- Email: [email protected]
PARCS code
annals of
NUCLEAR ENERGY Annals of Nuclear Energy 33 (2006) 646–652 www.elsevier.com/locate/anucene
Technical note
Analysis of the Peach Bottom flow stability test number 3 using the coupled RELAP5/PARCS code Anis Bousbia Salah *, Francesco D’Auria Dipartimento di Ingegneria Meccanica, Nucleari e della Produzione, Facolta` di Ingegneria, Universita` di Pisa. Via Diotisalvi 2, 56126 Pisa, Italy Received 30 January 2006; accepted 25 February 2006 Available online 17 April 2006
Abstract Nowadays, the coupled codes technique, which consists in incorporating three-dimensional (3D) neutron modeling of the reactor core into system codes, is extensively used for carrying out best estimate (BE) simulation of complex transient in nuclear power plants (NPP). This technique is particularly suitable for transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermal-hydraulics. Such complex interactions are encountered under normal and abnormal operating conditions of a boiling water reactors (BWR). In such reactors Oscillations may take place owing to the dynamic behavior of the liquidsteam mixture used for removing the thermal power. Therefore, it is necessary to be able to detect in a reliable way these oscillations. The purpose of this work is to characterize one aspect of these unstable behaviors using the coupled codes technique. The evaluation is performed against Peach Bottom-2 low-flow stability tests number 3 using the coupled RELAP5/PARCS code. In this transient dynamically complex neutron kinetics coupling with thermal-hydraulics events take place in response to a core pressure perturbation. The calculated coupled code results are herein assessed and compared against the available experimental data. Ó 2006 Elsevier Ltd. All rights reserved.
1. Introduction Instability events had been observed in several BWR NPPs during normal or abnormal operations (D’Auria, 2004). The oscillations may be originated by different reasons ranging from delays between pressure and density waves propagation velocities, to change in the flow regime, to the interaction between conduction and convection heat transfer, to the relationship between thermal-hydraulic and neutronic parameters, and to the presence of different parallel channels and loops in parallel or in series to the boiling channel. Generally two kinds of power oscillations have been observed in BWR cores. One is an in-phase (core-wide) and the other is an out-of-phase (regional) oscillation.
*
Corresponding author. Tel.: +39 050 2210354; fax: +39 050 2210384. E-mail addresses: [email protected] (A. Bousbia Salah), dauria@ docenti.ing.unipi.it (F. D’Auria). 0306-4549/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2006.02.012
The BWR instability is a complex phenomenon, which depends on the state of the thermal hydraulic behavior of the system, and on the neutronic feedback effects due to the void, fuel temperature and fuel time constants (Bousbia Salah, 2004). The current trend of increasing reactor powers and of applying natural circulation core cooling has major consequences for the stability of new BWR designs. These modifications have allowed BWRs to work at high nominal power, but they have also favored an increase in the reactivity feedback and a decrease in the response time, resulting in a lower stability margin when the reactor is operated at low mass flow and high nominal power (Ha¨nggi, 2001). Also, the increase in core size has led to a weaker spatial coupling of neutronic processes, which result in a stronger susceptibility to out-of-phase oscillations. Several incidents of coupled neutronic-thermohydraulic instabilities in operating BWRs occurred in the past as the ones observed in the LaSalle-2 and Caorso plants (D’Auria, 1997). Then many investigators have attempted
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652
to model and understand the instabilities occurring in BWRs both time domain and frequency analysis codes: Time domain codes, which include analysis tools specifically developed to simulate the transient behavior of plant systems; these codes have the capability to deal with the non-linear features of BWRs and are based in simulation techniques. Frequency domain codes, their purpose is the linear stability analysis of BWRs or other boiling systems. In the frequency domain, perturbing and Laplace transforming the neutron kinetics equations allow to easily include the fission power dynamics into the linear model for BWR stability. The coupled codes method is herein considered since it is particularly suited for simulating transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermalhydraulics (Bousbia Salah, 2004). However, only few applications of the coupled code technique to the BWR stability issues have been published in the open literature as the work of D’Auria et al. (2005), Hotta et al. (2001, 2003) and Miro´ et al. (2002). For the current framework, the coupled codes RELAP5/PARCS is considered. The validation of the technique has been performed against Peach Bottom-2 lowflow stability test PT3 (Carmichael and Niemi, 1978). This point is close to the stability boundary in the Power/Mass Flow map, and, besides, its axial power profile is not bottom peaked.
647
used in design and safety analysis, providing a one-to-one comparison to design calculations. Four test conditions for the low-stability tests were planned to be as close as possible to one of the following reactor operating conditions (Carmichael and Niemi, 1978): points along the rated power-flow control line (PT1 and PT2); points along the natural circulation power-flow control line (PT2, PT3, and PT4); extrapolated rod-block natural circulation power (test point PT3). The planned test conditions are shown in Fig. 1. The main objective of these tests is to provide a data base for the qualification of transient design methods used for reactor analysis at operating conditions. Three-dimensional time domains of the BWR stability analysis were performed for the core wide oscillation mode. In these transients dynamically complex events take place, and an in-phase oscillation has been developed. The tests were performed in the right boundary of the instability region of the
2. Peach bottom-2 low-flow stability tests It has been performed three turbine trip tests and four series of low-flow stability tests at Peach Bottom Unit 2 BWR during the first quarter of 1977 at the end of cycle 2. For both types of tests, the dynamic measurements were taken with a high speed digital data acquisition system capable of sampling over 150 signals every 6 ms and the core distribution measurements were taken from the plants local in-core flux detectors. The low-flow stability tests were intended to measure the reactor core stability margins at the limiting conditions
Fig. 2. Peach Bottom-2 low-flow stability tests (Carmichael and Niemi, 1978).
Fig. 1. Peach Bottom-2 EOC 2 test planned test operational time line.
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Table 1 Peach Bottom-2 low-flow stability test conditions Tests
Power (%)
Core mass flow rate (%)
Core inlet enthalpy (kJ/kg)
PT1 PT2 PT3 PT4
60.6 51.7 59.2 43.5
51.3 42.0 38.0 38.0
1183.93 1174.63 1228.13 1179.74
Power/Flow map as shown in Fig. 2. The reactor operating conditions at which the tests have been conducted are listed in Table 1. The stability test points PTl, PT2, and PT3 were carried out in decreasing stability order so that data from each test could be evaluated prior to continuing to the next test condition. In the current framework we focus our attention on the third experiment, i.e., PT3. The initial positions of the different movable control rods prior to this test are shown in Fig. 3. It should be noted that during the test, the resulting power rise was not enough high to activate the safety systems. 3. Calculation models To perform a numerical simulation of the considered experimental test the coupled RELAP5 Mod3.3/PARCSV2.5 code was used. The codes are run separately through the parallel virtual machine (PVM) processing way. In this scheme, practically, no modifications of the codes programs are carried out. PARCS (Joo et al., 1998) utilizes the thermal-hydraulics solution data for the moderator temperatures/densities and fuel temperatures calculated by RELAP5 to incorporate appropriate feedback effects into the cross sections. Likewise, RELAP5 takes the space-dependent power calculated in PARCS and
solves the heat conduction in the core heat structures, and the hydrodynamic conservation equations. The temporal coupling is explicit in nature, and the two codes are locked into the same time step. The information exchanged between the two codes is carried out through the MAPTAB file. In this file, association between the hydraulic and heat structure nodes of the RELAP5 to their corresponding nodes in the PARCS is defined. 3.1. Neutron modeling The PARCS code is used to evaluate in a three-dimensional space–time distribution the core power flux. For this purpose it uses a non-linear nodal method to resolve two energy group diffusion equations. In this framework, 18 fuel assembly types and one reflector element are considered. They are axially subdivided into 26 axial nodes. Therefore, the kinetic behavior of the core is then governed by divided into 435 compositions. Each composition is defined by material properties and burn up (exposure, spectral history control rod history, and delayed neutron parameters). This includes the macroscopic cross section for scattering, absorption, fission, assembly discontinuity factors, xenon absorption, and detector cross sections. In addition, six groups of effective delayed neutron and their relative decay constant are considered. All these data are provided into homogenized cross section library organized in a lookup based upon six fuel temperatures and six coolant densities. A bilinear interpolation scheme is used for intermediate values of (Tf, qm) as well as for the effective rodded fraction. In the current framework the cross section were derived from the (Solis et al., 2001) relative to the Peach Bottom Turbine Trip 2 (TT2) Benchmark, assuming that the state of the reactor in the low-flow stability tests did not changed significantly since, as reported in Fig. 1, only 10 days separate the two cycles of tests. 3.2. Thermal-hydraulic modeling
Fig. 3. PT3-Initial position of control rods pattern (blank: full withdrawn, 48: full insertion).
In order to simulate the PB-PT3 test, a nodalization of the Peach Bottom vessel components, coolant and steam loop was used for the system code RELAP5/Mod3.3. The nodalization was assessed and validated in former works by Bousbia Salah et al. (2004). The sketch of the adopted flow diagram is shown in Fig. 4. In this model, the four steam lines are lumped in two components, and each pump of the recirculation loop drives one jet pump (equivalent to the ten real ones). The core region, as shown in Fig. 5 is divided into 77 heated channels with 24 axial active meshes. These channels are chosen according to their thermal-hydraulic properties and repartition into the core Bousbia Salah et al. (2004). For the current framework only one channel is adopted to represent the whole core coolant bypass. The core region is modeled according to
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652
649
Fig. 4. Nodalization scheme of the Peach Bottom.
the RELAP5 code requirements; no more than nine branches for a single volume. Hence for each branch, channels with common characteristics were put together. These characteristics are principally the lattice type, channel power, and channel inlet flow area. 4. Coupled code simulation Therefore, to perform adequate coupled 3D Neutron Kinetic-Thermal-Hydraulic System Code calculations capable to get reliable results, a consolidated procedure should be used. Therefore, the following steps were followed and a detailed description for this procedure is described in Ref. Bousbia Salah (2004). 1. The RELAP5 code was run stand-alone for 100 s in order to allow the parameter to reach stable values.
2. The RELAP5 and PARCS codes were then run coupled in a steady state until a stability convergence value for keff (effective multiplication factor) was found. 3. The RELAP5 and PARCS codes were run coupled for a null transient to make it sure that the stable conditions exist. 4. The RELAP5 and PARCS were run in coupled PVM environment to perform the transient calculation.
4.1. Steady state coupled calculation The steady state coupled calculations with RELAP5/ PARCS were performed for the PT3 test case. Some tentative to perform the steady state calculations for the remaining tests but no convergence was reached. Reasons for calculation failure in getting stable steady state trend for
650
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652 1.6
1.4
Relative Power
1.2
1
0.8
0.6
0.4
Experimental Calculated
0.2 0
5
10
15
20
25
Axial Node
Fig. 6. Steady state mean power axial distribution.
Fig. 5. Core mapping distribution with 77 heated channel.
low-flow stability tests (PT1, PT2, and PT4) could be due to uncertainties related to the experimental measurements or to the limiting hypothesis used for the current simulation. In fact, in one hand we did not take into account the Xenon and Samarium effects, which is certainly different from the TT2 state. In the other hand, the feedback could not be so accurate since they are estimated through the cross sections lookup table, which considers only two independent thermal-hydraulic parameters (Tf, qm). A more accurate solution could be obtained when the void fraction is added as the third variable of the lookup table dimensions (Bousbia Salah, 2004). Results for the steady state conditions of PT3 are outlined against experimental data in Table 2, while Fig. 6 shows the steady state mean axial power distribution in comparison with the measured one. Good agreement is observed between the two trends. In Fig. 7, a two-dimensional (2D) core flux distribution is sketched. As can be verified in this map, there is a spatial flux asymmetry in the core. Indeed a good prediction of the 3D power distribution is imperative for the subsequent thermal-hydraulic-kinetic analysis of the core dynamics.
Table 2 Steady state reactor parameters Parameter
Measured
Calculated
Core thermal power (Mwt) Reactor flow (kg/s) Core inlet temperature (K) Core inlet enthalpy (kJ/kg) Pressure at core outlet (MPa)
1948.0 4907.7 544.1 1229.058 6.929231
1949.0 4918.8 542.1 1179.400 6.7215
Fig. 7. Steady state 2D flux core distribution.
4.2. Transient calculation The assessment of the coupled code calculations has been made considering one boundary condition perturbation case. The reactor is disturbed, as shown in Fig. 8, with two peaks pressure of 0.055 MPa. This magnitude of pressure gave a good signal-to-noise ratio in the neutron flux response and did not cause operational difficulties during the testing. The analyses were carried out and the results are presented next. Fig. 9 shows the pressure perturbation downstream in the turbine stop valve (TSV) zone. After the perturbation, the pressure oscillation decreases rapidly and, in few seconds, turns to the initial value. However,
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652
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It was observed that the reactor behavior can be identified as in-phase, because when the time dependent amplitudes of the several modes were calculated with the modal method (Maggini, 2004), it has been observed that the amplitude of the fundamental mode is the largest one while the other ones are almost negligible. In addition, the simulated evolution of the signals provided by the different LPRMs during the transients is always practically the same. 5. Conclusion Fig. 8. Two peaks pressure perturbation.
7.01
Pressure (MPa)
7.00
6.99
6.98
6.97
6.96 45
50
55
60
65
70
Time (s)
Fig. 9. Calculated pressure perturbation in the TSV zone.
the pressure perturbation will propagate through the steam lines at sonic velocity and reaches the core zone from the steam separator and from the downcomer. Consequently, as reported in Fig. 10, the core power experiences the same trend due mainly to its inherent void feedback reactivity. Some in-phase instability characteristics could be recognized for instance, frequencies in all the oscillations obtained in the analyses varied from 0.3 to 0.5 Hz, i.e., in the typical frequency range of this kind of instability events.
2.60
Power (GW)
2.40 2.20 2.00 1.80 1.60 1.40 45
50
55
60
Time (s)
Fig. 10. Total reactor core power.
65
70
In order to investigate and validate the coupled code technique in simulating the stability issues in BWR NPP, the RELAP5/PARCS code has been used for predicting the Peach Bottom-2 low-flow stability test number 3. Results for the steady state conditions of PT3 are show good agreement between the calculated and measured trends. For the transient, the calculations predict a complete damping of the steam lines pressure oscillations which is in conformity with the experimental observation. The same behavior was observed for the core power response, which exhibits damped in-phase oscillations ranging between 0.3 and 0.5 Hz. A more accurate solution could be obtained by considering the void fraction as a third variable in the cross sections lookup table. However, notwithstanding the mentioned limitations, it is possible to state that the present analysis, based upon the use of coupled code technique, allows to get realistic and meaningful information about the core power behavior at the stability boundaries that could be taken into account for the safety issues of a BWR reactor. References Bousbia-Salah, A., 2004. Overview of coupled system thermal-hydraulic 3D neutron kinetic code applications, PhD Thesis, Ref: 17033, Pisa University, Italy. Bousbia Salah, A., D’Auria, F., Bambara, M., 2004. Sensitivity analysis of the Peach Bottom turbine trip 2 experiment. Kerntechnik 69 (1–8), 2004. Carmichael, L.A., Niemi, R.O., 1978. Transient and stability tests at peach bottom atomic power station Unit 2 at end of cycle 2, EPRI Report NP-564. D’Auria, F. (Editor), 1997. The State of the Art Report on Boiling Water Reactor Stability. NEA/CSNI/R(96)21. D’Auria, F. (Project Coordinator), 2004. Neutronics/thermal-hydraulics coupling in LWR technology, vol. 2, CRISSUE-S WP2: State-of-theArt Report, OECD/NEAN. 5436. D’Auria, F., Lombardi Costa, A., Bousbia Salah, A., 2005. The boiling water reactor stability. Annex-10 of the IAEA-TECDOC-1474 on Natural Circulation in Water-cooled Nuclear Power Plants Phenomena, Models, and Methodology for System Reliability Assessments, pp. 281–320. Ha¨nggi, P., 2001. Investigating BWR stability with a new linear frequencydomain method and detailed 3D neutronics, PhD Thesis, Swiss Federal Institute of Technology, ETH. Hotta, A., Honma, M., Ninokata, H., Matsui, Y., 2001. BWR regional ´ E-I: application to densityinstability analysis by TRAC/BF1-ENTRE wave oscillation. Nuclear Technology 135, 1–16. Hotta, A., Anegawa, T., Hara, T., Ninokata, H., 2003. Simulation of boiling water reactor. Nuclear Technology one-pump trip transient by ´ E 142, 205–229. TRAC/BF1-ENTRE
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Joo, H.G., Barber, D., Jiang, G., Downar, T.J., 1998. PARCS, A MultiDimensional Two Group Reactor Kinetics Code Based on the Nonlinear Analytic Nodal Method, PU/NE-98-26. Maggini, F., 2004. Contributions to study instability in BWR: application to Peach Bottom-2 NPP. Laurea thesis etd-183309, University of Pisa.
Miro´, R., Ginestar, D., Verdu´, G., Hennig, D., 2002. A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis. Annals of Nuclear Energy 29, 1171–1194. Solis, J., Ivanov, K., Sarikaya, B., Olson, A., Hunt, K.W., 2001. Boiling Water Reactor Turbine Trip (TT) Benchmark, vol. 1. Final Specifications. NEA/NSC/DOC.
NUCLEAR ENERGY Annals of Nuclear Energy 33 (2006) 646–652 www.elsevier.com/locate/anucene
Technical note
Analysis of the Peach Bottom flow stability test number 3 using the coupled RELAP5/PARCS code Anis Bousbia Salah *, Francesco D’Auria Dipartimento di Ingegneria Meccanica, Nucleari e della Produzione, Facolta` di Ingegneria, Universita` di Pisa. Via Diotisalvi 2, 56126 Pisa, Italy Received 30 January 2006; accepted 25 February 2006 Available online 17 April 2006
Abstract Nowadays, the coupled codes technique, which consists in incorporating three-dimensional (3D) neutron modeling of the reactor core into system codes, is extensively used for carrying out best estimate (BE) simulation of complex transient in nuclear power plants (NPP). This technique is particularly suitable for transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermal-hydraulics. Such complex interactions are encountered under normal and abnormal operating conditions of a boiling water reactors (BWR). In such reactors Oscillations may take place owing to the dynamic behavior of the liquidsteam mixture used for removing the thermal power. Therefore, it is necessary to be able to detect in a reliable way these oscillations. The purpose of this work is to characterize one aspect of these unstable behaviors using the coupled codes technique. The evaluation is performed against Peach Bottom-2 low-flow stability tests number 3 using the coupled RELAP5/PARCS code. In this transient dynamically complex neutron kinetics coupling with thermal-hydraulics events take place in response to a core pressure perturbation. The calculated coupled code results are herein assessed and compared against the available experimental data. Ó 2006 Elsevier Ltd. All rights reserved.
1. Introduction Instability events had been observed in several BWR NPPs during normal or abnormal operations (D’Auria, 2004). The oscillations may be originated by different reasons ranging from delays between pressure and density waves propagation velocities, to change in the flow regime, to the interaction between conduction and convection heat transfer, to the relationship between thermal-hydraulic and neutronic parameters, and to the presence of different parallel channels and loops in parallel or in series to the boiling channel. Generally two kinds of power oscillations have been observed in BWR cores. One is an in-phase (core-wide) and the other is an out-of-phase (regional) oscillation.
*
Corresponding author. Tel.: +39 050 2210354; fax: +39 050 2210384. E-mail addresses: [email protected] (A. Bousbia Salah), dauria@ docenti.ing.unipi.it (F. D’Auria). 0306-4549/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2006.02.012
The BWR instability is a complex phenomenon, which depends on the state of the thermal hydraulic behavior of the system, and on the neutronic feedback effects due to the void, fuel temperature and fuel time constants (Bousbia Salah, 2004). The current trend of increasing reactor powers and of applying natural circulation core cooling has major consequences for the stability of new BWR designs. These modifications have allowed BWRs to work at high nominal power, but they have also favored an increase in the reactivity feedback and a decrease in the response time, resulting in a lower stability margin when the reactor is operated at low mass flow and high nominal power (Ha¨nggi, 2001). Also, the increase in core size has led to a weaker spatial coupling of neutronic processes, which result in a stronger susceptibility to out-of-phase oscillations. Several incidents of coupled neutronic-thermohydraulic instabilities in operating BWRs occurred in the past as the ones observed in the LaSalle-2 and Caorso plants (D’Auria, 1997). Then many investigators have attempted
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652
to model and understand the instabilities occurring in BWRs both time domain and frequency analysis codes: Time domain codes, which include analysis tools specifically developed to simulate the transient behavior of plant systems; these codes have the capability to deal with the non-linear features of BWRs and are based in simulation techniques. Frequency domain codes, their purpose is the linear stability analysis of BWRs or other boiling systems. In the frequency domain, perturbing and Laplace transforming the neutron kinetics equations allow to easily include the fission power dynamics into the linear model for BWR stability. The coupled codes method is herein considered since it is particularly suited for simulating transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermalhydraulics (Bousbia Salah, 2004). However, only few applications of the coupled code technique to the BWR stability issues have been published in the open literature as the work of D’Auria et al. (2005), Hotta et al. (2001, 2003) and Miro´ et al. (2002). For the current framework, the coupled codes RELAP5/PARCS is considered. The validation of the technique has been performed against Peach Bottom-2 lowflow stability test PT3 (Carmichael and Niemi, 1978). This point is close to the stability boundary in the Power/Mass Flow map, and, besides, its axial power profile is not bottom peaked.
647
used in design and safety analysis, providing a one-to-one comparison to design calculations. Four test conditions for the low-stability tests were planned to be as close as possible to one of the following reactor operating conditions (Carmichael and Niemi, 1978): points along the rated power-flow control line (PT1 and PT2); points along the natural circulation power-flow control line (PT2, PT3, and PT4); extrapolated rod-block natural circulation power (test point PT3). The planned test conditions are shown in Fig. 1. The main objective of these tests is to provide a data base for the qualification of transient design methods used for reactor analysis at operating conditions. Three-dimensional time domains of the BWR stability analysis were performed for the core wide oscillation mode. In these transients dynamically complex events take place, and an in-phase oscillation has been developed. The tests were performed in the right boundary of the instability region of the
2. Peach bottom-2 low-flow stability tests It has been performed three turbine trip tests and four series of low-flow stability tests at Peach Bottom Unit 2 BWR during the first quarter of 1977 at the end of cycle 2. For both types of tests, the dynamic measurements were taken with a high speed digital data acquisition system capable of sampling over 150 signals every 6 ms and the core distribution measurements were taken from the plants local in-core flux detectors. The low-flow stability tests were intended to measure the reactor core stability margins at the limiting conditions
Fig. 2. Peach Bottom-2 low-flow stability tests (Carmichael and Niemi, 1978).
Fig. 1. Peach Bottom-2 EOC 2 test planned test operational time line.
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Table 1 Peach Bottom-2 low-flow stability test conditions Tests
Power (%)
Core mass flow rate (%)
Core inlet enthalpy (kJ/kg)
PT1 PT2 PT3 PT4
60.6 51.7 59.2 43.5
51.3 42.0 38.0 38.0
1183.93 1174.63 1228.13 1179.74
Power/Flow map as shown in Fig. 2. The reactor operating conditions at which the tests have been conducted are listed in Table 1. The stability test points PTl, PT2, and PT3 were carried out in decreasing stability order so that data from each test could be evaluated prior to continuing to the next test condition. In the current framework we focus our attention on the third experiment, i.e., PT3. The initial positions of the different movable control rods prior to this test are shown in Fig. 3. It should be noted that during the test, the resulting power rise was not enough high to activate the safety systems. 3. Calculation models To perform a numerical simulation of the considered experimental test the coupled RELAP5 Mod3.3/PARCSV2.5 code was used. The codes are run separately through the parallel virtual machine (PVM) processing way. In this scheme, practically, no modifications of the codes programs are carried out. PARCS (Joo et al., 1998) utilizes the thermal-hydraulics solution data for the moderator temperatures/densities and fuel temperatures calculated by RELAP5 to incorporate appropriate feedback effects into the cross sections. Likewise, RELAP5 takes the space-dependent power calculated in PARCS and
solves the heat conduction in the core heat structures, and the hydrodynamic conservation equations. The temporal coupling is explicit in nature, and the two codes are locked into the same time step. The information exchanged between the two codes is carried out through the MAPTAB file. In this file, association between the hydraulic and heat structure nodes of the RELAP5 to their corresponding nodes in the PARCS is defined. 3.1. Neutron modeling The PARCS code is used to evaluate in a three-dimensional space–time distribution the core power flux. For this purpose it uses a non-linear nodal method to resolve two energy group diffusion equations. In this framework, 18 fuel assembly types and one reflector element are considered. They are axially subdivided into 26 axial nodes. Therefore, the kinetic behavior of the core is then governed by divided into 435 compositions. Each composition is defined by material properties and burn up (exposure, spectral history control rod history, and delayed neutron parameters). This includes the macroscopic cross section for scattering, absorption, fission, assembly discontinuity factors, xenon absorption, and detector cross sections. In addition, six groups of effective delayed neutron and their relative decay constant are considered. All these data are provided into homogenized cross section library organized in a lookup based upon six fuel temperatures and six coolant densities. A bilinear interpolation scheme is used for intermediate values of (Tf, qm) as well as for the effective rodded fraction. In the current framework the cross section were derived from the (Solis et al., 2001) relative to the Peach Bottom Turbine Trip 2 (TT2) Benchmark, assuming that the state of the reactor in the low-flow stability tests did not changed significantly since, as reported in Fig. 1, only 10 days separate the two cycles of tests. 3.2. Thermal-hydraulic modeling
Fig. 3. PT3-Initial position of control rods pattern (blank: full withdrawn, 48: full insertion).
In order to simulate the PB-PT3 test, a nodalization of the Peach Bottom vessel components, coolant and steam loop was used for the system code RELAP5/Mod3.3. The nodalization was assessed and validated in former works by Bousbia Salah et al. (2004). The sketch of the adopted flow diagram is shown in Fig. 4. In this model, the four steam lines are lumped in two components, and each pump of the recirculation loop drives one jet pump (equivalent to the ten real ones). The core region, as shown in Fig. 5 is divided into 77 heated channels with 24 axial active meshes. These channels are chosen according to their thermal-hydraulic properties and repartition into the core Bousbia Salah et al. (2004). For the current framework only one channel is adopted to represent the whole core coolant bypass. The core region is modeled according to
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652
649
Fig. 4. Nodalization scheme of the Peach Bottom.
the RELAP5 code requirements; no more than nine branches for a single volume. Hence for each branch, channels with common characteristics were put together. These characteristics are principally the lattice type, channel power, and channel inlet flow area. 4. Coupled code simulation Therefore, to perform adequate coupled 3D Neutron Kinetic-Thermal-Hydraulic System Code calculations capable to get reliable results, a consolidated procedure should be used. Therefore, the following steps were followed and a detailed description for this procedure is described in Ref. Bousbia Salah (2004). 1. The RELAP5 code was run stand-alone for 100 s in order to allow the parameter to reach stable values.
2. The RELAP5 and PARCS codes were then run coupled in a steady state until a stability convergence value for keff (effective multiplication factor) was found. 3. The RELAP5 and PARCS codes were run coupled for a null transient to make it sure that the stable conditions exist. 4. The RELAP5 and PARCS were run in coupled PVM environment to perform the transient calculation.
4.1. Steady state coupled calculation The steady state coupled calculations with RELAP5/ PARCS were performed for the PT3 test case. Some tentative to perform the steady state calculations for the remaining tests but no convergence was reached. Reasons for calculation failure in getting stable steady state trend for
650
A. Bousbia Salah, F. D’Auria / Annals of Nuclear Energy 33 (2006) 646–652 1.6
1.4
Relative Power
1.2
1
0.8
0.6
0.4
Experimental Calculated
0.2 0
5
10
15
20
25
Axial Node
Fig. 6. Steady state mean power axial distribution.
Fig. 5. Core mapping distribution with 77 heated channel.
low-flow stability tests (PT1, PT2, and PT4) could be due to uncertainties related to the experimental measurements or to the limiting hypothesis used for the current simulation. In fact, in one hand we did not take into account the Xenon and Samarium effects, which is certainly different from the TT2 state. In the other hand, the feedback could not be so accurate since they are estimated through the cross sections lookup table, which considers only two independent thermal-hydraulic parameters (Tf, qm). A more accurate solution could be obtained when the void fraction is added as the third variable of the lookup table dimensions (Bousbia Salah, 2004). Results for the steady state conditions of PT3 are outlined against experimental data in Table 2, while Fig. 6 shows the steady state mean axial power distribution in comparison with the measured one. Good agreement is observed between the two trends. In Fig. 7, a two-dimensional (2D) core flux distribution is sketched. As can be verified in this map, there is a spatial flux asymmetry in the core. Indeed a good prediction of the 3D power distribution is imperative for the subsequent thermal-hydraulic-kinetic analysis of the core dynamics.
Table 2 Steady state reactor parameters Parameter
Measured
Calculated
Core thermal power (Mwt) Reactor flow (kg/s) Core inlet temperature (K) Core inlet enthalpy (kJ/kg) Pressure at core outlet (MPa)
1948.0 4907.7 544.1 1229.058 6.929231
1949.0 4918.8 542.1 1179.400 6.7215
Fig. 7. Steady state 2D flux core distribution.
4.2. Transient calculation The assessment of the coupled code calculations has been made considering one boundary condition perturbation case. The reactor is disturbed, as shown in Fig. 8, with two peaks pressure of 0.055 MPa. This magnitude of pressure gave a good signal-to-noise ratio in the neutron flux response and did not cause operational difficulties during the testing. The analyses were carried out and the results are presented next. Fig. 9 shows the pressure perturbation downstream in the turbine stop valve (TSV) zone. After the perturbation, the pressure oscillation decreases rapidly and, in few seconds, turns to the initial value. However,
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It was observed that the reactor behavior can be identified as in-phase, because when the time dependent amplitudes of the several modes were calculated with the modal method (Maggini, 2004), it has been observed that the amplitude of the fundamental mode is the largest one while the other ones are almost negligible. In addition, the simulated evolution of the signals provided by the different LPRMs during the transients is always practically the same. 5. Conclusion Fig. 8. Two peaks pressure perturbation.
7.01
Pressure (MPa)
7.00
6.99
6.98
6.97
6.96 45
50
55
60
65
70
Time (s)
Fig. 9. Calculated pressure perturbation in the TSV zone.
the pressure perturbation will propagate through the steam lines at sonic velocity and reaches the core zone from the steam separator and from the downcomer. Consequently, as reported in Fig. 10, the core power experiences the same trend due mainly to its inherent void feedback reactivity. Some in-phase instability characteristics could be recognized for instance, frequencies in all the oscillations obtained in the analyses varied from 0.3 to 0.5 Hz, i.e., in the typical frequency range of this kind of instability events.
2.60
Power (GW)
2.40 2.20 2.00 1.80 1.60 1.40 45
50
55
60
Time (s)
Fig. 10. Total reactor core power.
65
70
In order to investigate and validate the coupled code technique in simulating the stability issues in BWR NPP, the RELAP5/PARCS code has been used for predicting the Peach Bottom-2 low-flow stability test number 3. Results for the steady state conditions of PT3 are show good agreement between the calculated and measured trends. For the transient, the calculations predict a complete damping of the steam lines pressure oscillations which is in conformity with the experimental observation. The same behavior was observed for the core power response, which exhibits damped in-phase oscillations ranging between 0.3 and 0.5 Hz. A more accurate solution could be obtained by considering the void fraction as a third variable in the cross sections lookup table. However, notwithstanding the mentioned limitations, it is possible to state that the present analysis, based upon the use of coupled code technique, allows to get realistic and meaningful information about the core power behavior at the stability boundaries that could be taken into account for the safety issues of a BWR reactor. References Bousbia-Salah, A., 2004. Overview of coupled system thermal-hydraulic 3D neutron kinetic code applications, PhD Thesis, Ref: 17033, Pisa University, Italy. Bousbia Salah, A., D’Auria, F., Bambara, M., 2004. Sensitivity analysis of the Peach Bottom turbine trip 2 experiment. Kerntechnik 69 (1–8), 2004. Carmichael, L.A., Niemi, R.O., 1978. Transient and stability tests at peach bottom atomic power station Unit 2 at end of cycle 2, EPRI Report NP-564. D’Auria, F. (Editor), 1997. The State of the Art Report on Boiling Water Reactor Stability. NEA/CSNI/R(96)21. D’Auria, F. (Project Coordinator), 2004. Neutronics/thermal-hydraulics coupling in LWR technology, vol. 2, CRISSUE-S WP2: State-of-theArt Report, OECD/NEAN. 5436. D’Auria, F., Lombardi Costa, A., Bousbia Salah, A., 2005. The boiling water reactor stability. Annex-10 of the IAEA-TECDOC-1474 on Natural Circulation in Water-cooled Nuclear Power Plants Phenomena, Models, and Methodology for System Reliability Assessments, pp. 281–320. Ha¨nggi, P., 2001. Investigating BWR stability with a new linear frequencydomain method and detailed 3D neutronics, PhD Thesis, Swiss Federal Institute of Technology, ETH. Hotta, A., Honma, M., Ninokata, H., Matsui, Y., 2001. BWR regional ´ E-I: application to densityinstability analysis by TRAC/BF1-ENTRE wave oscillation. Nuclear Technology 135, 1–16. Hotta, A., Anegawa, T., Hara, T., Ninokata, H., 2003. Simulation of boiling water reactor. Nuclear Technology one-pump trip transient by ´ E 142, 205–229. TRAC/BF1-ENTRE
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Joo, H.G., Barber, D., Jiang, G., Downar, T.J., 1998. PARCS, A MultiDimensional Two Group Reactor Kinetics Code Based on the Nonlinear Analytic Nodal Method, PU/NE-98-26. Maggini, F., 2004. Contributions to study instability in BWR: application to Peach Bottom-2 NPP. Laurea thesis etd-183309, University of Pisa.
Miro´, R., Ginestar, D., Verdu´, G., Hennig, D., 2002. A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis. Annals of Nuclear Energy 29, 1171–1194. Solis, J., Ivanov, K., Sarikaya, B., Olson, A., Hunt, K.W., 2001. Boiling Water Reactor Turbine Trip (TT) Benchmark, vol. 1. Final Specifications. NEA/NSC/DOC.