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MOD4.0 and application to LOCA of China DFLL-TBM
Fusion Engineering and Design 134 (2018) 35–42
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Modification on the contact model of LiPb and noncondensable gas in RELAP/SCDAPSIM/MOD4.0 and application to LOCA of China DFLL-TBM
T
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Qian Suna, Tianji Pengb, Zhiwei Zhoua, , Zhibin Chenc, Shisheng Wangc a
Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu, China c Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, CAS, Hefei, Anhui, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: DFLL-TBM In-TBM breeder box coolant leak Liquid lithium lead Modified RELAP/SCDAPS/MOD4.0
In-TBM breeder box coolant leak is one of four reference accidents identified for China Dual-functional Lithium Lead Test Blanket Module (DFLL-TBM), which will result in the pressurization of the TBM LiPb breeding zones and cooling system. In order to analyze In-TBM breeder box coolant leak accident, there is a need to simulate the mixing of liquid metal and non-condensable gas. While the current system safety code RELAP/SCDAPSIM/ MOD4.0 which was initially designed to predict the behavior of light water reactor systems is incapable of modeling the mixture of liquid metal fluids and non-condensable gas. This paper first briefly introduce the reason for RELAP/SCDAPS/MOD4.0’s incapability of modeling liquid metal in contact with a non-condensable gas. Then, a solution to solve the problem and the modification of the RELAP/SCDAPSIM/MOD4.0 code is proposed. Several typical problems involving liquid metal in contact with helium were simulated and the results demonstrate the feasibility and validity of the modified RELAP/SCDAPS/MOD4.0 in modeling the mixing of liquid metal and non-condensable gas. Last but not least, the modified RELAP/SCDAPS/MOD4.0 is used for transient analysis of In-TBM breeder box coolant leaks. Since both lead-lithium eutectic alloy and helium serve as TBM coolants, the Lithium Lead Cooling System (LLCS) and the Helium Cooling System (HCS) were modeled to investigate the thermal-hydraulic characteristic of the TBM system and its influence on ITER safety under the accident conditions. Results show that LLCS pressurization during In-TBM breeder box coolant leak is adequately handled by the safety accessories provided in LLCS and the highest temperature of the first wall is far below its melting point during the accident process.
1. Introduction The Dual-functional Lithium Lead Test Blanket Module (DFLL-TBM) has been developed by China for testing in ITER, which utilizes leadlithium eutectic alloy (LiPb) as tritium breeder, neutron multiplier and coolant [1,2]. The first wall facing the plasma is cooled by helium gas. As an initial examination of the safety impact that TBMs will have on ITER, the ITER IT requires the participating parties to analyze the following four accident scenarios: (1) in-vessel TBM coolant leaks, (2) inTBM breeder box coolant leaks, (3) ex-vessel TBM ancillary coolant leaks, and (4) complete loss of active TBM cooling [3]. In reference [4], the safety analyses of other 3 scenarios have been performed and discussed in detail. However, the second scenario has not been investigated yet. In-TBM Breeder Box Coolant Leak will cause the high pressure helium to discharge into the breeding box and result in the pressurization of the TBM LiPb breeding zones and its auxiliary system. In order to analyze the In-TBM Breeder Box Coolant Leak, there is a
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Corresponding author. E-mail address: [email protected] (Z. Zhou).
https://doi.org/10.1016/j.fusengdes.2018.06.020 Received 26 October 2017; Received in revised form 5 May 2018; Accepted 25 June 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
need to simulate the mixing of helium and Lead-Lithium fluids, while the current RELAP/SCDAPS/MOD4.0 cannot handle this problem. This paper first explains the reason for the current RELAP5’s inability to model liquid metal in contact with a non-condensable gas. Then a solution to solve this problem was introduced and code modification was made in the standard RELAP/SCDAPS/MOD4.0. By analyzing several cases using the modified RELAP/SCDAPS/MOD4.0 code, Fluent and theory correlation, the comparison results show that they are in good agreement with each other, which verify the accuracy and feasibility of the modified code. Finally the modified RELAP/SCDAPS/MOD4.0 is used in the safety analysis of In-TBM Breeder Box Coolant Leak in China DFLL-TBM. 2. DFLL-TBM system description DFLL-TBM [1,2] utilizes lead-lithium eutectic alloy as tritium breeder, neutron multiplier and coolant. Fig. 1 shows the basic design
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outlet temperature is around 400 ℃. Fig. 2(a–d) are schematic diagrams of helium flow in the radial-poloidal stiffening plate(rpSP), FW, inverted “L” shaped toroidal-poloidal stiffening plate (tpSP) and cover plate, respectively [4]. 3. Modification of RELAP5/MOD4.0 for DFLL-TBM The RELAP/SCDAPSIM/MOD4.0 hydrodynamic model is a one-dimensional, transient, two-fluid model for flow of a two-phase steam/ water mixture that can contain non-condensable components in the steam phase [5]. The basic differential equations are a system of 6 conservation equations: mass, energy and momentum for the liquid and the vapor phase of water. To include the non-condensable component in the gas phase, the following assumptions are considered:
• The non-condensable gas velocity is the same as the water vapour velocity. • The non-condensable gas temperature is the same as the water vapour temperature.
The general approach for addition of the non-condensable component consists of assuming that all properties of the gas phase are mixture properties of the steam/non-condensable gas mixture. The two mass continuity equations for liquid and vapour are unchanged and an additional mass conservation equation for the total non-condensable component is added [6]. The standard RELAP/SCDAPS/MOD4.0 version of the code can simulate systems with other fluids than water. However, it cannot simulate a mixture of a new fluid such as LiPb with any available RELAP/ SCDAPS/MOD4.0 non-condensable gas. The non-condensable gas calculation is based on the vapor phase of the fluid. Therefore, to simulate the mixing of helium and Lead-Lithium fluids, RELAP/SCDAPS/ MOD4.0 needs LiPb vapor phase properties when the liquid phase is in contact with helium [7].
Fig. 1. DFLL-TBM design scheme.
of DFLL-TBM. The structure of DFLL-TBM consists of a 484 mm (t) × 1660 mm (p) × 585 mm (r) rectangular steel box, which is reinforced by one radial–poloidal(r–p) and four toroidal–poloidal (t–p) stiffening plates(SPs). The four BPs constructed a three-stage helium distributing/collecting collector. The LiPb (2 MPa) flows into the module in the poloidal direction with the inlet/outlet temperatures of 480 ℃/700 ℃ to remove the volumetric nuclear heat in the breeding zones. The TBM FW and blanket structures are cooled by helium with mass flow rate of 1.35 kg/s at 8 MPa, whose inlet temperature is 340 ℃ and
3.1. Code modification The liquid phase physical properties of LiPb have been incorporated in the code [8]. A preliminary verification is also carried out for the single phase LiPb applications in this reference. To solve the problem of
Fig. 2. Schematic diagrams of helium flow within the TBM components. 36
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Cpg =
5 Rg 2
(5)
Cvg =
3 Rg 2
(6)
Dynamic viscosity [Pa.s]:
μg =
0.003285 T1/2
(7)
Internal energy [J]:
ug = ug 0 + Cvg (T −T0)
(8)
Enthalpy [J]:
h g = u g + p ⋅v
Fig. 3. Nodalization of communicating vessel.
(9)
Entropy [J/K]: simulating LiPb /Helium mixtures, two approaches can be considered in the modification of the code. One is avoiding the generation of LiPb vapor when the non-condensable gas appears [5]. The other one is implementing the vapor phase properties of LiPb into the code, similar to Jiang does for molten salt reactor system [6]. In this paper, the latter one is adopted. The first step of the code modification is adding the LiPb vapor phase properties, including saturation pressure, Psat ; density, ρg ; expansion coefficient, βg ; compression coefficient, k g ; heat capacity, Cpg , Cvg ; internal energy, ug ; enthalpy, hg ; entropy, sg and transport properties. The implemented properties of LiPb are in the forms of specific correlations, rather than the property tables that the original code adopts for the light and heavy water [7].The specific correlations are incorporated into subroutine STLIPB. The second step is modifying the code calculation process including defining the working range of temperature, pressure, and internal energy, using the given saturated temperature or saturated pressure to obtain other saturated parameters and calculation of the other physical parameters with any known parameters. The original modules calling the STLIPB are modified including the ISTATE, TSTATE, STATEP. The vapor phase property is assumed to be the ideal gas and satisfies the ideal gas state equation [6]. The vapor phase physical properties of LiPb can be obtained from the literature [9–11] for the lack of experimental data. Vapor property is not that important in the design and safety evaluation of DFLL-TBM due to the high boiling point of LiPb (about 2500 ℃). However, vapor data is required because the RELAP5 code structure is originally designed to simulate two-phase phenomena in water reactor systems [6.7]. The accuracy of the physical parameters of the vapor phase must be taken into account if there is a large number of LiPb in the vapor phase. The gram molecular mass of LiPb is calculated as R = 173 g/mol by taking it as a mean mass of the molecular lead and lithium- Li(17) Pb (83) [12]. The gas constant of LiPb: Rg = 48.05 J/kg/K. Vapor phase physical properties of LiPb: Saturation pressure [Pa]:
Psat = 1.5 × 1010 exp(−22900 Tsat )
sg = sg 0 + Cpg ln(T / T0) − Rg ln(P / P0)
T0 —Melting point temperature–508 K [13] 3.2. Verification of the modified RELAP/SCDAPS/MOD4.0 code In this part two typical problems were chosen to demonstrate the feasibility and validity of modeling the mixing of LiPb and non-condensable gas by the modified RELAP/SCDAPS/MOD4.0. 3.2.1. Communicating vessels Communicating vessels is a name given to a set of containers containing a homogeneous fluid: when the liquid settles, it balances out to the same level in all of the containers regardless of the shape and volume of the containers. A simple nodalization of a communicating vessel which contains the liquid LiPb and helium was shown in Fig. 3. The test section 100 and 102 both contains LiPb and helium gas. But the liquid level of pipe 100 is higher than the one of pipe 102. When the valves 101 opens at t = 10 s (the valve 103 keeps open all the time), LiPb will flow from 100 to 102 until it reach the same level in pipe 100 and 102. Fig. 4. show that, the void fraction of volume 100-07 is 0 initially. As time goes on, the liquid level decrease and the void fraction of volume 100-07 increase. While the 102-07 performs oppositely. The void fraction of 100-07 and 102-07 both keep at 50% when the two connected pipes got balanced which means LiPb reach the same level in pipe 100 and 102. From Fig. 5, we can see that the pressure of pipe 100 and 102 get balanced. This case proves that the modified RELAP/SCDAPS/MOD4.0 can simulate the problem of LiPb in contact with helium during transients. 3.2.2. One-dimensional pressure wave propagation In-TBM breeder box coolant leak will cause the high pressure helium to discharge into the breeding box and result in the pressurization
(1)
Density [kg/m3]:
ρg =
P Rg *T
(2)
Thermal expansion coefficient [1/K]:
βg = 1/ T
(3)
Isothermal compression coefficient [1/Pa]:
k g = 1/ P
(10)
(4) Fig. 4. Void fraction of communicating vessel.
Heat capacity [J/kg-K]: 37
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Fig. 5. Pressure of communicating vessel.
Fig. 6. Nodalization of one dimensional pressure propagation model (b < < L). (a) The phase plane of wave propagation in simple pipeline.
of the TBM LiPb breeding zones and auxiliary system. The pressure value difference between the LiPb and helium ancillary cooling systems is great. And the pressure variation of LiPb ancillary cooling systems is important to its structure safety. As shown in Fig. 6, a closed pipe was filled with LiPb and helium. Point A is the left endpoint of LiPb part and point C is the middle point of LiPb part. The LiPb was in 2 MPa and the helium was in 8 MPa. There is a thin film between the two fluids. At t = 0 s, the film bursts and this will cause a pressure wave disturbance spreading to the left pipe. In the simulation, a valve was used to model the film bursting. According to the theory of pressure wave propagation in simple pipeline [14], the phase plane of wave propagation in shown in Fig. 7(a). The solid line shows the positive pressure wave trajectory and the dotted line shows the trajectory of negative pressure wave. Fig. 7(b–g) shows the theoretical full cycle of one-dimensional pressure wave propagation [14] (Vs is the sound speed in LiPb). Point A is the left endpoint of the pipe, and the pressure wave will get a positive reflection here. Considering the infinite big space of the helium part, the pressure of helium can be thought as unchanged. Pressure of point B will keep at 8 MPa. The result of the modified RELAP/SCDAPS/MOD4.0 shows a good agreement with Fluent simulated and theoretical results [14] as shown in Figs. 8 and 9. From the results of the two typical phenomenon that model LiPb in contact with helium, it can be concluded that the modified RELAP/ SCDAPS/MOD4.0 code can be used to calculate mixing of helium and Lead-Lithium fluids and the accuracy and reliability of the calculation have also been verified.
Fig. 7. The full cycle of one-dimensional pressure wave propagation.
pressurizer of LLCS. Valve 917, was used to simulate the pressure safety valve (PSV) during accidents. Its status was decided by the LLCS loop pressure. It was closed in steady state and would be opened if the pressure of LLCS loop exceeded its setting pressure (2.1 MPa) in accidents. Valve 919 will be opened when the pressure of Dump Tank (918 P) exceeded PSV setting pressure (2.1 MPa) in accidents and then if the pressure dropped below 2 MPa it would be closed again. Fig. 11 shows the nodalization of Helium Cooling System loop. The modeled components include helium flow channels in the structure
4. DFLL-TBM system model The nodalization of Lithium Lead Cooling System (LLCS) loop and its secondary helium loop is shown in Fig. 10. The secondary side has been modeled using a RELAP time dependent volume (TDV) component as source and sink for helium at a pressure of 8 MPa. Pipe 914 which contains a cavity filled with helium plays the role of 38
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will be closed according to the HCS loop pressure during accident conditions. A computation of the steady state was intended to provide an initial condition for the transient analyses. In the steady state, it is assumed that there was no heat exchange between the two cooling loops. This assumption was reasonable provided the flow channel inserts in the breeder zones can be considered as ideal thermal insulation. But during the In-TBM breeder box coolant leak accident, heat exchange between the two primary cooling loops need to be considered. Convective heat transfer condition was set between the breeder zones and the helium flow channels. The steady-state calculation was carried out on the basis of an average heat flux of 0.3 MW/m2 on the first wall [4]. Table 1 compares the calculated steady-state parameters with the design parameters given in [15]. The steady-state result was used for the initial condition of the accident analyses. Valve700 between 900 P and 022 P was used to model the TBM channel rupture.
Fig. 8. Pressure of left endpoint A.
5. Accident analyses 5.1. Identification of causes and accident scenario This scenario leads to the following time sequence of events. The average surface heat flux on the TBM FW was increased to 120% level at 0.36 MW/m2 10 s prior to the TBM channel rupture occurs. After the break of helium tube, the internal helium leak pressurizes the TBM LiPb breeder zones and cooling system causing the relief system to open and drain to the dump tank. Once the pressure in the drain tank reaches the set pressure, a vent valve (919 V) above the dump tank (918 P) opens and relieves the helium pressure into the port cell. To assess the TBM integrity under an aggravating condition, the pump and circulators were assumed to coast down coincidently with the initiation of this accident. The time sequence of the accident is given in Table 2.
Fig. 9. Pressure of middle point C.
components (i.e., FW, stiffening plates, covers and collector manifolds) within the TBM, valves, inlet and outlet pipelines, a helium/water heat exchanger and a circulator. For the analysis of In-TBM breeder box coolant leak, the sixteen helium passes in the W-shaped TBM FW (each one is 15 mm*20 mm) were represented by two groups of “PIPE” components. In the accident, we assume that two helium passes were broken. A break area of 0.0006 m2 was considered. Therefore, one group was for two passes and the other group was for fourteen passes. The helium channel rupture location is PIPE022. Pipe 040/041/042 represent the helium channel in rpSP, tpSPs, covers respectively. Valve 247 and valve 293 are isolation valves of HCS loop and they are opened during normal condition and
5.2. Transient analysis results Due to the channel rupture inside TBM (t = 10 s), helium comes out impairing the heat removal from TBM and causes pressurization of LLCS loop (Fig. 12). Almost instantly (t = 10.0078 s) due to high pressure in LLCS loop, PSV 917 gets opened and lead-lithium starts getting dumped into dump tank 918 P. Once some of the LiPb gets dumped into Dump Tank, the path is free for helium. Helium enters
Fig. 10. Nodalization of Lithium Lead Cooling System (LLCS). 39
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Fig. 11. Nodalization of Helium Cooling System (HCS).
Table 1 Steady state result. Description Breeder zones Temperature at inlet (K) Temperature at outlet (K) Mass flow rate (kg/s) Pressure (MPa) HCS Temperature at inlet (K) Temperature at outlet (K) Mass flow rate (kg/s) Pressure (MPa)
Design data
RELAP5 value
Relative error
753 973 6.05 2
754 980 6.05 2
0.13% 0.72% 0% 0%
613 668 1.35 8
608 672 1.35 8
−0.82% 0.60% 0% 0%
Fig. 12. Pressure of LLCS. Table 2 Time sequence of In-TBM breeder box coolant leak. Time/s
Description
t=0
The average surface heat flux on the TBM FW was up to 0.36 MW/m2 The TBM channel rupture occurs Generating LOCA signal when HCS pressure was below 6 MPa Valve 917 open when the pressure of LLCS loop was beyond 2.1 MPa Rector trips on LOCA signal from HCS Plasma disruption and heat flux on the TBM FW was up to 5.52 MW/m2 for 0.1 s, and kept at 0.72 MW/m2 for 0.9 s Plasma quench; decay heat removal through thermal radiation Isolation valves 247 and 293 closed; pump and circulator trip
t = 10 t = t1 t = t2 t = t1+3 t1+3 < t < t1+4 t > t1+4 t = t1+10
Fig. 13. Pressure of HCS.
Cooling System (LLCS). As the pressure release process in LLCS gonging on, the flow rate decreases gradually. And after a period time’s oscillation, there is no fluid flows through the rapture. A total mass of 5.75 kg helium has been discharged into the LLCS in the accident. FW temperature during in TBM breeder box coolant leak case is given in Fig. 15. T = 0 s, fusion power increases by 20% and the average surface heat flux on the TBM FW was up to 0.36 MW/m2, When accident occurred at t = 10 s, the first wall temperature increased form 882.3 K at steady state to 900k. After the accident, the reactor didn’t shut down immediately and the first wall temperature kept on increasing. After 3 s of LOCA signal, Fast Plasma Shutdown System (FPSS) trips the reactor (t = 25.84 s). The plasma burst at t = 25.84 s and it cause the average surface heat flux on the TBM FW up to 0.72 MW/m2 within 1 s. At t = 26.84 s, the plasma quenched and the first wall
Dump Tank (DT) and pressure increases very fast and reaches DT PSV 919 setting pressure and helium starts coming out to port cell. But once the pressure of LLCS drops down to 2 MPa (t = 35.6 s), PSV 919 sits back and no more flow occurs. The pressure changes of the helium cooling system (HCS) are shown in Fig. 13. Due to break in TBM breeder box, helium comes out to LLCS and generates LOCA signal at T = 22.84 s when the pressure of HCS is bellowed 6 MPa. The isolation valves (247 and 293) of the HCS was closed after 10 s of LOCA signal (t = 32.84 s). Therefore, the TBM part of HCS continues to release pressure until its pressure drops down to 2 MPa, and the other parts of HCS maintains around 4.4 MPa. Fig. 14 describes the mass flow rate of valve 700. The break of the helium tube in TBM FW results in ingress helium into Lead Lithium 40
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dissipation through radiation. The LiPb and Helium (in TBM box) temperature during In-TBM Breeder Box Coolant Leak accident are shown in Figs. 16 and 17. The helium temperature will decrease first after the accident occurs because its volume expansion to breeding zones. When PSV 919 sits back and no more flow occurs, its temperature will increase as a result of decay heating and heat conduction from the high temperature breeder zones. Then the helium is cooled gradually by the radiation heat transfer through FW. The result shows a good agreement with reference [16]. It is found that the decay heat in the TBM can be removed efficiently. 6. Conclusions As a participant in the International Thermonuclear Experimental Reactor (ITER) Test Blanket Module (TBM) program, in addition to helium cooled solid breeder (HCSB) blanket [17–21], China has developed a Dual-functional Lithium Lead Test Blanket Module (DFLLTBM). In preparation of the regulatory safety files of ITER-TBM, a number of off-normal event sequences have been postulated. In order to analyze some of the postulated off-normal events, there is the need to simulate the mixing of Helium and Lead-Lithium fluids. RELAP/SCDAPS/ MOD4.0 is a widely-used Nuclear Safety Analysis code that can simulate reactor plants from normal transients to severe accidents. While the current RELAP/SCDAPS/MOD4.0 cannot handle the problem of liquid metal in contact with a non-condensable gas. By implanting the vapor phase properties of lead-lithium eutectic alloy and modifying the calculation process, the modified code overcomes its disability of modeling the coexistence of LiPb and non-condensable gas. The feasibility and validity of the modified code handing the mixing of LiPb and noncondensable gas were proved by two typical problems. In-TBM breeder box coolant leak accident is simulated by the modified code. LLCS pressurization during In-TBM breeder box coolant leak is adequately handled by the safety accessories provided in LLCS. The first wall temperature peaks at 943.4 K during the accident, which is far below the melting point 1278 ℃ of Be armor. The TBM temperature response exhibits an acceptable decay heat removal capability of the TBM. The present work is expected to be helpful for the design of the DFLL-TBM system in view of its thermal hydraulic characteristics. The extended RELAP/SCDAPS/MOD4.0 code can be used for the DFLL-TBM system safety analysis in the future.
Fig. 14. Mass flow rate of the rupture.
Fig. 15. FW temperature during In-TBM Breeder Box Coolant Leak accident.
Acknowledgment The authors gratefully acknowledge the support from the National Basic Research Program of China (2014GB116000).
Fig. 16. LiPb (in TBM box) temperature during Coolant Leak accident.
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Fig. 17. Helium (in TBM box) temperature during In-TBM Breeder Box Coolant Leak accident.
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Modification on the contact model of LiPb and noncondensable gas in RELAP/SCDAPSIM/MOD4.0 and application to LOCA of China DFLL-TBM
T
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Qian Suna, Tianji Pengb, Zhiwei Zhoua, , Zhibin Chenc, Shisheng Wangc a
Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Tsinghua University, Beijing, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu, China c Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, CAS, Hefei, Anhui, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: DFLL-TBM In-TBM breeder box coolant leak Liquid lithium lead Modified RELAP/SCDAPS/MOD4.0
In-TBM breeder box coolant leak is one of four reference accidents identified for China Dual-functional Lithium Lead Test Blanket Module (DFLL-TBM), which will result in the pressurization of the TBM LiPb breeding zones and cooling system. In order to analyze In-TBM breeder box coolant leak accident, there is a need to simulate the mixing of liquid metal and non-condensable gas. While the current system safety code RELAP/SCDAPSIM/ MOD4.0 which was initially designed to predict the behavior of light water reactor systems is incapable of modeling the mixture of liquid metal fluids and non-condensable gas. This paper first briefly introduce the reason for RELAP/SCDAPS/MOD4.0’s incapability of modeling liquid metal in contact with a non-condensable gas. Then, a solution to solve the problem and the modification of the RELAP/SCDAPSIM/MOD4.0 code is proposed. Several typical problems involving liquid metal in contact with helium were simulated and the results demonstrate the feasibility and validity of the modified RELAP/SCDAPS/MOD4.0 in modeling the mixing of liquid metal and non-condensable gas. Last but not least, the modified RELAP/SCDAPS/MOD4.0 is used for transient analysis of In-TBM breeder box coolant leaks. Since both lead-lithium eutectic alloy and helium serve as TBM coolants, the Lithium Lead Cooling System (LLCS) and the Helium Cooling System (HCS) were modeled to investigate the thermal-hydraulic characteristic of the TBM system and its influence on ITER safety under the accident conditions. Results show that LLCS pressurization during In-TBM breeder box coolant leak is adequately handled by the safety accessories provided in LLCS and the highest temperature of the first wall is far below its melting point during the accident process.
1. Introduction The Dual-functional Lithium Lead Test Blanket Module (DFLL-TBM) has been developed by China for testing in ITER, which utilizes leadlithium eutectic alloy (LiPb) as tritium breeder, neutron multiplier and coolant [1,2]. The first wall facing the plasma is cooled by helium gas. As an initial examination of the safety impact that TBMs will have on ITER, the ITER IT requires the participating parties to analyze the following four accident scenarios: (1) in-vessel TBM coolant leaks, (2) inTBM breeder box coolant leaks, (3) ex-vessel TBM ancillary coolant leaks, and (4) complete loss of active TBM cooling [3]. In reference [4], the safety analyses of other 3 scenarios have been performed and discussed in detail. However, the second scenario has not been investigated yet. In-TBM Breeder Box Coolant Leak will cause the high pressure helium to discharge into the breeding box and result in the pressurization of the TBM LiPb breeding zones and its auxiliary system. In order to analyze the In-TBM Breeder Box Coolant Leak, there is a
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Corresponding author. E-mail address: [email protected] (Z. Zhou).
https://doi.org/10.1016/j.fusengdes.2018.06.020 Received 26 October 2017; Received in revised form 5 May 2018; Accepted 25 June 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
need to simulate the mixing of helium and Lead-Lithium fluids, while the current RELAP/SCDAPS/MOD4.0 cannot handle this problem. This paper first explains the reason for the current RELAP5’s inability to model liquid metal in contact with a non-condensable gas. Then a solution to solve this problem was introduced and code modification was made in the standard RELAP/SCDAPS/MOD4.0. By analyzing several cases using the modified RELAP/SCDAPS/MOD4.0 code, Fluent and theory correlation, the comparison results show that they are in good agreement with each other, which verify the accuracy and feasibility of the modified code. Finally the modified RELAP/SCDAPS/MOD4.0 is used in the safety analysis of In-TBM Breeder Box Coolant Leak in China DFLL-TBM. 2. DFLL-TBM system description DFLL-TBM [1,2] utilizes lead-lithium eutectic alloy as tritium breeder, neutron multiplier and coolant. Fig. 1 shows the basic design
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outlet temperature is around 400 ℃. Fig. 2(a–d) are schematic diagrams of helium flow in the radial-poloidal stiffening plate(rpSP), FW, inverted “L” shaped toroidal-poloidal stiffening plate (tpSP) and cover plate, respectively [4]. 3. Modification of RELAP5/MOD4.0 for DFLL-TBM The RELAP/SCDAPSIM/MOD4.0 hydrodynamic model is a one-dimensional, transient, two-fluid model for flow of a two-phase steam/ water mixture that can contain non-condensable components in the steam phase [5]. The basic differential equations are a system of 6 conservation equations: mass, energy and momentum for the liquid and the vapor phase of water. To include the non-condensable component in the gas phase, the following assumptions are considered:
• The non-condensable gas velocity is the same as the water vapour velocity. • The non-condensable gas temperature is the same as the water vapour temperature.
The general approach for addition of the non-condensable component consists of assuming that all properties of the gas phase are mixture properties of the steam/non-condensable gas mixture. The two mass continuity equations for liquid and vapour are unchanged and an additional mass conservation equation for the total non-condensable component is added [6]. The standard RELAP/SCDAPS/MOD4.0 version of the code can simulate systems with other fluids than water. However, it cannot simulate a mixture of a new fluid such as LiPb with any available RELAP/ SCDAPS/MOD4.0 non-condensable gas. The non-condensable gas calculation is based on the vapor phase of the fluid. Therefore, to simulate the mixing of helium and Lead-Lithium fluids, RELAP/SCDAPS/ MOD4.0 needs LiPb vapor phase properties when the liquid phase is in contact with helium [7].
Fig. 1. DFLL-TBM design scheme.
of DFLL-TBM. The structure of DFLL-TBM consists of a 484 mm (t) × 1660 mm (p) × 585 mm (r) rectangular steel box, which is reinforced by one radial–poloidal(r–p) and four toroidal–poloidal (t–p) stiffening plates(SPs). The four BPs constructed a three-stage helium distributing/collecting collector. The LiPb (2 MPa) flows into the module in the poloidal direction with the inlet/outlet temperatures of 480 ℃/700 ℃ to remove the volumetric nuclear heat in the breeding zones. The TBM FW and blanket structures are cooled by helium with mass flow rate of 1.35 kg/s at 8 MPa, whose inlet temperature is 340 ℃ and
3.1. Code modification The liquid phase physical properties of LiPb have been incorporated in the code [8]. A preliminary verification is also carried out for the single phase LiPb applications in this reference. To solve the problem of
Fig. 2. Schematic diagrams of helium flow within the TBM components. 36
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Cpg =
5 Rg 2
(5)
Cvg =
3 Rg 2
(6)
Dynamic viscosity [Pa.s]:
μg =
0.003285 T1/2
(7)
Internal energy [J]:
ug = ug 0 + Cvg (T −T0)
(8)
Enthalpy [J]:
h g = u g + p ⋅v
Fig. 3. Nodalization of communicating vessel.
(9)
Entropy [J/K]: simulating LiPb /Helium mixtures, two approaches can be considered in the modification of the code. One is avoiding the generation of LiPb vapor when the non-condensable gas appears [5]. The other one is implementing the vapor phase properties of LiPb into the code, similar to Jiang does for molten salt reactor system [6]. In this paper, the latter one is adopted. The first step of the code modification is adding the LiPb vapor phase properties, including saturation pressure, Psat ; density, ρg ; expansion coefficient, βg ; compression coefficient, k g ; heat capacity, Cpg , Cvg ; internal energy, ug ; enthalpy, hg ; entropy, sg and transport properties. The implemented properties of LiPb are in the forms of specific correlations, rather than the property tables that the original code adopts for the light and heavy water [7].The specific correlations are incorporated into subroutine STLIPB. The second step is modifying the code calculation process including defining the working range of temperature, pressure, and internal energy, using the given saturated temperature or saturated pressure to obtain other saturated parameters and calculation of the other physical parameters with any known parameters. The original modules calling the STLIPB are modified including the ISTATE, TSTATE, STATEP. The vapor phase property is assumed to be the ideal gas and satisfies the ideal gas state equation [6]. The vapor phase physical properties of LiPb can be obtained from the literature [9–11] for the lack of experimental data. Vapor property is not that important in the design and safety evaluation of DFLL-TBM due to the high boiling point of LiPb (about 2500 ℃). However, vapor data is required because the RELAP5 code structure is originally designed to simulate two-phase phenomena in water reactor systems [6.7]. The accuracy of the physical parameters of the vapor phase must be taken into account if there is a large number of LiPb in the vapor phase. The gram molecular mass of LiPb is calculated as R = 173 g/mol by taking it as a mean mass of the molecular lead and lithium- Li(17) Pb (83) [12]. The gas constant of LiPb: Rg = 48.05 J/kg/K. Vapor phase physical properties of LiPb: Saturation pressure [Pa]:
Psat = 1.5 × 1010 exp(−22900 Tsat )
sg = sg 0 + Cpg ln(T / T0) − Rg ln(P / P0)
T0 —Melting point temperature–508 K [13] 3.2. Verification of the modified RELAP/SCDAPS/MOD4.0 code In this part two typical problems were chosen to demonstrate the feasibility and validity of modeling the mixing of LiPb and non-condensable gas by the modified RELAP/SCDAPS/MOD4.0. 3.2.1. Communicating vessels Communicating vessels is a name given to a set of containers containing a homogeneous fluid: when the liquid settles, it balances out to the same level in all of the containers regardless of the shape and volume of the containers. A simple nodalization of a communicating vessel which contains the liquid LiPb and helium was shown in Fig. 3. The test section 100 and 102 both contains LiPb and helium gas. But the liquid level of pipe 100 is higher than the one of pipe 102. When the valves 101 opens at t = 10 s (the valve 103 keeps open all the time), LiPb will flow from 100 to 102 until it reach the same level in pipe 100 and 102. Fig. 4. show that, the void fraction of volume 100-07 is 0 initially. As time goes on, the liquid level decrease and the void fraction of volume 100-07 increase. While the 102-07 performs oppositely. The void fraction of 100-07 and 102-07 both keep at 50% when the two connected pipes got balanced which means LiPb reach the same level in pipe 100 and 102. From Fig. 5, we can see that the pressure of pipe 100 and 102 get balanced. This case proves that the modified RELAP/SCDAPS/MOD4.0 can simulate the problem of LiPb in contact with helium during transients. 3.2.2. One-dimensional pressure wave propagation In-TBM breeder box coolant leak will cause the high pressure helium to discharge into the breeding box and result in the pressurization
(1)
Density [kg/m3]:
ρg =
P Rg *T
(2)
Thermal expansion coefficient [1/K]:
βg = 1/ T
(3)
Isothermal compression coefficient [1/Pa]:
k g = 1/ P
(10)
(4) Fig. 4. Void fraction of communicating vessel.
Heat capacity [J/kg-K]: 37
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Fig. 5. Pressure of communicating vessel.
Fig. 6. Nodalization of one dimensional pressure propagation model (b < < L). (a) The phase plane of wave propagation in simple pipeline.
of the TBM LiPb breeding zones and auxiliary system. The pressure value difference between the LiPb and helium ancillary cooling systems is great. And the pressure variation of LiPb ancillary cooling systems is important to its structure safety. As shown in Fig. 6, a closed pipe was filled with LiPb and helium. Point A is the left endpoint of LiPb part and point C is the middle point of LiPb part. The LiPb was in 2 MPa and the helium was in 8 MPa. There is a thin film between the two fluids. At t = 0 s, the film bursts and this will cause a pressure wave disturbance spreading to the left pipe. In the simulation, a valve was used to model the film bursting. According to the theory of pressure wave propagation in simple pipeline [14], the phase plane of wave propagation in shown in Fig. 7(a). The solid line shows the positive pressure wave trajectory and the dotted line shows the trajectory of negative pressure wave. Fig. 7(b–g) shows the theoretical full cycle of one-dimensional pressure wave propagation [14] (Vs is the sound speed in LiPb). Point A is the left endpoint of the pipe, and the pressure wave will get a positive reflection here. Considering the infinite big space of the helium part, the pressure of helium can be thought as unchanged. Pressure of point B will keep at 8 MPa. The result of the modified RELAP/SCDAPS/MOD4.0 shows a good agreement with Fluent simulated and theoretical results [14] as shown in Figs. 8 and 9. From the results of the two typical phenomenon that model LiPb in contact with helium, it can be concluded that the modified RELAP/ SCDAPS/MOD4.0 code can be used to calculate mixing of helium and Lead-Lithium fluids and the accuracy and reliability of the calculation have also been verified.
Fig. 7. The full cycle of one-dimensional pressure wave propagation.
pressurizer of LLCS. Valve 917, was used to simulate the pressure safety valve (PSV) during accidents. Its status was decided by the LLCS loop pressure. It was closed in steady state and would be opened if the pressure of LLCS loop exceeded its setting pressure (2.1 MPa) in accidents. Valve 919 will be opened when the pressure of Dump Tank (918 P) exceeded PSV setting pressure (2.1 MPa) in accidents and then if the pressure dropped below 2 MPa it would be closed again. Fig. 11 shows the nodalization of Helium Cooling System loop. The modeled components include helium flow channels in the structure
4. DFLL-TBM system model The nodalization of Lithium Lead Cooling System (LLCS) loop and its secondary helium loop is shown in Fig. 10. The secondary side has been modeled using a RELAP time dependent volume (TDV) component as source and sink for helium at a pressure of 8 MPa. Pipe 914 which contains a cavity filled with helium plays the role of 38
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will be closed according to the HCS loop pressure during accident conditions. A computation of the steady state was intended to provide an initial condition for the transient analyses. In the steady state, it is assumed that there was no heat exchange between the two cooling loops. This assumption was reasonable provided the flow channel inserts in the breeder zones can be considered as ideal thermal insulation. But during the In-TBM breeder box coolant leak accident, heat exchange between the two primary cooling loops need to be considered. Convective heat transfer condition was set between the breeder zones and the helium flow channels. The steady-state calculation was carried out on the basis of an average heat flux of 0.3 MW/m2 on the first wall [4]. Table 1 compares the calculated steady-state parameters with the design parameters given in [15]. The steady-state result was used for the initial condition of the accident analyses. Valve700 between 900 P and 022 P was used to model the TBM channel rupture.
Fig. 8. Pressure of left endpoint A.
5. Accident analyses 5.1. Identification of causes and accident scenario This scenario leads to the following time sequence of events. The average surface heat flux on the TBM FW was increased to 120% level at 0.36 MW/m2 10 s prior to the TBM channel rupture occurs. After the break of helium tube, the internal helium leak pressurizes the TBM LiPb breeder zones and cooling system causing the relief system to open and drain to the dump tank. Once the pressure in the drain tank reaches the set pressure, a vent valve (919 V) above the dump tank (918 P) opens and relieves the helium pressure into the port cell. To assess the TBM integrity under an aggravating condition, the pump and circulators were assumed to coast down coincidently with the initiation of this accident. The time sequence of the accident is given in Table 2.
Fig. 9. Pressure of middle point C.
components (i.e., FW, stiffening plates, covers and collector manifolds) within the TBM, valves, inlet and outlet pipelines, a helium/water heat exchanger and a circulator. For the analysis of In-TBM breeder box coolant leak, the sixteen helium passes in the W-shaped TBM FW (each one is 15 mm*20 mm) were represented by two groups of “PIPE” components. In the accident, we assume that two helium passes were broken. A break area of 0.0006 m2 was considered. Therefore, one group was for two passes and the other group was for fourteen passes. The helium channel rupture location is PIPE022. Pipe 040/041/042 represent the helium channel in rpSP, tpSPs, covers respectively. Valve 247 and valve 293 are isolation valves of HCS loop and they are opened during normal condition and
5.2. Transient analysis results Due to the channel rupture inside TBM (t = 10 s), helium comes out impairing the heat removal from TBM and causes pressurization of LLCS loop (Fig. 12). Almost instantly (t = 10.0078 s) due to high pressure in LLCS loop, PSV 917 gets opened and lead-lithium starts getting dumped into dump tank 918 P. Once some of the LiPb gets dumped into Dump Tank, the path is free for helium. Helium enters
Fig. 10. Nodalization of Lithium Lead Cooling System (LLCS). 39
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Fig. 11. Nodalization of Helium Cooling System (HCS).
Table 1 Steady state result. Description Breeder zones Temperature at inlet (K) Temperature at outlet (K) Mass flow rate (kg/s) Pressure (MPa) HCS Temperature at inlet (K) Temperature at outlet (K) Mass flow rate (kg/s) Pressure (MPa)
Design data
RELAP5 value
Relative error
753 973 6.05 2
754 980 6.05 2
0.13% 0.72% 0% 0%
613 668 1.35 8
608 672 1.35 8
−0.82% 0.60% 0% 0%
Fig. 12. Pressure of LLCS. Table 2 Time sequence of In-TBM breeder box coolant leak. Time/s
Description
t=0
The average surface heat flux on the TBM FW was up to 0.36 MW/m2 The TBM channel rupture occurs Generating LOCA signal when HCS pressure was below 6 MPa Valve 917 open when the pressure of LLCS loop was beyond 2.1 MPa Rector trips on LOCA signal from HCS Plasma disruption and heat flux on the TBM FW was up to 5.52 MW/m2 for 0.1 s, and kept at 0.72 MW/m2 for 0.9 s Plasma quench; decay heat removal through thermal radiation Isolation valves 247 and 293 closed; pump and circulator trip
t = 10 t = t1 t = t2 t = t1+3 t1+3 < t < t1+4 t > t1+4 t = t1+10
Fig. 13. Pressure of HCS.
Cooling System (LLCS). As the pressure release process in LLCS gonging on, the flow rate decreases gradually. And after a period time’s oscillation, there is no fluid flows through the rapture. A total mass of 5.75 kg helium has been discharged into the LLCS in the accident. FW temperature during in TBM breeder box coolant leak case is given in Fig. 15. T = 0 s, fusion power increases by 20% and the average surface heat flux on the TBM FW was up to 0.36 MW/m2, When accident occurred at t = 10 s, the first wall temperature increased form 882.3 K at steady state to 900k. After the accident, the reactor didn’t shut down immediately and the first wall temperature kept on increasing. After 3 s of LOCA signal, Fast Plasma Shutdown System (FPSS) trips the reactor (t = 25.84 s). The plasma burst at t = 25.84 s and it cause the average surface heat flux on the TBM FW up to 0.72 MW/m2 within 1 s. At t = 26.84 s, the plasma quenched and the first wall
Dump Tank (DT) and pressure increases very fast and reaches DT PSV 919 setting pressure and helium starts coming out to port cell. But once the pressure of LLCS drops down to 2 MPa (t = 35.6 s), PSV 919 sits back and no more flow occurs. The pressure changes of the helium cooling system (HCS) are shown in Fig. 13. Due to break in TBM breeder box, helium comes out to LLCS and generates LOCA signal at T = 22.84 s when the pressure of HCS is bellowed 6 MPa. The isolation valves (247 and 293) of the HCS was closed after 10 s of LOCA signal (t = 32.84 s). Therefore, the TBM part of HCS continues to release pressure until its pressure drops down to 2 MPa, and the other parts of HCS maintains around 4.4 MPa. Fig. 14 describes the mass flow rate of valve 700. The break of the helium tube in TBM FW results in ingress helium into Lead Lithium 40
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dissipation through radiation. The LiPb and Helium (in TBM box) temperature during In-TBM Breeder Box Coolant Leak accident are shown in Figs. 16 and 17. The helium temperature will decrease first after the accident occurs because its volume expansion to breeding zones. When PSV 919 sits back and no more flow occurs, its temperature will increase as a result of decay heating and heat conduction from the high temperature breeder zones. Then the helium is cooled gradually by the radiation heat transfer through FW. The result shows a good agreement with reference [16]. It is found that the decay heat in the TBM can be removed efficiently. 6. Conclusions As a participant in the International Thermonuclear Experimental Reactor (ITER) Test Blanket Module (TBM) program, in addition to helium cooled solid breeder (HCSB) blanket [17–21], China has developed a Dual-functional Lithium Lead Test Blanket Module (DFLLTBM). In preparation of the regulatory safety files of ITER-TBM, a number of off-normal event sequences have been postulated. In order to analyze some of the postulated off-normal events, there is the need to simulate the mixing of Helium and Lead-Lithium fluids. RELAP/SCDAPS/ MOD4.0 is a widely-used Nuclear Safety Analysis code that can simulate reactor plants from normal transients to severe accidents. While the current RELAP/SCDAPS/MOD4.0 cannot handle the problem of liquid metal in contact with a non-condensable gas. By implanting the vapor phase properties of lead-lithium eutectic alloy and modifying the calculation process, the modified code overcomes its disability of modeling the coexistence of LiPb and non-condensable gas. The feasibility and validity of the modified code handing the mixing of LiPb and noncondensable gas were proved by two typical problems. In-TBM breeder box coolant leak accident is simulated by the modified code. LLCS pressurization during In-TBM breeder box coolant leak is adequately handled by the safety accessories provided in LLCS. The first wall temperature peaks at 943.4 K during the accident, which is far below the melting point 1278 ℃ of Be armor. The TBM temperature response exhibits an acceptable decay heat removal capability of the TBM. The present work is expected to be helpful for the design of the DFLL-TBM system in view of its thermal hydraulic characteristics. The extended RELAP/SCDAPS/MOD4.0 code can be used for the DFLL-TBM system safety analysis in the future.
Fig. 14. Mass flow rate of the rupture.
Fig. 15. FW temperature during In-TBM Breeder Box Coolant Leak accident.
Acknowledgment The authors gratefully acknowledge the support from the National Basic Research Program of China (2014GB116000).
Fig. 16. LiPb (in TBM box) temperature during Coolant Leak accident.
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Fig. 17. Helium (in TBM box) temperature during In-TBM Breeder Box Coolant Leak accident.
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