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Benchmarking of the WIMS9/PARCS/TRACE code system for neutronic calculations of the Westinghouse AP1000TM reactor Mohamed A. Elsawi ∗ , Amal S. Bin Hraiz 1 Department of Nuclear Engineering, Khalifa University of Science, Technology, and Research (KUSTAR), Abu Dhabi, P.O. Box 127788, United Arab Emirates

h i g h l i g h t s • • • • •

AP1000 core conﬁguration is challenging due to its high degree of heterogeneity. The proposed code was used to model neutronics/TH behavior of the AP1000 reactor. Enhanced modeling features in WIMS9 facilitated neutronics modeling of the reactor. PARCS/TRACE coupled code system was used to model the temperature feedback effects. Final results showed reasonable agreement with publically available reactor data.

a r t i c l e

i n f o

Article history: Received 24 October 2014 Received in revised form 26 July 2015 Accepted 5 August 2015

a b s t r a c t The objective of this paper is to assess the accuracy of the WIMS9/PARCS/TRACE code system for power density calculations of the Westinghouse AP1000TM nuclear reactor, as a representative of modern pressurized water reactors (Gen III+). The cross section libraries were generated using the lattice physics code WIMS9 (the commercial version of the legacy lattice code WIMSD). Nine different fuel assembly types were analyzed in WIMS9 to generate the two-group cross sections required by the PARCS core simulator. The nine fuel assembly types were identiﬁed based on the distribution of Pyrex discrete burnable absorber (Borosilicate glass) and integral fuel burnable absorber (IFBA) rods in each fuel assembly. The generated cross sections were passed to the coupled core simulator PARCS/TRACE which performed 3-D, full-core diffusion calculations from within the US NRC Symbolic Nuclear Analysis Package (SNAP) interface. The results which included: assembly power distribution, effective multiplication factor (keff ), radial and axial power density, and whole core depletion were compared to reference Monte Carlo results and to a published reactor data available in the AP1000 Design Control Document (DCD). The results of the study show acceptable accuracy of the WIMS9/PARCS/TRACE code in predicting the power density of the AP1000 core and, hence, establish its adequacy in the evaluation of the neutronics parameters of modern PWRs of similar designs. The work reported here is new in that it uses, for the ﬁrst time, the combination of WIMS9/PARCS/TRACE codes to perform neutronics calculation for the Westinghouse’ AP1000TM reactor, as a representative of modern PWRs, with its challenging core conﬁguration. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Safety analysis of nuclear power plants is based on the application of complex computer codes that are able to predict the physical behavior of the system under normal and abnormal

∗ Corresponding author. Tel.: +971 2 501 8561; fax: +971 2 447 2442. E-mail addresses: [email protected] (M.A. Elsawi), [email protected], [email protected] (A.S.B. Hraiz). 1 Present address: Emirates Nuclear Energy Company (ENEC), Abu Dhabi, United Arab Emirates (UAE). http://dx.doi.org/10.1016/j.nucengdes.2015.08.008 0029-5493/© 2015 Elsevier B.V. All rights reserved.

conditions. Therefore, such computer codes must be extensively and continuously veriﬁed and validated in order to demonstrate their reliability. The need for such continuous veriﬁcation and validation activities is more pressing for legacy nuclear codes, which were developed for speciﬁc or standard systems, and now need to be validated for new reactor designs for which the operating parameters may lie outside the legacy code’s operating space. In this context, the current study presents an assessment of the suitability and accuracy of the WIMS9/PARCS/TRACE code system for power density calculation for the Westinghouse AP1000TM reactor core as a representative of modern pressurized water reactor designs (Generation III+) (Schulz, 2006). In this study, the lattice

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code used for few-group constant generation was WIMS9 (WIMS, 1999), the commercial version of the legacy WIMSD lattice physics code, which is currently developed and maintained by AMEC, Inc. (formerly, Serco/ANSWERS Software). For full-core power calculations, the U.S. NRC PARCS/TRACE (Downar et al., 2010) coupled neutron kinetics and thermal hydraulics code was used within the SNAP (Symbolic Nuclear Analysis Package) framework (SNAP, 2011). The Hot Full Power (HFP) conditions of the AP1000 reactor were simulated in this study covering the whole range of fuel burnup from the beginning of cycle (BOC) to the end of cycle (EOC). 2. AP1000 reactor core conﬁguration The Westinghouse AP1000TM is a Generation III+, two-loop pressurized water reactor (PWR) that uses a simpliﬁed, passive approach to safety (Schulz, 2006). The reactor is rated at 3400 MW(th) core power and, depending on the site condition, nominally 1117 MW(e). The fuel type is enriched UO2 and the reactor is cooled and moderated by light water. The reactor core

Fig. 1. Initial AP1000 core layout (ﬁrst cycle).

Fig. 2. AP1000 fuel assembly conﬁgurations.

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2.1. Fuel assembly description Each of the AP1000 fuel assemblies is comprised of a 17 × 17 square lattice array of which 264 are fuel rods, 24 are guide tubes for reactor control, and one central instrumentation tube (Westinghouse, 2007). Burnable absorbers, in the form of Pyrex (Borosilicate Glass) (Wagner and Parks, 2002) and Integral Fuel Burnable Absorber (IFBA) (Sanders and Wagner, 2002 and Simmons et al., 1987) rods are used to provide partial control of excess reactivity in the ﬁrst core. The Pyrex rods are removed for the core after ﬁrst cycle. The burnable absorber loading controls peaking factors and prevents the moderator temperature coefﬁcient of the core from becoming positive at normal operating conditions. Fig. 2 shows the different arrangements of the Pyrex and IFBA rods in the AP1000 fuel assemblies. According to Fig. 2, the Pyrex and IFBA rods are arranged in assemblies in three and ﬁve different conﬁgurations, respectively, giving rise to nine distinct assembly types in the AP1000 reactor core. Fig. 3 shows the core layout according to assembly types (including fuel enrichment and Pyrex and IFBA rod distribution). Fig. 3. Quarter-core layout of assemblies with the number of Pyrex (P) and IFBA (I) rods shown in each assembly.

2.2. Axial zoning of AP1000 core contains a matrix of fuel rods assembled into mechanically identical 157 fuel assemblies along with control and structural elements. The fuel assemblies are arranged in a pattern which approximates a right circular cylinder. There are three radial regions in the core that have different enrichments to establish a favorable power distribution. The enrichment of the fuel in the initial core ranges from 2.35% to 4.45%. The temperature coefﬁcient of reactivity of the core is highly negative. The core is designed for a fuel cycle of 18 months with a 93% capacity factor and a region average discharge burnups as high as 60,000 MWd/tU. Fig. 1 shows the AP1000 radial enrichment map. Light water and stainless steel reﬂectors surround the core from top, bottom, and in the radial direction. The thickness of the top, bottom, and radial reﬂector material is approximately 25, 25, and 38 cm, respectively.

Axial zoning of fuel rods refers to the non-uniform distribution of material along the fuel rod length. For Pyrex burnable absorber rods, the top and bottom 12 inches are ﬁlled with helium gas, whereas the middle area of the rod is made of Borosilicate absorber material (B2 O3 SiO2 ). For IFBA rods, the top and bottom 8 inches of each fuel rod contain UO2 fuel at reduced U-235 enrichment (3.2% in U-235 weight) and act as axial blanket for better neutron economy. The central region of the IFBA fuel rod is made of UO2 coated with a thin layer of ZrB2 absorber at the linear concentration of 0.772 mg/cm of B10 . For a non-IFBA fuel rod, the axial blanket region contains UO2 fuel at an enrichment of 1.58% in U-235 weight. Fig. 4 shows the axial zoning of AP1000 fuel rods. From the modeling standpoint, axial zoning of fuel rods has imposed a restriction on the size of the computational node in the axial direction in the full-core calculations (Section 3.3).

Fig. 4. Axial zoning of AP1000 fuel rods.

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Fig. 5. Computational ﬂow of the AP1000 model.

3. Computational procedure In this investigation, the common “two-step” procedure (Duderstadt and Hamilton, 1997; Zhong and Downar, 2003; Wang et al., 2012; Salazar and Franceschini, 2014) for performing reactor calculations was adopted, where cross section libraries were generated using the lattice physics code WIMS9, then a 3-D full core calculation was performed using the PARCS/TRACE coupled code. Fig. 5 shows a schematic of the ﬂow of calculations and the validation procedure of the AP1000 model . Fig. 6. WIMS9 modules used in homogenized cross section generation.

3.1. WIMS9 lattice cross section model description The core simulator PARCS can utilize many lattice codes to generate assembly or pin-level cross section data. The lattice code used in this investigation was WIMS9 (WIMS, 1999). The development of the commercial version of WIMS, which started with WIMS7, was the culmination of a major uniﬁcation program for the WIMS reactor physics codes with the combination of the capabilities of WIMSE and LWRWIMS in a single package. Additional improvements and many new features have been included in the WIMS9 release with a fundamental review of the resonance self-shielding methods (Newton and Hutton, 2002) and modeling of complex lattices (Newton and Hutton, 2002; Hutton et al., 2000a,b). WIMS9 utilizes the JEF2.2 library (JEF-2.2, OECD) with 172 energy groups which are collapsed into a fast and a thermal energy group. The energy groups are collapsed through ﬂux weighting, using the average ﬂux in each material mixture. A family of utility tools called WIMSBUILDER was used to simplify the input for WIMS9. The WIMSBUILDER tool collects the pin cell description, assembly geometry, operating conditions,

branch data, irradiation sequence, and calculation route from many input ﬁles to form a single input ﬁle to WIMS. The calculation route ﬁle describes the sequence of calculations to be performed by different WIMS9 modules. Of special importance are the PIP and CACTUS modules which perform ﬂux calculation using the collision probability method in 1-D, then a 2-D transport calculation in 6 energy groups, respectively. By default, CACTUS applies reﬂective boundary condition to all boundaries of the assembly. The CONDENSE module performs energy group collapse twice: after the ﬁrst ﬂux calculation by PIP (energy group collapse from 172 to 6 energy groups) and after the CACTUS calculation (energy group collapse from 6 to 2 energy groups). The SMEAR module performs the spatial homogenization of each fuel assembly and then the LED module writes to the cross section library. At the end of each calculational cycle, the BURNUP module performs depletion calculation and prepares for the next cycle. Fig. 6 shows the ﬂow of computation in WIMS9. The WIMS9 models for selected fuel assemblies are shown in Fig. 7.

Fig. 7. WIMS9 models of selected AP1000 fuel assemblies (E: fuel enrichment, P: No. of Pyrex rods, I: No. of IFBA rods).

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Fig. 8. WIMS9 model for radial reﬂector.

There are eight (8) intermediate grids and four (4) intermediate ﬂow mixing (IFM) grids along the length of fuel assemblies all made of ZIRLO. The axial representation of the grid spacers was done implicitly during the lattice calculations by smearing the material properties of the grid spacers into the moderator. The volume (density) of the moderator has been adjusted accordingly to account for the inclusion of grid spacers. Fig. 9. Axial nodalization of fuel assemblies (IMF = intermediate mixing ﬂow grid, Grid = spacer grid).

3.2. Reﬂector group constants generation Reﬂector homogenization is carried out next to construct an equivalent reﬂector to be used in the core calculations. Contrary to the fuel assemblies, the reﬂector does not contain ﬁssile material and therefore its ﬂux cannot be used for homogenization. To generate two-group cross sections for the reﬂector region, a typical ‘slab’ model was used. This slab model consists of a row of few (2∼3) fuel assemblies (to provide neutrons) and a representation of the reﬂector region as a mixture of steel (core bafﬂe and core barrel) and water. A sensitivity analysis has been performed to optimize the number of fuel assemblies needed to yield ‘reasonable’ two-group constants for the reﬂector. This analysis showed that using two fuel assemblies was optimum for reasonable reﬂector constants. A method is available in WIMS9 to enable corrections to be made to reﬂector cross sections so that better agreement can be achieved between WIMS transport solution and the whole-core diffusion solution. The method uses a transport solution (by CACTUS module) of the slab model including the calculation of the neutron

current at the core/reﬂector interface. Fig. 8 shows a WIMS9 model of the reﬂector (not to scale). Assembly discontinuity factors (ADF) have been generated by WIMS9 by including the keyword SURFACE in the LED module. The SURFACE keyword causes assembly edge ﬂuxes and currents to be written to the interface ﬁle which is generated by the CACTUS transport module. Many references are available which summarizes different techniques and algorithms for the generation of ADFs for reactor calculations (Pekicten, 2011; Colameco, 2010; Sandrin et al., 2011). The generation of the two-group constants for the axial reﬂector was more complex than that of the radial reﬂector. The structural materials above and below the active fuel length (top and bottom nozzles and top and bottom core plates) were approximated by an axial slice of ZIRLO® of thickness 26.42 cm in each direction of the core (top and bottom) and a representation of an axial slice of fuel assembly. The radial details of the fuel assemblies were smeared out to generate the equivalent axial slice of fuel assemblies.

Fig. 10. PARCS model of AP1000 core at axial levels 5 and 6.

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Table 1 Fuel temperature and moderator density and temperature branches. Fuel temperature (K) 300 600 900 1200

Moderator temperature (K)

Moderator density (g/cm3 )

617 580 560 530

0.5993 0.6779 0.7439 0.7930

3.3. Branching calculations To prepare for full-core calculations, a set of cross sections that covers possible operating, transient and accident conditions must be generated. To achieve this, burnup calculations, at appropriate burnup steps, must be performed followed by a set of branching calculations. In the current investigation, branching calculations were performed at the assembly level to account for the cross section variations with fuel temperature (Doppler Effect) and moderator temperature and density. Moderator densities were calculated at the corresponding moderator temperatures using online steam table calculators. The fuel temperature points listed in Table 1 are representative values. Including more temperature points would not signiﬁcantly inﬂuence the ﬁnal results as indicated by our sensitivity analyses. The burnup steps used in the calculations have been gradually increased from 100 MWd/MTU to 500 MWd/MTU to get xenon in equilibrium, then a constant burnup step of size 2 GWd/MTU has been used to burn the fuel to the completion of the ﬁrst cycle. Each major burnup step has been divided into 8 sub-steps for better numerical results. WIMS9 has the capability to sub-divide the major burnup steps into smaller steps using the NSTEPS directive.

Table 2 Conditions at Inlet and Outlet of TRACE Model. Parameter

Value at inlet

Value at outlet

Mass ﬂow rate (kg/hr) Pressure (MPa) Temperature (◦ C)

48.44 × 106 15.5 279.44

– 15.5 324.67

inlet mass ﬂow source, and outlet mass ﬂow sink components were deﬁned in the TRACE model. Appropriate boundary conditions were imposed at the inlet and outlet of the model components. The inlet conditions were mass ﬂow rate, pressure and coolant temperature, and the outlet conditions were pressure and temperature. The axial nodalization of the PARCS and TRACE models were identical. Table 2 summarizes the boundary conditions used in TRACE model of the AP1000 core:

3.4. PARCS/TRACE Full-core model description The PARCS core simulator (Downar et al., 2010) solves the time-dependent and steady-state neutron diffusion equation in 3D Cartesian and hexagonal core geometries. PARCS comes in two packages: coupled to TRACE for thermal-hydraulics feedback and as a standalone. The coupled version of PARCS has been used in this investigation. The coupled PARCS/TRACE code has been extensively used for core simulation and many validation and benchmark studies are available in the literature (Downar et al., 2010; Zhong and Downar, 2003; Wang et al., 2012; Brown et al., 2013). The Symbolic Nuclear Analysis Package (SNAP) framework (SNAP, 2011) was used to build the AP1000 core in PARCS. The discretization used for the PARCS model was two nodes per each fuel assembly per X- or Y-direction (i.e., a total of 4 nodes per assembly in the radial direction). A total of 112 reﬂector assemblies were used to model the radial reﬂector. The radial reﬂector assemblies take into account the core shroud and the core barrel. The axial direction of the core was modeled with 47 axial levels to capture the axial zoning of fuel assemblies (Section 2.2). The ﬁrst and last two axial levels were used to represent the bottom and top core reﬂectors (Fig. 9). Fig. 10 shows the radial conﬁguration of the core at axial levels 5 and 6 as they appear in SNAP interface. The solution of the neutronics problem was obtained using the PARCS hybrid solver (ANM/NEM) which employs a combination of an Analytical Nodal Method (ANM) and a Nodal Expansion Method (NEM). The negative thermal feedback for PARCS was provided by a TRACE model of the core in which each fuel assembly was modeled with a separate thermal ﬂuid channel. Due to the symmetry of the AP1000 core, only a quarter of the core was modeled in TRACE. Forty seven thermal ﬂuid channels, upper plenum, lower plenum,

Fig. 11. Percent relative error in rod-wise power distribution in assembly (G-9) near the beginning of cycle (BOC) [top] and near the end of cycle (EOC) [bottom] at hot full power (HFP) and equilibrium Xenon.

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4. Results and discussions The AP1000 core physics parameters calculated in this investigation are: • Assembly power distribution at the beginning and end of ﬁrst cycle. • Core effective multiplication factor. • Core radial and axial power distribution at the core’s beginning of cycle (BOC), middle of cycle (MOC), and end of cycle (EOC). • Whole core depletion (core reactivity vs. burnup). The by the First, a design

reference data used to benchmark the results generated proposed suite of codes are coming from two sources. Monte Carlo simulation of the same core with the same parameters used in this study (Ames, 2010), and the

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reactor’s design control document (DCD) published by the reactor manufacturer (Westinghouse, 2007). The Monte Carlo criticality calculations were performed using MCNP5 and the depletion calculations were performed using MCNPX 2.6.0 which has depletion/burnup/transmutation capabilities available for criticality studies (Pelowitz, 2008). The ENDF/B-VII.0 cross-section libraries were utilized for depletion and criticality calculations for fuel temperatures at 900 K and moderator temperature of 600 K. More details on the Monte Carlo simulation of the AP1000 reactor core can be found in (Ames, 2010). As a matter of fact, some of the results generated in the current investigation were not available in the reactor’s DCD and for those, we used the Monte Carlo simulation results for benchmark, if available. For other results, we used the DCD data as the main source for benchmark. Fig. 11 shows the percent relative error in rod-wise power distribution in assembly (G-9) at the core beginning and end of cycle,

Fig. 12. Normalized average power density in the core middle plane at beginning of cycle (BOC) (A), middle of cycle (MOC) (B), and end of cycle (EOC) (C) for unrodded core, at hot full power (HFP) and equilibrium xenon for burnup points 80 MWd/MTU, 28 GWd/MTU, and 42 GWd/MTU, respectively.

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Table 3 Comparison of WIMS9/PARCS results and reference data for AP1000 core maximum reactivity. Data Source

keff

% Relative error

AP1000 DCD MCNP5/MCNPX 2.6.0 WIMS9/PARCS/TRACE

1.2050 1.2039 1.2038

– 0.091 0.100

respectively. (Assembly G-9 is physically located near the center of the core, refer to Fig. 1.) The core was at hot full power (HFP) and equilibrium xenon conditions. The calculated results show good agreement with the AP1000 DCD reference data as the maximum percent relative error does not exceed 2% (Westinghouse, 2007). Table 3 shows a comparison between the value of the core maximum reactivity keff , calculated at a fuel temperature of 20 ◦ C, zero power, unborated water, and near the beginning of ﬁrst cycle of the core (BOC) and reference values reported in the AP1000 DCD and a Monte Carlo simulation of the same core (Ames, 2010). A good agreement between the Monte Carlo simulation and the current study calculation of keff can be seen in Table 3; no comments can be made about the DCD keff results are the details of its calculations are not available to the authors. Fig. 12 shows comparison between the calculated and published data for typical normalized power density distributions for oneeighth of the core for representative operating conditions. These conditions are as follows:

Fig. 13. PARCS/TRACE model prediction of the core relative axial power.

(1) Hot full power (HFP), beginning of cycle (BOC), unrodded, and equilibrium xenon. (2) Hot full power (HFP), middle of cycle (MOC), unrodded, and equilibrium xenon. (3) Hot full power (HFP), end of cycle (EOC), unrodded, and equilibrium xenon. In order to allow for the xenon to build up to equilibrium, the power density calculation for case (1) above was performed at a burnup point of about 80 MWd/MTU, which corresponds to about 45 days of reactor operation at full power. For cases (2) and (3) the burnup points at which the calculations were performed were selected as 28 GWd/MTU and 42 GWd/MTU, respectively. The results for the normalized average power density (power density divided by the average core power) shown are in good agreement with the data reported in the AP1000 DCD. The maximum relative error is about 2%. At the BOC, assembly average power density shows lower values for fuel assemblies located at the core periphery due to the large number of fresh IFBA rods existing in those assemblies (112, 88, and 72). These IFBA will depress the ﬂux signiﬁcantly and, consequently, less ﬁssion will occur in these assemblies. As time progresses from BOC to MOL and EOC, boron in the IFBA rods will be signiﬁcantly depleted and the assembly average power density starts to increase due to increased ﬁssions in assemblies located at the core periphery; this behavior is conﬁrmed in Fig. 12. For core inner assemblies, the behavior is reversed. The assembly average power density is larger at the BOC due to the higher neutron ﬂux resulting from the checkerboard arrangement and the smaller number of IFBA and Pyrex rods existing in these assemblies. As time progresses to MOL and EOC and due to fuel burnup, the average power density starts to decrease signiﬁcantly. Fig. 13 shows the axial relative power distribution, i.e., the average relative power fraction generated in each axial node of the core model during the ﬁrst cycle, as compared to data from the reactor’s DCD. The reference axial relative power is reported as measurements in the DCD. It can be clearly seen that the spacer grid model implemented during the lattice calculation was quite successful in

Fig. 14. AP1000 core reactivity vs. fuel burnup as predicted by PARCS and a Monte Carlo simulation.

capturing, to a reasonable degree, the impact of the grids on the axial ﬂux. Fig. 14 shows the core effective multiplication factor vs. the burnup. Monte Carlo data was used as a reference data for this calculation as no depletion data was available in the plant DCD. At the beginning of the calculation, a short time step was used to show the neutron poison effect resulting from the production of ﬁssion products into the reactor core at startup. At beginning of cycle (BOC), the boron in the Pyrex and IFBA rods act as a strong neutron Table 4 Core reactivity vs. burnup. Burnup (GWd/MTU)

keff (MCNP/MCNPX)

keff (PARCS)

Reactivity diff. (pcm)

0.00E + 00 0.48583 4.2 8.5 12.2 16.0 20.2 24.1 27.91 32.0 36.0 39.5

1.2589 1.22397 1.24966 1.24966 1.22192 1.18904 1.15411 1.12432 1.09247 1.05856 1.02466 1.0012

1.258 1.2229 1.2476 1.2490 1.2220 1.18721 1.1531 1.1221 1.09454 1.05701 1.02112 1.00321

57 71 132 42 5 130 76 176 173 139 338 200

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poison and depresses the reactivity of the core. As time progresses, the boron is depleted which results in the increase in keff . The core reactivity starts to decrease with the burnup. The core reaches a subcritical level at approximately ∼42 GWd/MTU. PARCS model results correctly and predicts the behavior of the core reactivity and the results show a reasonably good agreement with published MCNP5 simulation (Ames, 2010). Table 4 shows the reactivity changes vs. the core burnup. The maximum reactivity difference between PARCS and Monte Carlo is about 340 pcm. 5. Conclusions In this investigation, a steady state 3-D full-core model of Westinghouse AP1000 reactor was constructed using the WIMS9/PARCS/TRACE suite of codes. The model was validated against reference data published in the AP1000 Design Control Document (DCD) and from MCNP5 simulations available in the open literature. The simulation results of the current study, including fuel rod-wise power distribution, core reactivity, assembly radial and axial power distribution, and core reactivity vs. fuel burnup, were generally in reasonably good agreement with the reference data. This will encourage further investigation of other neutronics parameters of the AP1000 reactor utilizing the proposed WIMS9/PARCS/TRACE suite of codes. Further research is ongoing to model different operational transients and accident scenarios using the proposed WIMS9/PARCS/TRACE suite of codes and our ﬁndings will be reported in separate papers. References Ames II, D.E., 2010. High Fidelity Nuclear Energy System for Optimization towards Environmentally Benign, Sustainable, and Secure Energy. The Department of Nuclear Engineering, Texas A&M University, USA (Ph.D. Dissertation). Brown, R.B., Ludewig, H., Aronson, A., Todosow, M., 2013. Neutronic evaluation of a PWR with fully ceramic microencapsulated fuel. Ann. Nucl. Energy, 62 (2013).

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