RMC Capability of Multi-cycle HFP Full Core Burnup Simulation. Department of Engineering Physics, Tsinghua University, Beijing , China b

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1 RMC Cpbility of Multi-cycle HFP Full Core Burnup Simultion Shichng Liu, Gng Wng, Jingng Ling b, Feng Yng, Zonghun Chen, Xioyu Guo, Qu Wu, JunJun Guo, Yishu Qiu, Xio Tng, Zegung Li c, Kn Wng Deprtment of Engineering Physics, Tsinghu University, Beijing , Chin b Deprtment of Nucler Science nd Engineering, Msschusetts Institute of Technology, Cmbridge, Msschusetts, 02139, USA c Institute of Nucler nd New Energy Technology, Tsinghu University, Beijing, , Chin wngkn@mil.tsinghu.edu.cn; liu-sc13@mils.tsinghu.edu.cn Abstrct - Monte Crlo method is very ttrctive for high fidelity simultions of nucler rectors. However, rel nucler rectors re complex systems with multi-physics intercting nd coupling. In order to perform the high fidelity multi-physics simultions of rel rectors, mny dvnced methods nd cpbilities must be developed in new genertion Monte Crlo codes, including on-the-fly temperture dependent cross sections tretment, neutronics/ therml-hydrulics coupling, full-core detiled burnup clcultion, criticl serching, djoint-weighted dynmic prmeters clcultions, equilibrium non method,monte Crlo refueling cpcity, nd restrt cpcity for burnup clcultion. In this pper, these mentioned for multiple burnup cycles simultions in Hot Full power condition of PWR full core hve been developed in RMC nd pplied to the two cycles burnup clcultions of BEAVRS benchmrk. The prmeters given in BEAVRS benchmrk were clculted nd compred with the mesured vlues of BEAVRS benchmrk nd results of MC21, which show good greements. This work pves the wy for Monte Crlo code in lifecycle simultions of nucler rector cores. I. INTRODUCTION With the incresing demnds of high fidelity neutronics nlysis nd the development of computer technology, Monte Crlo method becomes more nd more importnt especilly in criticl nlysis of initil core nd shielding clcultions, due to its dvntges such s flexibility in geometry tretment, the bility to use continuous-energy pointwise cross-sections, the esiness to prllelize nd high-fidelity of simultions. However, nucler rectors re complex systems with multi-physics intercting nd coupling. For exmples, nuclides re generted or depleted during the lifecycle of rectors, nd therml-hydrulics hs feedbcks on mteril temperture nd density nd thus nucler cross sections. Rectivity control systems such s soluble boron nd control rods re djusted during the opertions of rectors to mintin the criticlity of power plnts. Moreover, when the concentrtion of soluble boron rech zero, the rector should be refueled to undergo the next burnup cycle. All of the fctors mentioned bove should be considered the high fidelity multi-physics simultions of rel rectors or benchmrks clcultions such s BEAVRS MIT BEAVRS benchmrk [1]. In this pper, the bilities mentioned bove for multiple burnup cycles simultions in Hot Full power condition of PWR full core hve been developed in RMC for multiphysics coupling nd lifecycle simultions of nucler rectors. BEAVRS benchmrk ws selected s n exmple nd RMC ws pplied full core two cycles burnup clcultion of BEAVRS. The prmeters given in BEAVRS benchmrk will be clculted nd compred with the mesured vlues of BEAVRS benchmrk. For other prmeters such s pin power distributions, they re compred to the results of MC21. II. COMPUTATIONAL METHODS Some dvnced methods hve been proposed for PWR full Core two cycles burnup clcultion, including the hybrid coupling method with on-the-fly cross sections tretment, lyered prllelism bsed on MPI/OpenMP prllel model for full-core detiled burnup clcultion, criticl serching for criticl boron concentrtion, djointweighted dynmic prmeters clcultions, inline equilibrium non method, Monte Crlo refueling cpcity, nd restrt cpcity for burnup clcultion. 1. Hybrid coupling method with on-the-fly cross sections tretment RMC ws coupled with sub-chnnel code COBRA, equipped with on-the-fly temperture-dependent cross section tretment to consider the therml-hydrulic feedbck nd temperture effects on nuclides cross sections. For on-the-fly temperture-dependent cross section tretment, the Trget motion smpling (TMS) method bsed on the ry trcking [2] is used for resolved resonnce region nd on-the-fly interpoltion of therml scttering dt ws developed in RMC to consider the therml scttering nd bound effect [3]. For therml-hydrulic coupling, considered the dvntges nd disdvntges of externl nd internl couplings, new hybrid coupling method is developed.

2 Hybrid coupling mens trnsforming dt vi externl files of therml hydrulics code nd mnging ll the useful dt by internl memory in neutronics code. The hybrid coupling method cn reduce the difficulty of modeling nd improve the verstility of coupling by mnging ll the useful dt by internl memory in neutronics code, while mking good use of the existing therml-hydrulics codes. Detils of the reliztions nd dvntges of the hybrid internl/externl coupling scheme cn be referred to references [4, 5]. 2. Lyered prllelism bsed on MPI/OpenMP prllel model The huge memory consumption is the bottleneck of full-core detiled burnup clcultions of PWR. Therefore, severl methods hve been proposed to solve the memory problem, such s domin decomposition, dt decomposition nd lyered prllelism bsed on MPI/OpenMP prllel model. On the other hnd, future computer pltforms move towrd lrger numbers of nodes nd processor cores per node coupled with lower memory vilble, s shown in Fig.1. These new rchitectures encourge hybrid prllel lgorithm in Monte Crlo simultion. Therefore, lyered prllelism bsed on MPI/OpenMP prllel model ws developed [6] nd pplied to the burnup clcultions of BEAVRS, s shown in Fig.2. trnsport. Then the ws clculted bsed on derivtives nd k. In RMC, the second-order differentil opertor method ws used. 2 dk 1 d k k 2 d 2! d 4. Inline equilibrium non method For some wekly coupled systems such s lrge PWR core, instbility problems hve been found in burnup clcultions such s oscilltions in power nd flux. The oscilltions re minly cused by xenon. In this pper, the inline equilibrium xenon method [8] ws used to del with the problem of xenon. In this method, the xenon concentrtion ws clculted nlyticlly bses on flux nd depletion time. ( I + ) f N t 1 exp t (2) I f exp I I f NI t 1 exp It I t exp It 2 (1) (3) 5. Monte Crlo refueling cpbility Memory Memory... Memory Fig. 1 Distributed-shred Memory Prllel NOW Super Computer MPI Process thred thred thred MPI Process thred thred thred MPI Process thred thred thred The opertion of nucler power plnt is long term process including initil cycle, trnsition cycles nd equilibrium cycles by fuel refueling fter ech cycle. For exmple, Fig. 3 is the Cycle 2 refueling pttern of BEAVRS. In the wy, the build-in refueling cpcity ws developed in RMC code [9]. The build-in refueling is relized by building mp between mteril informtion, rection rtes tllies, geometry cell, nd burnup informtion in depletion solver. The refueling process ws performed utomticlly through the inner mnipultion of RMC once the users hve input the refueling scheme. The refueling cpbility of RMC cn hndle full core burnup problems with more thn millions of burnup regions. Fig. 2 MPI process nd OpenMP threds Prllel Model 3. Criticlity serch In opertion of rectors, the criticl boron concentrtion in coolnt keep serching nd updting to mintin the criticl condition. The criticlity serch cpbility bsed on differentil opertor method ws developed in RMC [7].The first-order nd higher-order derivtives of K eff re estimted to solve Tylor expnsion eqution, s shown in Eqution 1. The first-order nd higher-order derivtives of K eff re tllied during the neutron Fig. 3 Cycle 2 refueling pttern of BEAVRS

3 III. RESULTS 1. Benchmrk descriptions BEAVRS benchmrk is specifictions nd mesured results for two cycles of PWR which ws proposed by the MIT Computtionl Rector Physics Group. Both the mesured dt of hot zero power (HZP) nd hot full power (HFP) re given in BEAVRS. The geometry model of BEAVRS core ws built by RMC, s shown in Fig Fig. 5 Rdil chnnels of BEAVRS core (COBRA) The whole core is divided into 10 xil segments, nd ech fuel pin nd poison pin re treted s single burnup region, summing up to burnup regions totlly. There re no rdil rings divisions in ech fuel pin. The most burned fuel pin hs bout 100 isotopes t the end of first cycle, nd bout 150 isotopes t the end of second cycle. On the bsic of neutronics/therml-hydrulics coupling in HFP condition, the lyered prllelism bsed on MPI/OpenMP ws dopted to del with the memory problem of full-core detiled burnup clcultion. The lrge scle prllelism ws performed on Tinhe2 super computer. 70 nodes with 1680 processes were used, ech node hs 64G memory. The lyered prllelism ws pplied to ech node, in which the configurtion of 2 MPI 12 OpenMP/MPI ws dopted. This configurtion of lyered prllelism is consistent with the hrdwre rchitecture of clcultion nodes of Tinhe2 super computer, which hs two CPU nd twelve codes per CPU in ech node. Through the lyered prllelism, the memory footprint of ech code in full core detiled burnup clcultions cn be reduced effectively, so s to meet the requirement of single node in Tinhe-2 super computer (24 cores per node shring 64G memory). 3. Criticl boron concentrtion comprisons Fig. 4 Rdil nd xil cross section of BEAVRS core 2. Computtionl model nd conditions For the coupling in HFP conditions, three feedbck should be considered, including the temperture of coolnt nd fuel, the density of coolnt nd the boron concentrtion in coolnt. To consider the xil distributions of fission power nd coolnt density, the ctive core is divided into 10 xil segments. For therml-hydrulics model in COBRA, only n octnt of core hs been considered for the 193 fuel ssemblies in the full core. Therefore, the grid of 31 chnnels, ech contining n individul fuel ssembly, mking up the lower tringulr region of the qurter-core shown in Fig. 5. Ech ssembly is divided into 10 xil segments. As the boron concentrtion in coolnt chnges in different burnup steps, the cpcity of criticl serch ws used to chnge the boron concentrtion in ech burnup step ccording to keep the rector criticl. The criticl boron concentrtion clculted by RMC re compred with the benchmrk results. For the first cycle, the power is not constnt s shown in Fig.6, nd the verge power is 75% full power. Therefore, the bunrup clcultions of 75% nd 100% full power re performed. The results re compred with benchmrk in Fig.7. The criticl boron concentrtion of 75% power ws closer to the benchmrk results thn full power. After cycle 1, the refueling ws crried out. As the power history of cycle 2 ws lmost in full power, so 100% power ws dopted for the burnup clcultion. The results re compred with benchmrk in Fig.8. The mximum discrepncy of boron concentrtion is 48 ppm for cycle 1 nd 46 ppm for cycle 2.

4 Fig. 9 Pin power distributions t different burnup of RMC Fig. 6 Power history of Cycle 1 Fig. 10 Pin power distributions t different burnup of MC21 Fig. 7 Criticl boron concentrtion of Cycle Fig. 11 Pin power distributions of Cycle 2 5. Detectors responses comprisons Fig. 8 Criticl boron concentrtion of Cycle 2 The rdil detectors responses in the instrument rod locted in the center of some ssemblies were lso clculted nd compred with the benchmrk results. The detectors responses t , 4587 nd in cycle 1 were compred in Fig. 12 ~Fig.14. It cn be found tht the lrge discrepncies pper in the periphery of core where power ws reltively smll. 4. Pin power distributions comprisons Beside the criticl boron concentrtion, the pin power distributions of , 4587 nd in cycle 1 ws lso compred with tht of MC21 [10] in Fig.9 & 10. Pin power distributions gree well for both two codes. The pin power distributions of cycle 2 clculted by RMC re shown in Fig.11.

5 R P N M L K J H G F E D C B A % 1.6% % -0.8% 2.5% % 1.6% 1.9% 5.9% % -2.8% -2.1% % 3.9% 2.1% 3.1% % -2.5% -3.6% -1.3% 4.9% % 4.1% -2.5% 3.7% % -1.8% -3.1% -1.6% 0.6% 3.4% 4.1% 4.9% % 0.3% 0.8% 2.0% % -2.9% -0.5% % 3.1% -1.8% -1.7% -2.9% % -2.5% -0.8% % 3.1% -1.3% -2.1% % -0.3% -1.3% -5.2% % 1.0% Fig. 12 Comprisons of detectors response t R P N M L K J H G F E D C B A % -5.0% -3.6% -1.4% -1.3% % -2.3% -3.7% -2.9% -1.1% 0.5% % -4.1% -4.1% -1.3% -1.0% 0.6% % -2.1% 1.2% % -3.4% -2.1% 1.0% 1.9% 2.8% 3.2% 0.2% % 0.1% 1.3% -1.9% % -2.5% 0.4% % -2.3% -2.4% -0.9% -6.7% % -3.4% 2.7% % -5.1% -4.4% -3.9% % -2.9% -5.2% -2.3% % -4.6% Fig. 13 Comprisons of detectors response t 4587 The mximum reltive errors nd Root-men-squre (RMS) errors t three bunrp steps were compred mong RMC, MC21 nd SIMULATE-3 in Tble I nd Tble II. Noticing tht both MC21 nd SIMULATE-3 were using the qurter core model for clcultions, the reltive errors of RMC re in the sme level compred with the other two codes. Tble I. Mximum reltive errors for three codes RMC 9.9% 6.7% 7.6% MC21 7.7% 3.2% 4.5% SIMULATE-3 9.0% 3.5% 3.0% Tble II. RMS errors for three codes RMC 2.9% 3.1% 3.8% MC21 2.5% 1.2% 2.1% SIMULATE-3 2.5% 1.1% 1.1% IV. CONCLUSIONS The multi-physics coupling nd lifecycle simultions is crucil for relistic rectors simultions nd benchmrks clcultions such s MIT BEAVRS benchmrk. In order to perform the high fidelity two cycles burnup clcultion in hot full power, severl dvnced techniques were developed in RMC. The results of RMC gree well with the reference vlues of BEAVRS benchmrk nd lso gree well with those of MC21. This work proves the fesibility nd ccurcy of RMC in multi-physics coupling nd lifecycle simultions of nucler rectors % -1.7% % -5.6% -3.8% % -3.3% -1.9% % -7.0% -3.9% % -2.8% -2.7% -1.6% % -5.6% -5.7% -0.2% % -1.2% % -6.1% -3.2% 1.7% 1.5% % -0.3% 0.9% 4.2% % -2.1% 2.7% % -5.4% -0.4% 1.9% -2.4% % 2.3% % 0.6% -1.7% % 1.1% -5.2% 0.4% % 1.3% Fig. 14 Comprisons of detectors response t ACKNOWLEDGMENTS This work is prtilly supported by Ntionl Science nd Technology Mjor Project of Lrge Advnced PWR Nucler Power Plnt in Chin (2011ZX ), Project / by Ntionl Nturl Science Foundtion of Chin, nd Science nd Technology on Rector System Design Technology Lbortory. REFERENCES 1. N. HORELIK, et l. "Benchmrk for Evlution nd Vlidtion of Rector Simultions (BEAVRS), v " Proc. Int. Conf. Mthemtics nd Computtionl Methods Applied to Nuc. Sci. & Eng. (2013). 2. S. LIU, et l. "Development of on-the-fly temperturedependent cross-sections tretment in RMC code." Annls of Nucler Energy 94, (2016).

6 3. S. LIU, et l. "Rection rte tlly nd depletion clcultion with on-the-fly temperture tretment." Annls of Nucler Energy 92, (2016). 4. J. GUO, et l. Neutronics/Therml-Hydrulics Coupling with RMC nd CTF for BEAVRS Benchmrk Clcultion, 2016 ANS Winter meeting (2016). 5. S. LIU, et l. "BEAVRS full core burnup clcultion in hot full power condition by RMC code." Annls of Nucler Energy 101, (2017). 6. F. YANG, et l. Multi-Node nd Multi-Core Performnce Studies of Monte Crlo Code RMC, 2016 ANS Annul meeting (2016). 7. G. WANG, et l. Implementtion of Mteril nd Geometry Criticlity Serch in RMC Code, 2016 ANS Annul meeting (2016). 8. Z. CHEN, et l. Implementtion of Inline Equilibrium non Method in RMC Code, 2015 ANS Annul meeting (2015). 9. S. LIU, et l., Development of mssive-dt bsed build-in refueling cpcity in Monte Crlo code RMC for full-core detiled burnup simultions, 8th Interntionl Symposium on Symbiotic Nucler Power Systems for 21st Century (2016). 10. K. DANIEL, A. BRIAN, R. PAUL. Anlysis of select BEAVRS PWR benchmrk cycle 1 results using MC21 nd OpenMC, PHYSOR2014, Kyoto, Jpn, September 28 October 3 (2014)