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Benchmark calculations of pressurizer model for Maanshan nuclear power plant using TRACE code
Nuclear Engineering and Design 239 (2009) 2343–2348
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Benchmark calculations of pressurizer model for Maanshan nuclear power plant using TRACE code Yi-Hsiang Cheng a,∗ , Jong-Rong Wang b , Hao-Tzu Lin b , Chunkuan Shih a a b
Department of Engineering and System Science, National Tsing Hua University, No. 101, Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC Institute of Nuclear Energy Research, No. 1000, Wen-Hua Road, Longtan, Taoyuan 32546, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 19 August 2008 Received in revised form 3 July 2009 Accepted 10 July 2009
a b s t r a c t The pressurizer plays an important role in controlling the pressure of the primary coolant system in pressurized water reactor (PWR) nuclear power plants. An accurate modeling of the pressurizer is needed to determine the pressure response of the primary coolant system, and thus to successfully simulate overall PWR nuclear power plant behavior during transients. The purpose of this study is to develop a pressurizer model, and to assess its pressure transients using the TRACE code version 5.0. The benchmark of the pressurizer model was performed by comparing the simulation results with those from the tests at the Maanshan nuclear power plant. Four start-up tests of the Maanshan nuclear power plant are collected and simulated: (1) turbine trip test from 100% power (Test PAT-50); (2) large-load reduction at 100% power (Test PAT-49); (3) net-load trip at 100% power (Test PAT-51); and (4) net-load trip at 50% power (Test PAT-21). The simulation results show that the predictions of the pressure response are in reasonable agreement with the power plant’s start-up tests, and thus the pressurizer model built in this study is successfully verified and validated. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of predicting the behavior of nuclear power plant components with accuracy is well recognized after the Three Mile Island accident. For the pressurized water reactor (PWR), the pressurizer is an important component to control the pressure in the primary coolant system. It provides a surge volume for system coolant expansion and contraction, such that the system pressure can be controlled above saturation. Thus, many separate effect tests, such as the ATWS tests at the PACTEL test facility (Riikonen, 1998), the pressurizer tests at MIT (Kim, 1984), and the Neptununs Y05 tests at Delft University of Technology (Peterson, 1984), were conducted to observe the dynamic behavior in the pressurizer. Meanwhile, numerous efforts have been undertaken on code verification and validation. The ability of a code to predict the pressure behavior during operational transients and recovery procedures with accuracy is highly crucial. Earlier studies show that the transient behavior predicted by the equilibrium models diverges from the experimental phenomena especially during rapid reactor transients (Kim and Griffith, 1987). Therefore, non-equilibrium models based on the two-region or three-region concept were developed to enhance the predic-
∗ Corresponding author. Tel.: +886 3 5742371; fax: +886 3 5720724. E-mail addresses: [email protected] (Y.-H. Cheng), [email protected] (C. Shih). 0029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2009.07.025
tion accuracy (Abdallah et al., 1982; Bake et al., 1986; Kim et al., 2006). Furthermore, the incorporation of more accurate heat transfer models into the existing physical models also enhances the pressure transient predictions for the pressurizer system. Weaver (2004) modified the interfacial condensation model for the RELAP3D code; Prelewicz et al. (2005) used thermal front tracking model for the RELAP5/MOD 3.3 code. In this study, we model the pressurizer system of the Maanshan nuclear power plant for the TRACE code (USNRC, 2007). TRACE (TRAC/RELAP Advanced Computational Engine), developed by the USNRC, is an advanced, best-estimate reactor systems code for analyzing neutronic-thermal-hydraulic behavior in light water reactors. TRACE consolidates the capabilities of the four codes, TRAC-P, TRAC-B, RELAP 5 and RAMONA, into one modernized code. The code is well designed to perform analyses of loss-of-coolant accidents (LOCAs), operational transients, accident scenarios, phenomena in experimental facilities. Models for multidimensional two-phase flow, non-equilibrium thermo-dynamics, heat transfer, reflood, level tracking, and reactor kinetics are included. Furthermore, a client application – SNAP (the Symbolic Nuclear Analysis Package) – is developed by Applied Programming Technology, Inc. for conveniently creating and editing input decks. Thus, the process of performing reactor systems analysis is simplified by using the SNAP client application. Therefore, the pressurizer model of the Maanshan nuclear power plant is edited by using the SNAP graphical user environment for the TRACE code for a part of the work of Wang et al. (2009). The
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To cut the calculation complexity and the time for calculation, the internal energy and motion equations converted from the conservative forms of the energy and momentum equations are derived firstly as (7). Rather than using the internal energy equation for gas, TRACE uses the internal mixture energy conservation equation, which is much easier to deal with transitions from two-phase to single-phase flow for the finite volume approach. The internal mixture energy conservation equation is as (8).
Nomenclature e hl hv f fi − → V P q
internal energy (m2 /s2 ) liquid enthalpy of the bulk liquid (J/kg) vapor enthalpy of the bulk vapor (J/kg) force per unit volume (N/m3 ) interfacial friction factor velocity vector (m/s) fluid pressure (Pa) heat transfer rate per unit volume (W/m3 )
− ∂(˛g eg ) ∂˛ − → → + ∇ · ˛g eg Vg = −P − P ∇ · ˛Vg ∂t ∂t
Greek symbols ˛ gas volume fraction density (kg/m3 ) interfacial mass-transfer rate (positive from liquid to gas) (kg/m3 s) Subscripts d direct heating as energy source g gas mixture i interfacial l liquid w wall
+ qig + qwg + qdg + hv ∂[(1 − ˛)l el + ˛g eg ] − → − → + ∇ · [(1 − ˛)l el Vl + ˛g eg Vg ] ∂t − → − → = −P ∇ · [(1 − ˛) Vl + ˛Vg ] + qwl + qwg + qdl + qdg Motion equations are also obtained as: → − → − − → − → − → ∂ Vl 1 [ f + fwl − ( Vi − Vl )] − − → − → + V l · ∇ Vl = − ∇ P + i +→ g l (1 − ˛)l ∂t − → −→ − → − → − → ∂Vg − [− fi + fwg − (Vg − Vi )] − 1 → − → + Vg · ∇ Vg = − ∇ P + +→ g g ˛g ∂t
(7)
(8)
(9)
(10)
2.1. Interfacial drag force pressure transients are further analyzed for the four represented start-up tests conducted at the Maanshan nuclear power plant in 1985 as benchmark calculations. 2. Governing equations TRACE uses two-fluid, two-phase field equations that consist of mass, energy, and momentum conservations for the liquid and gas fields. The model considers (1) heat transfer from the interface to gas and to liquid, and heat transfer from surfaces of structures to the fluid; and (2) contributions from the stress tensor due to shear at metal surfaces or phase interfaces within the averaging volume. The time and volume averaged mass equations are:
∂(1 − ˛)l − → + ∇ · (1 − ˛)l Vl = − ∂t
(1)
− ∂˛g → + ∇ · ˛g Vg = ∂t
(2)
The time and volume averaged energy equations are:
2.3. Wall condensation and boiling
(4)
2.4. Heat Conduction
The time and volume averaged momentum equations are: − → ∂(1 − ˛)l Vl − →− → + ∇ · (1 − ˛)l Vl Vl + (1 − ˛)∇ P ∂t → − → − − → → g − Vi = fi + fwl + (1 − ˛)l −
TRACE models the fluid-wall shear force using a friction factor approach. Regarding the Pre-CHF regime, wall drag force is only applied to the liquid phase.
(3)
∂˛g (eg + Vg 2 /2) P − → + Vg 2 /2)Vg ) + ∇ · ˛g (eg + g ∂t
− → −→ − → − → → = qig + qwg + qdg + ˛g − g · Vg + hv + (− fi + fwg ) · Vg
2.2. Wall drag force
When the wall temperature above the liquid level is lower than the saturation temperature, condensation of vapor on the wall is calculated. If the wall temperature above the liquid level is higher than the saturation temperature, natural convection in the vapor region occurs. Natural convection in the liquid region is considered when the wall temperature below the liquid level is lower than the saturation temperature. When the wall temperature below the liquid level is higher than the saturation temperature, heat transfer occurs by boiling.
∂(1 − ˛)l (el + Vl 2 /2) P − → + Vl 2 /2) Vl + ∇ · (1 − ˛)l (el + l ∂t − → − → − − → → → = qil + qwl + qdl + (1 − ˛)l − g · Vl − hl + ( fi + fwl ) · Vl
The transfer of mass, energy and momentum between gas–liquid phases are modeled by the flow-regime dependent thermal-hydraulic equations. In TRACE, there are three categories of flow regimes: Pre-CHF (bubbly/slug and annular/mist regimes), Stratified, and Post-CHF (inverted flow regime). The interfacial drag force for the bubbly/slug flow regime is based on the drift flux model, while TRACE treats the annular/mist flow regime as a superposition of interfacial drag on a liquid film and on entrained droplets.
The thermal history of the wall structure is obtained from the solution of the general heat-conduction equation.
(5)
3. Pressurizer model 3.1. Descriptions of pressurizer
− → ∂˛g Vg − → − → − → − →− → → g + Vi + ∇ · ˛g Vg Vg + ˛∇ P = − fi + fwl + ˛g − ∂t
(6)
The Maanshan nuclear power plant in Taiwan is a Westinghouse 3-loop PWR plant with a total thermal output of 2785 MWth. The
Y.-H. Cheng et al. / Nuclear Engineering and Design 239 (2009) 2343–2348
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with level error signal. The backup heater is fully turned on only when the level error signal exceeds the setpoint of +5% and the pressure error signal is less than the setpoint of −172.4 kPa. On the other hand, the backup heater may be turned full off if the pressure error signal is greater than −117.2 kPa. The proportional heater and backup heater are totally turned off if the water level is lower than 14%, no matter the pressure is high or low. Therefore, the water level for heater cutoff is 1.55 m. The PORVs open when the pressure-difference setpoint 689.5 kPa is reached, and the PORVs close when the pressure difference drops down to 551.6 kPa. The release capability for each of the three PORVs is 79.38 kg/s. The SVs open when the pressuredifference setpoint 1620.3 kPa is reached, and the SVs close as the pressure difference is lower than 1620.3 kPa. The release capability for each of the three SVs is 143.64 kg/s. The pressurizer system is modeled in the power plant scale, and the main parameters of the pressurizer are listed in Table 1. 3.2. Pressurizer model for TRACE
Fig. 1. Inner structure of pressurizer.
pressurizer is made up of a steel tank which contains saturated water in the lower section and saturated steam in the upper section at normal operation. It is connected to the hot leg of the loop No. 2 through a surge line. Important components in the pressurizer include sprayer, electric heaters, power-operated relief valves (PORVs), safety valves (SVs), surge line, and relief tank, as seen in Fig. 1. The sprayer, the PORVs and the SVs are equipped at the top of the tank, while electric heaters are immersed in the water. The sprayer and the electric heaters are used to control the system pressure during load transients. When the reactor power increases, the coolant volume increases correspondingly such that the coolant surges into the pressurizer. In such case, the sprayer is activated to spray water from the top of the tank to limit the pressure by condensing the steam. When the reactor power decreases, the coolant volume decreases and the coolant surge out the pressurizer. At this time, some of the water flashes to steam due to pressure drop. The electric heaters are activated to heat up the water in the tank to maintain the desired operating pressure. The sprayer is activated by the pressure-difference setpoint. In normal operating condition, a low fluid flow rate of 0.126 kg/s is sprayed into the pressurizer. When the pressure difference exceeds 172.4 kPa, the flow rate starts to increase. The flow rate increases linearly from 0.126 kg/s to 44 kg/s when the pressure difference increases from 172.4 kPa to 517.1 kPa. The electric heaters can be classified into proportional heater and backup heater. The control of the proportional heater and backup heater is based on the pressure-difference setpoints and water-level setpoints. The proportional heater adds one half of the rated heating rate to the liquid at normal operation, generates power of 376 kW at a full rate if the pressure error signal is less than −103.4 kPa, and is fully turned off if the pressure error signal is greater than +103.4 kPa. The backup heater can only be fully turned on or off, and is controlled by the pressure error signal together
The pressurizer model was built by the SNAP client, and then converted to the input decks for the TRACE code. TRACE includes several hydraulic components: PIPEs, PLENUMs, PRIZERs (pressurizers), CHANs (BWR fuel channels), PUMPs, JETPs (jet pumps), SEPDs (separators), TEEs, TURBs (turbines), HEATRs (feedwater heaters), CONTANs (containment), VALVEs, and VESSELs. Powered and heated components are POWER, FLPOWER (fluid power), HTSTR (heat structure). RADENC (radiation enclosures) component simulates radiation heat transfer between surfaces. FILL and BREAK components supply the coolant-flow and pressure boundary conditions. In this study, the PIPE component is used to model the feature of the pressurizer. The FILL component models the phenomena of insurge and outsurge at the surge nozzle, the spray mechanism through the spray nozzle, and the pressure relief by letting steam exit through the power-operated relief valves (PORVs) and safety valves (SVs). The HTSTR component is added at the bottom of the pressurizer to model the heaters. To fulfill the control procedures of the open position of the spray valve, the opening and closing of PORVs and SVs, the proportional heater and backup heater, the control systems in TRACE (including trips, signal variables, control blocks, and component action tables) are properly combined for the TRACE code to follow. The fill table of the FILL component is edited to simulate the flow insurge and outsurge as the boundary condition of the pressurizer model. Therefore, the mass flow rates relative to time must be initially given. However, flow meters were not installed along the surge line to measure the flow rates during the tests conducted in 1985. We managed to adjust the mass flow rates at the surge nozzle by matching the calculated water level inside the pressurizer with those from the test data. Therefore, trial and error is applied to search out the proper inputs of the mass flow rates. All of the plant tests collected in this study have their records of the
Table 1 Main parameters of the pressurizer. Parameter Dimension Flow length (m) Flow area (m2 ) Volume (m3 ) Hydraulic diameter (m)
11.74 3.58 39.64 2.13
Nominal condition Water level (%) Operating pressure (MPa) Operating temperature (K)
56.5 15.4 617
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variations in water level. Consequently, the time-varying mass flow rates input to the fill table for each test are successfully obtained. After constructing the geometric model of the pressurizer, the boundary conditions, such as the insurge and outsurge flow rates, the insurge and outsurge flow temperatures, and the outlet pressures of the SVs and PORVs, and given. Then, each test retrieves its fluid initial conditions in the pressurizer body by using the steadystate calculation function in TRACE. 4. Results and discussion Four start-up tests of the Maanshan nuclear power plant, (1) turbine trip test from 100% power (Test PAT-50), (2) large-load reduction at 100% power (Test PAT-49), (3) net-load trip at 100% power (Test PAT-51) and 4) net-load trip at 50% power (Test PAT21), were collected for the verification purpose. In the following, the test procedures and the test criteria are firstly described (TPC, 1985), and then the pressurizer transients simulated by the TRACE code version 5.0 are shown. (1) turbine trip test from 100% power The turbine trip test was initiated by manually tripping the turbine while the plant was operating at full power (2785 MW). As a result, the reactor was directly tripped with control rods in full-in position. The decrease in the reactor coolant temperature led a large flow outsurge of the pressurizer. The test must meet the following criteria: (a) (b) (c) (d)
No pressurizer safety valves should open. No steam generator safety valves should open. Safety injection system should not be started. The response time of RTD (residence time distribution) should not be greater than the test value (6 s). (e) Neutron flux should be reduced to be less than 15% rated within 2 s after the turbine trip. (f) All the control rods should be inserted. (2) large-load reduction at 100% power The large-load reduction test was initiated by reducing the steam flow passing through the turbine from 100 to 50% of the rated capacity. This test must prove that the rod control system and the steam dump system can be automatically initialized, and the reactor power can be reduced from 100 to 50% corresponding to the reduction in steam flow. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. (3) net-load trip at 100% power
Fig. 2. Water level during the 100% turbine trip test.
The 100% net-load trip test was initiated by manually rejecting load while the plant was operating at full power (2785 MW). All the control systems were in auto mode. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. (4) net-load trip at 50% power The 50% net-load trip test was initiated by manually rejecting load while the plant was operating at 50% power. All the control systems were in auto mode. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. To simulate these transients, the initial conditions and the boundary conditions must be input. Table 2 lists the specified initial conditions of each test. The boundary conditions are obtained from the trial and error procedure as described above. For the turbine trip test from 100% power, the solid line in Fig. 2 shows the water levels during the 100% turbine trip test. The circle points in Fig. 2 represent the resultant water level when the mass flow rates at FILL component are well adjusted. Fig. 3 plots the calculated pressurizer pressure histories together with the measured
Table 2 Initial conditions of the four start-up tests.
Case 1 Case 2 Case 3 Case 4 a b
Thermal power (MWth)
RCS cold leg temp. (K)
RCSa hot leg temp. (K)
PZRb pressure (MPa)
PZR level (%)
2752.5 2802.7 2802.7 1397.7
565.9 565.8 565.2 565
599.5 599.8 599.3 582.8
15.3 15.4 15.4 15.4
56.5 57 56.6 40.5
RCS = reactor coolant system PZR = pressurizer
Y.-H. Cheng et al. / Nuclear Engineering and Design 239 (2009) 2343–2348
Fig. 3. Comparisons between the measured and calculated pressurizer pressure histories during the 100% turbine trip test.
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Fig. 5. Comparisons between the measured and calculated pressurizer pressure histories during the 100% large-load reduction test.
Fig. 4. Water level during the 100% large-load reduction test. Fig. 6. Water level during the 100% net-load trip test.
pressure histories. This figure reveals that the pressure histories in the pressurizer predicted by the TRACE code are in agreement with the test data. In this test, only the backup heater is activated due to the depressurization in the pressurizer system. For the large-load reduction at 100% power, the flow rates input in the FILL component result in that the calculated water levels meet the measured water levels, as shown in Fig. 4 Fig. 4. Comparisons between the measured and calculated pressurizer pressure during the transient is shown in Fig. 5. It can be seen that the calculated pressure histories follow the test data, caused by a combination of insurge, outsurge, spray actuation, and electric heater action. However, discrepancies between the calculated and the measured pressure histories are observed. In this simulation, the pressure response is over-reactive when the pressure is increasing. Fig. 6 shows that the calculated water levels meet the measured water levels in the net-load trip at 100% power transient. The calculated and the measured pressurizer pressures during the transient are plotted in Fig. 7. As revealed from this figure, the calculated pressure histories follow the trend of the test data, caused by a combination of insurge, outsurge, spray actuation, opening of PORVs and electric heater action. The calculated pressure in this net-load trip at 100% power test reaches the sprayer setpoint +172.4 kPa at 175 s and the PORVs setpoint +689.5 kPa at 183 s. Therefore, the sprayer starts to spray cool liquid into the pressurizer to suppress
Fig. 7. Comparisons between the measured and calculated pressurizer pressure histories during the 100% net-load trip test.
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is, respectively, with 40, 20 and 10 meshes in its axial orientation. From Figs. 3, 5, 7 and 9, we can see that the numerical solutions are not very sensitive to the number of mesh cells. Therefore, the coarser meshes provide the transient prediction as reliable as the finer meshes in these simulation cases. The errors between the prediction and the measurement are evaluated by the standard deviation sampled from the data points of 40, 20 and 10 mesh cells. The error measurement show that the transient prediction by the pressurizer model built in this study has the worst standard deviation of 3% occurring in the net-load trip at 100% power test. 5. Conclusions
Fig. 8. Water level during the 50% net-load trip test.
This study develops a pressurizer model for the Maanshan nuclear power plant, and assesses the pressure behavior in the pressurizer system using the TRACE code version 5.0. The pressurizer model is constructed of the inherent hydraulic components in TRACE, including the PIPE, the FILL, and the HTSTR components. Furthermore, the control systems in TRACE, including trips, signal variables, control blocks, and component action tables, are used to control the opening and closing of PORVs and SVs, the open position of the spray valve, the proportional heater and backup heater. For benchmark calculations, four start-up tests: (1) turbine trip test from 100% power, (2) large-load reduction at 100% power, (3) netload trip at 100% power and (4) net-load trip at 50% power, are collected and simulated. The time-dependent surge flow rates at the surge nozzle are given as the boundary conditions. The fluid initial conditions are obtained by using the steady-state calculation function in TRACE. The predicted pressure transients are compared with the test data, and the results show that the comparisons are in reasonable agreement. This study benchmarks the pressurizer model for TRACE code’s calculation, and fulfills the component level verification of our native PWR. References
Fig. 9. Comparisons between the measured and calculated pressurizer pressure histories during the 50% net-load trip test.
the pressure at 175 s. However, the pressure in the pressurizer is not suppressed instantly due to the continuous hot water surging. Consequently, the PORVs open at 183 s to release the steam such that the pressure in the pressurizer is successfully suppressed. Regarding the net-load trip at 50% power test, Fig. 8 also shows that the calculated water levels meet the measured water levels. The calculated and the measured pressurizer pressures during the transient are plotted in Fig. 9. The calculated pressure histories follow the test data, caused by a combination of insurge, outsurge, spray actuation, and electric heater action. The calculated pressure in this net-load trip at 50% power test reaches the sprayer setpoint +172.4 kPa at 165 s. Therefore, the sprayer is activated, and then the pressure is successfully suppressed. However, discrepancies between the calculated and the measured pressure histories are also observed. The sensitivity of the mesh cells is also observed. In these simulation cases, the pressurizer body (modeled by the PIPE component)
Abdallah, A.M., Maria, A.H., Rabie, M.A., Nagy, M.E.S., 1982. Pressurizer transients dynamic model. Nuclear Engineering and Design 73 (3), 447–453. Bake, S.M., No, H.C., Park, I.N., 1986. A non-equilibrium three-region model for transient analysis of pressurized water reactor pressurizer. Nuclear Technology, 74. Kim, S., 1984. An experimental and analytical model of a PWR pressurizer during transients. Doctor of Philosophy Thesis. Massachusetts Institute of Technology, Department of Nuclear Engineering. Kim, S.-N., Griffith, P., 1987. PWR pressurizer modeling. Nuclear Engineering and Design 102 (2), 199–209. Kim, T.-W., Kim, J-.W., Park, G.-C., 2006. Development of nonequilibrium pressurizer model with noncondensible gas. Nuclear Engineering and Design 236, 375– 384. Peterson, A.C., 1984. TRAC-PF1/MOD1 Independent Assessment: NEPTUNUS Pressurizer Test Y05. Sandia National Laboratories, Albuquerque, New Mexico, USA, NUREG/CR.3919. p. 49. Prelewicz, D., Mortensen, G.A., Barber, D., Bolander, M., Fletcher, D., Caraher, D., Wang, W, 2005. RELAP5 Status Report. Spring 2005 CAMP Meeting. Dubrovnik, Croatia, May 2–4, 2005. Riikonen, V., 1998. ATWS Experiments with PACTEL: Pressurizer Experiments Lappeenrantam. VTT Energy TEKOJA 1/98. Taiwan Power Company (TPC), 1985. Maanshan Start-Up Test Report. U. S. Nuclear Regulatory Commission (USNRC), 2007. TRACE V5.0 User Manual. Wang, J.-R., Lin, H.-Z., Cheng, Y.-H., Wang, W.-C., Shih, C., 2009. TRACE modeling and its verification using Maanshan PWR start-up tests. Annals of Nuclear Energy 36 (4), 527–536. Weaver, W., 2004. Improvements to the pressurizer component. In: International Relap Users Group Meeting, Sun Valley, Idaho, USA, August 25–27.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Benchmark calculations of pressurizer model for Maanshan nuclear power plant using TRACE code Yi-Hsiang Cheng a,∗ , Jong-Rong Wang b , Hao-Tzu Lin b , Chunkuan Shih a a b
Department of Engineering and System Science, National Tsing Hua University, No. 101, Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC Institute of Nuclear Energy Research, No. 1000, Wen-Hua Road, Longtan, Taoyuan 32546, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 19 August 2008 Received in revised form 3 July 2009 Accepted 10 July 2009
a b s t r a c t The pressurizer plays an important role in controlling the pressure of the primary coolant system in pressurized water reactor (PWR) nuclear power plants. An accurate modeling of the pressurizer is needed to determine the pressure response of the primary coolant system, and thus to successfully simulate overall PWR nuclear power plant behavior during transients. The purpose of this study is to develop a pressurizer model, and to assess its pressure transients using the TRACE code version 5.0. The benchmark of the pressurizer model was performed by comparing the simulation results with those from the tests at the Maanshan nuclear power plant. Four start-up tests of the Maanshan nuclear power plant are collected and simulated: (1) turbine trip test from 100% power (Test PAT-50); (2) large-load reduction at 100% power (Test PAT-49); (3) net-load trip at 100% power (Test PAT-51); and (4) net-load trip at 50% power (Test PAT-21). The simulation results show that the predictions of the pressure response are in reasonable agreement with the power plant’s start-up tests, and thus the pressurizer model built in this study is successfully verified and validated. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of predicting the behavior of nuclear power plant components with accuracy is well recognized after the Three Mile Island accident. For the pressurized water reactor (PWR), the pressurizer is an important component to control the pressure in the primary coolant system. It provides a surge volume for system coolant expansion and contraction, such that the system pressure can be controlled above saturation. Thus, many separate effect tests, such as the ATWS tests at the PACTEL test facility (Riikonen, 1998), the pressurizer tests at MIT (Kim, 1984), and the Neptununs Y05 tests at Delft University of Technology (Peterson, 1984), were conducted to observe the dynamic behavior in the pressurizer. Meanwhile, numerous efforts have been undertaken on code verification and validation. The ability of a code to predict the pressure behavior during operational transients and recovery procedures with accuracy is highly crucial. Earlier studies show that the transient behavior predicted by the equilibrium models diverges from the experimental phenomena especially during rapid reactor transients (Kim and Griffith, 1987). Therefore, non-equilibrium models based on the two-region or three-region concept were developed to enhance the predic-
∗ Corresponding author. Tel.: +886 3 5742371; fax: +886 3 5720724. E-mail addresses: [email protected] (Y.-H. Cheng), [email protected] (C. Shih). 0029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2009.07.025
tion accuracy (Abdallah et al., 1982; Bake et al., 1986; Kim et al., 2006). Furthermore, the incorporation of more accurate heat transfer models into the existing physical models also enhances the pressure transient predictions for the pressurizer system. Weaver (2004) modified the interfacial condensation model for the RELAP3D code; Prelewicz et al. (2005) used thermal front tracking model for the RELAP5/MOD 3.3 code. In this study, we model the pressurizer system of the Maanshan nuclear power plant for the TRACE code (USNRC, 2007). TRACE (TRAC/RELAP Advanced Computational Engine), developed by the USNRC, is an advanced, best-estimate reactor systems code for analyzing neutronic-thermal-hydraulic behavior in light water reactors. TRACE consolidates the capabilities of the four codes, TRAC-P, TRAC-B, RELAP 5 and RAMONA, into one modernized code. The code is well designed to perform analyses of loss-of-coolant accidents (LOCAs), operational transients, accident scenarios, phenomena in experimental facilities. Models for multidimensional two-phase flow, non-equilibrium thermo-dynamics, heat transfer, reflood, level tracking, and reactor kinetics are included. Furthermore, a client application – SNAP (the Symbolic Nuclear Analysis Package) – is developed by Applied Programming Technology, Inc. for conveniently creating and editing input decks. Thus, the process of performing reactor systems analysis is simplified by using the SNAP client application. Therefore, the pressurizer model of the Maanshan nuclear power plant is edited by using the SNAP graphical user environment for the TRACE code for a part of the work of Wang et al. (2009). The
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Y.-H. Cheng et al. / Nuclear Engineering and Design 239 (2009) 2343–2348
To cut the calculation complexity and the time for calculation, the internal energy and motion equations converted from the conservative forms of the energy and momentum equations are derived firstly as (7). Rather than using the internal energy equation for gas, TRACE uses the internal mixture energy conservation equation, which is much easier to deal with transitions from two-phase to single-phase flow for the finite volume approach. The internal mixture energy conservation equation is as (8).
Nomenclature e hl hv f fi − → V P q
internal energy (m2 /s2 ) liquid enthalpy of the bulk liquid (J/kg) vapor enthalpy of the bulk vapor (J/kg) force per unit volume (N/m3 ) interfacial friction factor velocity vector (m/s) fluid pressure (Pa) heat transfer rate per unit volume (W/m3 )
− ∂(˛g eg ) ∂˛ − → → + ∇ · ˛g eg Vg = −P − P ∇ · ˛Vg ∂t ∂t
Greek symbols ˛ gas volume fraction density (kg/m3 ) interfacial mass-transfer rate (positive from liquid to gas) (kg/m3 s) Subscripts d direct heating as energy source g gas mixture i interfacial l liquid w wall
+ qig + qwg + qdg + hv ∂[(1 − ˛)l el + ˛g eg ] − → − → + ∇ · [(1 − ˛)l el Vl + ˛g eg Vg ] ∂t − → − → = −P ∇ · [(1 − ˛) Vl + ˛Vg ] + qwl + qwg + qdl + qdg Motion equations are also obtained as: → − → − − → − → − → ∂ Vl 1 [ f + fwl − ( Vi − Vl )] − − → − → + V l · ∇ Vl = − ∇ P + i +→ g l (1 − ˛)l ∂t − → −→ − → − → − → ∂Vg − [− fi + fwg − (Vg − Vi )] − 1 → − → + Vg · ∇ Vg = − ∇ P + +→ g g ˛g ∂t
(7)
(8)
(9)
(10)
2.1. Interfacial drag force pressure transients are further analyzed for the four represented start-up tests conducted at the Maanshan nuclear power plant in 1985 as benchmark calculations. 2. Governing equations TRACE uses two-fluid, two-phase field equations that consist of mass, energy, and momentum conservations for the liquid and gas fields. The model considers (1) heat transfer from the interface to gas and to liquid, and heat transfer from surfaces of structures to the fluid; and (2) contributions from the stress tensor due to shear at metal surfaces or phase interfaces within the averaging volume. The time and volume averaged mass equations are:
∂(1 − ˛)l − → + ∇ · (1 − ˛)l Vl = − ∂t
(1)
− ∂˛g → + ∇ · ˛g Vg = ∂t
(2)
The time and volume averaged energy equations are:
2.3. Wall condensation and boiling
(4)
2.4. Heat Conduction
The time and volume averaged momentum equations are: − → ∂(1 − ˛)l Vl − →− → + ∇ · (1 − ˛)l Vl Vl + (1 − ˛)∇ P ∂t → − → − − → → g − Vi = fi + fwl + (1 − ˛)l −
TRACE models the fluid-wall shear force using a friction factor approach. Regarding the Pre-CHF regime, wall drag force is only applied to the liquid phase.
(3)
∂˛g (eg + Vg 2 /2) P − → + Vg 2 /2)Vg ) + ∇ · ˛g (eg + g ∂t
− → −→ − → − → → = qig + qwg + qdg + ˛g − g · Vg + hv + (− fi + fwg ) · Vg
2.2. Wall drag force
When the wall temperature above the liquid level is lower than the saturation temperature, condensation of vapor on the wall is calculated. If the wall temperature above the liquid level is higher than the saturation temperature, natural convection in the vapor region occurs. Natural convection in the liquid region is considered when the wall temperature below the liquid level is lower than the saturation temperature. When the wall temperature below the liquid level is higher than the saturation temperature, heat transfer occurs by boiling.
∂(1 − ˛)l (el + Vl 2 /2) P − → + Vl 2 /2) Vl + ∇ · (1 − ˛)l (el + l ∂t − → − → − − → → → = qil + qwl + qdl + (1 − ˛)l − g · Vl − hl + ( fi + fwl ) · Vl
The transfer of mass, energy and momentum between gas–liquid phases are modeled by the flow-regime dependent thermal-hydraulic equations. In TRACE, there are three categories of flow regimes: Pre-CHF (bubbly/slug and annular/mist regimes), Stratified, and Post-CHF (inverted flow regime). The interfacial drag force for the bubbly/slug flow regime is based on the drift flux model, while TRACE treats the annular/mist flow regime as a superposition of interfacial drag on a liquid film and on entrained droplets.
The thermal history of the wall structure is obtained from the solution of the general heat-conduction equation.
(5)
3. Pressurizer model 3.1. Descriptions of pressurizer
− → ∂˛g Vg − → − → − → − →− → → g + Vi + ∇ · ˛g Vg Vg + ˛∇ P = − fi + fwl + ˛g − ∂t
(6)
The Maanshan nuclear power plant in Taiwan is a Westinghouse 3-loop PWR plant with a total thermal output of 2785 MWth. The
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with level error signal. The backup heater is fully turned on only when the level error signal exceeds the setpoint of +5% and the pressure error signal is less than the setpoint of −172.4 kPa. On the other hand, the backup heater may be turned full off if the pressure error signal is greater than −117.2 kPa. The proportional heater and backup heater are totally turned off if the water level is lower than 14%, no matter the pressure is high or low. Therefore, the water level for heater cutoff is 1.55 m. The PORVs open when the pressure-difference setpoint 689.5 kPa is reached, and the PORVs close when the pressure difference drops down to 551.6 kPa. The release capability for each of the three PORVs is 79.38 kg/s. The SVs open when the pressuredifference setpoint 1620.3 kPa is reached, and the SVs close as the pressure difference is lower than 1620.3 kPa. The release capability for each of the three SVs is 143.64 kg/s. The pressurizer system is modeled in the power plant scale, and the main parameters of the pressurizer are listed in Table 1. 3.2. Pressurizer model for TRACE
Fig. 1. Inner structure of pressurizer.
pressurizer is made up of a steel tank which contains saturated water in the lower section and saturated steam in the upper section at normal operation. It is connected to the hot leg of the loop No. 2 through a surge line. Important components in the pressurizer include sprayer, electric heaters, power-operated relief valves (PORVs), safety valves (SVs), surge line, and relief tank, as seen in Fig. 1. The sprayer, the PORVs and the SVs are equipped at the top of the tank, while electric heaters are immersed in the water. The sprayer and the electric heaters are used to control the system pressure during load transients. When the reactor power increases, the coolant volume increases correspondingly such that the coolant surges into the pressurizer. In such case, the sprayer is activated to spray water from the top of the tank to limit the pressure by condensing the steam. When the reactor power decreases, the coolant volume decreases and the coolant surge out the pressurizer. At this time, some of the water flashes to steam due to pressure drop. The electric heaters are activated to heat up the water in the tank to maintain the desired operating pressure. The sprayer is activated by the pressure-difference setpoint. In normal operating condition, a low fluid flow rate of 0.126 kg/s is sprayed into the pressurizer. When the pressure difference exceeds 172.4 kPa, the flow rate starts to increase. The flow rate increases linearly from 0.126 kg/s to 44 kg/s when the pressure difference increases from 172.4 kPa to 517.1 kPa. The electric heaters can be classified into proportional heater and backup heater. The control of the proportional heater and backup heater is based on the pressure-difference setpoints and water-level setpoints. The proportional heater adds one half of the rated heating rate to the liquid at normal operation, generates power of 376 kW at a full rate if the pressure error signal is less than −103.4 kPa, and is fully turned off if the pressure error signal is greater than +103.4 kPa. The backup heater can only be fully turned on or off, and is controlled by the pressure error signal together
The pressurizer model was built by the SNAP client, and then converted to the input decks for the TRACE code. TRACE includes several hydraulic components: PIPEs, PLENUMs, PRIZERs (pressurizers), CHANs (BWR fuel channels), PUMPs, JETPs (jet pumps), SEPDs (separators), TEEs, TURBs (turbines), HEATRs (feedwater heaters), CONTANs (containment), VALVEs, and VESSELs. Powered and heated components are POWER, FLPOWER (fluid power), HTSTR (heat structure). RADENC (radiation enclosures) component simulates radiation heat transfer between surfaces. FILL and BREAK components supply the coolant-flow and pressure boundary conditions. In this study, the PIPE component is used to model the feature of the pressurizer. The FILL component models the phenomena of insurge and outsurge at the surge nozzle, the spray mechanism through the spray nozzle, and the pressure relief by letting steam exit through the power-operated relief valves (PORVs) and safety valves (SVs). The HTSTR component is added at the bottom of the pressurizer to model the heaters. To fulfill the control procedures of the open position of the spray valve, the opening and closing of PORVs and SVs, the proportional heater and backup heater, the control systems in TRACE (including trips, signal variables, control blocks, and component action tables) are properly combined for the TRACE code to follow. The fill table of the FILL component is edited to simulate the flow insurge and outsurge as the boundary condition of the pressurizer model. Therefore, the mass flow rates relative to time must be initially given. However, flow meters were not installed along the surge line to measure the flow rates during the tests conducted in 1985. We managed to adjust the mass flow rates at the surge nozzle by matching the calculated water level inside the pressurizer with those from the test data. Therefore, trial and error is applied to search out the proper inputs of the mass flow rates. All of the plant tests collected in this study have their records of the
Table 1 Main parameters of the pressurizer. Parameter Dimension Flow length (m) Flow area (m2 ) Volume (m3 ) Hydraulic diameter (m)
11.74 3.58 39.64 2.13
Nominal condition Water level (%) Operating pressure (MPa) Operating temperature (K)
56.5 15.4 617
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variations in water level. Consequently, the time-varying mass flow rates input to the fill table for each test are successfully obtained. After constructing the geometric model of the pressurizer, the boundary conditions, such as the insurge and outsurge flow rates, the insurge and outsurge flow temperatures, and the outlet pressures of the SVs and PORVs, and given. Then, each test retrieves its fluid initial conditions in the pressurizer body by using the steadystate calculation function in TRACE. 4. Results and discussion Four start-up tests of the Maanshan nuclear power plant, (1) turbine trip test from 100% power (Test PAT-50), (2) large-load reduction at 100% power (Test PAT-49), (3) net-load trip at 100% power (Test PAT-51) and 4) net-load trip at 50% power (Test PAT21), were collected for the verification purpose. In the following, the test procedures and the test criteria are firstly described (TPC, 1985), and then the pressurizer transients simulated by the TRACE code version 5.0 are shown. (1) turbine trip test from 100% power The turbine trip test was initiated by manually tripping the turbine while the plant was operating at full power (2785 MW). As a result, the reactor was directly tripped with control rods in full-in position. The decrease in the reactor coolant temperature led a large flow outsurge of the pressurizer. The test must meet the following criteria: (a) (b) (c) (d)
No pressurizer safety valves should open. No steam generator safety valves should open. Safety injection system should not be started. The response time of RTD (residence time distribution) should not be greater than the test value (6 s). (e) Neutron flux should be reduced to be less than 15% rated within 2 s after the turbine trip. (f) All the control rods should be inserted. (2) large-load reduction at 100% power The large-load reduction test was initiated by reducing the steam flow passing through the turbine from 100 to 50% of the rated capacity. This test must prove that the rod control system and the steam dump system can be automatically initialized, and the reactor power can be reduced from 100 to 50% corresponding to the reduction in steam flow. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. (3) net-load trip at 100% power
Fig. 2. Water level during the 100% turbine trip test.
The 100% net-load trip test was initiated by manually rejecting load while the plant was operating at full power (2785 MW). All the control systems were in auto mode. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. (4) net-load trip at 50% power The 50% net-load trip test was initiated by manually rejecting load while the plant was operating at 50% power. All the control systems were in auto mode. This test must meet the following criteria: (a) No reactor trip or turbine trip. (b) Safety injection system should not be started. (c) Pressurizer safety valves and steam generator safety valves should not open. (d) The system should reach a stable status without human interposition during the test. To simulate these transients, the initial conditions and the boundary conditions must be input. Table 2 lists the specified initial conditions of each test. The boundary conditions are obtained from the trial and error procedure as described above. For the turbine trip test from 100% power, the solid line in Fig. 2 shows the water levels during the 100% turbine trip test. The circle points in Fig. 2 represent the resultant water level when the mass flow rates at FILL component are well adjusted. Fig. 3 plots the calculated pressurizer pressure histories together with the measured
Table 2 Initial conditions of the four start-up tests.
Case 1 Case 2 Case 3 Case 4 a b
Thermal power (MWth)
RCS cold leg temp. (K)
RCSa hot leg temp. (K)
PZRb pressure (MPa)
PZR level (%)
2752.5 2802.7 2802.7 1397.7
565.9 565.8 565.2 565
599.5 599.8 599.3 582.8
15.3 15.4 15.4 15.4
56.5 57 56.6 40.5
RCS = reactor coolant system PZR = pressurizer
Y.-H. Cheng et al. / Nuclear Engineering and Design 239 (2009) 2343–2348
Fig. 3. Comparisons between the measured and calculated pressurizer pressure histories during the 100% turbine trip test.
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Fig. 5. Comparisons between the measured and calculated pressurizer pressure histories during the 100% large-load reduction test.
Fig. 4. Water level during the 100% large-load reduction test. Fig. 6. Water level during the 100% net-load trip test.
pressure histories. This figure reveals that the pressure histories in the pressurizer predicted by the TRACE code are in agreement with the test data. In this test, only the backup heater is activated due to the depressurization in the pressurizer system. For the large-load reduction at 100% power, the flow rates input in the FILL component result in that the calculated water levels meet the measured water levels, as shown in Fig. 4 Fig. 4. Comparisons between the measured and calculated pressurizer pressure during the transient is shown in Fig. 5. It can be seen that the calculated pressure histories follow the test data, caused by a combination of insurge, outsurge, spray actuation, and electric heater action. However, discrepancies between the calculated and the measured pressure histories are observed. In this simulation, the pressure response is over-reactive when the pressure is increasing. Fig. 6 shows that the calculated water levels meet the measured water levels in the net-load trip at 100% power transient. The calculated and the measured pressurizer pressures during the transient are plotted in Fig. 7. As revealed from this figure, the calculated pressure histories follow the trend of the test data, caused by a combination of insurge, outsurge, spray actuation, opening of PORVs and electric heater action. The calculated pressure in this net-load trip at 100% power test reaches the sprayer setpoint +172.4 kPa at 175 s and the PORVs setpoint +689.5 kPa at 183 s. Therefore, the sprayer starts to spray cool liquid into the pressurizer to suppress
Fig. 7. Comparisons between the measured and calculated pressurizer pressure histories during the 100% net-load trip test.
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is, respectively, with 40, 20 and 10 meshes in its axial orientation. From Figs. 3, 5, 7 and 9, we can see that the numerical solutions are not very sensitive to the number of mesh cells. Therefore, the coarser meshes provide the transient prediction as reliable as the finer meshes in these simulation cases. The errors between the prediction and the measurement are evaluated by the standard deviation sampled from the data points of 40, 20 and 10 mesh cells. The error measurement show that the transient prediction by the pressurizer model built in this study has the worst standard deviation of 3% occurring in the net-load trip at 100% power test. 5. Conclusions
Fig. 8. Water level during the 50% net-load trip test.
This study develops a pressurizer model for the Maanshan nuclear power plant, and assesses the pressure behavior in the pressurizer system using the TRACE code version 5.0. The pressurizer model is constructed of the inherent hydraulic components in TRACE, including the PIPE, the FILL, and the HTSTR components. Furthermore, the control systems in TRACE, including trips, signal variables, control blocks, and component action tables, are used to control the opening and closing of PORVs and SVs, the open position of the spray valve, the proportional heater and backup heater. For benchmark calculations, four start-up tests: (1) turbine trip test from 100% power, (2) large-load reduction at 100% power, (3) netload trip at 100% power and (4) net-load trip at 50% power, are collected and simulated. The time-dependent surge flow rates at the surge nozzle are given as the boundary conditions. The fluid initial conditions are obtained by using the steady-state calculation function in TRACE. The predicted pressure transients are compared with the test data, and the results show that the comparisons are in reasonable agreement. This study benchmarks the pressurizer model for TRACE code’s calculation, and fulfills the component level verification of our native PWR. References
Fig. 9. Comparisons between the measured and calculated pressurizer pressure histories during the 50% net-load trip test.
the pressure at 175 s. However, the pressure in the pressurizer is not suppressed instantly due to the continuous hot water surging. Consequently, the PORVs open at 183 s to release the steam such that the pressure in the pressurizer is successfully suppressed. Regarding the net-load trip at 50% power test, Fig. 8 also shows that the calculated water levels meet the measured water levels. The calculated and the measured pressurizer pressures during the transient are plotted in Fig. 9. The calculated pressure histories follow the test data, caused by a combination of insurge, outsurge, spray actuation, and electric heater action. The calculated pressure in this net-load trip at 50% power test reaches the sprayer setpoint +172.4 kPa at 165 s. Therefore, the sprayer is activated, and then the pressure is successfully suppressed. However, discrepancies between the calculated and the measured pressure histories are also observed. The sensitivity of the mesh cells is also observed. In these simulation cases, the pressurizer body (modeled by the PIPE component)
Abdallah, A.M., Maria, A.H., Rabie, M.A., Nagy, M.E.S., 1982. Pressurizer transients dynamic model. Nuclear Engineering and Design 73 (3), 447–453. Bake, S.M., No, H.C., Park, I.N., 1986. A non-equilibrium three-region model for transient analysis of pressurized water reactor pressurizer. Nuclear Technology, 74. Kim, S., 1984. An experimental and analytical model of a PWR pressurizer during transients. Doctor of Philosophy Thesis. Massachusetts Institute of Technology, Department of Nuclear Engineering. Kim, S.-N., Griffith, P., 1987. PWR pressurizer modeling. Nuclear Engineering and Design 102 (2), 199–209. Kim, T.-W., Kim, J-.W., Park, G.-C., 2006. Development of nonequilibrium pressurizer model with noncondensible gas. Nuclear Engineering and Design 236, 375– 384. Peterson, A.C., 1984. TRAC-PF1/MOD1 Independent Assessment: NEPTUNUS Pressurizer Test Y05. Sandia National Laboratories, Albuquerque, New Mexico, USA, NUREG/CR.3919. p. 49. Prelewicz, D., Mortensen, G.A., Barber, D., Bolander, M., Fletcher, D., Caraher, D., Wang, W, 2005. RELAP5 Status Report. Spring 2005 CAMP Meeting. Dubrovnik, Croatia, May 2–4, 2005. Riikonen, V., 1998. ATWS Experiments with PACTEL: Pressurizer Experiments Lappeenrantam. VTT Energy TEKOJA 1/98. Taiwan Power Company (TPC), 1985. Maanshan Start-Up Test Report. U. S. Nuclear Regulatory Commission (USNRC), 2007. TRACE V5.0 User Manual. Wang, J.-R., Lin, H.-Z., Cheng, Y.-H., Wang, W.-C., Shih, C., 2009. TRACE modeling and its verification using Maanshan PWR start-up tests. Annals of Nuclear Energy 36 (4), 527–536. Weaver, W., 2004. Improvements to the pressurizer component. In: International Relap Users Group Meeting, Sun Valley, Idaho, USA, August 25–27.