- Email: [email protected]
MOD4.0
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Thermal-hydraulics and neutronic code coupling for RELAP/SCDAPSIM/ MOD4.0
T
Sabahattin Akbasa, Victor Martinez-Quirogab, Fatih Aydoganc, , Chris Allisonb, Abderrafi M. Ougouagd ⁎
a
Institute of Science, Gazi University, Milas No 15 Street, Teknikokullar, 06500 Ankara, Turkey Innovative Systems Software 3585 Briar Creek, Ammon, ID 83406, USA c Department of Mechanical Engineering, Jacksonville University, USA d Idaho National Laboratory, Idaho Falls, ID, USA b
ABSTRACT
The design and analysis of energy systems requires robust and reliable computer codes that produce realistic results. The governing equations and closure models must represent the physical behaviors of the energy systems. Nuclear power plants, as the quintessential example of complex energy systems, must be modeled with such high-fidelity and accurate nuclear system codes in which thermal-hydraulics, neutronics and fuel performance models must be coupled for in order to produce high-fidelity predictions. Most commonly, the interplay between the various subsystems of a nuclear power plant (nuclear fuel, fluids, neutronics, control rods, power conversion, etc.) is modeled through a combination of different codes that are externally coupled. The objective of this paper is to present work that couples the RELAP/SCDAP SIM/MOD4.0 code with the NESTLE neutronic code within the 3DKIN package, thus providing the latter with updated neutron kinetic capabilites. The version of the RELAP/SCDAPSIM/MOD4.0 code used in this work has been developed by Innovate System Software (ISS) and is the latest in the series of such code versions developed as part of the international SCDAP Development and Training Program (SDTP) for best-estimate analysis to model reactor transients including severe accident phenomena. The new feature of 3DKIN enhances the simulation of the Nuclear Power Plants (NPP) response under accidental and operational scenarios in which high reliability of neutronic feedback is needed. The RELAP/SCDAPSIM code is described and the improvements implemented in it are presented, including nodal kinetics library as well the coupling method that is applied. Finally, a BWR transient with unexpected injection of subcooled water as specified in an OECD Benchmark has been simulated in order to assess the reliability of the package and the performance of the coupling. Results are compared to those of the other OECD benchmark participants. The comparison of fuel temperature, effective multiplication factor (keff) and power distribution results display good agreement with values within the range of those of other participants.
1. Introduction The computational tools used in nuclear industry can simulate complex nuclear systems. The nuclear systems include nuclear fuel, control rods, reactor internals, fluid systems, control systems, safety systems, energy conversion components (such as turbine), pump, condensers, preliminary heat exchangers, steam-seperators, valves, pipes and other heat sources and heat sinks. To model all these systems and components, some specific codes are utilized. For instance, some of the following codes used commonly:
• reactor physics codes for modeling core neutronics, cross-section preparation and/or lattice physics codes or cross section libraries, • thermal hydraulic codes that encompass system codes, containment codes, computational fluid dynamics, sub-channel codes. All of these can simulate the thermal and hydraulic behavior of the coolant and/ or working fluid,
⁎
• fuel performance
under irradiation.
codes that simulate the nuclear fuel behavior
In the early decades of nuclear power, each of these types of codes were developed and implemented individually. However, the strong interaction between the various physical phenomena of neutronics, reactor thermal hydraulics, fuel performance, containment physics, and others, has been recognized to necessitate the coupling between these codes. Coipled codes capture the interplay between the various physics phenomena and hence model the feedback between them. Feedback effects can be observed in several transients in nuclear power plants. Some example transients include:
• Inadvertent control rod withdrawal (uneven feedback) • Control rod ejection (strong local feedback) • Start-up of a cold or a boron free loop (uneven feedback) • External asymmetrical boron dilution (uneven feedback)
Corresponding author at: Mechanical Engineering, Jacksonvile University, 2800 University Blvd N., Jacksonville, FL 32211, USA. E-mail address: [email protected] (F. Aydogan).
https://doi.org/10.1016/j.nucengdes.2019.01.009 Received 13 March 2018; Received in revised form 30 December 2018; Accepted 5 January 2019 Available online 08 February 2019 0029-5493/ © 2019 Published by Elsevier B.V.
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Acronyms ANM BE BWR FDM ISS SCDAP NEM
NGFM NPP NK PWR SS TH RS4 LWR LWRCT
Analytic Nodal Method Best Estimate Boiling Water Reactor Finite Differential Method Innovate System Software SCDAP Development and Training Program Nodal Expansion Method
• Transients with potential for inherent boron dilution (uneven feedback) • Anticipated transients without scram (uneven feedback) • Cool-down transients with re-criticality potential (steam or feed
Nodal Green’s Function Method Nuclear Power Plant Neutron Kinetics Pressure Water Reactor Steady-State Thermal-Hydraulics RELAP/SCDAPSIM/MOD4.0 Light Water Reactor LWR Core Transient
complex configurations codes that incorporate TH and 3-D NK would be required. Especially for full nuclear core applications integrated with primary and power conversion coolant cycles, detailed coupling between TH and NK codes is required for modeling strong interaction between NK and TH behaviors for steady-state and transients (design basis accidents, anticipated transient without scram and severe accidents). The following coupled codes are some of the existing codes used for the accurate and realistic evaluation of NK and TH behavior: TRACE/PARCS (Xu et al., 2006), RELAP5/PARCS (Barber et al., 1999), ATHLET/DYN3D (Kozmenkov et al., 2007) and RELAP/SCDAPSIM/ MOD4.0/PARCS and NESTLE (Martinez-Quiroga et al., 2015, 2016). The code prediction of this coupling method is also demonstrated for a Boiling Water Reactor (BWR) transient to demonstrate how developed coupling works such as, TRACE/PARCS (Gajev et al., 2014), CATHARECRONOS2-FLICA4 (Mignot et al., 2004), DYN3D/ATHLET (Grundmann et al., 2004), RELAP5/PARCS (Salah et al., 2005), TRAC-BF1/NEM/ COBRA-TF (Solis et al., 2002). This paper presents a coupling of RELAP/SCDAPSIM/MOD4.0 and NESTLE within 3DKIN package. The scenario of a BWR transient with unexpected subcooled water injection was utilized to benchmark the code predictions with the other code predictions by using a OECD benchmark. Section 2 shows a brief description of RELAP/SCDAPSIM/MOD4.0 and NESTLE in 3DKIN package. Section 3 describes the selected OECD scenario for this paper. Section 4 describes the code models and nodalization diagrams. Section 5 demontrates the results of the code for the selected OECD bencmark.
lines break-uneven feedback)
In nuclear power plants there are strong feedback effects between thermal hydraulic (TH), fuel performance (FP), and neutron kinetics (NK) and static neutronic physical behaviors that require accordingly coupled codes. The temperature distribution in nuclear fuel is calculated by the TH and neutronics codes. In turn, the temperature distribution is used by the reactor physics codes since effective neutron cross sections depend on the temperature distribution of fuel and moderator. The NK code predicts the neutron flux and power distribution, which is used by the thermal hydraulic codes. The fuel performance codes use information provided by both the TH and neutronics codes. Although there is a data exchange between all of these codes, the coupling methods between them are different from one another as the parameters that are exchanged vary and the time scales of the various phenomena are substantially different. Thus, the coupling schemes can also vary substantially: for example some codes and situations may require data exchanges only for certain specific parameters that are not exchanged between other pairs of codes and under other situations. Furhtermore, the exchanges have to occur with different frequencies (e.g., at every computational time step or not). To reduce the cost of the fully coupled codes using realistic feedback effects, some codes incorporate other code models to utilize limited feedback effects. For instance, NK codes include simple TH models and some TH codes utilize basic 1-D NK modeling capability. Even though these simple models for the representation of NK or TH does not provide realistic feedback effects, the combination of several coupled models can provide simple treatment of feedback effects on the codes. However, inasmuch as the predictions of the neutronics models depend strongly on fuel, coolant and moderator temperatures, and though for some problems NK with simple incorporated TH or TH codes with simple NK may suffice, for most realistic applications that involve
2. Coupling of thermal-hydraulic code of RELAP5/SCDAPSIM/ MOD4.0 and 3DKIN package 3DKIN is a nodal kinetics package that has been included into RELAP/SCDAPSIM/MOD4.0 (RS4) as an option for RS4 users that do not have their own 3D reactor kinetics package. 3DKIN package is based on models and correlations of NESTLE (Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator) 5.2.1, a NK code developed
Fig. 1. Diagram of 3DKIN series coupling. 175
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at North Carolina State University (North Carolina State University, 2003). Code architect has been modified and reprogrammed in FORTRAN 90/95/2000 standards to keep the implicit solution of the neutron diffusion equation as an internal library of RS4 (Fig. 1). New input cards have been included in RS/M4 for user-friendly mapping of LWRs Cartesian geometries (Hexagonal geometries are also possible to be simulated). Although it is not as powerful as the NESTLE code, it is a useful option for coupled calculations. 3DKIN package solves few-group neutron diffusion equation utilizing Nodal Expansion Method (NEM) for spatial discretization. It can simulate either eigenvalue or eigenvalue initiated transient problems, thus they can be applied for simulating operation transients at constant power (by the use of the eigenvalue simulation at each time advancement) or transient problems for an initial neutron flux distribution (eigenvalue initiated transients). Depletion is also available for operational simulations. Two or four energy groups can be utilized for solving the neutron diffusion equation. NEM is based upon quartic polynomial expansion equations and a non-linear iterative strategy (outer-inner iteration) is employed for solving the resulting matrix system. The utilized package solves either Nodal or Finite Differential Method (FDM). Quartic polynomial expansion is employed for the transverse integrated fluxes, and transverse leakage is represented by a quadratic polynomial. Furthermore, discontinuity factors are applied to correct for homogenization errors. For transient problems, diffusion equation employs a first-order difference operator and precursor equations are analytically solved assuming that fission rate behaves linearly over a time-step. In these problems, the delayed neutron precursor groups are specified by the user. As regards XS libraries, they are externally parameterized in macroscopic models that includes composition type, control rod state (in/out) and burnup (fuel depletion can be also modeled for operational simulations). In addition, all cross sections are expressed in terms of a Taylor series expansion depending on coolant density, coolant temperature, effective fuel temperature and soluble poison concentration. Finally, I-Xe and Pm-Sm chains are modeled with several options for calculating their number densities (i.e. equilibrium, transient, peak Sm- no Xe, no Sm nor Xe, or frozen), and decay groups are used to model decay heat. As regards neutron flux solution, FDM outer-inner iteration strategy is employed taking advantage of the Chebyshev polynomials for accelerating the convergence. For NEM, a non linear iterative method is also applied after a sufficient number of outer iterations are completed. Fig. 2 shows the structure of the iterative method. As it can be seen in the diagram, for achieving the convergence it is required a continuous updating of TH data after each outer iteration. Hence, it was decided to define an implicit coupling between TH and neutronics for RS4 time advancement in order to enhance the stability, accuracy and robustness of the iterative method. With this approach, if there is no convergence in the neutron flux solution, TH data are updated with the provisional estimation of the power distribution without advancing to a new time step. Once new TH values are computed, outer-inner iteration is restarted at the same level and new cycle is run. This process is iteratively repeated until convergence is achieved. After that, RS4 starts a new time advancement following the same numerical scheme. As it can be seen, the coupling is completely implicit because both neutronics and TH data solutions are computed by the use of a coupled set of equations that are function of the current and previous time step solutions estimates. In order to verify the programming and the integration of the 3DKIN package within RS4, three testing problems were carried out based on the sample XS libraries and core configurations supplied with NESTLE neutronic model (Martinez-Quiroga et al., 2016). In our previous publication (published in NUTHOS conference), we have already studied and published three cases, which are (1) Eigenvalue problem, (2) Eigenvalue initiated transient problem, and (3) Depletion problem. Cold water injection transient without screaming the reactor core is selected as the validation case in the scope of this paper.
3. Description of the selected BWR transient In order to verify the programming of neutronic as well as the proper coupled data exchange, a series of coupled calculations have been carried out with RS4-3DKIN codes. Since international LWR core transient (LWRCT) benchmarks, based on well-defined problems with a complete set of input data, are used to assess the discrepancies between three-dimensional space-time kinetics codes in transient calculations, a specific case of an OECD benchmark has been selected for this article. The chosen scenario/case is a BWR transient with unexpected injection of subcooled water (Fig. 3) without scramming the reactor (case D1 of the NEACRP LWR core transients benchmark (Finnemann and Galati, 1992; Finnemann et al., 1993)). One of the goals of this transient is to test the reactivity feedback effects of density variation and Doppler broadening in core power distribution. The selected benchmark provides results of eight national and industrial institutions that will be used to evaluate the result of RS43DKIN coupled simulations. Just as a reminder, the aim of this comparison is not to validate the accuracy of supplied sample input decks and the neutronic code but to demonstrate 3DKIN reliability and to test the performance by using a BWR nuclear power plant. In a BWR reactor vessel (Fig. 4), there are a reactor core that mainly consists of fuel assemblies and control rods in the center, equipment for generating steam for a turbine, such as a steam-water separator and a steam dryer in the upper part of the vessel, equipment for reactorpower control, such as control rod guide tubes and control rod drive housings in the lower part of the vessel, and a core shroud, jet pumps etc. that surrounds the reactor core and composes the coolant flow path in the periphery of reactor core. 4. Modelling and simulation of the nuclear power plant The selected BWR case for modelling and simulation consists of subprompt critical reactivity excursions generated by rapid cold water injection or core pressurization events. The selected case has neutronic and thermohydraulic feedback-effects. This section demonstrates two main components of modelling that will be described in this section in detail: (1) neutronic modelling based on 3DKIN module for the BWR core and (2) thermal hydraulic modelling of RELAP/SCDAPSIM/ MOD4.0 for the BWR’s TH system.
Fig. 2. Diagram of the NEM non-linear outer inner iteration method. 176
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neutron flux (a measure of the neutron population) as a consequence of the neutrons interaction with the fuel and moderator (and other materials) within the reactor core. The computed value of the flux, in turn, is used to calculate reaction rates, including the volumetric rate at which fission reactions take place and hence the power density distribution, and essential input to safety analysis modeling. The governing equations solved by NK codes are the time-dependent multi-group neutron diffusion equations and their associated delayed neutron precursor equations (Duderstadt and Hamilton, 1976; Bandini, 1990). For light water applications most NK codes use two neutron energy groups, though occasionally as many as four groups may be used. In this study, two neutron energy groups (thermal and fast neutron groups) and six delayed neutron groups are used for neutron modeling in the calculations. 3D cross-section (transport, absorption, nu-fission, kappafission, nu) values (XSs) of NEACRP LWR core are used in the selected transient benchmark (Finnemann and Galati, 1992; Finnemann et al., 1993) The 3D NK model has been prepared based on the 3D cross-sections given for the selected OECD benchmark. The cross-sectional view (based on Xand Y dimensions) of the BWR reactor is shown in Figs. 5 and 6. The full core consist of ten different fuel macroelement compositions (as shown in Fig. 5) and 19 composition types. The length of each square fuel macroelement and macrocell in the radial reflector, is 30.48 cm. Axially, the reactor is subdivided into 14 layers, each 30.48 cm high, as shown in Fig. 7. The fuel composition of each axial layer is individually defined (Fig. 7).
Fig. 3. Inlet subcooling vs. time for D1 transient (Finnemann and Galati, 1992; Finnemann et al., 1993).
4.1. Neutronics modelling In coupled NK-TH codes (or code systems), the NK part, which computes the neutron flux as a function of time (and space in most instances), uses the neutron diffusion equation as a model for the physics. Furthermore, most of coupled NK-TH codes use one of the various modern nodal methods as their neutronic solver for the multidimensional, multi-group neutron diffusion equations (Lawrence, 1986; Sutton and Aviles, 1996). These nodal methods such as Nodal Expansion Methods (NEM) (Finnemann, 1975), Analytic Nodal Method (ANM) (Smith, 1979), the Nodal Green’s Function Method (NGFM) (Lawrence 1979), and the more efficient Semi-Analytic Nodal Method (Rajic and Ougouag, 1989), have been implemented using different approaches in current NK codes. Neutron kinetics (NK), or time-dependent neutronics, deals with modeling of time evolution of the
4.2. Thermal-hydraulics model RELAP/SCDAPSIM/MOD4.0 is a Best Estimate (BE) code designed
Fig. 4. Typical BWR reactor system (Roth and Aydogan, 2015). 177
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Fig. 5. BWR initial map.
Fig. 7. BWR macroelement type 1.
MOD3.2 models, developed by the US Nuclear Regulatory Commission, in combination with advanced numerics, advanced programming, techniques and SDTP member-developed models and user options (more detailed information can be found in reference (Pérez et al., 2015)). In particular, RELAP/SCDAPSIM/MOD4.0, the latest in the series of the SDTP-developed versions, is the first version of RELAP or SCDAP/RELAP5 completely rewritten to FORTRAN 90/95/2000 standards. It implies that RELAP5 database is dynamically allocated, making easier and faster the coupling with other codes with the use of pointers and structures. The input model (Fig. 8) of RELAP/SCDAPSIM/ MOD4.0 to simulate the TH behaviour of the the core and the BWR system has been prepared based on the selected OECD benchmark. The channels (from 1 to 4) shown on the right side of Fig. 8 are the representative channels for the channels of Fig. 6. The core has been simulated with 4 concentric channels linked to 4 different active fuel heat structures, and a bypass. It has also been included for simulating the peripheral region. As regards -3DKIN and RELAP/SCDAPSIM model, main features of the supplied decks are given in Table 1. Fig. 6. BWR core map.
5. Results
to run a wide range of conditions from normal operating conditions up through severe accidents (Allison and Hohorst, 2010). RELAP/SCDAPSIM uses the publicly available RELAP5/MOD3.3 and SCDAP/RELAP5/
NK and TH modelling and the developed coupling codes have been demonstrate in the previous sections of the paper. In this section, the results will be demonstrated for the selected OECD Benchmark. Even 178
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Fig. 8. RS4 nodalization.
though the selected OECD benchmark does not demonsrate all the results of TH and NK parameters, the benchmark of OECD participants were given based on selected parameters of NK and TH. Firstly, the keff results of the developed coupled code is benchmarked with the OECD participants for the steady state BWR core results in Table 2. The keff
change from 0.952429 to 0.99999. For the steady state calculation, the axial and radial power distributions are compared with the results given in the OECD benchmark (Figs. 9 and 10). The cross-sectional modelling of NK code can be revisited to improve the top-half results of normalized axial power. Even
Table 1 Main design parameters of RS4-3DKIN for core modeling (Finnemann and Galati, 1992; Finnemann et al., 1993). Parameters
Value
Neutronic
Number of fuel rods Number of reflector elements UO2 density Zircaloy density Outer clad diameter Inner clad diameter Pellet diameter Fuel rod pitch Reference effective fuel temp. Number of composition types Fast neutron inverse velocity Thermal neutron inverse velocitv Prompt energy release per fission Total delayed neutron fraction
196 64 10.412 g/cm3 6.6 g/cm3 1.430 cm 1.267 cm 1.237 cm 1.875 cm 573.15 K 19 (10 fuel XS macro elements) 3.58 × 10−8 cm−1/s 2.27 × 10−6 cm−1/s 3.20 × 10−11 J/fission 0.00760
Thermal-hydraulic
Core thermal power Total inlet mass flow rate Core pressure Core inlet subcooling Core configuration Reference coolant density
1800 MW 13,000 Kg/s 67.0 bar 46.52 KJ/Kg 17 × 17 × 14 (30.48 cm × 30.48 cm × 30.48 cm) 47.627 lb/ft3
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Table 2 Keff results.
keff
ARROTTA
DYNAS
TNK-XC
KICOM
QUANDRY-EN
STAND
QUABOX
RS4-PARCS
RS4-3DKIN
0.99999
0.98563
0.98764
0.9844
0.96788
0.991
0.98639
0.961342
0.952429
Fig. 9. Axial core power distribution.
Fig. 11. Core power for transient problem.
Fig. 10. Radial distribution of core averaged densities for steady state problem. Fig. 12. Core averaged fuel temperature difference with respect to steady-state.
though our coupling results are in the range of other code predictions range, the top half axial power can be improved by using more detailed NK models. Conclusions of the benchmark point out TH modelling as the main factor of the dispersed results for the SS power distributions. It is also worth to mention that supplied RS4 radial core configuration for TH was significantly simple (4 concentric channels for 10 fuel composition types and 185 neutronic nodes) in comparison with the standalone simulations of the participants (one fluid channel per each fuel bundle). With that modelling, no one-to-one TH/NK feedback exists for each fuel bundle composition type, and greater deviations in criticality and keff value must be expected. Fig. 10 shows how the limited number of radial TH channels affects to the reactivity feedback. RS4-3DKIN simulation results of average density are relatively similar to the average results of the benchmark participants. On the contrary, results for the axial distribution of the core power showed a good agreement (see Fig. 9). This was due to a finer meshing coupling between RS/MOD4.0 and 3DKIN (12 TH and NK nodes for the active fuel bundles). Therefore, the reported discrepancies are related with the TH modeling and not with the
reliability of RS4-3DKIN coupling. After steady state runs, transient runs for cold water injection (as described in section 2) have been performed. Time dependent problem was executed in a Intel i5-640 PC (3,3 GHz and 4 GB of RAM) with Windows 7 64 bits OS. RS4 was compiled with Intel Fortran 2016 XE Composer 32 bits compiler. The total CPU time was 70.28 s for a simulation transient of 30 s. The time step used for the whole simulation was 2.5·10−2 s With respect to the simulation, transient problem starts with a sudden injection of subcooled water at core inlet. For these conditions, density is suddenly reduced also increasing the thermal neutrons moderation and core power. A maximum peak (165.6% of the initial power) is achieved 1.8 s after the initiation of the water injection (Fig. 11). As a result of the power excursion, fuel average temperature starts to increase (Fig. 12). It causes a negative reactivity feedback because of Doppler broadening dependency that compensates the effect of the water subcooling and stops the power excursion. Finally core 180
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Fig. 16. Difference of radial relative power (Δ = t0-t20). Fig. 13. Radial power at t = 0 s (transient, initial).
similar trends for the increasing of the fuel temperature. The trend of fuel-temperature change depend on several parameters: the detailed modelling of fuel bundle, fuel rods and the physical modelling of the core which effect the convective and conductive heat transfer characteristics as well as heat capacitance of the fuel and non-fuel elements. Very detailed comparison is necessary to figure out all these models among these codes but the benchmark used does not provide detailed information to clarify which parameter is the dominant on for defining why RS4-3DKIN has more fuel temperature than other ones. Figs. 13–16 demonstrates the difference of the radial power of the reactor core for different time of the transient. 6. Conclusions In this study, RELAP/SCDAPSIM/MOD4.0 and NESTLE codes are coupled. The code results have been benchmarked with other codes by using a OECD benchmark. 3DKIN package including NESTLE has been demonstrated as the neutronic interface between NK and TH modesuls to simplify the coupling process. This coupling allows usre friendly coupling TH/NK calculations. Steady-state and transient (with unexpected injection of subcooled water) problems in OECD Benchmark have been simulated. Our results have been compared with the benchmark results of other seven codes. RS4-3DKIN simulation results of average density are higher than other benchmark participants at the mid-section of the radial core since only 4 representative core channels have been used. The top axial core power distribution is higher than other benchmark calculations even though our code predictions are between other code prediction range. Even though our coupling results are in the range of other code predictions range, the top half axial power can be improved by using more detailed NK models. Despite the differences between the results of OECD benchmark’s participants and the limitations of the meshing modeling in the supplied RELAP5 input decks, RS4-3DKIN results showed that the transient results are in the other code results range. Continuation of the validations of RS4-3DKIN coupled code will demonstrate more code capabilities for other validation cases in the future.
Fig. 14. Difference of radial relative power (Δ = t0-t5).
Fig. 15. Difference of radial relative power (Δ = t0-t10).
power is stabilized around the 132% of the initial core power at t = 11 s. The code of ARROTTA has decreasing fuel temperature. Some of the codes have stable fuel temperatures at the last part of the transient. The codes of RS4-3DKIN, TNK_XC, STAND and QUANDRY-EN have
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nucengdes.2019.01.009.
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Thermal-hydraulics and neutronic code coupling for RELAP/SCDAPSIM/ MOD4.0
T
Sabahattin Akbasa, Victor Martinez-Quirogab, Fatih Aydoganc, , Chris Allisonb, Abderrafi M. Ougouagd ⁎
a
Institute of Science, Gazi University, Milas No 15 Street, Teknikokullar, 06500 Ankara, Turkey Innovative Systems Software 3585 Briar Creek, Ammon, ID 83406, USA c Department of Mechanical Engineering, Jacksonville University, USA d Idaho National Laboratory, Idaho Falls, ID, USA b
ABSTRACT
The design and analysis of energy systems requires robust and reliable computer codes that produce realistic results. The governing equations and closure models must represent the physical behaviors of the energy systems. Nuclear power plants, as the quintessential example of complex energy systems, must be modeled with such high-fidelity and accurate nuclear system codes in which thermal-hydraulics, neutronics and fuel performance models must be coupled for in order to produce high-fidelity predictions. Most commonly, the interplay between the various subsystems of a nuclear power plant (nuclear fuel, fluids, neutronics, control rods, power conversion, etc.) is modeled through a combination of different codes that are externally coupled. The objective of this paper is to present work that couples the RELAP/SCDAP SIM/MOD4.0 code with the NESTLE neutronic code within the 3DKIN package, thus providing the latter with updated neutron kinetic capabilites. The version of the RELAP/SCDAPSIM/MOD4.0 code used in this work has been developed by Innovate System Software (ISS) and is the latest in the series of such code versions developed as part of the international SCDAP Development and Training Program (SDTP) for best-estimate analysis to model reactor transients including severe accident phenomena. The new feature of 3DKIN enhances the simulation of the Nuclear Power Plants (NPP) response under accidental and operational scenarios in which high reliability of neutronic feedback is needed. The RELAP/SCDAPSIM code is described and the improvements implemented in it are presented, including nodal kinetics library as well the coupling method that is applied. Finally, a BWR transient with unexpected injection of subcooled water as specified in an OECD Benchmark has been simulated in order to assess the reliability of the package and the performance of the coupling. Results are compared to those of the other OECD benchmark participants. The comparison of fuel temperature, effective multiplication factor (keff) and power distribution results display good agreement with values within the range of those of other participants.
1. Introduction The computational tools used in nuclear industry can simulate complex nuclear systems. The nuclear systems include nuclear fuel, control rods, reactor internals, fluid systems, control systems, safety systems, energy conversion components (such as turbine), pump, condensers, preliminary heat exchangers, steam-seperators, valves, pipes and other heat sources and heat sinks. To model all these systems and components, some specific codes are utilized. For instance, some of the following codes used commonly:
• reactor physics codes for modeling core neutronics, cross-section preparation and/or lattice physics codes or cross section libraries, • thermal hydraulic codes that encompass system codes, containment codes, computational fluid dynamics, sub-channel codes. All of these can simulate the thermal and hydraulic behavior of the coolant and/ or working fluid,
⁎
• fuel performance
under irradiation.
codes that simulate the nuclear fuel behavior
In the early decades of nuclear power, each of these types of codes were developed and implemented individually. However, the strong interaction between the various physical phenomena of neutronics, reactor thermal hydraulics, fuel performance, containment physics, and others, has been recognized to necessitate the coupling between these codes. Coipled codes capture the interplay between the various physics phenomena and hence model the feedback between them. Feedback effects can be observed in several transients in nuclear power plants. Some example transients include:
• Inadvertent control rod withdrawal (uneven feedback) • Control rod ejection (strong local feedback) • Start-up of a cold or a boron free loop (uneven feedback) • External asymmetrical boron dilution (uneven feedback)
Corresponding author at: Mechanical Engineering, Jacksonvile University, 2800 University Blvd N., Jacksonville, FL 32211, USA. E-mail address: [email protected] (F. Aydogan).
https://doi.org/10.1016/j.nucengdes.2019.01.009 Received 13 March 2018; Received in revised form 30 December 2018; Accepted 5 January 2019 Available online 08 February 2019 0029-5493/ © 2019 Published by Elsevier B.V.
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Acronyms ANM BE BWR FDM ISS SCDAP NEM
NGFM NPP NK PWR SS TH RS4 LWR LWRCT
Analytic Nodal Method Best Estimate Boiling Water Reactor Finite Differential Method Innovate System Software SCDAP Development and Training Program Nodal Expansion Method
• Transients with potential for inherent boron dilution (uneven feedback) • Anticipated transients without scram (uneven feedback) • Cool-down transients with re-criticality potential (steam or feed
Nodal Green’s Function Method Nuclear Power Plant Neutron Kinetics Pressure Water Reactor Steady-State Thermal-Hydraulics RELAP/SCDAPSIM/MOD4.0 Light Water Reactor LWR Core Transient
complex configurations codes that incorporate TH and 3-D NK would be required. Especially for full nuclear core applications integrated with primary and power conversion coolant cycles, detailed coupling between TH and NK codes is required for modeling strong interaction between NK and TH behaviors for steady-state and transients (design basis accidents, anticipated transient without scram and severe accidents). The following coupled codes are some of the existing codes used for the accurate and realistic evaluation of NK and TH behavior: TRACE/PARCS (Xu et al., 2006), RELAP5/PARCS (Barber et al., 1999), ATHLET/DYN3D (Kozmenkov et al., 2007) and RELAP/SCDAPSIM/ MOD4.0/PARCS and NESTLE (Martinez-Quiroga et al., 2015, 2016). The code prediction of this coupling method is also demonstrated for a Boiling Water Reactor (BWR) transient to demonstrate how developed coupling works such as, TRACE/PARCS (Gajev et al., 2014), CATHARECRONOS2-FLICA4 (Mignot et al., 2004), DYN3D/ATHLET (Grundmann et al., 2004), RELAP5/PARCS (Salah et al., 2005), TRAC-BF1/NEM/ COBRA-TF (Solis et al., 2002). This paper presents a coupling of RELAP/SCDAPSIM/MOD4.0 and NESTLE within 3DKIN package. The scenario of a BWR transient with unexpected subcooled water injection was utilized to benchmark the code predictions with the other code predictions by using a OECD benchmark. Section 2 shows a brief description of RELAP/SCDAPSIM/MOD4.0 and NESTLE in 3DKIN package. Section 3 describes the selected OECD scenario for this paper. Section 4 describes the code models and nodalization diagrams. Section 5 demontrates the results of the code for the selected OECD bencmark.
lines break-uneven feedback)
In nuclear power plants there are strong feedback effects between thermal hydraulic (TH), fuel performance (FP), and neutron kinetics (NK) and static neutronic physical behaviors that require accordingly coupled codes. The temperature distribution in nuclear fuel is calculated by the TH and neutronics codes. In turn, the temperature distribution is used by the reactor physics codes since effective neutron cross sections depend on the temperature distribution of fuel and moderator. The NK code predicts the neutron flux and power distribution, which is used by the thermal hydraulic codes. The fuel performance codes use information provided by both the TH and neutronics codes. Although there is a data exchange between all of these codes, the coupling methods between them are different from one another as the parameters that are exchanged vary and the time scales of the various phenomena are substantially different. Thus, the coupling schemes can also vary substantially: for example some codes and situations may require data exchanges only for certain specific parameters that are not exchanged between other pairs of codes and under other situations. Furhtermore, the exchanges have to occur with different frequencies (e.g., at every computational time step or not). To reduce the cost of the fully coupled codes using realistic feedback effects, some codes incorporate other code models to utilize limited feedback effects. For instance, NK codes include simple TH models and some TH codes utilize basic 1-D NK modeling capability. Even though these simple models for the representation of NK or TH does not provide realistic feedback effects, the combination of several coupled models can provide simple treatment of feedback effects on the codes. However, inasmuch as the predictions of the neutronics models depend strongly on fuel, coolant and moderator temperatures, and though for some problems NK with simple incorporated TH or TH codes with simple NK may suffice, for most realistic applications that involve
2. Coupling of thermal-hydraulic code of RELAP5/SCDAPSIM/ MOD4.0 and 3DKIN package 3DKIN is a nodal kinetics package that has been included into RELAP/SCDAPSIM/MOD4.0 (RS4) as an option for RS4 users that do not have their own 3D reactor kinetics package. 3DKIN package is based on models and correlations of NESTLE (Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator) 5.2.1, a NK code developed
Fig. 1. Diagram of 3DKIN series coupling. 175
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at North Carolina State University (North Carolina State University, 2003). Code architect has been modified and reprogrammed in FORTRAN 90/95/2000 standards to keep the implicit solution of the neutron diffusion equation as an internal library of RS4 (Fig. 1). New input cards have been included in RS/M4 for user-friendly mapping of LWRs Cartesian geometries (Hexagonal geometries are also possible to be simulated). Although it is not as powerful as the NESTLE code, it is a useful option for coupled calculations. 3DKIN package solves few-group neutron diffusion equation utilizing Nodal Expansion Method (NEM) for spatial discretization. It can simulate either eigenvalue or eigenvalue initiated transient problems, thus they can be applied for simulating operation transients at constant power (by the use of the eigenvalue simulation at each time advancement) or transient problems for an initial neutron flux distribution (eigenvalue initiated transients). Depletion is also available for operational simulations. Two or four energy groups can be utilized for solving the neutron diffusion equation. NEM is based upon quartic polynomial expansion equations and a non-linear iterative strategy (outer-inner iteration) is employed for solving the resulting matrix system. The utilized package solves either Nodal or Finite Differential Method (FDM). Quartic polynomial expansion is employed for the transverse integrated fluxes, and transverse leakage is represented by a quadratic polynomial. Furthermore, discontinuity factors are applied to correct for homogenization errors. For transient problems, diffusion equation employs a first-order difference operator and precursor equations are analytically solved assuming that fission rate behaves linearly over a time-step. In these problems, the delayed neutron precursor groups are specified by the user. As regards XS libraries, they are externally parameterized in macroscopic models that includes composition type, control rod state (in/out) and burnup (fuel depletion can be also modeled for operational simulations). In addition, all cross sections are expressed in terms of a Taylor series expansion depending on coolant density, coolant temperature, effective fuel temperature and soluble poison concentration. Finally, I-Xe and Pm-Sm chains are modeled with several options for calculating their number densities (i.e. equilibrium, transient, peak Sm- no Xe, no Sm nor Xe, or frozen), and decay groups are used to model decay heat. As regards neutron flux solution, FDM outer-inner iteration strategy is employed taking advantage of the Chebyshev polynomials for accelerating the convergence. For NEM, a non linear iterative method is also applied after a sufficient number of outer iterations are completed. Fig. 2 shows the structure of the iterative method. As it can be seen in the diagram, for achieving the convergence it is required a continuous updating of TH data after each outer iteration. Hence, it was decided to define an implicit coupling between TH and neutronics for RS4 time advancement in order to enhance the stability, accuracy and robustness of the iterative method. With this approach, if there is no convergence in the neutron flux solution, TH data are updated with the provisional estimation of the power distribution without advancing to a new time step. Once new TH values are computed, outer-inner iteration is restarted at the same level and new cycle is run. This process is iteratively repeated until convergence is achieved. After that, RS4 starts a new time advancement following the same numerical scheme. As it can be seen, the coupling is completely implicit because both neutronics and TH data solutions are computed by the use of a coupled set of equations that are function of the current and previous time step solutions estimates. In order to verify the programming and the integration of the 3DKIN package within RS4, three testing problems were carried out based on the sample XS libraries and core configurations supplied with NESTLE neutronic model (Martinez-Quiroga et al., 2016). In our previous publication (published in NUTHOS conference), we have already studied and published three cases, which are (1) Eigenvalue problem, (2) Eigenvalue initiated transient problem, and (3) Depletion problem. Cold water injection transient without screaming the reactor core is selected as the validation case in the scope of this paper.
3. Description of the selected BWR transient In order to verify the programming of neutronic as well as the proper coupled data exchange, a series of coupled calculations have been carried out with RS4-3DKIN codes. Since international LWR core transient (LWRCT) benchmarks, based on well-defined problems with a complete set of input data, are used to assess the discrepancies between three-dimensional space-time kinetics codes in transient calculations, a specific case of an OECD benchmark has been selected for this article. The chosen scenario/case is a BWR transient with unexpected injection of subcooled water (Fig. 3) without scramming the reactor (case D1 of the NEACRP LWR core transients benchmark (Finnemann and Galati, 1992; Finnemann et al., 1993)). One of the goals of this transient is to test the reactivity feedback effects of density variation and Doppler broadening in core power distribution. The selected benchmark provides results of eight national and industrial institutions that will be used to evaluate the result of RS43DKIN coupled simulations. Just as a reminder, the aim of this comparison is not to validate the accuracy of supplied sample input decks and the neutronic code but to demonstrate 3DKIN reliability and to test the performance by using a BWR nuclear power plant. In a BWR reactor vessel (Fig. 4), there are a reactor core that mainly consists of fuel assemblies and control rods in the center, equipment for generating steam for a turbine, such as a steam-water separator and a steam dryer in the upper part of the vessel, equipment for reactorpower control, such as control rod guide tubes and control rod drive housings in the lower part of the vessel, and a core shroud, jet pumps etc. that surrounds the reactor core and composes the coolant flow path in the periphery of reactor core. 4. Modelling and simulation of the nuclear power plant The selected BWR case for modelling and simulation consists of subprompt critical reactivity excursions generated by rapid cold water injection or core pressurization events. The selected case has neutronic and thermohydraulic feedback-effects. This section demonstrates two main components of modelling that will be described in this section in detail: (1) neutronic modelling based on 3DKIN module for the BWR core and (2) thermal hydraulic modelling of RELAP/SCDAPSIM/ MOD4.0 for the BWR’s TH system.
Fig. 2. Diagram of the NEM non-linear outer inner iteration method. 176
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neutron flux (a measure of the neutron population) as a consequence of the neutrons interaction with the fuel and moderator (and other materials) within the reactor core. The computed value of the flux, in turn, is used to calculate reaction rates, including the volumetric rate at which fission reactions take place and hence the power density distribution, and essential input to safety analysis modeling. The governing equations solved by NK codes are the time-dependent multi-group neutron diffusion equations and their associated delayed neutron precursor equations (Duderstadt and Hamilton, 1976; Bandini, 1990). For light water applications most NK codes use two neutron energy groups, though occasionally as many as four groups may be used. In this study, two neutron energy groups (thermal and fast neutron groups) and six delayed neutron groups are used for neutron modeling in the calculations. 3D cross-section (transport, absorption, nu-fission, kappafission, nu) values (XSs) of NEACRP LWR core are used in the selected transient benchmark (Finnemann and Galati, 1992; Finnemann et al., 1993) The 3D NK model has been prepared based on the 3D cross-sections given for the selected OECD benchmark. The cross-sectional view (based on Xand Y dimensions) of the BWR reactor is shown in Figs. 5 and 6. The full core consist of ten different fuel macroelement compositions (as shown in Fig. 5) and 19 composition types. The length of each square fuel macroelement and macrocell in the radial reflector, is 30.48 cm. Axially, the reactor is subdivided into 14 layers, each 30.48 cm high, as shown in Fig. 7. The fuel composition of each axial layer is individually defined (Fig. 7).
Fig. 3. Inlet subcooling vs. time for D1 transient (Finnemann and Galati, 1992; Finnemann et al., 1993).
4.1. Neutronics modelling In coupled NK-TH codes (or code systems), the NK part, which computes the neutron flux as a function of time (and space in most instances), uses the neutron diffusion equation as a model for the physics. Furthermore, most of coupled NK-TH codes use one of the various modern nodal methods as their neutronic solver for the multidimensional, multi-group neutron diffusion equations (Lawrence, 1986; Sutton and Aviles, 1996). These nodal methods such as Nodal Expansion Methods (NEM) (Finnemann, 1975), Analytic Nodal Method (ANM) (Smith, 1979), the Nodal Green’s Function Method (NGFM) (Lawrence 1979), and the more efficient Semi-Analytic Nodal Method (Rajic and Ougouag, 1989), have been implemented using different approaches in current NK codes. Neutron kinetics (NK), or time-dependent neutronics, deals with modeling of time evolution of the
4.2. Thermal-hydraulics model RELAP/SCDAPSIM/MOD4.0 is a Best Estimate (BE) code designed
Fig. 4. Typical BWR reactor system (Roth and Aydogan, 2015). 177
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Fig. 5. BWR initial map.
Fig. 7. BWR macroelement type 1.
MOD3.2 models, developed by the US Nuclear Regulatory Commission, in combination with advanced numerics, advanced programming, techniques and SDTP member-developed models and user options (more detailed information can be found in reference (Pérez et al., 2015)). In particular, RELAP/SCDAPSIM/MOD4.0, the latest in the series of the SDTP-developed versions, is the first version of RELAP or SCDAP/RELAP5 completely rewritten to FORTRAN 90/95/2000 standards. It implies that RELAP5 database is dynamically allocated, making easier and faster the coupling with other codes with the use of pointers and structures. The input model (Fig. 8) of RELAP/SCDAPSIM/ MOD4.0 to simulate the TH behaviour of the the core and the BWR system has been prepared based on the selected OECD benchmark. The channels (from 1 to 4) shown on the right side of Fig. 8 are the representative channels for the channels of Fig. 6. The core has been simulated with 4 concentric channels linked to 4 different active fuel heat structures, and a bypass. It has also been included for simulating the peripheral region. As regards -3DKIN and RELAP/SCDAPSIM model, main features of the supplied decks are given in Table 1. Fig. 6. BWR core map.
5. Results
to run a wide range of conditions from normal operating conditions up through severe accidents (Allison and Hohorst, 2010). RELAP/SCDAPSIM uses the publicly available RELAP5/MOD3.3 and SCDAP/RELAP5/
NK and TH modelling and the developed coupling codes have been demonstrate in the previous sections of the paper. In this section, the results will be demonstrated for the selected OECD Benchmark. Even 178
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Fig. 8. RS4 nodalization.
though the selected OECD benchmark does not demonsrate all the results of TH and NK parameters, the benchmark of OECD participants were given based on selected parameters of NK and TH. Firstly, the keff results of the developed coupled code is benchmarked with the OECD participants for the steady state BWR core results in Table 2. The keff
change from 0.952429 to 0.99999. For the steady state calculation, the axial and radial power distributions are compared with the results given in the OECD benchmark (Figs. 9 and 10). The cross-sectional modelling of NK code can be revisited to improve the top-half results of normalized axial power. Even
Table 1 Main design parameters of RS4-3DKIN for core modeling (Finnemann and Galati, 1992; Finnemann et al., 1993). Parameters
Value
Neutronic
Number of fuel rods Number of reflector elements UO2 density Zircaloy density Outer clad diameter Inner clad diameter Pellet diameter Fuel rod pitch Reference effective fuel temp. Number of composition types Fast neutron inverse velocity Thermal neutron inverse velocitv Prompt energy release per fission Total delayed neutron fraction
196 64 10.412 g/cm3 6.6 g/cm3 1.430 cm 1.267 cm 1.237 cm 1.875 cm 573.15 K 19 (10 fuel XS macro elements) 3.58 × 10−8 cm−1/s 2.27 × 10−6 cm−1/s 3.20 × 10−11 J/fission 0.00760
Thermal-hydraulic
Core thermal power Total inlet mass flow rate Core pressure Core inlet subcooling Core configuration Reference coolant density
1800 MW 13,000 Kg/s 67.0 bar 46.52 KJ/Kg 17 × 17 × 14 (30.48 cm × 30.48 cm × 30.48 cm) 47.627 lb/ft3
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Table 2 Keff results.
keff
ARROTTA
DYNAS
TNK-XC
KICOM
QUANDRY-EN
STAND
QUABOX
RS4-PARCS
RS4-3DKIN
0.99999
0.98563
0.98764
0.9844
0.96788
0.991
0.98639
0.961342
0.952429
Fig. 9. Axial core power distribution.
Fig. 11. Core power for transient problem.
Fig. 10. Radial distribution of core averaged densities for steady state problem. Fig. 12. Core averaged fuel temperature difference with respect to steady-state.
though our coupling results are in the range of other code predictions range, the top half axial power can be improved by using more detailed NK models. Conclusions of the benchmark point out TH modelling as the main factor of the dispersed results for the SS power distributions. It is also worth to mention that supplied RS4 radial core configuration for TH was significantly simple (4 concentric channels for 10 fuel composition types and 185 neutronic nodes) in comparison with the standalone simulations of the participants (one fluid channel per each fuel bundle). With that modelling, no one-to-one TH/NK feedback exists for each fuel bundle composition type, and greater deviations in criticality and keff value must be expected. Fig. 10 shows how the limited number of radial TH channels affects to the reactivity feedback. RS4-3DKIN simulation results of average density are relatively similar to the average results of the benchmark participants. On the contrary, results for the axial distribution of the core power showed a good agreement (see Fig. 9). This was due to a finer meshing coupling between RS/MOD4.0 and 3DKIN (12 TH and NK nodes for the active fuel bundles). Therefore, the reported discrepancies are related with the TH modeling and not with the
reliability of RS4-3DKIN coupling. After steady state runs, transient runs for cold water injection (as described in section 2) have been performed. Time dependent problem was executed in a Intel i5-640 PC (3,3 GHz and 4 GB of RAM) with Windows 7 64 bits OS. RS4 was compiled with Intel Fortran 2016 XE Composer 32 bits compiler. The total CPU time was 70.28 s for a simulation transient of 30 s. The time step used for the whole simulation was 2.5·10−2 s With respect to the simulation, transient problem starts with a sudden injection of subcooled water at core inlet. For these conditions, density is suddenly reduced also increasing the thermal neutrons moderation and core power. A maximum peak (165.6% of the initial power) is achieved 1.8 s after the initiation of the water injection (Fig. 11). As a result of the power excursion, fuel average temperature starts to increase (Fig. 12). It causes a negative reactivity feedback because of Doppler broadening dependency that compensates the effect of the water subcooling and stops the power excursion. Finally core 180
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Fig. 16. Difference of radial relative power (Δ = t0-t20). Fig. 13. Radial power at t = 0 s (transient, initial).
similar trends for the increasing of the fuel temperature. The trend of fuel-temperature change depend on several parameters: the detailed modelling of fuel bundle, fuel rods and the physical modelling of the core which effect the convective and conductive heat transfer characteristics as well as heat capacitance of the fuel and non-fuel elements. Very detailed comparison is necessary to figure out all these models among these codes but the benchmark used does not provide detailed information to clarify which parameter is the dominant on for defining why RS4-3DKIN has more fuel temperature than other ones. Figs. 13–16 demonstrates the difference of the radial power of the reactor core for different time of the transient. 6. Conclusions In this study, RELAP/SCDAPSIM/MOD4.0 and NESTLE codes are coupled. The code results have been benchmarked with other codes by using a OECD benchmark. 3DKIN package including NESTLE has been demonstrated as the neutronic interface between NK and TH modesuls to simplify the coupling process. This coupling allows usre friendly coupling TH/NK calculations. Steady-state and transient (with unexpected injection of subcooled water) problems in OECD Benchmark have been simulated. Our results have been compared with the benchmark results of other seven codes. RS4-3DKIN simulation results of average density are higher than other benchmark participants at the mid-section of the radial core since only 4 representative core channels have been used. The top axial core power distribution is higher than other benchmark calculations even though our code predictions are between other code prediction range. Even though our coupling results are in the range of other code predictions range, the top half axial power can be improved by using more detailed NK models. Despite the differences between the results of OECD benchmark’s participants and the limitations of the meshing modeling in the supplied RELAP5 input decks, RS4-3DKIN results showed that the transient results are in the other code results range. Continuation of the validations of RS4-3DKIN coupled code will demonstrate more code capabilities for other validation cases in the future.
Fig. 14. Difference of radial relative power (Δ = t0-t5).
Fig. 15. Difference of radial relative power (Δ = t0-t10).
power is stabilized around the 132% of the initial core power at t = 11 s. The code of ARROTTA has decreasing fuel temperature. Some of the codes have stable fuel temperatures at the last part of the transient. The codes of RS4-3DKIN, TNK_XC, STAND and QUANDRY-EN have
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nucengdes.2019.01.009.
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