Research on thermal hydraulic behavior of small-break LOCAs in AP1000

Nuclear Engineering and Design 263 (2013) 380–394

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Research on thermal hydraulic behavior of small-break LOCAs in AP1000 W.W. Wang, G.H. Su ∗ , W.X. Tian, S.Z. Qiu State Key Laboratory of Multiphase Flow in Power Engineering, Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China

h i g h l i g h t s • • • •

A RELAP5 model for RCS and passive safety systems in AP1000 was developed. A spectrum of cold leg small break LOCAs was analyzed. The PCTs are far below the limit value of 1478 K and meet the safety criterion. This article is useful for design and operation of AP1000 and other plants.

a r t i c l e

i n f o

Article history: Received 25 June 2012 Received in revised form 12 May 2013 Accepted 17 June 2013

a b s t r a c t As a Generation III+ reactor that received Final Design Approval by U.S. NRC, AP1000 employs a series of nature forces, such as gravity, natural circulation and compressed gas, to enhance plant safety. Although plenty of work has been done around AP600 and its updated version AP1000 both experimentally and theoretically in the past few decades, thermal hydraulic behavior of small break LOCAs in AP1000 has not been fully understood and further studies are still required. In the present study, the response of AP1000 to a spectrum of cold leg small break LOCAs is simulated and analyzed using RELAP5/MOD3.4, including 2-in. break, 4-in. break, 8-in. break as well as 10-in. break which approaches the upper limit size for small break LOCAs in AP1000. Based on the calculation results, it indicates that the passive safety systems employed by AP1000, including CMTs, ACCs, IRWST, PRHRS and ADS, combine to provide continuous passive safety injection and residual heat removal. During cold leg small break LOCAs, the core uncovery and fuel heat up do not occur. The peak cladding temperatures (PCTs) during the accident process are far below the Appendix K limit value of 1478 K/2200 ◦ F and meet the safety criterion. Results show that the accidental consequence can be mitigated effectively and thus the safety of AP1000 during cold leg small break LOCAs is proven. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Since the TMI-2 accident in March 1979, the small break LOCA issue and related nuclear power plant safety has attracted the attention of researchers in the nuclear engineering field (Kawanishi et al., 1991). Around this issue, plenty of work has been done both experimentally and theoretically. As a Generation III+ reactor that received Final Design Approval by U.S. NRC, AP1000 employs a series of passive safety systems which rely only on redundant/fail-safe valves, gravity, natural circulation and compressed gas to ensure its safety feature rather than active components such as diesel generators and pumps (Boyack and Lime, 1995a,b, April). The passive safety systems mentioned

∗ Corresponding author. Tel.: +86 29 82663401; fax: +86 29 82663401. E-mail address: [email protected] (G.H. Su). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.06.004

above have a great difference from conventional PWRs. In support of AP600 and AP1000 design, plenty of tests on integral and separate effects facilities were performed to obtain data for safety analysis codes in accordance with Part 52 of Title 10 of the Code of Federal Regulations, namely 10CFR52 (U.S. NRC, 1992). Among the integral effect tests, Westinghouse conducted testing in two integral experimental facilities: the full-height, fullpressure facility SPES-2 (simulatore per esperienze di sicurezza) located in Piacenza, Italy (Friend et al., 1998; Wright et al., 1996) and the reduced-height, reduced-pressure facility APEX (Advanced Plant EXperiment) located at Oregon State University (OSU), USA (Hochreiter et al., 1995; Welter et al., 2005; Wright, 2007). The mission of the SPES-2 program was to provide data on the high pressure and depressurization phases of LOCAs, while the APEX program emphasized late phase depressurization, transition to IRWST injection and long-term cooling (Bessette and Marzo, 1999). In addition, NRC conducted independent testing programs at two facilities.

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Nomenclature flow area (m2 ) energy (J) specific internal energy (J/kg) gravitational acceleration (9.8 m/s2 ) pump head (m) specific enthalpy (J/kg) pump head multiplier pump torque multiplier pressure (Pa) power (W) pump torque (N m) time (s) velocity (m/s) v specific volume (m3 /kg) W mass flow rate (kg/s) three dimensional 3D ACC accumulator automatic depressurization system ADS ANS American nuclear society APEX Advanced Plant EXperiment BDBA beyond design basic accident Combustion Engineering CE CFR Code of Federal Regulations CHF critical heat flux CMT core makeup tank design certification DC DEDVI double-ended rupture of direct vessel injection DNBR departure from nuclear boiling ratio DVI direct vessel injection integral system test IIST IRWST in-containment refueling water storage tank in-vessel core melt retention IVR LOCA loss of coolant accident long term cooling LTC MFW main feed water nuclear steam supply system NSSS OSU Oregon State University PBL pressure balance line PCT peak cladding temperature passive containment cooling system PCCS PMS protection and safety monitoring system PRHR HX Passive Residual Heat Removal Heat eXchanger PRHR passive residual heat removal PRHRS passive residual heat removal system psi pounds per square inch PSIS passive safety injection system PWR pressurized water reactor passive core cooling system PXS PZR pressurizer RCP reactor coolant pump reactor coolant system RCS ROSA rig of safety assessment RPV reactor pressure vessel reactor vessel RV SBLOCA small break loss of coolant accident SG steam generator SPES simulatore per esperienze di sicurezza Three Mile Island TMI A E e g H h Mh Mt P Q T t u

Greek symbols ␣ void fraction surface tension (N/m) ␴ ␳ density (kg/m3 )

381

Subscripts liquid phase f g gas phase fg phasic difference in inlet outlet out 1 pump one-phase condition 2 pump two-phase fully degraded condition

The full-height, full-pressure facility ROSA (rig of safety assessment) located in Tokai-mura, Japan focusing on the high-pressure and depressurization phases and the initiation of IRWST injection (Kukita et al., 1996; Tasakaa et al., 1988). Also, NRC contracted with OSU to carry out a testing program which primarily focused on beyond design basis accident (BDBA) scenarios, providing counterpart tests to the ROSA program (Bessette and Marzo, 1999). Similar integral tests were also conducted at the reduced-height, reduced-pressure facility IIST (integral system test) to evaluate the performance of the passive core cooling system of a Westinghouse three-loop PWR during cold leg small break LOCAs (Chang et al., 2002, 2003, 2006). The separate effect tests included PRHR HX tests (Yonomoto et al., 1998), ADS tests, core makeup tank tests (Yonomoto et al., 1997), passive containment cooling system (PCCS) tests, DNBR tests and in-vessel core melt retention (IVR) tests (Westinghouse, 2004). Meanwhile, small-, intermediate – and large-break LOCAs were simulated numerically for AP600, AP1000 and related integral test facilities to verify the passive safety system design. Based on the large commercial codes RELAP5, WCOBRA/TRAC and TRAC-PF, thermal-hydraulic behaviors of intermediate-break LOCAs (Boyack and Lime, 1995, April, July) and large-break LOCAs (Fisher, 1992; Frepoli et al., 2004; Kemper et al., 1992; Lime and Boyack, 1994; Zhang et al., 1998) were investigated. As for small break LOCAs, the RELAP5 code (Hassan and Banerjee, 1996; Wang and Xie, 2010; Xie, 2010) and a modified version of WCOBRA/TRAC (Bajorek et al., 2001) were applied. What is more, coupling analysis between the reactor coolant system (RCS) and the containment was performed in the case of small break LOCAs in AP600 based on RELAP5 as well as the CONTAIN program which was used for containment simulation (Muftuoglu, 2004). In addition, the NOTRUMP code developed by Westinghouse was used to analyze small break LOCAs in AP1000. Several typical small break LOCA transients, including inadvertent ADS actuation, 2-in. cold leg break, 10-in. cold leg break and DEDVI (double-ended rupture of direct vessel injection line), were analyzed using NOTRUMP (Westinghouse, 2004). Although much work has been done in the past few decades, mechanisms that control small break LOCAs in AP1000 have not been fully understood. Moreover, owing to proprietary of Westinghouse technical documentation, very little information can be obtained in open literature and further studies are still needed. In the present work, the response of the passive safety systems in AP1000 to a spectrum of cold leg small break LOCAs is investigated using RELAP5/MOD3.4 (RELAP5, 2001). The break is located at the bottom of one cold leg in the loop containing the CMTs. Former studies on conventional PWRs have shown that such a break is expected to be more limiting than breaks located at higher locations because they allow the RCS to drain to a lower level (Bajorek et al., 2001). The break spectrum covers 2-in., 4-in., 8-in. and 10-in. cold leg small break LOCAs. Detail description on thermal-hydraulic behavior during the break spectrum mentioned above will be presented in the following.

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2. Description of AP1000 passive safety features AP1000 is a two-loop, 3400 MW Westinghouse-designed PWR which received final design certification (DC) in December 2005 by NRC (Schulz, 2006). The first four AP1000 nuclear power units are now under construction in China, including two units in Sanmen, Zhejiang Province and two units in Haiyang, Shandong Province (Harrop and Poirier, 2010; Matzie, 2008). Recently on February 2012, NRC approved the construction of two new reactors in Georgia State, the first authorized in over 30 years since the TMI-2 accident in USA (http://en.wikipedia.org/wiki/AP1000). The AP1000 passive core cooling system (PXS) is shown schematically in Fig. 1 (Schulz, 2006). Two core makeup tanks (CMTs), two nitrogen-pressurized accumulators (ACCs) and one incontainment refueling water storage tank (IRWST) replace the high, medium and low pressure safety injection systems in conventional PWRs respectively. A full-pressure Passive Residual Heat Removal Heat eXchanger (PRHR HX) with C-shaped tubes submerged in the IRWST provides a decay heat removal path connecting the pressurizer-side hot leg with the corresponding steam generator exit plenum. As water level in the CMTs drops, four stages of automatic depressurization system (ADS) valves open sequentially to provide a controlled depressurization of the primary system. According to the ADS design feature for AP1000, the ADS-1/2/3 valves are clustered into two groups. The ADS-1 valves are 4-in. motor valves. The ADS-2 and ADS-3 valves are both 8-in. motor valves. In addition, 14-in. squib valves are adopted for the ADS-4 (Westinghouse, 2004). The ADS stages 1–3 vent the pressurizer to the two spargers immersed in the IRWST and the ADS stage 4 vents the loop hot legs directly to the containment (Fisher, 1992; Reyes, 2004). Specially, the reactor coolant pumps (RCPs) are integrated into the steam generator channel head in the AP1000 design which is different from conventional PWRs (Westinghouse, 2004). The integration cancels the loop seal of coolant loop piping, namely the pump suction leg in conventional PWRs. It should be noticed that the existence of the loop seal may result in temporary core uncovery and fuel heat up during cold leg small break LOCAs due to the loop seal venting process in which the steam generated in the core must go through the loop seal section to exit via the break (Kukita et al., 1990; Lee, 1987; Tasakaa et al., 1988). As for AP1000, in contrast, the loop seal venting process is eliminated and the potential for core uncovery and fuel heat up is reduced to a great extent (Kemper and Vertes, 1990; Muftuoglu, 2004).

3. Description of RELAP5 model A preliminary RELAP5 model for AP1000 has been developed which represents all of the major primary, secondary and passive safety system components and the nodalization scheme is shown in Fig. 2. Note that both loops are explicitly modeled, including the hot leg, steam generator, the two cold legs and associated pumps (Fisher, 1992). The loop containing the pressurizer and PRHRS (passive residual heat removal system) is denoted by number “1” and the loop containing the CMTs is denoted by number “2”. The RPV (reactor pressure vessel) model is accurately detailed and contains representation of nearly all internal components. Pipe 114 and Pipe 116 represents the core mean channel and hot channel, respectively. The core bypass is taken into consideration by Pipe 115. In addition, the RPV downcomer is split into two azimuthal regions to reflect asymmetric behavior of the two loops (Aktas, 2003; Hassan and Banerjee, 1996). The pressurizer upper head is modeled with Branch 440 and the pressurizer cylindrical body together with the lower head is modeled with seven-cell Pipe 441. In general, good agreement with experimental and plant data can

be obtained with this nodalization (RELAP5, 2001). For the steam generator simulation, eight axial nodes scheme is adopted for small break LOCAs in which the variation of heat transfer in the axial direction plays an important role in determining the outcome of the transient (RELAP5, 2001). All valves in the passive safety injection system (PSIS) are check valves connecting the CMTs, ACCs and IRWST to the two DVI lines. The CMT tank is divided into ten control volumes in the vertical direction and the ACCs are modeled as two lumped parameter components Accum 865 and Accum 885 in RELAP5. It is reported in reference Yonomoto et al. (1998) that in the ROSA/AP600 test facility, the IRWST internal space is divided into two regions by a separation plate to avoid atypical interactions between the PRHR HX tubes and the ADS spargers which may affect the natural circulation flow around the PRHR HX tubes. Therefore, it is reasonable to model the PRHR HX space and the ADS sparger space separately in the IRWST. The nodalization for the IRWST consists of three stacks of vertical volumes representing the liquid pool and convering vapor space and thus the 3D effects, such as thermal stratification and internal flow within the IRWST can be considered. The three stacks represent the ADS sparger bay (Pipe 801), the connecting bay (Pipe 802) and the PRHR bay (Pipe 803) and they are connected laterally by crossflow junctions. The initial inventory of the liquid in the IRWST is such that the liquid–vapor interface is in the elevation eight of the model (Weaver, 1996). The PRHR HX is located in the PRHR bay. As for the two ADS spargers, they are simplified to a vertical pipe and in connection with the fifth volume of the ADS sparger bay (Pipe 801). In addition, the connecting bay acts as the safety injection water source from the IRWST. It should be pointed out that in the NOTRUMP code, the IRWST is modeled as two connected fluid nodes roughly. The lower node is connected to the DVI line as the source of injection water and the upper node acts as a sink for the ADS discharge flow from the pressurizer and meanwhile as a heat sink for the PRHR HX (Westinghouse, 2004). With respect to the PRHR HX modeling, similar to the treatment method of the steam generator U-tubes (RELAP5, 2001), the Cshaped heat transfer tube bundle consisting of 689 tubes is lumped into a single pipe. Then the lumped pipe is divided into three sections according to different heat transfer mechanisms (Weaver, 1996; Yonomoto et al., 1998): the upper horizontal section, the vertical section and the bottom horizontal section (Wang et al., 2012). The existing reactor safety analyses have demonstrated that the RCP behavior in a PWR significantly affects the progression of the postulated accident. The most important behavior of RCPs is the two-phase head and torque degradation from a safety viewpoint (Choi et al., 2008). In the RELAP5 code, the pump model contains four-quadrant homologous curves for single-phase operation. In accordance with reference Fisher (1992), two-phase head and torque multipliers and degradation data are from Combustion Engineering Inc. (CE) pump data (Chen and Quapp, 1980; Kastner and Seeberger, 1983; Korenchan, 1984) because they are thought to be more representative than SEMISCALE pump data which are widely used all the time (RELAP5, 2001). In two-phase conditions, pump head and torque are given in the following (Choi et al., 2008; Lane et al., 2008; RELAP5, 2001): H = H1 − Mh (˛)(H1 − H2 )

(1)

T = T1 − Mt (˛)(T1 − T2 )

(2)

where H1 and T1 are single-phase head and torque respectively; H2 and T2 are values corresponding to two-phase fully degraded conditions; Mh and Mt are head and torque degradation multipliers as functions of void fraction ˛. The reactor fission power is obtained by point reactor neutron kinetics model with six groups of delayed neutrons (RELAP5,

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Fig. 1. AP1000 passive core cooling system.

Fig. 2. RELAP5 nodalization scheme for AP1000.

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2001) and the 1979 decay heat standard for light-water reactors (ANS, 1979) is used to represent the core decay power for AP1000 (Bajorek et al., 2001; Reyes and Hochreiter, 1998; Welter et al., 2005). Time dependent control volumes (TMDPVOLs) are adopted to model the containment and a constant containment pressure of 14.7 psi (i.e. one atmospheric pressure) is assumed during small break LOCAs (Westinghouse, 2004). 4. Steady-state results

Table 1 Steady-state initial condition of AP1000 obtained by RELAP5. Parameters

Rated value

RELAP5 value

NSSS power (MW) Pressurizer pressure (MPa) Loop flow rate (kg/s) 1/2a RPV inlet temperature (K) RPV outlet temperature (K) SG secondary outlet pressure (MPa) SG secondary steam flow rate (kg/s)

3415 15.517 7591.3 553.817 594.261 5.766 942.6

3414.84 15.558 7616.1/7591.1 552.29/552.25 593.03/593.03 5.727/5.726 945.4/943.6

a

Prior to conducting analysis for small break LOCA transients, a steady-state RELAP5 run is performed to simulate the full-power operation of the plant. The RELAP5 code provides useful control components for selfinitialization option which can reduce the time, effect and cost in obtaining a satisfactory steady-state (RELAP5, 2001). Among those control components, the PUMPCTL controller component is used to control the reactor coolant pump speed to achieve a desired primary flow rate. An error signal E is generated by subtracting the actual flow rate from desired flow rate and then dividing the result by a user-supplied constant (S): E=

V1 − V2 S

(3)

This error signal is used to compute a new pump speed Y for the next time advancement according to the relationship:



Y

n+1

=G

 tn

E + T1

t0

Edt

T2



+ Y0

(4)

where G is the gain, T1 and T2 are time constants applied to the proportional part and integral part respectively, Y0 is the initial pump speed. In addition, the RCS pressure control is achieved by adding a TMDPVOL as a replacement for the pressurizer. The TMDPVOL connecting to the pressurizer-side hot leg is defined to contain liquid at the desired RCS pressure and at a temperature near the hot leg rated value (RELAP5, 2001). After a satisfactory steady-state is obtained, a null transient run for several hundreds of seconds is executed to check the stabilization of the system model (Chung et al., 1994). The null transient results are set as the initial conditions for further transient calculation. During the null transient, the PUMPCTL controller component is disabled and the TMDPVOL for pressure control is replaced again by the pressurizer. The resulting steady-state data are listed in Table 1. It shows that the main thermal-hydraulic parameters obtained by RELAP5 agree well with the AP1000 rated values (Westinghouse, 2004).

loop 1/loop 2.

5. Transient results A spectrum of cold leg small break LOCAs in the loop containing the CMTs, including 2-in., 4-in., 8-in. and 10-in. small breaks, are simulated by triggering the trip valve (break valve 199) connecting to the broken cold leg (CL-2a). The protection and safety monitoring system (PMS) setpoints and time delay assumed in the analysis are listed in Table 2 (Westinghouse, 2004). 5.1. Small break LOCA chronology A typical small break LOCA transient in AP1000 can be divided into four different phases, namely the blow-down phase, the natural circulation phase, the ADS blow-down phase and the IRWST injection phase (Friend et al., 1998; Wright et al., 2007). After a small break occurs in the cold leg, with loss of mass and energy through the break, the primary system undergoes depressurization. When the RCS pressure drops to the PZR low-pressure setpoint 12.41 MPa (1800 psi), a reactor scram signal is generated and causes the reactor shutdown. With further decrease of the RCS pressure to the PZR low–low pressure setpoint 11.72 MPa (1700 psi), the “S” signal is generated and results in opening of the CMT and PRHR HX isolation valves. Once the CMTs and PRHR HX are actuated, two natural circulation flow paths are established through which the core decay heat is removed effectively. The CMTs inject cold borated water into the RCS through the DVI lines owing to gravity-driven natural circulation and thus hot liquid from the cold legs collects gradually at the top of the CMTs. This phenomenon is referred to as the CMT recirculation mode (Wright, 2007). The PRHR HX is located above the RCS, providing sufficient inlet and outlet pressure difference which drives the coolant to flow from one hot leg, through the PRHR HX, and back into its associated steam generator outlet plenum and cold legs. Through the PRHR HX, the residual heat is transferred to the IRWST internal fluid by free convection or boiling on the outer wall

Table 2 PMS setpoints and time delay assumption in SBLOCA analysis for AP1000. Function

Setpoint assumed in SBLOCA analysis

Time delay(s)

Reactor trip on low PZR pressure “S” signal on low–low PZR pressure SG main feed water valves start to close SG main steam valves start to close RCPs trip PRHRS isolation valve starts to open CMT injection starts ACC injection starts on low RCS pressure ADS-1 valves start to open ADS-2 valves start to open ADS-3 valves start to open ADS-4a valves start to open ADS-4b valves start to open IRWST injection starts

12.41 MPa (1800 psi) 11.72 MPa (1700 psi) After “S” signala After low PZR pressure signal After “S” signal After “S” signal After “S” signal 4.83 MPa (700 psi) 20 s after 67.5% liquid volume in any CMT 70 s after ADS-1 actuation 120 s after ADS-2 actuation 20.0% liquid volume in any CMT and 120 s after ADS-3 actuation 60 s after ADS-4a actuation RCS pressure less than 0.19 MPa (27.7 psi)b

2.0 0.0 2.0 6.0 6.0 15.0 15.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

a b

“S” signal: safety system actuation signal. 27.7 psi = 13.0 psi + 14.7 psi and 14.7 psi is the assumed containment pressure.

W.W. Wang et al. / Nuclear Engineering and Design 263 (2013) 380–394

of the heat transfer tubes (Reyes, 2006; Sibamoto and Yonomoto, 2006; Yonomoto et al., 1998). If the RCS pressure drops enough to produce a safety injection actuation signal (i.e. the “S” signal for AP1000) during a small break LOCA in a PWR, the NRC require that all reactor coolant pumps must be stopped to reduce coolant loss out the break (Burchill, 1982). Consequently, the “S” signal in AP1000 trips the reactor coolant pumps and then the primary system is cooled down by different types of natural circulation depending on the primary system inventory; that is single phase natural circulation, two phase natural circulation and reflux condensation (Duffey and Sursock, 1987; Wright, 2007). The CMT operation will switch from recirculation mode to draining mode due to flashing in the CMTs and pressure balance line (PBL) or gaseous flow from the cold legs (Reyes and Nelson, 2007; Sibamoto and Yonomoto, 2006). After that, water level in the CMTs drops continuously which determines the action of the four stages of ADS valves. When water level in any CMT drops to 67.5%, motor valves in the ADS-1 depressurization lines open gradually. Later on, the ADS-2 and ADS-3 valves are actuated sequentially after certain time delay following opening of the previous stage of depressurization valves. After water level falls below 20%, the ADS-4 squib valves open and begin to discharge toward the containment. When the RCS pressure reaches 4.83 MPa (700 psi), the ACC injection starts. After the primary system pressure drops to 0.19 MPa (27.7 psi), 13.0 psi higher than the containment pressure (14.7 psi), injection from the IRWST initiates, marking the end of small break LOCA transients and the beginning of long term cooling (LTC) phase.

385

Fig. 3. Shut-down rod reactivity and core thermal power.

5.2. General system response After the reactor scram signal, the shut-down rods drop automatically after a time delay of 2 s. A total of 4% (5.33$) negative reactivity will be inserted within a time of 3.368 s (Ke and Xu, 2009; Westinghouse, 2004) and then the core thermal power falls rapidly to a low decay power level. Fig. 3 shows the time dependent reactivity by shut-down rods and the resulting core thermal power in the case of different break sizes.

Fig. 4. Break discharge flow rate.

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Fig. 5. Break void fraction.

The break discharge mass flow rates and break void fractions are shown in Figs. 4 and 5, respectively. As the accident progresses, the break undergoes subcooled, two-phase and saturated steam blow-down successively (No, 1983; Zhou et al., 1998). The subcooled blow-down phase is characterized by a high break flow rate and lasts only a relatively short time. The break flow rate decreases following the RCS depressurization. When the RCS pressure drops to the saturation pressure corresponding to the coolant temperature, the blow-down turns to two-phase blowdown mode and the break flow declines to a low level following liquid flash near the break and depressurization in the RCS. Finally, the saturated steam blow-down occurs when the break cold leg becomes steam-filled and the break flow rate is negligible. Fig. 5 also shows that the subcooled blow-down phase lasts for a longer time for a larger break size. In addition, fluctuation of the break void fraction after the transients proceed to the saturated steam blow-down phase is mainly caused by DVI injection from the IRWST. Fig. 6 indicates pressures in the RCS and the SG secondary side during small break LOCAs. In the initial stage, primary-tosecondary heat transfer in the SGs is an important means of energy removal from the RCS and determines the RCS depressurization rate (Bajorek et al., 2001). The pressure in the SG secondary side first increases quickly and then decreases slowly due to SG heat transfer. The RCS depressurizes rapidly as mass and energy are lost through the break. As coolant flashes in the hottest parts of the RCS, the depressurization in the primary side slows and then stalls (Boyack and Lime, 1995, July). The primary side exists in a quasi-steady-state condition with the secondary side (Wright, 2007). For smaller size breaks, 2-in. SBLOCA for example, a RCS

pressure plateau lasts for a longer time when the SG heat transfer becomes insignificant. After that, the RCS pressure drops below the secondary side pressure as a result of continuous energy removal by the PRHR HX and the CMTs. Once the ADS is actuated, the primary system depressurizes rapidly again to allow passive safety injection from the CMTs, ACCs and IRWST. When the break size increases, duration of the pressure plateau becomes shorter. The pressure asymmetry effect in SG secondary side due to loop arrangement, 2-in. SBLOCA for example, is shown in detail in Fig. 7. It indicates that the secondary side pressure of SG-1 in the pressurizer side loop is higher than that of SG-2 after break. The asymmetry response is mainly caused by the pressurizer outsurge in the initial stage which flows into the SG-1 primary side and then feeds the SG-1 primary side with hotter fluid than that in SG-2 (Fig. 8). Then a greater heat transfer rate in SG-1 results in a higher secondary side pressure than that of SG-2. Such a phenomenon was also reported in the ROSA/AP600 test facility (Kukita et al., 1996; Sibamoto and Yonomoto, 2006). Correspondingly, the hot side and cold side of Utube in SG-1 will drain earlier than those in SG-2 due to more vapor generation in the U-tube primary inventory (Fig. 9). The accumulation of steam in the top of SG U-tubes results in the decrease of driving head for natural circulation and finally terminates it (Kawanishi et al., 1991; Tasakaa et al., 1988). The RCS is thermally decoupled from the SGs after the U-tubes void completely (Kukita et al., 1996) and the primary-to-secondary heat transfer becomes insignificant. Similar results are also observed for larger size breaks, such as 4-in., 8-in. and 10-in. small break LOCAs. The core void fraction distribution in axial direction for 2-in. small break LOCA is shown in Fig. 10. The amount of steam produced

W.W. Wang et al. / Nuclear Engineering and Design 263 (2013) 380–394

387

Fig. 6. RCS and SG secondary side pressures.

in the reactor core can be obtained based on steady-state energy balance (Kukita et al., 1990; Welter et al., 2005): Wcore =

Q hfg + hin

(5)

where Wcore is the steam generation rate in the core, Q is the core decay power, hfg is the latent heat under a certain pressure and hin is the core inlet subcooling.

Fig. 7. SG pressure asymmetry effect due to loop arrangement.

It indicates in Fig. 10 that in the transient process, the core outlet control volume (Volume 114-10) reaches the saturation condition firstly as the hottest portion of the RCS due to depressurization flash and decay heat addition to the coolant. With development of the accident, which is marked by an arrow in Fig. 10, nucleate boiling progresses from top to bottom region of the core and finally the entire core is cooled by nucleate boiling (Boyack and Lime, 1995, July). The higher void fraction appears at the higher elevation of the core from beginning to end during the small break LOCA process.

Fig. 8. PZR collapsed liquid level.

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Fig. 9. SG U-tube collapsed liquid level.

Fig. 12. Cladding temperature.

code (Westinghouse, 2004), a void fraction limit value ˛ = 90% was chosen as the indicator of the onset of core dryout CHF predicted by the Griffith–Zuber correlation (Bjornard and Griffith, 1977; Zuber et al., 1961). From Fig. 11, it can be seen that the maximum core outlet void fraction does not exceed the limit line of ˛ = 0.9 except a few points and will not endanger the core safety, especially for 10in. small break with the break size approaching the upper limit size for small break LOCAs (Westinghouse, 2004). The Griffith–Zuber correlation is expressed in the following form (Leung et al., 1981):

 qCHF = (1 − ˛)0.131g hfg

Fig. 10. Core void fraction distribution.

Furthermore, Fig. 11 displays the core outlet void fractions for a spectrum of break size. It is obvious that with increase of the break size, the core outlet void fraction becomes higher. In the verification simulation for AP1000 small break LOCAs using the NOTRUMP

Fig. 11. Core outlet void fraction.

g(f − g ) g2

1/4 (6)

The cladding temperatures at the hottest point of the core fuel pin are shown in Fig. 12. It indicates that the cladding temperatures present a continuous decrease trend in general. The changing trend of the cladding temperature is in accordance with that of the RCS pressure approximately. It is well accepted that the peak cladding temperature (PCT) is used for the principle indication of small break LOCA consequence for licensing analysis (Burchill, 1982). Fig. 12 shows that the PCTs are well below the Appendix K upper limit value of 1478 K/2200 ◦ F (U.S. NRC, 1992) and meet the safety criterion. Hence it proves that the passive safety systems can remove the core decay power and mitigate the consequence of small break LOCAs effectively. An interesting phenomenon is observed in the present study that, an obvious reverse flow occurs in the broken cold leg (CL-2a) in the initial stage of small break LOCAs. The reason can be attributed to a sudden decrease of local pressure at the break location which draws fluid from the bottom of the core. By comparison, flow rate in the intact cold legs (CL-1a, 1b and 2b) basically keeps forward flow and shows a nearly same trend. Moreover, with increase of the break size, amplitude of the reverse flow becomes large (Fig. 13). The transient pump velocity is shown in Fig. 14. After pump coastdown, the pump velocity decreases sharply. However, the pump connecting to the broken cold leg (Pump-2a) undergoes a temporary acceleration process, especially for larger size breaks, such as 8-in. and 10-in. small break LOCAs. The pump acceleration can also be referred to local pressure decrease at the break location mentioned previously which accelerate fluid through the pump. In the remaining time, the pumps have little or no influence on the course of the transient and continue to freewheel at low speeds, increasing resistance of the cold leg flow (Boyack and Lime, 1995, July).

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Fig. 13. Cold leg flow rare.

Fig. 14. Pump velocity.

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Fig. 15. Energy removal rates of PRHRS and CMTs compared to the core decay power.

Fig. 16. CMT normalized liquid level.

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Fig. 17. Integrated energy removal from the RCS.

Fig. 18. Passive safety injection flow rate by CMTs, ACCs and IRWST.

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Fig. 19. ADS flow rate.

5.3. Passive residual heat removal behavior The energy removal rates of the PRHRS and CMTs as well as the core decay power are shown in Fig. 15. As for the CMTs, the heat removal power in the recirculation mode is given by: Q = Win hin − Wout hout

(7)

where W is the recirculation flow rate and h is the coolant enthalpy. The subscripts “in” and “out” indicate the CMT inlet and outlet parameters, respectively. The coolant can be either single-phase or two-phase. In a general form, the flow rate W is given in the following: W = (f uf ˛f + g ug ˛g )A

(8)

The enthalpy h is converted by: h = e + Pv

effect of the PRHRS depends on the ADS actuation, after which it becomes insignificant (Friend et al., 1998; Yonomoto et al., 1998). Compared to the PRHRS, the CMTs only play a minor role in the energy removal process. With increase of the break size, the effect of the CMTs becomes more and more limited because switch from the recirculation mode to the draining mode in the CMTs starts earlier in the transients (see Fig. 16). The integrated energy removal from the RCS during small break LOCAs is shown in Fig. 17. The heat removal paths include heat transfer to the SGs and PRHRS as well as heat discharge through the break and ADS (ADS-1/2/3 and ADS-4). Specially, the integrated heat discharge E through the break and ADS can be obtained by:



E=

t

(Wh)dt

(10)

0

(9)

It can be concluded from Fig. 15 that for smaller size breaks, such as 2-in. and 4-in. small break LOCAs, the total heat transfer power of the PRHRS and CMTs exceeds the core decay power soon after reactor shutdown and thus the core residual heat can be removed effectively. A similar conclusion was also obtained in the ROSA/AP600 test facility (Kukita et al., 1996; Sibamoto and Yonomoto, 2006; Yonomoto et al., 1998). However, in the case of larger size breaks, such as 8-in. and 10-in. small break LOCAs, the total heat transfer power is lower than the core decay power in the initial stage after actuation and then drops quickly when the core outlet void fraction becomes very high (Fig. 11), degrading heat transfer to the PRHR HX (Boyack and Lime, 1995, July). The

where the discharge flow rate W and the discharge coolant enthalpy h are given by Eqs. (8) and (9), respectively. In the initial stage, the effect of the SGs cannot be neglected, especially for smaller size breaks. It is obvious that in the case of 2-in. SBLOCA, heat transfer to the SGs is a dominant form of heat removal path. With increase of the break size, a reverse heat transfer phenomena in SG (i.e. secondary-to-primary heat transfer) becomes more and more obvious after the RCS pressure drops below the secondary side pressure. In the interim between the SG isolation and the ADS actuation, the PRHRS provides significant heat removal together with recirculation flow to the CMTs and discharge flow through the break (Wright et al., 1996). An important fact is that the ADS actuation essentially ends the PRHRS heat transfer which was also observed in small break LOCA tests conducted at

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the SPES-2 integral facility (Friend et al., 1998). However, the ADS itself provides a more efficient heat removal path in small break LOCAs. For larger size breaks, heat discharge through the break becomes predominant absolutely. (5) 5.4. Passive safety injection behavior After small break LOCAs, the CMTs (860 and 880), ACCs (865 and 885) and IRWST (812 and 822) combine to provide continuous passive safety injection to the reactor (Fig. 18). Fig. 18 shows that the CMTs are actuated in the initial stage and flow rate from the CMTs last for a long time until activation of the IRWST. The ACCs provide high flow borated water in a short time after the RCS pressure drops below 4.83 MPa (700 psi). After injection from the ACCs begins, flow rate from the CMTs is reduced or even temporary stopped due to backpressure increase in the DVI lines which reduces the driving head in the CMT natural circulation loop (Boyack and Lime, 1995, April; Wright, 2007; Yonomoto et al., 1997). The flow rates from the CMTs and ACCs show a negative relationship. In addition, the IRWST injection exhibits an oscillatory behavior which was reported in the integral test facilities SPES-2, APEX and ROSA/AP600. Such a phenomenon is related to the ADS-4 discharge from the hot legs (Bessette and Marzo, 1999).

(6)

(7)

(8)

5.5. ADS discharge behavior The ADS discharge flow rate is shown in Fig. 19. Flow through the break actually ends (Fig. 4) when the ADS is actuated because the larger flow area provides a lower resistance flow path (Friend et al., 1998). Once the ADS-4 is tripped, the ADS-1/2/3 discharge flow rate becomes insignificant for the same reason. It can be concluded that the lower flow rate through the ADS-1 valves is mainly caused by smaller flow areas compared to that of the ADS-2 and ADS-3 valves. In addition, actuation of the ADS-1/2/3 results in a reduction in pressure at the top of the pressurizer and cause the coolant in the upper plenum to flow toward the pressurizer (Friend et al., 1998; Kukita et al., 1996). As a result, the collapsed liquid level in the pressurizer rises markedly (Fig. 8). After the fourth stage of ADS is opened, draining of the pressurizer water takes place again and the collapsed liquid level in the pressurizer decreases (Takeuchi et al., 1999). 6. Conclusions Thermal hydraulic response of AP1000 to a spectrum of cold leg small break LOCAs is obtained based on RELAP5/MOD3.4. Main conclusions obtained in this study are summarized in the flowing: (1) With proceeding of the small break LOCAs, the water that flows through the break undergoes subcooled, two-phase and saturated steam blow-down successively determined by the system condition. (2) The RCS rapidly depressurizes to the secondary side pressure as mass and energy are lost through the break. For a smaller size break, a RCS pressure plateau lasts for a longer time. In comparison of larger breaks, the pressure plateau lasts only for a short time. Activation of the ADS accelerates the RCS depressurization. After the RCS pressure drops below the secondary side pressure, a reverse heat transfer in the SGs occurs. (3) A pressure asymmetry effect in the SG secondary sides is observed. The secondary side pressure in SG-1 in the pressurizer side loop is higher than that of SG-2 after break due to the pressurizer outsurge flow. Meanwhile, the pressurizer outsurge results in early U-tube draining in SG-1. (4) The core outlet control volume reaches a saturation condition firstly and the nucleate boiling progresses from top to bottom

(9)

(10)

393

region of the core in the transient process. The maximum core outlet void fraction in small break LOCAs does not exceed the limit line of ˛ = 0.9 and the core dryout CHF is not considered to occur. The fuel cladding temperatures present a continuous decrease trend in general. The PCTs are far below the Appendix K upper limit value of 1478 K/2200 ◦ F. It proves that the passive safety systems in AP1000 combine to remove the core decay power and mitigate the consequence of small break LOCAs effectively. In the initial stage, an obvious reverse flow occurs in the broken cold leg caused by a sudden decrease of local pressure at the break location. Correspondingly, the pump connecting to the broken cold leg undergoes a temporary acceleration process, especially for larger size breaks. For smaller size breaks, the total heat transfer power of PRHRS and CMTs exceeds the core decay power soon after reactor shutdown and the residual heat can be removed effectively. But in the case of larger size breaks, the total heat transfer power is lower than the core decay power in the whole transient process. With progress of the transients, heat transfer power of the PRHR HX degrades. The break, SGs, PRHRS together with the ADS provide continuous heat removal paths to ensure the reactor safety. For smaller size breaks, heat transfer to the SGs is a dominant heat transfer form. While for larger size breaks, heat discharge through the break becomes predominant. The CMTs, ACCs and IRWST provide continuous passive safety injection to the reactor. Flow rates from CMTs and ACCs show a negative relationship. The IRWST injection flow exhibits an oscillatory behavior which is related to the ADS-4 coolant outflow from the hot legs. Stages 1–4 of the ADS combine to realize continuous depressurization in a controlled manner. Flow through the break actually ends after the ADS actuation. Once the ADS-4 is actuated, the ADS-1/2/3 discharge flow rate becomes insignificant.

Acknowledgments This work is supported by National Natural Science Foundation of China (11125522) and National Natural Science Foundation of China (11075124).

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