ML15076A020

Appendix a - Examination of Mixed Enrichment Core Loading for the Ncsu Pulstar Reactor

ML15076A020
Person / Time
Site:	North Carolina State University
Issue date:	03/12/2015
From:	Hawari A I, Wormald J L North Carolina State University
To:	Office of Nuclear Reactor Regulation
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Nt-'('II-',,\R RFACTOR PROGRAM \0101 I (',,\ROI.I\.,\ STAT t'NIVI-.RSI'I YAppendix AExamination of Mixed Enrichment Core Loadingfor the NCSU PULSTAR ReactorA. I. HawariJ. L. WormaldNuclear Reactor ProgramDepartment of Nuclear EngineeringNorth Carolina State UniversityRaleigh, NC 27695-7909March 12, 2015 SummaryMCNP6 simulations were performed of the I MWth North Carolina State University (NCSU)PULSTAR reactor core to quantify the potential for the utilization of U02 fuel assemblies that areenriched to 6% in 235U within the currently licensed Technical Specifications. The fuel assembliesbelonged to the "sister" PULSTAR reactor that was located at the Buffalo Materials Researchcenter (BMRC) at the State University of New York (SUNY) at Buffalo. Except for enrichment,these assemblies are identical in materials and configuration to the assemblies that are currently inuse at the NCSU PULSTAR. Moreover, their utilization at BMRC was demonstrated up to apower of 2 MWth. The constructed MCNP6 model was found to yield good agreement withoperational PULSTAR data including measurements of excess reactivity (Figure 3.2), rod worth(Table 3.2) and assembly peaking factors (Figure 3.3). Using this model, key technicalspecification parameters were predicted for representative core configurations that include mixedenrichment (4% and 6%) loading of fuel assemblies (see Figures 4.3 -4.9 and Tables 4.1 -4.3).The examined mixed enrichment configurations based on the loading of one 6% assembly or two6% assemblies (e.g., reflected core 9-1 and 9-2) have been found to meet such limits withsubstantial margin. In addition, for configurations such as cores 9-1 and 9-2 the pin power peakingfactor remains below the limit by a set 15% margin. In all cases, the PULSTAR was shown tomaintain its overall negative feedback behavior with a power coefficient of less than -300pcm/MW. Consequently, these results indicate that the insertion of 6% fuel in pre-selectedlocations of the PULSTAR core should meet the limits set by the current Technical Specifications.

Table of Contents1.0 Introduction .......................................................................................................................... 11.1 Objective .......................................................................................................................... 11.2 Background ............................................................................................................... 11.3 M ethods ............................................................................................................................ 11.4 Excess Reactivity H istory ........................................................................................... 21.5 Excess Reactivity N eeds .............................................................................................. 22.0 PULSTAR Core Configurations ..................................................................................... 43.0 MCNP Core Modeling and Comparison to Historical Data ............................................ 43.1 Core M odel ....................................................................................................................... 43.2 M ethods for Calculation of Core Reactivity Param eters ............................................ 43.3 Com parison of M CN P and M easured Data ................................................................ 104.0 M CNP M odeling of M ixed Enrichm ent Cores ............................................................. 124.1 Calculation of Core K inetic Param eters .................................................................... 124.2 M ixed Enrichm ent Core Configurations .................................................................... 154.3 Results ............................................................................................................................ 165.0 Conclusions ........................................................................................................................ 236.0 References .......................................................................................................................... 24 List of TablesTable 1.1 D efinition of reactor states ............................................................................................................ 1Table 1.2 Summary of core configurations of the NCSU PULSTAR research reactor ............................ 3Table 1.3 Minimum desirable excess reactivity -routine operations ..................................................... 4Table 3.1 MCNP parameters and data library processing for defined core states .................................. 5Table 3.2 Summary of parameters for historic core configurations ............................................................ 11Table 4.1 Summary of single 6% assembly loading ............................................................................... 16Table 4.2 Summary of reactivity parameters for representative mixed enrichment core configurations ... 18Table 4.3 Summary of MCNP6 core kinetics for representative mixed enrichment configurations .......... 22 List of FiguresFigure 1.1. A schematic of the PULSTAR reactor core .......................................................................... 2Figure 1.2. NCSU PULSTAR reactor core and excess reactivity history .............................................. 3Figure 3.1. PULSTAR core configurations ............................................................................................. 5Figure 3.2. A comparison of the measured and calculated PULSTAR excess reactivity history ........... 10Figure 3.3. Reflected core 8 assembly power peaking map ....................................................................... 11Figure 4.1. MCNP models of reflected core 8 and a representative reflected core 9-4 .......................... 12Figure 4.2. PULSTAR mixed enrichment core configurations ............................................................... 15Figure 4.3. Permitted single 6% fuel loading positions (green) ............................................................ 17Figure 4.4. Reflected core 8 assembly power peaking factor map ....................................................... 18Figure 4.5. Reflected core 9-1 assembly power peaking factor map ..................................................... 19Figure 4.6. Reflected core 9-2 assembly power peaking factor map ..................................................... 19Figure 4.7. Reflected core 9-3 assembly power peaking factor map ..................................................... 20Figure 4.8. Reflected core 9-4 assembly power peaking factor map ..................................................... 20Figure 4.9. Pin power peaking factor map of reflected cores 8, 9-1, 9-2, 9-3 and 9-4 .......................... 21Figure 4.10. Reflected core 8 linear regression for calculation of Doppler coefficient ......................... 22

\ ( CL 1: A R R I -A ("I OR PR OG R AN I \0WHICAROLINASIXI 1,N1VLRS1'1Y I1.0 Introduction1.1 ObjectiveThe objective of this work is to examine the use of a mixed enrichment core design that utilizesunirradiated 6% enriched fuel from the BMRC at SUNY Buffalo with 4% enriched fuel (currentlyresident in the core) to operate the NCSU PULSTAR reactor. A total of nine 6% fuel assembliesare available for utilization in the PULSTAR core. All mixed enrichment core configurations arerequired to be analyzed and shown to meet the current licensed Technical Specifications (TS) ofthe PULSTAR before loading in the core and utilization in reactor operations.1.2 BackgroundThe PULSTAR reactor is an open-pool I MWth reactor. Its core is composed of an array of 5 x5fuel assemblies with 6x6 available fuel positions. The empty assembly positions have traditionallybeen used to house either graphite or beryllium reflectors (see Figure 1.1 below). Each assemblyis composed of a 5x5 array of U02 fuel pins that are enriched to 4% in 231U. The reactor has beenoperated under eight core configurations for 1541 MWd with a core average bum-up of less than5 GWd/MTU and a corresponding maximum fuel bum-up and assembly average bum-up of nomore than 15 GWd/MTU and 10 GWd/MTU, respectively. Control of the core is achieved throughthe movement of three Ag-In-Cd (80%-15%-5%) control rods. A fourth control rod of the samecomposition exists; however, this rod was designed for reactor pulsing in the original coreconfiguration and has since been disabled, remaining locked in position above the core. The coreis surrounded by six experimental beam tubes which penetrate the concrete reactor biologicalshield into the pool and may be emptied of water to permit the streaming of neutrons toexperimental facilities external to the reactor pool. Of these beam ports three are empty, andlower the available excess reactivity of the core. During operation the reactor is generally at fullpower; however, most reactivity properties, specifically excess reactivity and control rod worths,are referenced to the cold clean state. The reactor states are defined in Table 1.1.Table 1.1 Definition of reactor statesReactor State Power (MW) Bulk Moderator Average FuelTemperature (°F) Temperature (°F)Cold Clean 0 70 70Hot Zero Power < 0.0001 100 100Full Power 1 105 2931.3 MethodsThe MCNP6 Monte Carlo code was used for this work to simulate the PULSTAR reactor [ 1 ]. Theresults of the MCNP simulations were compared to historically measured data collected during theoperation of the PULSTAR starting in 1972. Subsequently, the MCNP model was used to predictcore characteristics for the current core and for potential core configurations that include 6%enriched assemblies. The MCNP6 code was selected due to its capability to model with high1/24 fidelity three dimensional geometries, which is of particular importance to modeling smallheterogeneous cores, and for its ability to account for core depletion in the analysis. Details of theMCNP6 analysis are given in Section 3.Figure 1.1. A schematic of the PULSTAR reactor core and surroundings in its current configuration (i.e.,reflected core 8). The dark squares on the top and left sides of the core represent the beryllium reflectors.1.4 Excess Reactivity HistoryThe initial 5x5 unreflected core, the standard core, had a measured excess reactivity of 2047percent milli-rho (pcm). To date reflected core 8 has a measured excess reactivity of 2442 pcm.The core has demonstrated an excess reactivity below the licensed limit of 3970 pcm over theentire power history from September 1972 to the current date [2]. A brief overview of the historicalcore configurations is listed in Table 1.2 (see layouts in Figure 3.1). The measured excessreactivity over the power history is summarized in Figure 1.2. Each core in the excess reactivityhistory is labeled by a number corresponding chronologically to the core name in Table 1.2.Current reactivity consumption is estimated to be 0.2 pcm/MWhr.1.5 Excess Reactivity NeedsOperational demand for experimentation requires that the reactor be maintained at full power for30-40 hours per week, resulting in a bum-up of approximately 300 pcm per year. To continueoperation of the PULSTAR, fresh fuel must be loaded in the core to ensure sufficient excessreactivity. To satisfy the operational need for excess reactivity, it is proposed to utilize the nine6% enriched U02 assemblies from the Buffalo PULSTAR reactor [3,4], currently in the possessionof the NCSU PULSTAR facility. The current net operational excess reactivity is approximately692 pcm accounting for experiments, feedback, and equilibrium xenon effects. The minimumexcess reactivity required for routine operation of 6-8 hours daily at 1 MW is nearly 1750 pcm, assummarized in Table 1.3. A drop below this value will prevent the reactor from achieving2/24 criticality. Therefore, the PULSTAR is expected to become xenon limited in approximately 2.3years.Table 1.2 Summary of core configurations of the NCSU PULSTAR research reactorCore Name Operation Core Configuration/Modifications Operation DatesI'-Standard 0-95 MWd 5x5 array of 4% enriched assemblies Aug-1972 to Feb-1977Core2-Reflected 95-162 MWd 5 Graphite reflectors inserted in row Apr- 1977 to Jun- 1979Core 1 A6-E63-Reflected Fuel movement from A I-A5 to F2-F6;Core 3 162-861 MWd 5 Graphite reflectors inserted in Al- Jun-1979 to Mar-1999A54-Reflected 861-969 MWd Graphite reflectors in Al-A5 replaced Mar-1999 to Jun-2005Core 4 with 5 Beryllium reflectorsBeryllium reflectors moved to A2-A6;5-Reflected Graphite reflectors moved to AI, B 1Cre 5e 969-1186 MWd and D1-FI; Fuel reconfigured and 5 Jun-2005 to Jun-2009fresh 4% enriched assemblies insertedin C I and B6-E63 Graphite reflectors in DI-FI moved6-Reflected to C l-E 1; Fission chamber movedCor 6- 1186-1241 MWd from F6 to A6; Fuel reconfigured and Jun-2009 to Oct-20 10Core 6 assemblies removed in reflected core5 inserted into C3-C5 and E3-E47-Reflected Fuel reconfigured and 4 assembliesCor 7 1241-1425 MWd replaced with fresh 4% assemblies Oct-2010 to Nov-2011Core 7 inserted into C3 and D3-D58-Reflected 1425-Current MWd Graphite reflectors in Al-E l replaced ..... ..Core 8 with Beryllium reflectors35003000 FC.)UU2500 F20001500Measurement825. 6 T4 5't v V;V 43/4 Kv1000 [5000 200 400 600 800 1000 1200 1400Operation Time [MWd]Figure 1.2. NCSU PULSTAR reactor core and excess reactivity history. The labels for each region correspondto the core configurations in chronological order, as listed in Table 1.2.3/24 Table 1.3 Estimated minimum excess reactivity -routine operationsXenon 300 pcmIsothermal Temperature Coefficient 120 pcmPower Defect (1 MW) 330 pcmBeam-Tube 4&5 (present core) 150 pcmBeam-Tube 6 (positron array) 750 pcmRotating Exposure Ports 100 pcmTOTAL 1750 pcm2.0 PULSTAR Core ConfigurationsAvailable historical data from measurements of excess reactivity, control rod worth values,shutdown margin, and power peaking factors for each core configuration provide information forconfirming neutronic calculations and models including the effects of fuel bum-up and coreshuffling. The fuel and reflector positions for each core configuration listed in Table 1.2 areillustrated in chronological order in Figure 3.1 below. Each fuel assembly is labeled according toits numeric index in the upper right comer, enrichment in the lower right, and core position in theupper left. This labeling allows the movement of individual assemblies to be modeled and trackedduring bum-up calculations while including the core configuration changes. Although the nominalfuel enrichment is specified as 4%, the enrichment specified by the fuel manufacturer is 4.026%[2,5]. This value was used to simulate the starting composition of the original 1972 "Standard"PULSTAR core.3.0 MCNP Core Modeling and Comparison to Historical Data3.1 Core ModelMCNP6 was utilized to model the steady-state neutronic characteristics of PULSTAR reactor [1].The model geometry and material compositions were set according to OEM specifications (i.e.manufacturer datasheets) and recent measurements of core components. For all materials theENDF/B-VII cross-sections libraries were used [6]. The temperatures of the moderator and fuelmaterials were modified using the TMP card of MCNP to the temperature corresponding to thesimulated core state, as defined in Table 1.1. Cross-section libraries were modified using theNJOY99 code to capture the thermal neutron scattering in light water and Doppler broadening forthe resonances in 235U and 238U [7]. The hydrogen library for H20 was generated using thestandard "H in H20" input available for the NJOY99 package [7]. The moderator density was setto the corresponding value at 1 atm at the temperature for the core state, as define in Table 1.1,using the NIST database [8,9]. The corresponding parameters and processed ENDF/B-VII libraryfor each defined core state are listed in Table 3.1.3.2 Methods for Calculation of Core Reactivity ParametersThe PULSTAR reactor MCNP model was compared to the historical measurements of excessreactivity (as illustrated in Figure 1.2), rod worth values, shutdown margin, and power peakingfactors. Modeling of the PULSTAR over the power history included the effects of bum-up andfuel movement, as illustrated by the core configurations in Figure 3.1. Additional comparisons4/24 were made for reflected core 8 by comparing measurements of assembly worth performed in May2014 to MCNP6 calculations.Table 3.1 MCNP parameters and data library processing for defined core statesTemperature (IF) ENDF/B-VII TemperatureReactor State Power (MeV) Moderator Density(MW) Moderator Fuel (g/cm3)Moderator Fuel (H in H20) (235U, 238U)Cold Clean 0 70 70 2.516x 10-08 2.516x10°08 0.99797134Hot Zero Power 100 100 2.536x 10-08 2.536x 10-08 0.993049690.0001Full Power 1 105 293 2.703x 10-08 3.602x10-08 0.99200516W15 STANDARD COREM REFLECTED CORE NO.I*MTATMO IRTAIVIG RGAT#MI RffATM iO aPOI I I "MmIFo=I "=I"OmM1 REFLECTED CORE NO.45 REFLECTED CORE NO.3Figure 3.1. PULSTAR core configurations. Each grid position is labeled by its alpha-numeric index (upperleft). Assemblies (pink) are labeled by assembly number (upper right) and enrichment (lower right).5/24 M REFLECTED CORE NO.L EM REFLECTED CORE NOAFO IM1 RFLECTED CORE NO.7 M1 REFLECTED CORE NO.8Figure 3.1 (continued)Burn-up CalculationsThe PULSTAR bum-up was performed sequentially for all the historical configurations of thereactor starting from the standard core through the current operational time of reflected core 8.Each configuration was depleted through three successive steps:1. Bum for 3 days at 1 MW with all rods withdrawn to establish equilibrium xenon2. Bum for the remainder of the cycle length (MWd) for the given core configuration at 1MW with all rods withdrawn3. Bum for 30 days at zero power to allow the fission products, specifically xenon, to decayThis three step procedure was adopted after it was shown through sensitivity analysis that changingthe number of bum-up steps (e.g., 10 steps of 10 days vs. I step of 100 days) did not affect thechange in kefr over the operation period.6/24 To simulate full power (1 MW) in MCNP during depletion, the temperatures, density, andprocessed data libraries of the fuel and moderator were set according to Table 3.1 (as defined inSection 3.1). The PULSTAR has an asymmetrical geometry and assembly positions have beenshuffled periodically over the core history. As a result of these core changes and lack of symmetry,the isotopic inventory of the PULSTAR may vary as a function of core position. Accurate trackingof the fuel inventory as a function of core was achieved by defining an array of 6250 cells for thefuel -10 axial sub-divisions for each fuel pin- and explicitly defining a material card for each cell.The isotope inventory of each of these materials was tracked for each depletion step. During corereconfigurations (e.g., shuffling) each fuel cell was appropriately moved with its correspondingassembly and axial position. To ensure an accurate fuel inventory during the bum, all second tieractinides and fission products contained within the MCNP CINDER database were tracked byutilizing the "BOPT 1 14" card [10]. At each core reconfiguration, the density of each fuel cellwas renormalized to the mass output from the MCNP bum-up of the previous core configurationto account for isotopes that were not tracked by MCNP.Each burn step used the kcode card:kcode 500 1.00000 50 550 100000 0such that 250,000 particles are generated per bum-up step, which corresponds to more than30,000,000 collisions per step. The keff calculated at each bum-up step has a statistical uncertaintyof less than +/--160 pcm, and the rate of change of fuel composition was found to be insensitive toan increase of particles per burn-up step beyond 250,000.Excess Reactivity (pexcess)In MCNP the excess reactivity may be estimated directly by modeling the reactor with all rodswithdrawn in the cold clean condition, as defined in Table 1.1. To model this state, the fuel andmoderator temperatures, density and processed ENDF/B-VII data libraries are set according toTable 3.1 (as defined in Section 3.1). The excess reactivity is calculated as the relative deviationof the MCNP kerr estimate from the critical state (keff = 1) in the cold clean condition, as givenbelowPexcess = (keff -1)/keff. Equation 3-1Acceptable results with errors of around 8 pcm in the keff calculation were obtained using the kcodecardkcode 100000 1.017 200 1000 300000 0The measured excess reactivity is estimated using the measured rod worth curves. In thesemeasurements the reactivity insertions due to rod withdrawal are typically small and the reactor isoperated with a period, T, of around 30 seconds. The reactivity is calculated in these measurementsusing the following expression for the inhour equation,7/24 6 = 169 = i=11 + X.iTEquation 3-2where j3 are the delayed neutron fractions, X i are delayed neutron decay constants and r is thereactor period. The measured reactivity was estimated using delayed neutron fraction for eachgroup that were scaled from the reference value [11]. The scaling factor was set such that the sumof the delayed neutron fraction for each group (i.e., P3eff) was equal to the average MCNP P3eff overthe core history (i.e., 745 pcm).Beta Effective (Peff)Beta effective defines the impact of delayed neutrons on the reactivity of the core. The total keffof the reactor must be equal to sum of the prompt and delayed neutron components which may beexpressed askeff = keff prompt + keffl eff, Equation 3-3where kefflprompt is the multiplication factor due to prompt neutrons, keff is the total effectivemultiplication factor and P3eff is the effective delayed neutron factor (i.e., beta effective). Betaeffective has been estimated to be 745 pcm. In MCNP the delayed neutron factor was determinedby utilizing the TOTNU card to calculate keff under the cold-clean condition (see Tables 1.1 and3.1) with and without delayed neutrons. Beta effective was estimated directly using the followingexpression13eff = keff-keffprompt Equation 3-4keffControl Rod WorthFor estimation of control rod worth using MCNP, the core is modeled in the cold-clean condition.The reactivity worth of a given control rod is calculated as the reactivity difference of the modelin the cold clean condition with all rods withdrawn and with the corresponding rod or rods fullyinserted. For each core configuration the control rod worth values were calculated for each rod.In addition to the control rod worth, the shutdown margin (SDM) was estimated, where the SDMis defined as the amount of reactivity by which the reactor would be subcritical from its presentcondition assuming all control rods are fully inserted except for the rod of highest reactivity worththat is assumed to be fully withdrawn [2]. This quantity may be estimated for the PULSTAR asSDM = Pexcess -Pgang + Phigh, Equation 3-5where phigh is the rod worth of the highest worth rod. The gang rod worth (pgang) was estimated asthe sum of the worth of the safety I (psi), safety 2 (ps2), and regulating rods (Preg). The highestworth rod is selected from safety 1, safety 2 and regulating rod, and excludes the non-operationalshim rod. The SDM must be less than -400 pcm.8/24 Assembly WorthThe worth of a single assembly is the change in excess reactivity of the reactor when that assemblyis removed. In MCNP the reactivity worth of an assembly is calculated as the difference in excessreactivity predicted for the model with all rods withdrawn, and for the model with all rodswithdrawn and that assembly re-defined as water (moderator).Power Peaking Factor CalculationsThe power peaking factors in the PULSTAR are traditionally measured by inserting a neutronprobe in each assembly and measuring the neutron flux as the probe is withdrawn from theassembly. In this case the power peaking factor is taken as the ratio of the highest axial neutronflux in an assembly to the average of all measured neutron flux values in the core. In MCNP theestimation of power peaking factors may be performed by calculating the fission energy depositionrate within each discrete fuel unit in the core. In this case, each fuel pin was divided into 10 axialcells resulting in 6250 fuel cells in the core. An F7 fission energy deposition tally was calculatedin each of the 6250 cells used to model the fuel with the cross-sections, moderator density, andtemperatures corresponding to the cold-clean condition, and with the control rods in the MCNPpredicted gang critical position. The power peaking factor for each pin was calculated as the ratioof the maximum fission energy deposition, F7 tally, of the 10 axial cells in the pin to the averagefission rate of the 6250 fuel material cells in the core. The pin power peaking factor, F', may bedefined asFn power of hotest cell in pinn , phot/(P)cell'Q -average power of all cells in the coreEquation 3-6where phot is the power of the hottest axial cell in pin n and (P)celi is the average power of all 250axial layers in the core. The greatest pin power peaking factor is the power peaking factor for thecore, FQ, and is compared to the Technical Specifications limit of 2.92. Assembly averaged powerpeaking factors were calculated by first averaging the fission rate in each pin within each axialzone and within a single assembly. Subsequently the assembly power peaking factor, F' for eachassembly was calculated as the ratio of the maximum fission rate of the 10 axial layers to theaverage fission rate of all 250 axial layers in the core. The assembly power peaking factor may bedefined aspower of hotest axial layer assembly in a = hot layerQ average power of all layers in the core a I\rlayer'Equation 3-7whereaphot layer is the sum of the pin powers in the hottest axial layer of assembly a and (PMlayeris the average power of all 250 axial layers in the core. The greatest assembly averaged powerpeaking factor is the assembly power peaking factor for the core, FQA. The assembly powerpeaking factors estimated from MCNP may be considered analogous to the measured flux peakingfactors, and as such provide a basis for comparison of the measured and calculated powerdistribution in the PULSTAR.9/24 3.3 Comparison of MCNP and Measured DataBefore using the MCNP model to predict safety related parameters for future core configurations,comparison to historical data was performed. This included data for excess reactivity, rod worthvalues, and assembly peaking factors. Each parameter was calculated as described above. Theexcess reactivity as a function of operational time, illustrated in Figure 3.2, demonstrates that themeasured values are in reasonable agreement with those predicted using MCNP6. The MCNP6estimated rod worth values, SDM, and assembly averaged peaking factors are compared tomeasurement in Table 3.2. The rods are listed as safety I (Si), safety 2 (S2), regulating (Reg),shim, and gang. The right value for each configuration column is the MCNP6 estimate whereasthe left value is the measurement. The peaking factors listed are the assembly peaking factor forthe core, with the exception of the standard core where the comparison is based on the pin powerpeaking factor due to the availability of such experimental data. As was found for the excessreactivity, the MCNP6 predicted parameters are within reasonable agreement with measurement.The power peaking factor distribution was also used for comparing MCNP6 predictions andmeasurement, as demonstrated in Figure 3.3 for reflected core 8. Each fuel assembly is labeledaccording to its numeric index in the upper right and core position in the upper left. The assemblypeaking factor calculated using MCNP6 is listed in the lower right of each cell and the measuredpeaking factor is listed in the lower left. The assembly peaking factors predicted by MCNP6 werewithin 10% of measurements near the core interior and within 30% near the core periphery.3500MCNP63000 v Measurement 82500 2.32000 5 64., V4 , 4VI IV iG~ 150010005000 200 400 600 800 1000 1200 1400Operation Time [MWd]Figure 3.2. A comparison of the measured and calculated PULSTAR excess reactivity history. The labels foreach region correspond to the core configurations in chronological order, as listed in Table 1.2.10/24 Table 3.2. Summary of parameters for historic core configurations (For each core the right column is theMCNP value and the left column is the measured value). For the standard core the comparison is made basedon pin power peaking factors as the measurement is more representative of this parameter.Standard Reflected Reflected Reflected Reflected Reflected Reflected ReflectedCore Core 1 Core 3 Core 4 Core 5 Core 6 Core 7 Core 8Meas Cale Meas Cale Meas Cak Meas Calc Meas Calc Meas Cale Meas Cale Meas Calesi(m 4165 4596 4084 4286 2655 2910 2943 3193 2348 2665 2583 2460 2246 2499 1991 2713(pcm)S2 2631 2933 3185 3297 2267 2326 2502 2504 2961 3199 2808 3314 2695 3275 2246 3048(pcm)Reg 2521 2769 2379 2623 3982 4029 3664 3784 2787 2982 2757 2842 2634 2927 2297 3135(pcm)Shim(pcm) 1644 1867 1899 2091 2961 3062 2696 2891 3727 3537 4492 3906 3982 3956 3522 3596(pcm)Gang 9316 10299 9648 10205 8903 9265 9110 9481 8096 8846 8168 8616 7576 8701 6534 8895(pcm)SDM -3104 -3621 --3578 -----------(pcm) 3462 2301 2307 3858 4066 3145 3521 3459 3380 2041 2655 1612 2812FQA 2.8 2.69 2.07 1.84 2.1 1.84 1.80 1.71 1,62 1.71 1.90 1.76 1.89 1.90 1.76 1.84In addition to rod worth values, excess reactivity, and power peaking factors, recent assemblyworth measurements allow for further comparison between MCNP calculations and measurementfor reflected core 8. The assembly worth values of F6 and F2 in reflected core 8 were measuredand found to be 200 pcm and 610 pcm respectively. The MCNP predicted assembly worth valuesare 270 pcm and 650 pcm for F6 and F2 respectively.e [ FUELLOCATIN ASSEMBLYF1ISSION MEAS CALCCHAMBERFigure 3.3. Reflected core 8 assembly power peaking map. Assembly peaking factors in fuel assemblies (pink)are listed for measurement (lower left) and calculation (lower right)11/24 4.0 MCNP Modeling of Mixed Enrichment Cores4.1 Calculation of Core Kinetic ParametersMixed enrichment configurations of the PULSTAR reactor were evaluated by changing theenrichment and density in the reflected core 8 model for each assembly loaded with 6% enrichedfuel. The excess reactivity, assembly worth, and power peaking factor were calculated usingMCNP6 for the case of loading a single 6% assembly to establish the positions in which "single"assemblies may be loaded without violating Technical Specifications limits. The excess reactivity(Equation 3-1) and assembly worth are computed as described in Section 3.2. In addition to excessreactivity, assembly worth, power peaking factor, rod worths, shutdown margin, and core kineticswere evaluated for representative mixed enrichment core configurations and for reflected core 8(e.g., see Figures 4.1 and 4.2 below). The rod worth values and shutdown margins are calculatedas described in Section 3.2. The calculation of core kinetics are described below and include themoderator feedback coefficient, reactivity insertion rate, void coefficient, Doppler feedbackcoefficient, power defect, and P3eff. Additional calculations were performed for pin power andassembly power peaking factor maps using the approach described in Section 3.2.Figure 4.1. MCNP models of reflected core 8 (left) and a representative reflected core 9-4 (right).Reactivity Parameter CalculationsThe PULSTAR has various characteristic reactivity parameters which may be estimated by MonteCarlo methods, including excess reactivity, rod worth, assembly worth, reactivity insertion rate,beta effective, and feedback coefficients. The feedback coefficients of interest were the moderator,Doppler, and void coefficients. The procedure for calculating each parameter is described in itsspecified section below. In general, all reactivity effects were calculated under similar conditionsto those of the excess reactivity. The reactivity calculated for a simulated core condition is the sumtotal of the excess and the change in reactivity due to changes from the cold clean condition; wherethe cold clean condition is a xenon free core at 70 OF. This estimation may be expressed moreconcisely as,12/24 P ---- Pexcess + Ap, Equation 4-1where p is the calculated reactivity for a particular state, Pexcess is the reactivity in the cold cleancondition with all rods withdrawn, and Ap is the effect on reactivity of a change in the core statefrom cold clean condition. The calculated reactivity p is the output of MCNP and may be used todetermine the reactivity feedback of changes in the core state. All feedback coefficients weredetermined assuming a linear model between reactivity and the varied parameter expressed as,P = Pexcess + QGAG, Equation 4-2where p is the reactivity, AG is the change in a parameter which describes the core state (e.g., fueltemperature) and aG is the linear feedback coefficient corresponding to the parameter G. If p isestimated for multiple values of G then under the assumption the of a linear feedback, the slope ofa linear least squares regression of p and G is considered the estimate of aG. As in the case of theprevious calculations all materials were modeled with ENDF/B-VII cross-section libraries, whichwere treated with NJOY99 for Doppler broadening or to produce thermal scattering kernels whennecessary (see Section 3.1). The kcode line used in the calculation of reactivity feedbackcoefficients waskcode 100000 1.017 200 1000 300000 0The total number of particles run (80,000,000 tracked; 20,000,000 skipped) produced a value ofkeff value with a statistical uncertainty of approximately 8 pcm. Unless otherwise specified all rodsare assumed fully extruded in all the calculations described below.Rod Reactivity Insertion RateThe operation of the reactor requires the direct insertion of reactivity through withdrawal of controlrods, most commonly in a gang configuration. To model the reactivity insertion rate resultingfrom control rod movement in MCNP, the keff of the core was estimated in the cold clean conditionwith the rods in two gang positions, 12" and 15" insertion. These values were chosen as theybound the critical position at cold clean where the sensitivity or reactivity to rod position is bothlinear and greatest. The resulting reactivity insertion rate, 05, is calculated asL=Ph Equation 4-3where Ap is the change in reactivity between the rod positions, Ah is the 3" change in rod position,and lh is the rod withdraw rate of 7.5"/min. The reactivity insertion rate due to rod withdrawal hasa limit of 100 pcm/s.Moderator CoefficientThe isothermal temperature coefficient (aT), referred to operationally as the moderator feedbackcoefficient, measures the effect of core temperature on reactivity. Operationally this effect ismeasured by varying the flow rate in the secondary side of the heat exchanger at low core powers(<1 kW). When the core is in an isothermal condition both moderator temperature and fueltemperature are approximately the same such that the isothermal coefficient measures the13/24 combined effect of the moderator and fuel. In MCNP this coefficient was estimated with a linearcomparison between the cold clean condition and the zero power condition (see Tables 1.1 and3.1).Void CoefficientsVoids occur in the moderator of the PULSTAR as either microscopic cavities or by the insertionof in core probes. To simulate voids, the water in two channels was re-defined as void. Thechannels chosen were the two right of center in assembly D4. These pins correspond to positionsthat may be measured using in-core probes. The void coefficient was calculated per Equation 4-2, using the channel volume of 56.9 cm3.The reactivity difference was taken as that between theexcess reactivity and the reactivity of the core with the voided channels.Doppler CoefficientThe Doppler coefficient in the PULSTAR is a measure of the negative reactivity insertion due tothe rise in fuel temperature from the hot zero power state to the full power state (see Table 1.1).Doppler broadening in a low-bum-up core such as the PULSTAR occurs primarily in 238U;however, effects from 235U may also be present. To examine the effect of Doppler broadening onthe reactivity of the MCNP model, ACER libraries for 238U and 235U were prepared using NJOY99and the corresponding ENDF/B-VII libraries. The fuel temperature input card, TMP card, andcorresponding Doppler broadened libraries for U-235 and U-238 were varied homogenously forall fuel cells as function of temperature (100 'F, 142 'F, 179 'F, 217 'F, 293 'F) while maintaininga homogeneous moderator temperature, using the thermal cross-sections of H in H20 and densityappropriate for 100 'F (see hot zero power in Table 3.1). The Doppler coefficient of reactivity(aF) is the slope between the reactivity and fuel temperature, per Equation 4-2.Power DefectThe change in operation state from hot zero power to full power in the NCSU PULSTAR isassociated with a distinct change in reactivity, which is both a combination of the moderator andDoppler feedback effects known as the power defect, (cQp). This power defect may be calculatedper Equation 4-2 by comparing the reactivity with all rods withdrawn in the hot zero power andfull power states as described in Table 3.1.Power Peaking Factor CalculationsAs discussed in Section 3.2, the MCNP estimation of power peaking factors may be determinedby calculating the fission energy deposition rate within each discrete fuel unit in the core. An F7fission energy deposition tally was calculated in each of the 6250 cells used to model the fuel withthe cross-sections, moderator density, and temperatures corresponding to the cold clean condition,and with the control rods in the MCNP predicted gang critical position. The cold clean conditionis considered to be the most conservative case with respect to axial power peaking as including thereactivity losses due to power defect results in withdrawal of control rods and thus a more uniformpower distribution. The pin power peaking for each pin was calculated as the ratio of the maximumfission energy deposition, F7 tally, of the 10 axial cells in the pin to the average fission rate of the6250 fuel material cells in the core. The highest pin power peaking factor is the power peakingfactor for the core, FQ, and has a Technical Specifications limit of 2.92.14/24 4.2 Mixed Enrichment Core ConfigurationsCore configurations containing a single 6% enriched assembly were considered. MCNP6calculations were performed where a single 6% assembly was inserted in a selected position thatoriginally contained a 4% enriched assembly in reflected core 8 to examine the core limits usingsuch fuel loading patterns. Multiple 6% loading patterns were considered for positions that didnot violate safety limits for single 6% assembly loading, and are shown in Figure 4.2. Each fuelassembly is labeled according to its numeric index in the upper right comer, enrichment in thelower right, and core position in the upper left. The 6% assemblies have not yet been given anumeric designation.515 REFLECTED CORE .-1515 REFI.CTED CORE NO.9-25V5 RFMMLECTD COR NO.3W REFLECTED CORE NO.5-4mumEJ ramFigure 4.2. PULSTAR mixed enrichment core configurations based on the insertion of 6% assemblies inselected positions of row F and/or column 6. Each grid position is labeled by its alpha-numeric index (upperleft). Assemblies (pink) are labeled by assembly number (upper right) and enrichment (lower left).15/24 4.3 ResultsThe MCNP6 model was used to characterize the reactivity behavior of the PULSTAR in its currentconfiguration (reflected core 8), and possible configurations for reflected core 9 with 6% enrichedfuel assemblies. The excess reactivity, 6% assembly worth, and power peaking factors for eachsingle 6% assembly loading is summarized in Table 4.1. The license limit for excess reactivity,assembly worth, and power peaking factors are 3970 pcm, 1590 pcm, and 2.92 respectively.Permitted and non-permitted single 6% assembly loading positions are illustrated in Figure 4.3.The core position is designated in the upper left comer of each cell. Each assembly locationdesignates a 6% assembly loaded in that position with the core excess reactivity in the upper rightcomer, the assembly worth in the lower left comer, and the power peaking factor, FQ, in the lowerright. Positions where single 6% assembly loading is permitted based on Technical Specificationslimits are green, whereas positions where single 6% assembly loading is not permitted are red.Table 4.1. Summary of single 6% assembly loading.Core Position Excess Reactivity 6% Assembly FQLoaded (pcm) Worth (pcm)B2 3010 1812 2.62B3 3112 1917 2.73B4 3135 2036 2.87B5 3008 1564 2.76B6 2789 714 2.57C2 3127 2143 2.63C3 3061 1856 2.70C4 3147 2030 2.91C5 2990 1559 2.81C6 2847 773 2.53D2 3048 2282 2.82D3 3092 1963 2.91D4 3145 2191 3.15D5 2986 1706 3.07D6 2858 803 2.56E2 3036 1673 2.76E3 3005 1477 2.83E4 3025 1634 3.09E5 2997 1302 3.01E6 2797 590 2.56F2 2779 825 2.52F3 2865 936 2.53F4 2916 1075 2.55F5 2829 848 2.52F6 2701 367 2.5216/24 COREGRID EXCESSLDC:ATOCNCT REACTIVITYGREATEST COREASSEMBLY PEAJK(N.CHAMMFRI ORTHVO.TH FACTORFigure 4.3. Permitted single 6% fuel loading positions (green). The excess reactivity, greatest assembly worthand core power peaking factor are listed for single 6% fuel loaded in that position. Positions considered notpermitted for 6% loading are red.As described in Section 4.3, mixed enrichment core configuration with multiple 6% enrichedassemblies were considered where the 6% assemblies were loaded into permitted core positionsindicated in Figure 4.2. The excess reactivity, rod worth values, SDM, reactivity insertion rate,and core pin peaking factors are tabulated in Table 4.2 for representative mixed enrichment coreswith multiple 6% assemblies as illustrated in Figure 4.2. The rods are listed as safety I (S 1), safety2 (S2), regulating (Reg), shim, and gang. The power peaking factor is the maximum pin powerpeaking factor in the core. The license limits (as specified in the technical specifications) forexcess reactivity, SDM, reactivity insertion rate, and power peaking factor are less than 3970 pcm,less than -400 pcm, less than 100 pcm/s, and less than 2.92 respectively. These core parametersare estimated to be within the safety limits for all multiple 6% assembly mixed enrichment coreconfigurations considered (see Figure 4.2). A sensitivity analysis of the power peaking factor tothe critical rod position demonstrated that the power peaking factor predicted by MCNP6 variesby no more than 5% for ganged rod positions within 50 pcm of the critical position. Assemblyaveraged power peaking factors maps for reflected core 8 and representative reflected core 9configurations loaded with multiple 6% assemblies are illustrated in Figure 4.4-4.8. Pin Powerpeaking factor maps for reflected core 8 and the representative reflected core 9 mixed enrichmentconfigurations are illustrated in Figure 4.9. Core positions are indicated in the upper left of eachcell while the assembly numeric index for 4% enriched assemblies is indicated in the upper right.The 6% enriched assemblies from the SUNY Buffalo PULSTAR have not yet been given anumeric index. Assembly peaking factors are indicated in the lower right of each cell and theassembly worth of 6% enriched assemblies is indicated in lower left. The MCNP6 calculatedpeaking factors for all reflected core 9 cases are within 10% of those calculated for reflected core17/24

8. The predicted worth of a single 6% enriched fuel in multiple loading reflected core 9configurations considered were determined to be below the 1590 pcm license limit for reactivityinsertion by a single fuel assembly.Table 4.2 Summary of MCNP6 core parameters for representative mixed enrichment core configurationsReflected Reflected Reflected Reflected ReflectedCore 8 Core 9-1 Core 9-2 Core 9-3 Core 9-4Pexcess 3970 2604 2895 3160 3214 3735(pcm)SI (pcm) 2713 2621 2534 2532 2357S2 (pcm) 3048 2935 2930 2839 2630Reg (pcm) 3135 3171 3043 3162 3133Shim(pcm 3596 3594 3698 3642 3651(pcm)Gang 8895 8728 8507 8533 8120(pcm)SDM(pm -400 -2812 -2661 -2304 -2156 -1253(pcm)S(pcm/s) 100 68 68 65 65 62FQ 2.92 2.56 2.51 2.54 2.59 2.78Based on the above table, representative cores 9-1 and 9-2 are considered acceptable for loading.The pexcess and SDM are comfortably within the set technical specifications limits. Cores 9-3 and9-4 would be precluded based on the power peaking factor (FQ) as its value falls outside a marginof 15% that is set to be greater than the maximum deviation between the calculated andexperimentally estimated values (see Table 3.2). In this case, if FQ for cores 9-3 and 9-4 ismultiplied by 1.15 it would yield a value greater than 2.92.FUELASSEMBLYLOCATION NUMBERS1 ASSEMBLYASEBYPOWER~FSNORTH 044118 FACTORFigure 4.4. Reflected core 8 assembly power peaking factor map. Each grid position is labeled by its alpha-numeric index (upper left). Assemblies (pink) are labeled by assembly number (upper right) for 4% enrichedfuel only. Assembly power peaking factor (lower right) and measured assembly worth (lower left) are listed.18/24 IS FUELGRID BYLOCATIO NUMBERASSEMBLYASSEMBLY POVER'.#IORTH PEAKINGFACTORFigure 4.5. Reflected core 9-1 assembly power peaking factor map. Assembly power peaking factor (lowerright) and assembly worth for 6% enrich fuel (lower left) are listed.amU ASSEMBLYLOCATION NUMBERASSEMBLYASSEMBLY POWERVORTH PEAKINGFACTORFigure 4.6. Reflected core 9-2 assembly power peaking factor map. Assembly power peaking factor (lowerright) and assembly worth for 6% enrich fuel (lower left) are listed.19/24 I I ( i I \ I ý 1 11 1 \ ( I ( ) I ý I I I \, ( ) ( , I ý \ ý, 1 ) 1 \ I i I ( 'I, I ý ( j 1 1 \, "I I "1 1 t \ 1 1 1 ý ý I I ')FUIELGRD ASSEMBLYLOCATION NUMBERNUMBERASSEMBLYASSEMBLY POVERFS ORTH PEAKINGFACTORFigure 4.7. Reflected core 9-3 assembly power peaking factor map. Assembly power peaking factor (lowerright) and assembly worth for 6% enrich fuel (lower left) are listed.ASSEMBSLYASSEMBLY POWERFISSOCIN WORTH PEAKINGCHAMBuER MFACTORFigure 4.8. Reflected core 9-4 assembly power peaking factor map. Assembly power peaking factor (lowerright) and assembly worth for 6% enrich fuel (lower left) are listed.20/24 RCSABCD12 345 6 Rc91 23 45 6ABCDF ..F F .CRc9-2 1 2 3 4 5 6 RC9-3 1 2 3 4 5 6A AB BC CD DE ERc94 1 2 3 4 5 6 oW~0.600 *0.901.0B 1.11.31.4C 1.51.61.71.8D2.12.22.3E 242.52.42.7F F.C. 2.8209Figure 4.9. Pin power peaking factor map of reflected cores 8, 9-1, 9-2, 9-3 and 9-4.21/24 The reactivity feedback coefficients were computed for core 8 and the various configurations ofreflected core 9. The calculation of the Doppler coefficient for reflected core 8 using linearregression with Equation 4-2, is illustrated in Figure 4.10 for both beginning of cycle (1425 MWd)and the current state (1541 MWd). The calculated feedback coefficients and P3etf are tabulated inTable 4.3. The Doppler and moderator coefficients have a relative uncertainty due to the statisticaluncertainty in keff of nearly 5% and 10% respectively. The void coefficients have a relativeuncertainty of nearly 10%. The power defect for each configuration has a statistical uncertaintyof around 20 pcm. With the exception of the moderator feedback coefficient, all feedbackcoefficients and P3eff were calculated to change by less than 10% between different coreconfigurations.300028002600m 240022002000 L50A RC8 (1425MWd)0 RC8 (154 IMWd)100 150 200 250 300350Temperature [°F]Figure 4.10. Reflected core 8 linear regression for calculation of Doppler coefficient. Operation times of 1425MWd (begging of cycle) and 1541 MWd (current cycle state) for reflected core 8 are given, as illustrated inFigure 3.2Table 4.3 Summary of MCNP6 core kinetics for representative mixed enrichment configurations.Reflected Reflected Reflected Reflected ReflectedCore 8 Core 9-1 Core 9-2 Core 9-3 Core 9-4IT (pcm/°F) -3.44 -2.96 -3.44 -3.28 -2.38aF (pcm/°F) -1.66 -1.68 -1.64 -1.65 -1.58atv -1.09 -1.09 -1.13 -1.16 -1.08(pcm/cm3)CIp -335 -341 -334 -341 -349(pcm/MW)I3eff (Pcm) 742 716 733 740 73822/24 5.0 ConclusionsAn MCNP6 Monte Carlo model was created to simulate the NCSU PULSTAR reactor's neutroniccharacteristics. Using this model, it was demonstrated that reasonable agreement exists betweenmeasured and calculated excess reactivity (as a function of operating time), rod worth values, andassembly averaged power peaking factors. Furthermore, the model was shown to reliably predictthe historic PULSTAR core behavior in comparison to measurements. Therefore, based on thismodel, analysis was performed of the current reflected core 8, with the insertion of fuel assembliesthat are enriched to 6% (by weight) with 235U. Such assemblies were obtained from thedecommissioned PULSTAR reactor at the BMRC of SUNY Buffalo and are currently stored atthe NCSU PULSTAR facility.The performed MCNP analysis showed that, for several representative "reflected core 9"configurations, no reactivity parameters associated with the safe insertion of fuel and safe start-upof the core violate the PULSTAR's Technical Specifications. This includes the total core excessreactivity (limited to less than 3970 pcm), the worth of a single inserted assembly (limited to lessthan 1590 pcm), the shutdown margin for the cold clean condition (limited to less than -400 pcm),the maximum reactivity insertion rate through rod withdrawal (limited to less than 100 pcm/s), andthe maximum core pin power peaking factor (limited to less than 2.92). The examined mixedenrichment configurations based on the loading of one 6% assembly or two 6% assemblies (e.g.,reflected core 9-1 and 9-2) have been found to meet such limits with substantial margin. Inaddition, for configurations such as cores 9-1 and 9-2 the pin power peaking factor remains belowthe limit by a set 15% margin. In all cases, the PULSTAR maintained its overall negative feedbackbehavior as demonstrated by a power coefficient of reactivity that is less than -300 pcm/MW.23/24 6.0 References[1] J. T. Goorley et al., "Initial MCNP6 Release Overview MCNP6 Version 1.0," Los AlamosNational Laboratory report LA-UR- 13-22934 (2013).[2] Safety Analysis Report, North Carolina State University PULSTAR Reactor, License No. R-120, Docket No. 50-297 (1997).[3] Buffalo Materials Research Center Hazards Summary Report, Revision II, September 23,1963.[3] Buffalo Materials Research Center Safety Evaluation Report, NUREG-0982, May 1983.[5] Specifications for PULSTAR Fuel Assemblies, American Machine & Foundry Co., YorkDivision, April 1970 (York, Pennsylvania).[6] M. B. Chadwick et al., Nuclear Data Sheets, vol. 112, 2887 (2011).[7] R. E. MacFarlane, D. W. Muir, "The NJOY Nuclear Data Processing System Version 91,"Los Alamos National Laboratory report LA-12740-M (1994).[8] Wagner, W., Pruss, A., "The IAPWS formulation 1995 for the thermodynamic properties ofordinary water substance for general and scientific use," J. Phys. Chem. Ref Data, 31, 2, 387-535, (2002).[9] Saul, A., Wagner, W., "A Fundamental Equation for Water Covering the Range From theMelting Line to 1273 K at Pressures up to 25000 MPa, "J. Phys. Chem. Ref Data, 1989, 18,4, 1537-1564, (1989).[10] W. B. Wilson et al., "Recent Development of the CINDER'90 Transmutation Code and DataLibrary for Actinide Transmutation Studies," Proc. GLOBAL'95 Int. Conf. on Evaluation ofEmerging Nuclear Fuel Cycle Systems, September 11-14, 1995, Versailles, France, pp. 848(1995).[11] J. R. Lamarsh, H. Goldstein ed., Introduction to Nuclear Reactor Theory, Addison-Wesley,June 1966 (Reading, Massachusetts).24/24