The Virtual Environment for Reactor Applications (VERA) core physics benchmark problem #6, 3D Hot Full Power (HFP) assembly, from the Consortium for Advanced Simulation of Light Water Reactors (CASL) was simulated using the MC21 continuous energy Monte Carlo code coupled with the COBRA-IE subchannel thermal-hydraulics code using the R5EXEC coupling framework.
Progress in Nuclear Energy 101 (2017) 338e351 Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene MC21/COBRA-IE and VERA-CS multiphysics solutions to VERA core physics benchmark problem #6 Brian N Aviles a, *, Daniel J Kelly a, David L Aumiller b, Daniel F Gill b, Brett W Siebert a, Andrew T Godfrey c, Benjamin S Collins c, Robert K Salko c a b c Naval Nuclear Laboratory, Knolls Atomic Power Laboratory, Schenectady, NY, USA Naval Nuclear Laboratory, Bettis Atomic Power Laboratory, West Mifflin, PA, USA Oak Ridge National Laboratory, Bethel Valley Road, Oak Ridge, TN, USA a r t i c l e i n f o a b s t r a c t Article history: Received 12 September 2016 Received in revised form January 2017 Accepted 19 May 2017 Available online June 2017 The Virtual Environment for Reactor Applications (VERA) core physics benchmark problem #6, 3D Hot Full Power (HFP) assembly, from the Consortium for Advanced Simulation of Light Water Reactors (CASL) was simulated using the MC21 continuous energy Monte Carlo code coupled with the COBRA-IE subchannel thermal-hydraulics code using the R5EXEC coupling framework The converged MC21/COBRA-IE solution was compared to results from CASL's VERA-CS code system, MPACT coupled to COBRA-TF (CTF) MPACT is a three-dimensional (3D) whole core transport code, executed in a 2D/1D approach employing planar method of characteristics (MOC) solutions with SP3 in the axial direction, and CTF is a subchannel thermal-hydraulics code designed for Light Water Reactor analysis Eigenvalues agreed within 63 pcm, axially-integrated normalized radial fission distributions agreed within ±0.2% (root mean square (RMS) difference of 0.1%), local volume-averaged fuel pin temperatures agreed within ỵ8.8/-4.3 C (RMS difference of 3.9 C), and local subchannel coolant temperatures agreed within ỵ0.8/-1.5 C (RMS difference of 0.5 C) A sensitivity study to guide tube heat transfer indicated that a statistically-significant increase in reactivity and shift in radial pin power distribution occurred within the assembly when guide tube heating was enabled © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: Multiphysics MC21 COBRA-IE VERA MPACT CTF Introduction CASL (CASL, 2014) VERA Core Physics Benchmark Progression Problems (Godfrey, 2014) are designed to aid multiphysics researchers with a set of single reactor physics and coupled reactor physics/thermal-hydraulics problems of increasing complexity Problem #6 is a single Westinghouse 17 Â 17-type fuel assembly at beginning-of-cycle (BOC) and hot full power (HFP) conditions based on Watts Bar Nuclear (WBN1) initial core loading The purpose of Problem #6 is to demonstrate that coupled reactor physics and thermal-hydraulics can be iterated to mutuallyconsistent solutions To date, coupled solutions for VERA Problem #6 based on deterministic neutron transport and thermalhydraulics subchannel codes have been published (Palmtag, 2013), but a coupled Monte Carlo/thermal-hydraulics subchannel code solution has not yet been published for this benchmark * Corresponding author E-mail address: brian.aviles@unnpp.gov (B.N Aviles) High-fidelity reactor simulations that include Monte Carlo for pin-resolved neutron transport coupled with thermal-hydraulics codes solving for flow and temperature distributions at the subchannel level have been reported in the literature (see text and references in Daeubler et al., 2015; Ivanov et al., 2015; Gill et al., 2017; Lepp€ anen et al., 2015; Bennett et al., 2016; Pecchia et al., 2015; Ellis et al., 2017; Kotlyar and Shwageraus, 2016) At the Naval Nuclear Laboratory, MC21 (Griesheimer et al., 2015) and COBRAIE (Aumiller et al., 2015) coupling via R5EXEC (Aumiller et al., 2016) has been described previously (Gill et al., 2014) as have running strategies for performing coupled Monte Carlo/thermal-hydraulics analyses (Gill et al., 2015) This research utilizes these tactics and submits a high-fidelity MC21/COBRA-IE solution for Benchmark Problem #6 These results are compared with results from the core simulator being developed by CASL, VERA-CS (Sieger, 2015; Kochunas et al., 2015), which includes the deterministic neutron transport code, MPACT (Collins and Godfrey, 2015; MPACT Team, 2015), coupled to the subchannel thermal-hydraulics code, CTF (Salko and Avramova, 2014) COBRA-IE and CTF share a common http://dx.doi.org/10.1016/j.pnucene.2017.05.017 0149-1970/© 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 COBRA code ancestor but have undergone different development paths over the past 15 years; COBRA-IE improvements are geared towards analyzing Loss-of-Coolant accidents, and CTF improvements are geared towards nominal PWR and BWR operating conditions VERA problem #6 reactor physics and thermal hydraulics model description Specifications for Problem #6 are provided by Godfrey (2014) and describe a Westinghouse 17 Â 17-type fuel assembly at BOC and HFP steady-state conditions with boron concentration at 1300 ppm There are no burnable poison or control rod clusters in Problem #6 Because of symmetry in the assembly, a ¼-assembly radial model is employed Figs and present the radial and axial assembly geometry, respectively There are 72 fuel rods, 81 coolant subchannels, and guide tubes All fuel pins and water subchannels are modeled explicitly in all analysis codes, and each guide tube is modeled as an unheated cylinder with water flowing inside From the specification, 9% of the total flow accounts for bypass flow Of this, one third is assumed to flow through the guide tubes, resulting in 0.7085 kg/s (1.5620 lbm/s) flowing through all guide tube channels in this ¼-assembly model The instrument tube in the center of the assembly in the specification is modeled as a guide tube in MC21/COBRA-IE to be consistent with VERA-CS Because the guide tube inner radius and thickness (0.561 cm and 0.041 cm, respectively) are similar to the instrument tube inner radius and thickness (0.559 cm and 0.046 cm, respectively), this assumption is deemed valid In both models, heat transfer through guide tube walls is turned off such that the water flowing in the guide tubes remains unheated A sensitivity to this assumption is performed with MC21/COBRA-IE in which conduction through the guide tube walls is allowed and the water within the guide tubes is heated The left plot in Fig shows the MC21 geometry at an axial elevation with a spacer grid (75.0 cm) In order to model spacer grids correctly and to preserve flexibility in assigning subchannels, multiple intra-channel regions were required in the MC21 model and appropriate axially-varying materials are assigned using the axial material capability in MC21 Thicknesses of these intrachannel regions were determined to preserve masses of the Zircaloy (intermediate) and Inconel (top and bottom) spacer grids In Fig Problem #6 axial geometry (from Godfrey, 2014) Fig ¼-assembly radial geometry showing fuel rod, guide tube, and subchannel numbering scheme 339 340 B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 the MC21 figure, lines through the subchannels denote MC21 subchannel subdivisions The COBRA-IE and CTF fuel rod/channel model is shown on the right in Fig at an axial elevation with no spacer grid There are 49 axial mesh in the 365.76 cm active core region, which is the domain of the COBRA-IE and CTF models The axial mesh definition from VERA Problem #3 (Godfrey, 2014) is used in both MC21/COBRA-IE and VERA-CS The lower and upper core plates and bottom and top nozzles are modeled in both reactor physics codes to ensure proper axial neutronic treatment Cross section treatment for MC21 and MPACT is as follows: ENDF/B-VII.1 is used for the MC21 cross section library and contains 55 BOC nuclides Non-water materials have cross sections ranging from 500 K to 1600 K in 50 K increments up to 900 K and 100 K increments thereafter Water cross sections range from 500 K to 650 K at 10 K intervals MPACT employs a 47 energy group cross section library based on ENDF/B VII.0 data with subgroup parameters to capture selfshielding effects Coupled code execution strategy 3.1 MC21/COBRA-IE The procedure developed by Gill et al (Gill et al., 2014 and Gill et al., 2015) in which R5EXEC (formerly known as PVMEXEC) is used to couple MC21 and COBRA-IE is employed in this research R5EXEC was created to couple and control transient codes (Aumiller et al., 2016), but it can also be used to couple a transient thermal-hydraulics subchannel code like COBRA-IE to a steadystate reactor physics code like MC21 The kinetics coupling option in R5EXEC is used to transfer data on common defined regions via a well-defined API at user-specified synchronization points R5EXEC allows many reactor physics and thermal-hydraulics parameters to be passed via the API, but Problem #6 only requires region-wise powers to be transmitted from MC21 to COBRA-IE, and regionwise solid and liquid temperatures and liquid densities to be transferred from COBRA-IE to MC21 An R5EXEC session is launched in which a transient COBRA-IE simulation is initiated At each userspecified synchronization point, COBRA-IE sends local densities and temperatures as input for MC21 material properties and cross section interpolation, and COBRA-IE is paused while an MC21 keigenvalue solution is performed When the MC21 calculation is complete, it returns region-wise powers to COBRA-IE and R5EXEC continues the COBRA-IE transient simulation Stability of the coupled MC21/COBRA-IE solution is achieved by exchanging data between the reactor physics and thermalhydraulics codes at an interval smaller than the time needed for transient COBRA-IE to achieve a steady-state solution This is analogous to a physics-based under-relaxation scheme in which the change in thermal-hydraulic parameters is controlled by timestep size rather than by an under-relaxation factor In this coupled analysis, parameters are exchanged between MC21 and COBRA-IE 14 times during the COBRA-IE transient, as shown in Table The COBRA-IE transient encompassed a 55 s transient to ensure full flow conditions were achieved (the residence time for water in the coolant subchannels is less than s) The data exchanges occur at a higher frequency during the earlier portion of the transient as the thermal-hydraulic solution is developing The following metrics are inspected to assess convergence of MC21/ COBRA-IE: MC21 eigenvalue trajectory, Table MC21/COBRA-IE data exchange intervals during COBRA-IE transient Data exchange index COBRA-IE transient simulation time point (s) 10 11 12 13 14 0.01 0.50 2.50 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 MC21 Shannon entropy, and COBRA-IE L2 and L∞ norms of local fuel temperature and coolant density As will be shown in the Results section, additional parameter exchanges between MC21 and COBRA-IE beyond the eighth exchange not improve convergence for Problem #6 At each reactor physics calculation, MC21 utilizes 200 active generations (50 discarded generations) and 10 million neutrons per generation for a total of billion active neutrons per MC21 execution These are enough neutron histories to drive local pin power uncertainties below 0.7% as will be demonstrated in the Results section 3.2 VERA-CS As described in Sieger (2015), MPACT calls CTF at every outer iteration, at which time MPACT passes CTF region-wise powers The CTF solution is run as a transient; however, it is run until the thermal-hydraulics solution is considered steady before passing temperatures and densities back to MPACT All data is passed between the two codes using an API that was developed in CTF for driving solutions from other code systems (Salko et al., 2015) Thus, the coupling of MPACT and CTF is a direct coupling, with MPACT directly calling procedures in CTF to initialize the code, execute the solution, pass powers to CTF, and receive temperatures and densities from CTF The coupled iteration strategy is done using Picard iteration with an under-relaxation of parameters passed between MPACT and CTF Convergence is achieved when MPACT satisfies eigenvalue and fission source convergence criteria Temperature and density changes are monitored to determine if the subgroup calculation needs to be re-executed to obtain new shielding parameters for cross section generation MPACT was executed using the 2D/1D technique with transport-corrected P0 2D MOC in the radial planes and SP3 in the axial direction Results 4.1 MC21/COBRA-IE convergence metrics Fig presents the MC21 eigenvalue trajectory and COBRA-IE transient progression during the 14 MC21/COBRA-IE data exchanges The 95% confidence interval is shown with each eigenvalue, and all are less than ±3.0E-5 The eigenvalue at the first exchange is an outlier because MC21 is being fed temperatures and densities from an under-developed COBRA-IE transient solution COBRA-IE transient progression described in Table is shown on B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 341 Fig MC21 eigenvalue convergence and COBRA-IE transient progression during MC21/COBRA-IE data exchanges the y2-axis, indicating that data exchanges are more frequent during the initial stages of the developing COBRA-IE solution Four data exchanges occur before the COBRA-IE transient is 10% complete at s of simulated time, followed by more widely-spaced data exchanges as further physical under-relaxation is no longer needed to achieve the mutually-consistent solution between MC21 and COBRA-IE Based on the MC21 eigenvalue trajectory, the reactor physics solution is converged by the eighth data exchange Further data exchanges result in statistically-equivalent eigenvalues Batch-wise eigenvalues and Shannon entropy for MC21 during the first and eighth data exchanges are presented in Fig Although 50 discarded batches are not sufficient to converge the fission source in the first MC21/COBRA-IE data exchange as indicated by Shannon entropy (also true of the second data exchange, not shown), all subsequent data exchanges exhibit a converged source prior to 50 discarded batches This is because the previous fission source, which is used as the initial source guess at the next data exchange, approaches the converged MC21/COBRA-IE solution Thus, 50 discarded batches are not sufficient to converge the source in the first two MC21 executions, but early data exchanges are used only to start the coupled analysis on the path to convergence After the first few data exchanges, the fission source is converged after 50 discarded batches, at which time tallies can be accumulated Two billion active neutron histories are sufficient for this 3D ¼-assembly model to drive all local uncertainties in fission rate to a target of 0.5% occur in the bottom plane, as shown in the uncertainty distribution map on the right in Fig MC21 requires ~6000 wall clock seconds per execution (tracking and tallies) for 2.5 billion tracked neutrons (active plus inactive batches) using 50 nodes containing two 12core Intel Xeon E5-2680v3 2.5 GHz (Haswell) processors (1200 total cores) COBRA-IE execution time is a small fraction of the total simulation time Figs and present COBRA-IE convergence metrics for local fuel temperature and relative change in coolant density, respectively, as measured by the L2 and L∞ norms with respect to the final (exchange index 14) fuel temperature and coolant density distributions The L2 norms for both the fuel temperature and relative change in coolant density were normalized by the square root of the number of regions (3528 fuel temperature regions and 4410 coolant density regions including guide tube water, respectively) Thus, the following norms are used to monitor convergence in the COBRA-IE solution (N ¼ 14 in Figs and 7): L∞ norm of fuel temperature: n T f À T N f ∞ for n ¼ 1; N À (1) L2 norm of fuel temperature: n T f À T N f ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # Fuel Regions for n ¼ 1; N À (2) L∞ norm of relative change in coolant density: n rc À rN c rN c ∞ for n ¼ 1; N À L2 norm of relative change in coolant density: (3) 342 B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 Fig MC21 batch-wise shannon entropy and eigenvalue convergence during initial and eighth data exchanges Fig Distribution of MC21 relative uncertainty in relative power density (RPD) for CASL problem #6 3D ¼-Assembly, billion neutrons B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 343 Fig COBRA-IE convergence metrics for fuel temperature Fig COBRA-IE convergence metrics for coolant density rn ÀrN c N c rc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # Coolant Regions where, for n ¼ 1; N À (4) T nf ¼ vector of local fuel temperatures for data exchange index n, TN f ¼ vector of local fuel temperatures at the final data exchange N, rnc ¼ vector of local subchannel coolant densities for data exchange index n, and 344 B.N Aviles et al / Progress in Nuclear Energy 101 (2017) 338e351 Table Calculated eigenvalue for CASL P6 ¼-Assembly Code Eigenvalue (95% CI) MC21/COBRA-IE VERA-CS 1.16424 (2.6E-05) 1.16361 rNc ¼ vector of local subchannel coolant densities at the final data exchange N From Figs and 7, both L2 and L∞ norms decrease as the COBRAIE transient solution develops and data is exchanged with MC21 until data exchange eight, at which time convergence metrics not improve given the chosen data exchange and MC21 neutron history schemes (a simulation was run with 20 data exchanges, and the COBRA-IE norms decreased no further) Final COBRA-IE convergence metrics indicate that fuel temperature is converged to