECCS for the mitigation of LOCA. Table 3 shows the parameters of the ECCS design for the large break LOCA. Time delay of LPCI actuation is assumed 30 s due to the starting of the emergency diesel generators. LPCI is conservatively assumed to start at a pressure of 0.8 MPa which is less than the designed value. Actuation of ADS is not considered in the blowdown phase. The refill phase is also successively calculated. It continues until the lower plenum is full of Table 3. ECCS design for large break LOCA Low pressure coolant injection system(LPCI)
Number of units: Capacity: Time delay: Design pressure:
Automatic depressurization system (ADS)
Location: Flow area: Time delay:
4 805 kg s-1 30 s 1.0 MPa Hot-leg 0.22 m 2
30 s
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ECCS water. Heat transfer from the fuel rods to the coolant is neglected during the refill phase. 3.1.2. Calculation results
The pressure trend during the blowdown phase of the 100 % cold-leg break LOCA is exhibited in Fig. 16. The cladding temperature is shown in Fig. 17. The blowdown phase is completed at 41 s after the break and the refill phase is completed at 44 s. The LPCI system is actuated at 33 s. The cladding temperature at the core middle sharply increases to about 800°C in the initial stage due to the degradation of cooling capability and power redistribution, and thereafter, the increase speed of the temperature is slower. The intact line flow drives upward flow, while the break flow does downward flow in the core. Figure 18 shows the flowrates at various positions in the core and the intact line. Consequently, flow stagnation appears in the core. If the flow in the intact line is not considered, the core coolability is better because the downward flow to the break is prevailing. 30
!
With Intact Line Flow I
m
20
No Intact Line Flow
a.
2- i
I
10
2
a.
L
0
10
20 30 Time(sec)
40
50
Fig. 16. Pressure trend in 100% cold-leg break LOCA (blowdown analysis). 1050 .Core Middle(with Intact Line Flow)
--
,.j
~
~
Core Middle(No Intact Line Flow)
550
I~
"~'~""'~'qr~ 300
,
0
co re Bottom I
I
I
15 Time(sec) 30
,
I
45
Fig. 17. Fuel cladding temperature in 100% cold-leg break LOCA (blowdown analysis).
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2OOO lOO0 A|
A
!
i -1000 ,-;- -2000 -3000 0
Core Top Hot-leg(Intact) Cold-Leg (Intact) Core Bottom I
I
10
20
Time(sec)
Fig. 18. Flowrates in 100% cold-leg break LOCA (with intact line flow). In the case of 100 % hot-leg break LOCA, the pressure and the cladding temperature are depicted in Figs 19 and 20, respectively. The blowdown phase ends at 33 s after the break and the refill phase is completed at 40 s. The LPCI system is actuated at 30 s. The cladding temperature at the core middle sharply increases at the beginning due to the redistribution of stored energy in the fuel and a power spike caused by a positive reactivity. Figure 21 shows the reactor thermal power in the cold-leg and hot-leg break LOCAs. The reactor power shows a peak at 0.2 s in the hot-leg break because the core flow is accerelated. The positive reactivity is inserted by increasing the coolant density in the core. On the other hand, the power peak does not appear in the cold-leg break LOCA since the core flow is decelerated. However, the peak temperature is 550°C, which is much lower than the case of cold-leg break LOCA. The cladding temperature decreases after the peak due to the high coolability in the core. This is because the core is cooled by the upward flow by using the coolant inventory in the downcomer and the lower plenum. In the case of hot-leg break, effect of the intact line flow is not large as shown in Fig. 20 since the directions of the intact line flow is the same as the break flow.
2s[ [ 2O
With Intact Line Flow J
15
.}
I
lo
|
0 0
10
20 30 Time(sec)
40
50
Fig. 19. Pressure trend in 100% hot-leg break LOCA (blowdown analysis).
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500
i
400
I--
Core Bottom , ! ,
200 0
10
~ i
--"--'-'-'Core ToPl
20 Time(sec)
,
i 40
30
,2o
Fig. 20. Fuel cladding temperature in 100% hot-leg break LOCA (blowdown analysis).
m
Cold-Leg I Hot-Leg
o ~L
"6 40 @
t
rr
0 ~
0.0
2.5
5.0 • Time(sec)
7.5
10.0
Fig. 21. Reactor thermal power in the blowdown phase.
3.2. Reflood analysis 3.2.1. Calculation condition Two out of four LPCI systems are assumed to be available. Therefore, the total available flowrate of ECCS during the reflood is 1610 kg -1 sec. The length of the ADS line is assumed 13 m. The static head in the suppression chamber pool is not considered in the calculation of the pressure loss of the ADS line. The reflood analysis is only carried out in the case of 100% cold-leg break LOCA because this leads to a severer result than the hotleg break LOCA. The calculation starts from the output data from the blowdown analysis with the intact line flow.
3.2.2. Calculation results The reflood phase starts from 44 s after the break. Figure 22 represents the cladding temperatures at the core bottom, middle and top. PCT is 980°C which appears at the core
Development of a LOCA analysis code
1000~
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~ Core Bottom Gore Middle Top
750
Gore
i
~. 250 0
50
100
150
Time(sec)
20O
Fig. 22. Fuel cladding temperature after the break. middle at 56 s. This is sufficiently lower than the limit temperature of stainless steel cladding, 1260°C (Coffman Jr, 1976). The core middle is quenched at 170s. The cladding temperature at the core bottom rapidly drops at 74 s due to the quench. The cladding temperature at the core top exhibits a peak value at about 64 s, and gradually decreases to the quench point. Since the quench front level proceeds from the core bottom to the top in the present calculation using the quench front velocity correlation, the core top is to be quenched later than the core middle as depicted in Fig. 23. Figure 24 describes the history of the heat transfer coefficient at the PCT position, 3.3 m elevation of the core. The flow regime is changed to the subcooled film boiling at about 70 s and finally reaches the subcooled nucleate boiling due to the quench at about 180 s. This means that the saturation liquid level is higher than the quench front level, which is the flow pattern of type B in Fig. 12. This behavior of SCLWR is different from that in PWR. The general trend of the reflood phase in PWR shows that the core above the quench front level is cooled by the 15
10 QuenchFront I DowncomerLevel
s
0 ~
0
70
Time($ec)
140
210
Fig. 23. Quench front and downcomer water levels in the reflood phase.
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J.H. Lee et al. 10 5
i '°litf 1
r 0
0
0 70
' Time(sec)
~ 140
210
Fig. 24. Heat transfer coefficientat the PCT position. two-phase flow regime (Okubo and Murao, 1985; Akimoto and Murao, 1992) which is type A in Fig. 12. The heat transfer coefficient is smaller in the two-phase flow regime than the subcooled film boiling flow regime. This difference is attributed to the friction loss from the upper plenum to the break. Steam generated in the core is release through the ADS line in SCLWR, while it goes through S/G to the break in PWR.
4. CONCLUSIONS In this study, a LOCA analysis code, named SCRELA, is developed for the supercritical-pressure light water cooled reactors. The code consists of the blowdown and the reflood analysis modules, both of which are validated in comparison with the REFLATRAC code. The analysis of the 100% cold-leg break LOCA of SCLWR shows that PCT is 980°C, which is sufficiently lower than the limit of the stainless steel cladding, 1260°C. In addition, the following information is obtained for the SCLWR LOCA. Isolation of the intact line leads to higher core coolability during the blowdown phase because the coolant stagnation is avoided in the core. Actuation of ADS helps the reflooding by releasing steam generated in the core. SCRELA is expected to be applied to the LOCA analyses of other types of supercritical-pressure light water cooled reactors which cannot be analyzed by the existing codes.
REFERENCES
Akimoto, H. and Murao, Y. (1992) Development of reflood model for two fluid model code based on physical models used in REFLA code, J. Nucl. Sci. Technol. 29, 642. Coffman Jr, F. D. (1976) LOCA Temperature Criterion for Stainless Steel Clad Fuel. NUREG-0065. Duffey, R. B. and Porthouse, D. T. C. (1973) The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Des. 25, 379.
Development of a LOCA analysis code
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Jevremovic, T., Oka, Y and Koshizuka, S. (1994) Core design of direct-cycle, supercritical-water cooled fast breeder reactor, Nucl. Technol. 108, 24. Koshizuka, S., Shimamura, K. and Oka, Y. (1994) Large-break loss-of-coolant accident analysis of a direct-cycle supercritical-pressure light water reactor, Ann. Nucl. Energy 21, 177. Mistubishi Heavy Industries Ltd (1988) The Methodology of the ECCS Analysis for the Mistubishi's PWR (Large LOCA). MAPI-1035. Oka, Y. and Koshizuka, S. (1993) Conceptual design of a supercritical-pressure, directcycle light water reactor, Nucl. Technol. 103, 295. Oka, Y., Koshizuka, S., Jevremovic, T. and Okano, Y. (1995), Systems design of directcycle supercritical-water cooled fast reactors, Nucl. Technol., 109, 1. Okubo, T. and Murao, Y. (1985) Assessment of core thermo-hydrodynamic models of REFLA-1D code with CCTF data for reflood phase of PWR-LOCA, J. ofNucl. Sci. Technol. 22, 987. Jones Jr, O. C. (1981) Nuclear reactor safety heat transfer, Hemisphere, 403.