NEUTRONIC AND THERMAL HYDRAULIC ANALYSIS OF THE GEOLOGICAL SURVEY TRIGA REACTOR. Nicolas Shugart

Transcription

1 NEUTRONIC AND THERMAL HYDRAULIC ANALYSIS OF THE GEOLOGICAL SURVEY TRIGA REACTOR by Niolas Shugart

2 Copyright by Niolas E. Shugart 2013 All Rights Reserved

3 A Thesis submitted to the Faulty and the Board of Trustees of the Colorado Shool of Mines in partial fulfillment of the requirements for the degree of Master of Siene (Nulear Engineering) Golden, Colorado Date Signed: Niolas Shugart Signed: Dr. Jeffrey King Thesis Advisor Golden, Colorado Date Signed: Dr. Jeffrey King Assistant Professor and Interim Head Nulear Siene and Engineering Program ii

4 ABSTRACT The United States Geologial Survey TRIGA Reator (GSTR) is a 1 MW reator loated in Lakewood, Colorado. In support of the GSTR s reliensing efforts, this projet developed and validated a Monte Carlo N-Partile Version 5 (MCNP5) model of the GSTR reator. The model provided estimates of the exess reativity, power distribution and the fuel temperature, water temperature, void, and power reativity oeffiients for the urrent and limiting ore. The MCNP5 model predits a limiting ore exess reativity of $6.48 with a peak rod power of 22.2 kw. The fuel and void reativity oeffiients for the limiting ore are strongly negative, and the ore water reativity oeffiient is slightly positive, onsistent with other TRIGA analyses. The average fuel temperature reativity oeffiient of the full power limiting ore is $/K while the average ore void oeffiient is $/K from 0-20 % void. The ore water temperature reativity oeffiient is $/K. Following the neutronis analysis, the projet developed RELAP5 and PARET-ANL models of the GSTR hot-rod fuel hannel under steady state and transient onditions. The GSTR limiting ore, determined as part of this analysis, provides a worst ase operating senario for the reator. During steady state operations, the hot rod of the limiting ore has a peak fuel temperature of 829 K and a minimum departure from nuleate boiling ratio of After a $3.00 pulse reativity insertion the fuel reahes a peak temperature is 1070 K. Examining the model results several seonds after a pulse reveals flow instabilities that result from weaknesses in the urrent two-hannel model. iii

5 TABLE OF CONTENTS ABSTRACT... iii LIST OF FIGURES... vii LIST OF TABLES... x LIST OF SYMBOLS... xii ACKNOWLEDGMENTS... xv CHAPTER 1 INTRODUCTION... 1 CHAPTER 2 BACKGROUND TRIGA Reators TRIGA Fuel Rods Geologial Survey TRIGA Reator Code Seletion Monte Carlo N-Partile Temperature Adjustments in MCNP MCNP ENDF Libraries and Zironium Cross-Setions Reator Exursion and Leak Analysis Program Program for the Analysis of Reator Transients...26 CHAPTER 3 NEUTRONICS ANALYSIS Introdution Desription of the Geologial Survey TRIGA Reator Desription of the GSTR Core Model Fuel Depletion Analysis Desription of the Limiting Core iv

6 Full-Power Model Validation Control Rod Calibration Critial Control Rod Position Flux Profile Reliensing Analysis Limiting Core Exess and Shutdown Reativity Margins Reator Power Distribution Reativity Calulations Summary and Conlusions...70 CHAPTER 4 THERMAL-HYDRAULIC ANALYSIS Introdution Desription of the Geologial Survey TRIGA Reator Summary of Neutronis Analysis of the GSTR Desription of the Thermal-Hydrauli Models Steady-State RELAP Model Transient RELAP Model PARET Model Testing Methodology Thermal-Hydrauli Results Model Calibration Steady-State Results Transient Results v

7 4.6. Summary and Conlusions CHAPTER 5 SUMMARY AND CONCLUSIONS CHAPTER 6 SUGGESTIONS FOR FUTURE RESEARCH REFERENCES CITED APPENDIX A GSTR MCNP5 MODEL APPENDIX B RELAP STEADY STATE MODEL APPENDIX C RELAP TRANSIENT MODEL APPENDIX D PARET MODEL vi

8 LIST OF FIGURES Figure 2.1. GSTR ore during operation....7 Figure 2.2. Shematis of the TRIGA fuel types used in the GSTR Figure 2.3. The different ontrol rod types used in the GSTR ompared to a fuel rod Figure 2.4. The GSTR Core with the different experimental failities shown...14 Figure 2.5. Example of a heat struture in RELAP with 10 nodes in two different materials with non-uniform mesh lengths Figure 3.1. The GSTR ore, highlighting the refletor, ontrol rods, and fuel Figure 3.2. Shematis of the TRIGA fuel types used in the GSTR Figure 3.3. Diagram of the two ontrol rod types used in the GSTR, showing how the fuel and void followers line up to a regular fuel element Figure 3.4. Radial and axial views of the MCNP model of the GSTR ore in the urrent operating onfiguration Figure 3.5. Fuel layout in the urrent GSTR operating ore Figure 3.6. Composition of an 8.5 wt.% E-Ring fuel element before and after 25 atom % uranium 235 depletion Figure 3.7. Radial view of the GSTR limiting ore...42 Figure 3.8. Example ross-setions of fresh and depleted GSTR ontrol rods Figure 3.9. Measured and alulated reativity worth urves for the regulating rod Figure Measured and alulated reativity worth urves for the transient rod Figure Measured and alulated reativity worth urves for shim rod Figure Measured and alulated reativity worth urves for shim rod Figure Multipliation fators alulated by the GSTR model using the ombinations of neutron libraries listed in Table Figure Gold foil ativity following a one-hour ativation as predited by MCNP and measured by the GSTR staff vii

9 Figure Point-to-average flux ratios in the GSTR entral thimble Figure Power profile for the GSTR limiting ore operating at 1.1 MW...61 Figure Calulated multipliation fator for the GSTR limiting ore as a funtion of fuel temperature Figure Calulated fuel temperature reativity oeffiient for the GSTR limiting ore as a funtion of fuel temperature Figure Calulated multipliation fator for the GSTR limiting ore as a funtion of ore water temperature Figure Calulated ore water temperature reativity oeffiient for the GSTR limiting ore as a funtion of ore water temperature Figure Fators ontributing to the multipliation fator of the 5W ase in Figure 18 as a funtion of ore water temperature Figure Calulated multipliation fator for the GSTR limiting ore as a funtion of ore void fration Figure Calulated ore void reativity oeffiient for the GSTR limiting ore as a funtion of ore void fration Figure 4.1. The GSTR ore, highlighting the refletor, ontrol rods, and fuel Figure 4.2. TRIGA stainless steel lad fuel rod Figure 4.3. Radial view of the GSTR operating ore Figure 4.4. Radial view of the GSTR limiting ore Figure 4.5. Axial power fator alulated by the MCNP model of the GSTR limiting ore Figure 4.6. Radial power fator alulated by the MCNP model of the GSTR limiting ore Figure 4.7. Steady state RELAP model of the GSTR Figure 4.8. Layout of the axial and radial nodes of the fuel rod in the RELAP and PARET models of the GSTR limiting ore Figure 4.9. Transient RELAP model of the GSTR Figure Fuel temperature profiles as a funtion of gap thikness Figure Peak fuel temperatures as a funtion of rod power at different gap sizes in an aluminum lad rod viii

10 Figure Peak fuel temperature as a funtion of rod power at different gap sizes in a stainless steel lad rod Figure Generalized temperature urves for the GSTR fuel rods and hannels as a funtion of power Figure Steady state hot-rod temperature profile for the middle of the hot-rod for the GSTR at full power (1.1 MW) Figure Departure from nuleate boiling ratio as a funtion of position along the hotrod fuel element...96 Figure Power during a $1.50 pulse modeled in both PARET and RELAP Figure Peak fuel temperature during a $1.50 pulse modeled in both PARET and RELAP Figure Inserted and total reativity during a $1.50 pulse modeled in both PARET and RELAP Figure Temperatures and powers alulated as a funtion of time for the GSTR hot rod during a $3.00 pulse Figure Calulated void fration in the hot-hannel as a funtion of time during a $3.00 pulse Figure Inserted and alulated reativities as a funtion of time during $3.00 pulse Figure Temperatures and powers alulated as a funtion of time for the GSTR hot rod during a $2.75 pulse Figure Temperatures and powers alulated as a funtion of time for the GSTR hot rod during a $2.50 pulse Figure Temperatures and powers alulated as a funtion of time for the GSTR hot rod during a $2.00 pulse Figure Calulated void fration in the hot-hannel as a funtion of time during a $2.00 pulse ix

11 LIST OF TABLES Table 2.1. GSTR Fuel types and basi information Table 3.1. GSTR fuel types...31 Table 3.2. Isotopes onsidered in the depletion analysis Table 3.3. Average alulated rod powers and fuel, ladding, and hannel water temperatures by type and ring for the urrent GSTR ore at full power Table 3.4. Average surutual material, ore water and ladding temperatures used in the model of the urrent GSTR ore at full power...46 Table 3.5. Changes between the low power and full power MCNP models of the urrent GSTR onfiguration Table 3.6. Average alulated rod powers and fuel, ladding, and hannel water temperatures by type and ring for the limiting GSTR ore at full power Table 3.7. Average strutural material, ore water and ladding temperatures used in the limiting GSTR ore model at full power Table 3.8. Control rod alibration results Table 3.9. Test ases onsidered in Figure Table Critial ontrol rod position verifiation data Table Exess and shutdown margins of the limiting ore Table Input parameters for the reativity oeffiient analysis Table Integral fuel reativity as a funtion of temperature...64 Table Integral void reativity as a funtion of ore void fration Table 4.1. GSTR fuel types used in the limiting ore thermal-hydrauli analysis Table 4.2. Prompt fuel temperature reativity data for the GSTR limiting ore Table 4.3. Void reativity data for the GSTR limiting ore Table 4.4. Six-group delayed neutron frations used in the transient thermal-hydrauli models (Lewis, 2008) x

12 Table 4.5. Axial node lengths in the hot hannel segments of the GSTR Table 4.6. Radial node lengths in the heat struture segment of thikness in the RELAP model of the GSTR Table 4.7. Calulation of the flow area used in the steady state thermal-hydrauli analyses Table 4.8. Flow area alulations for the GSTR limiting ore used in the transient analysis Table 4.9. Reativity insertion sequene for a $3 pulse Table Peak powers and temperatures prediated by the hot hannel analysis for a $3.00 pulse of the GSTR limiting ore xi

13 LIST OF SYMBOLS A - initial ativity following irradiation in the GSTR (Bq). A flow - Flow area of the hannel (m) A au - atomi weight of gold (g) D e - equivalent hydrauli diameter (m)r Εn - average oolant enthalpy (J/kg) E - energy produed (MWH) E Sm149 - fission yield of samarium-149 (atoms/fission) F - MCNP tally result (atoms/b-m) f - frition fator G - mass flow rate (kg/s) g - aeleration due to gravity (m/s 2 ) h - enthalpy i numeri index k - MCNP reativity alulation result k eff - effetive multipliation fator in a reator l - partile trak length (m) M - number of ative yles M Au - mass of the gold foil (g) M U mass of Uraniuim-236 burned (g) m - individual yle number n - node index N - arbitrary number, Chapter 2 xii

14 N - number of rods in ore, Chapter 3 N a - Avagrado s number OD - Outer Diameter of fuel element (m) P - reator power (W) Pr - pressure (Pa) Pi - pith (m) P rod - power in a rod (kw) P(v,T) - distribution of the target veloities in the experiment(m/s) PF - peaking fator q - heat soure per unit volume (J/m 3 ) R - relative error Ṙ- reation rate (1/s) R fuel - thermal resistivity of the fuel ((m 2 K)/W) R lad - thermal resistivity of the ladding((m 2 K)/W) S - approximation of standard deviation SPR - soure partile rate (N/s) t - time T - duration of the irridation (s) TR - MCNP tally result from the model T l - the enterline temperature of the fuel rod (K) T 1/2 - half-life of gold-198 (s) U - internal energy (J) - veloity of the target (m/s) xiii

15 v - veloity of inident partiles (m/s) x - quantity of interest from an MCNP alulation - average value of x - average value of x squared z - axial oordinate (positive diretion is upwards) α - fitting oeffiient used in RELAP alulations β - fitting oeffiient used in RELAP alulations Β eff - effetive delayed neutron fration δ - energy per fission (MeV) γ - fitting oeffiient used in RELAP alulations ρ - density (kg/m 3 ) ρ - reativity ($) ν - number of neutrons per fission σ - mirosopi ross-setion of an stationary nulei (b) σ abs - adsorption ross setion of samarium 149 (b). σ f - fission ross setion of uraniu 235 (b) Σ tot - total neutron ross-setion (b) φ - fitting oeffiient used in RELAP alulations ξ- random number between 0-1 xiv

16 ACKNOWLEDGMENTS This projet, whih has taken the better part of two years of my life, is an interesting stepping-stone in my aademi areer, and has been an amazing learning opportunity in both life and nulear engineering. I would never have been able to ahieve this without the support of my adviser, Dr. Jeffrey King, and his belief in my own potential, even when I sometimes doubted it myself. I would like to thank you Dr. King, not for making this enjoyable, or fun, beause it wasn t, but for making this perhaps one of the greatest learning opportunities I will ever reeive, and I look forward to ompleting my Dotorate with you. Some things in life should not be fun, but they should be right, or at least provide a reasonable result within the unertainty bounds of the problem, and this was a lesson you taught me over the past three years. Even if oasionally your drive for perfetion seemed to onflit with my desire for progress I realize now that sometimes it just has to be right. I would also like to thank my friends and o-workers whose help and support keep me going, and whose ideas helped me in many of the more diffiult parts of this analysis, even if it was just as someone to boune ideas off of. Speifially I would like to thank Jeremy Washington for his help on MCNP5, Weston Collins for his assistane brainstorming the thermal-hydrauli problems, and Jason Sexauer, Daniel Suhr, Savannah Fitzwater, Sarah Morgan, Jared Hughes and Brady Nun for their support over the past two years. Finally, I would like to thank my ommittee for their support, espeially Dr. Olson without whose help the PARET model would ever have ome into existene. xv

17 CHAPTER 1 INTRODUCTION 1. The United States Geologial Survey (USGS) onstruted the Geologial Survey TRIGA Reator (GEST) to perform neutron irradiation experiments in support of their mission to provide relevant sientifi information about the planet (United States Geologial Survey, 2008). The GSTR provides neutron ativation and radioisotope prodution apabilities for the USGS and also supports the Colorado Shool of Mines (CSM), providing CSM s new Nulear Siene and Engineering Program with aess to the faility for researh and teahing purposes. The NRC granted the original GSTR faility a liense after onstrution finished in February of 1969; however, this liense expired on February 24, As part of the liense renewal proess, the NRC required that the GSTR s original safety analysis be updated to reflet the urrent operating onditions, legal requirements, and analysis methods. This projet developed a suite of omputational models to give the GSTR aess to the modern analysis tools needed for reliensing. These tools will also assist in the development of future experiments at the GSTR. The new omputational tools inlude neutroni, steady state thermal-hydrauli, and transient thermal-hydrauli operation models of the GSTR. This projet used the Monte Carlo N-Partile (MCNP) ode (X-5 Monte Carlo Team, 2003) to onstrut the neutronis model, the Reator Exursion and Leak Analysis Program (RELAP) (Information Systems Laboratories, In., 2010b) to develop the thermal-hydraulis model, and the Program for the Analysis of Reator Transients (PARET) ode (Woodruff and Smith, 2001) to onfirm the thermalhydraulis models. 1

18 Previous work at CSM developed an initial version of the MCNP model of the GSTR. While mostly omplete, the model had not been validated and needed to be updated to reflet the limiting ore analyses requested by the NRC. Therefore, the first goal of the present projet was to update and validate the existing MCNP model of the GSTR. Validation onsists of testing the model s ability to math experimental data olleted by the GSTR staff, inluding neutron flux profiles, ontrol rod worth urves, ritial rod positions, and ore exess and shutdown reativity values. This validation effort is a ritial step in the GSTR s re-liensing effort, as the validated MCNP model determines many of the parameters requested by the NRC. The steady-state thermal-hydrauli model was onstruted based on previous re-liensing models reated for other TRIGA reators (Marum and Woods and Reese, 2011; Marum, 2008; Oregon State University Radiation Center, 2010). This model represents the hot-hannel within the GSTR ore, and allows the steady-state heat flux from the hot rod, as well as the ladding, fuel, and hannel water temperatures, to be predited under steady-state operating onditions. A transient reator model evaluates the reator during operational transients, power pulses, and off-normal onditions. The MCNP model s preditions for the thermal feedbak oeffiients from the reator will inform a point-kinetis model to represent the bulk ativity of the reator ore. The model represents the ore average behavior, and the results are saled using the power fator to represent individual rods, or areas of the GSTR ore. objetives: In order to support the GSTR s reliensing effort, this thesis inludes several distint 1) omplete and validate the MCNP model of the GSTR and demonstrate the model s ability to predit reator onditions, 2

19 2) analyze the GSTR s limiting ore onfiguration, 3) onstrut and validate a RELAP steady-state model of the hot fuel hannel, 4) predit the departure from nuleate boiling ratio (DNBR) for the hot rod under steady state operating onditions for the limiting ore onfiguration, 5) onstrut and validate PARET and RELAP models for transient onditions in the ore, and 6) predit the transient behavior of the reator under the limiting ore onfiguration. While the geometry and material definitions in the original MCNP model of the GSTR were mostly omplete (aside from error heking), the model needed proper validation to ensure that it aurately predits the behaviors of the urrent GSTR ore. Objetive one foused on demonstrating this through several methods. The integral ontrol-rod worth urves for the model have been mathed to experimental data from the GSTR. The omputed ontrol rod ritial positions math the experimentally determined positions to within the model s unertainty and a safety fator to ompensate for measurement and error. The model preditions satisfy the GSTR Tehnial Speifiations during operation and shutdown onditions, inluding limits on the exess and shutdown reativity margins. The model also predits reasonably aurate foil ativation rates and axial fluxes in the GSTR entral thimble irradiation faility. Mathing the model s preditions to experimental results from the GSTR provides assurane that the model an support the analyses requested by the NRC. The seond objetive ensures that the GSTR is able to funtion safely under the worstase set of operating onditions. The purpose of the limiting ore is to set a bounding ondition on ore onfigurations that an be run without endangering the publi. A good limiting ore should push the limits of the urrent GSTR safety guidelines. Under these onditions, if the 3

20 GSTR an still operate safely, then, in theory, any less hallenging ore onfigurations will also be safe. To ensure this is true, the limiting ore s ritial onditions must meet all of the limits established in the GSTR s tehnial speifiations. The limiting ore alulations identify the hot rod and provide a detailed power profile for the fuel within this rod. The MCNP model also alulates the fuel temperature reativity oeffiient, moderator temperature reativity oeffiient, and void reativity oeffiient for the limiting ore. The reator must safely remove the heat generated during normal operation without ausing fuel damage. The RELAP model developed in objetive three demonstrates this. Like the MCNP model, the RELAP model requires validation to ensure that the results given by the model are aurate. Initially this validation examined the reorded temperatures from the reator s thermoouples; however, the unertainty in this data was too large to provide meaningful validation. Instead, a omparison to similar TRIGA reator models ensured that, from a safety perspetive, the model s preditions are onsistent, and meet the needs of the reliensing analysis. The NRC requires that the departure from nuleate boiling ratio (DNBR) for the GSTR be alulated as part of the re-liensing proess. Departure from nuleate boiling is a ondition where a thin film of vapor overs a fuel element, signifiantly dereasing the ability of that element to transfer heat to the oolant. In these onditions, the fuel element s temperature inreases rapidly as the heat generated by the rod annot esape. Objetive four uses the RELAP model to alulate the DNBR for the hot rod hannel. Sine the hot rod hannel is a limiting ase for the GSTR, the hot hannel DNBR also serves as the worst DNBR within the GSTR. 4

21 Objetive five fouses on developing a model for the transient behavior of the GSTR. RELAP ontains a point-kinetis model that, when applied to a two-hannel RELAP model, allows the steady-state model to approximate the transient behavior of the reator. This model, however needs some form of validation, whih omes from analyzing the differenes between the RELAP model and a similar model developed using PARET. The PARET ode simulates the transient behavior of test reators, and uses a oupled point kinetis and thermal-hydrauli model to predit the transient onditions within a reator ore simular to RELAP (Woodruff and Smith, 2001; Adoo et al., 2011; Woodruff et al., 1996). This allows PARET to provide a seond ase to ompare to the results of the RELAP model to, as the proposed limiting ore is unique from any ore urrently or historially used at the GSTR. Objetive six ensures that the limiting ore will operate safely under transient onditions. Similar to the MCNP analysis, the RELAP and PARET analyses verify the safe operating bounds of the GSTR during transient onditions with the limiting ore. The next hapter desribes TRIGA reators and the GSTR in detail, as well as the methodology for the seletion of eah of the analysis odes, and details on how eah ode funtions. Chapter 3 then desribes the neutroni analysis, inluding the MCNP reator model, in detail. Chapter 4 desribes the RELAP and PARET models, and the thermal-hydrauli analysis preformed for the GSTR. All of the results are summarized in Chapter 5, while Chapter 6 lists possible future work. Appendix A ontains the MCNP 5 model of the GSTR operating ore. Appendix B ontains the RELAP steady-state model, Appendix C ontains the RELAP two-hannel transient model, and Appendix D has the PARET model. 5

22 CHAPTER 2 BACKGROUND 2. This projet fouses on simulating the behavior of the U.S. geologial Survey TRIGA Reator (GSTR) with three different omputer odes: MCNP5, RELAP5 and PARET-ANL. Eah ode fouses on a speifi aspet of the reator s operation. Sine TRIGA reators are researh, not power, reators, this analysis is different from that for a ommerial power plant, as a TRIGA reator requires fewer features to ensure the safety of the publi ompared to larger ommerial reators. This hapter inludes a desription of the unique features of TRIGA reators, as well as the bakground of the three odes used in this projet TRIGA Reators General Atomis designed the Training Researh and Isotope - General Atomis (TRIGA) reator in the 1960 s to serve as a rugged researh and training reator suitable for training future nulear engineers without any major risk of endangering students or the publi (Fouquet, Razvi, and Whittemore, 2003). TRIGA reators are the most numerous form of researh reator, with 66 failities urrently in operation (General Atomis, 2011a). TRIGA reators are designed with strong negative thermal feedbaks, making the reator highly resistant to ore damage even in extreme situations (Fouquet, Razvi, and Whittemore, 2003). These features are ommon to every TRIGA reator, even though the speifi details of the ore geometry or ore dimensions hange from reator to reator (Nulear Installation Safety Division, 2004a). A TRIGA reator operates through ontrolled nulear fission in a manner idential to large energy prodution reators. TRIGA reators, however, require muh less infrastruture to 6

23 operate safely. Most TRIGA reators, inluding the GSTR, are housed at the bottom of large pools that provide both shielding and the primary method of ooling for the reator (Nulear Installation Safety Division, 2004b). The GSTR onsists of a reator ore housing the fuel elements in a irular grid surrounded by a graphite refletor. Figure 2.1 shows an image of the GSTR in operation. As Figure 2.1 shows, a TRIGA ore tends to be ompat, leading to a high rate of neutron leakage from the ore. While this leakage is an integral part of the TRIGA reator s inherent safety, it also allows for neutron irradiation without having to signifiantly re-design the ore (Nulear Installation Safety Division, 2004a). TRIGA reators inorporate inherent safety features, where natural fores, as opposed to engineered or operator-ontrolled mehanis, ensure the safety of the reator and publi in an Figure 2.1. GSTR ore during operation m

24 emergeny situation (Fouquet, Razvi, and Whittemore, 2003). Edward Teller proposed the design to reate a reator that would shut down without any human interation and without fuel damage if the ontrol rods were ompletely removed from the reator ore (General Atomis, 2011b). The TRIGA reator s uranium-zironium-hydride fuel provides the majority of this safety (Nulear Installation Safety Division, 2004a). TRIGA reator fuel has an inherently large negative temperature reativity oeffiient (Simnad, 1981). The largest ontributor to this effet omes from the inlusion of hydrogen within the fuel to moderate the neutrons. Beause the hydrogen inluded in the fuel heats with the fuel, a warm neutron effet redues the moderating ability of the fuel as reator power inreases (General Atomis, 2011b). As the hydrogen in the fuel heats up, its ability to moderate neutron energy (and thus inrease the effetive fission ross setion of the uranium within the fuel) dereases, while the exess energy within eah hydrogen atom beomes available to be transferred to passing neutrons, hardening the neutron spetrum (Clifford, Hopkins, and West, 1966). This enourages neutrons to leave the fuel and enter the surrounding water, inreasing the role of neutron apture outside of the fuel, and reduing overall reativity (Haake and Krase, 1967). At the same time, the harder (faster) neutron spetrum enourages parasiti neutron apture within the U-238 present in the fuel, further reduing the number of fissions (Nulear Installation Safety Division, 2004b). Finally, neutrons that esape into the water will be thermalized, but will have some diffiulty returning into the fuel through the ladding materials one at thermal energies (Nulear Installation Safety Division, 2004b). This effetively inreases the net loss of neutrons from the ore. These three fators ontribute to provide the prompt negative temperature feedbak inherent in TRIGA fuel (Nulear Installation Safety Division, 2004a). 8

25 TRIGA reators differ from ommerial power reators in a number of key areas that ause unique situations during re-liensing. Researh reators are typially muh smaller than ommerial power reators. The GSTR s power output of 1 MW th is approximately 1/3000 th that of a typial ommerial nulear power plant (whih typially produes 1 GW e ). The lower power output of a TRIGA reator requires less safety and operational infrastruture ompared to ommerial power reators (Nulear Installation Safety Division, 2004b). From a thermalhydraulis standpoint, the muh lower power output requires less extensive ooling systems than ommerial power reators (Nulear Installation Safety Division, 2004b). The small size of a TRIGA reator allows the reator to reah a old shutdown state within minutes of a SCRAM, as the power output of the deay produts an be ompletely removed through natural onvetion in the reator pool (Nulear Installation Safety Division, 2004b). Uranium-zironium-hydride fuel also allows TRIGA reators to pulse. In pulsed operations, one ontrol rod is rapidly removed from the ore, adding a large amount of reativity to the reator (Nulear Installation Safety Division, 2004b). The fuel reats to the temperature inrease aused by the sudden inrease in power by providing a large amount of negative reativity, whih limits the rate of the nulear reation and prevents fuel damage. During the brief duration of the pulse, the reator an operate at a power level of several gigawatts, allowing for safe experiments requiring large, short duration, neutron fluxes TRIGA Fuel Rods General Atomis developed several different TRIGA fuel rod onfigurations (Tomsio, 1986) (Table and Figures 2.2a and 2.2b). The GSTR uses three different fuel rod types, one whih is lad in aluminum (Figure 2.2a), and two of whih are lad in stainless steel (Figure 2b). All three types use a uranium-zironium hydride fuel enrihed to less than 20 wt.% uranium-235 9

26 graphite top fitting graphite top fitting samarium trioxide dis m samarium trioxide dis 8.81 m m pin to pin fuel meat (3.607 m diameter) m m pin to pin fuel meat (3.632 m outer diameter) zironium plug (0.635 m diameter) m aluminum ladding (0.076 m thik, m outer diameter) m stainless steel ladding (0.051 m thik, m outer diameter) 8.81 m bottom fitting bottom fitting a) aluminum lad fuel b) stainless steel lad fuel Figure 2.2. Shematis of the TRIGA fuel types used in the GSTR. 10

27 (Simnad, 1981). Both fuel types have a length of m (Figures 2.2a and 2.2b) (Tomsio, 1986). The aluminum lad fuel has an outer diameter of 3.76 m (Figure 2a) while the stainless steel lad fuel has an outer diameter of 3.73 m (Figure 2b). Internally, the fuel is sandwihed between two graphite plugs above and below the fuel meat to redue neutron leakage out of the top and bottom of the fuel rod (Figures 2a and 2b). Early TRIGA fuel rods inluded disks of samarium to at as a burnable neutron absorber; however, General Atomis stopped manufaturing these elements after 1964 (Tomsio, 1986). The present analysis ignores the effets of the burnable absorber, as all of the fuel at the GSTR is old enough that the burnable absorber has been depleted. Table 2.1 shows the basi properties of the fuel types urrently in the GSTR. All of the fuel in the GSTR is enrihed to < 20 wt.% uranium-235, although the amount of uranium within the fuel meat (by weight perent) differs 8 wt.% to 12 wt.% based on the fuel rod design from. General Atomis also developed a fuel rod lad with Inoloy (Tomsio, 1986); however, the GSTR has never used this type of element. The aluminum-lad fuel is the oldest TRIGA reator fuel manufatured by General Atomis (Day, 2004). The fuel meat within an aluminum-lad rod ontains 8 wt.% uranium, and is m tall (Figure 2.2a). The GSTR still uses several aluminum-lad fuel rods, whih are Table 2.1. GSTR Fuel types and basi information. Weight Perent Fuel Type Enrihment (%) Cladding Material Uranium in Fuel Meat (%) 8 % aluminum - lad < 20 aluminum 8 8.5% stainless steel- lad < 20 stainless steel % stainless steel - lad < 20 stainless steel 12 11

28 limited to the outer fuel rings in response to onerns over the lower melting temperature of aluminum (Day, 2004). The stainless-steel lad fuel within the GSTR is a mixture of 8.5 wt.% and 12 wt.% fuel. The fuel in all stainless steel lad fuel element is 38.10m long. A zironium plug is loated in the middle of the fuel meat (see Figure 2b) as a onsequene of the manufaturing tehniques used in manufaturing the U/ZrH fuel (Tomsio, 1986). The dimensions of TRIGA fuel pins are not onsistent and vary from reator to reator and bath to bath. The dimensions in Figures 2.2a and 2.2b form the basis for all of the fuel modeling efforts in this thesis Geologial Survey TRIGA Reator The Geologial Survey TRIGA Reator (GSTR) is a 1 MW th TRIGA Mark I reator housed at the Denver Federal Center loated in Lakewood, Colorado. The reator ore is ontained in a water-filled pool 2.13 m wide and 7.62 m deep. Figure 2.1 shows the reator ore of the GSTR. The reator ore is m in radius from the inside of the lazy susan and m inhes tall with 126 fuel loations loated around a entral thimble. A graphite refletor surrounds the ore and is designed to redue neutron leakage out the sides of the reator (see Figure 2.1). These fuel loations are split into six onentri fuel rings labeled B through G. Four ontrol rods are loated in the C- and D-Rings of the ore. Outside of the ore, a radial graphite refletor limits radial neutron leakage (the fuel itself is designed to minimize axial leakage). The refletor also houses a lazy susan irradiation faility in a groove fixed within the graphite refletor, as shown in Figure 1. 12

29 There are four ontrol rods within the GSTR (see Figure 2.3 a, 2.3b and 2.3). Three are fuelfollowed boron-enrihed graphite ontrol rods (Figure 2.3a), while the forth is a void-followed pulse rod (Figure 2.3b). The rod drives above the reator raise the rods during normal operation. All four rods inorporate an eletro-magneti SCRAM feature. During a SCRAM, the eletromagnet that binds the ontrol rods to their drives deativates, allowing gravity to pull the rod bak into the ore. As part of the GSTR tehnial speifiations, the ore must shutdown (beome subritial) with three of the four rods inserted to allow for the possibility of a rod beoming stuk. The GSTR s fuel followed ontrol rods are referred to as the shim 1, shim 2, 38.1 m graphite top of ore 38.1 m absorber 38.1 m fuel fuel 38.1 m graphite bottom of ore void a) fuel followed ontrol rod b) void followed ontrol rod ) fuel rod Figure 2.3. The different ontrol rod types used in the GSTR ompared to a fuel rod. 13

30 and regulating rods. These rods ontain a fuel element following the boron enrihed graphite (see Figure 2.3a), whih redues the impat of removing the ontrol rod on the ore flux profile. The final ontrol rod, the transient rod, is void followed, (see Figure 2.3b), and uses an eletropneumati rod drive instead of the mehanial system used by the other three ontrol rods. This system an quikly ejet the transient rod from the ore to initiate a pulse operation. Otherwise, the transient rod serves the same funtion as the other three rods; however, the pneumati drive is not as sensitive as the mehanial rod drives. The void follower redues the total reativity worth of the transient rod. lazy susan entral thimble external irridation tubes B-Ring C-Ring D-Ring E-Ring F-Ring G-Ring refletor ontrol rods m m m Figure 2.4. The GSTR Core with the different experimental failities shown 14

31 There are three primary experimental failities within the GSTR - the entral thimble loated within the reator ore, and the lazy susan and external irradiation tubes loated outside of the ore (see Figure 2.4). Loated in the middle of the ore, the entral thimble provides a high-flux irradiation loation. Normally, the entral thimble is water filled, but an be evauated to provide a beam tube for radiography. The lazy susan sits outside of the ore in an insert plaed in the GSTR s graphite refletor (see Figures 2.1 and 2.4). A pneumati system allows the forty sample loations within the lazy susan to be remotely loaded and unloaded and a mehanial drive rotates the lazy susan around the ore. Originally designed for isotope prodution, the GSTR urrently uses the lazy susan for sample irradiation. Two irradiation tubes sit outside of the refletor. A reator operator must manually insert samples into the tubes from outside of the reator tank by lowering or raising the sample into the reator by hand Code Seletion Within the last 14 years, multiple TRIGA reators have sought re-liensing, or have sought alterations to their lienses to alter their apabilities (Marum, 2008; Jensen and Newell, 1998). As a result of their age and large number, many TRIGA reator failities have developed independent tools to support reliensing analysis (Merroun et al., 2009; Mesquita, 2007; Miller and Feltus, 2000; Huda and Rahman, 2004; Housiadas, 2002). In the ase of the GSTR, a partially ompleted MCNP5 neutronis model already existed from previous work at CSM. Given the diffiulty in onstruting an aurate model from srath, this projet finishes and validates the partially ompleted model. This model is desribed in detail in Chapter 3. 15

32 While several ustom odes for thermal-hydraulis have been developed or were in the proess of being validated (Merroun et al., 2009; Mesquita, 2007; Miller and Feltus, 2000; Housiadas, 2002; Kazeminejad, 2008), most of these odes were not foused on a re-liensing senarios, or were only in the early stages of validation. A survey of existing thermal-hydraulis odes indiated that the RELAP pakage has been in use for safety analysis for deades and for researh reators as early as the late 1990 s (Jensen and Newell, 1998). RELAP is designed speifially for nulear appliations, and used extensively inside and outside of the United States (Marum, 2008; Jensen and Newell, 1998; Mesquita, 2007; Anderson, 2010; Ferreri, 1995; Binh el at., 2007; Antariksawan et al., 2005; Maria, 2010; Marum, Woods and Reese, 2009). Aside from RELAP, the newer TRACE ode (whih ombines RELAP and several other thermal-hydraulis odes, and is intended to eventually replae RELAP) is also used in some appliations (Cheng et al., 2009; Takasuo, 2006). The present projet seleted RELAP based on the odes history of use for researh reators modeling. The work done by Oregon State University (OSU) in re-liensing their TRIGA reator provided a basis for the GSTR analysis. The OSU analysis ombined MCNP and RELAP results to produe the reliensing data requested by the NRC. A detailed desription of the OSU RELAP model (Marum, 2008) provided the basis for this projet s RELAP model. PARET-ANL ombines point-kinetis with a thermal-hydrauli model to provide apabilities similar to RELAP (Woodruff et al., 1996; Hamidouhe et al., 2004). The ode is optimized for researh-sized reators, unlike RELAP, whih is primarily designed for large ommerial power reators (Adoo et al., 2011; Woodruff, 1982; Jonah, 2011). Previous 16

33 validation work has also used PARET (Huda and Rahman, 2004). This bakground led the projet to using PARET to provide a omparison to the RELAP alulations Monte Carlo N-Partile Monte Carlo N-Partile (MCNP) is a Monte Carlo partile transport ode extensively used in the nulear researh field for its ability to simulate a wide range of partile transport senarios inluding reator design, shielding, and dosimetry problems (Hendriks et al., 2000; X- 5 Monte Carlo Team, 2003a). MCNP5 is the most reent release of MCNP and uses a ombination of random numbers paired with different tables and funtions to simulate the probabilisti behavior of a random partile traveling within different materials. MCNP an simulate neutrons, eletrons and photons (X-5 Monte Carlo Team, 2003a). The Los Alamos National Laboratory develops MCNP5 and its variants. All of the neutroni alulations for the GSTR reliensing effort are based MCNP5 version An MCNP input file is referred to as a dek (a legay term from when atual deks of ards provided the program inputs) that ontain the geometri, material, and input parameters for the problem, inluding the partile soure and any detetors for partile fluxes or reation rates the user wishes to define. The ode begins by reating a partile either from a user-defined soure or through a alulated fission soure profile (in the ase of a ritiality alulation). Whih material the partile is urrently in determines the distane that partile travels before an interation ours with one of the atoms in the material (as defined by material ards and the appropriate ross-setion library). MCNP alulates this distane by (Carter and Cashwell, 1975): ( ) ( ). (2.1) 17

34 After traveling this length, an interation ours based on the material the partile is within. If there are multiple nulides in the region, another random number determines whih nulide the partile interats with. At this point the partile will either have been removed from the simulation (as a result of some form of apture reation), or a new energy, diretion and speed are determined, and the proess begins again (Carter and Cashwell, 1975). A general weakness of Monte Carlo odes, inluding MCNP5, omes from the ode s inability to generate general information not speified in the input dek. A user sets onditions within the dek to trak, and when a partile triggers one of these onditions (a fission reation, or entering a speifi portion of the geometry for existene) that data is reorded for the output file (X-5 Monte Carlo Team, 2003b). After the program has finished the run (from either user settings, or a manual interrupt) the results are plaed in the output file based on the user s onditions speified in the input file (X-5 Monte Carlo Team, 2003b). As MCNP is designed as a generi partile transport problem solver, the simulation an run in two ways. The primary method uses a generi soure that an funtion using any of the partiles found in MCNP (X-5 Monte Carlo Team, 2003b). With this soure, the geometry, distribution, and energy of the partiles an be set in the input dek. Partiles are reated by the ode based on the soure definition, and run through the desribed proess until they are absorbed or killed (a setting an also stop MCNP from ontinuing to trak the partile if it exists for too long), at whih point the soure reates another partile (X-5 Monte Carlo Team, 2003b). This ontinues until a pre-set limit is reahed, either time or number of partiles (X-5 Monte Carlo Team, 2003a). 18

35 The ritiality, or k-ode, mode only funtions with neutrons (X-5 Monte Carlo Team, 2003b). In this mode, MCNP treats fission reations as aptures that set the loation for the next generation of neutrons in the simulation (X-5 Monte Carlo Team, 2003a). Unlike the basi soure definition, whih simply runs until a set time or number of partiles has been reahed, a k-ode alulation uses many iterations of several (usually over 10,000) partiles eah. The first several iterations (defined by the user) determine the shape of the soure distribution based on the loations of the fission events (Brewer, 2009). One MCNP determines the soure distribution for a given yle, multipliation fator for that yle is determined by omparing the number of fission neutrons reated with the number of neutrons that began the yle (Brewer, 2009). This ratio determines multipliation fator and many iterations are needed to minimize the unertainty in the alulation (Brewer, 2009). All the neutroni simulations run in support of the GSTR re-liensing effort use the k-ode method. MCNP is also apable of traking partile flux, urrent, energy disposition and interations within an area of interest through the use of tallies (X-5 Monte Carlo Team, 2003a). These tallies an be set to over a surfae, volume, or a single point within the geometry of the problem. All tallies are normalized to be per starting partile (X-5 Monte Carlo Team, 2003a). MCNP is also apable of approximating reations using a flux alulation with ENDF reations (X-5 Monte Carlo Team, 2003a). Reation rates in MCNP use (X-5 Monte Carlo Team, 2003a; Lewis, 2008): ( ) ( ) (2.2) 19

36 The statistial unertainty of a monte arlo answer is proportional to the number of partiles traked in the simulation through the Strong Law of Large Numbers (Artstein and Vitale, 1975), but an inherent problem is that if another situation omes up, another simulation must be run (X-5 Monte Carlo Team, 2003a). Generally speaking, in eah iteration, the relative error (R) for some measured quantity is alulated as (Carter and Cashwell, 1975):, (2.3) where:. (2.4) MCNP uses these values to generate the ovariane and orrelation for the problem (X-5 Monte Carlo Team, 2003a). A Monte Carlo simulation alulates preision using the Strong Law of Large Numbers (Artstein and Vitale, 1975). Under this law, the average value will approah the expeted value as the number of attempts to find that value approahes infinity (Artstein and Vitale, 1975). Sine an infinite number of runs annot be done, MCNP alulates the preision of any value given as a funtion of the number of attempts run. In short, while any individual partile (or even bath of partiles) may not represent the physial situation, a suffiiently large number may provide a reasonable approximation for the physial system. MCNP measures this preision through a standard deviation alulation (X-5 Monte Carlo Team, 2003a): 20

37 ( ) (2.5) Temperature Adjustments in MCNP The MCNP5 distribution inludes the makxsf utility whih allows for manipulation of ross-setion libraries, Doppler-broadening of existing ross setions, and interpolation between existing sets of thermal sattering (S(α,β)) data (Brown, 2006). Like MCNP5, makxsf reads an input file to allow the user to aess the funtions of the makxsf ode. A user an opy rosssetion data from existing libraries (datasets) into a new library. New ross-setions an be Doppler-broadened based on a lower-temperature dataset. Should the dataset also ontain probability tables for unresolved resonanes, makxsf an interpolate the tables if a highertemperature dataset is provided (Brown, 2006), otherwise the lower-temperature probability table is simply opied over to the new library. Finally S(α,β) data interpolation is also possible if both a lower and higher temperature S(α,β) datasets are available (Brown, 2006). Doppler broadening with makxsf inorporates several portions of the NJOY and DOPPLER odes (Brown, 2006; Muir and MaFarlane, 1994). NJOY is a ode designed to proess nulear ross-setions and ontains the BROADR subroutine, whih is also inluded in makxsf and DOPPLER (Muir and MaFarlane, 1994). BROADR alters neutron ross-setions through a temperature-veloity relationship to find a temperature and veloity where the ross setions math aording to (Muir and MaFarlane, 1994): ( ) ( ) ( ) (2.6) 21

38 The DOPPLER ode expands this method to work on the ACE (A Compat ENDF) format ross-setion data, as opposed to the raw ENDF (Evaluated Nulear Data File) data whih NJOY starts with (Brown, 2006). The makxsf ode uses DOPPLER for probability tables as well, through a simple interpolation between two data points (Brown, 2006) MCNP ENDF Libraries and Zironium Cross-Setions The impat of ross-setion seletion on the neutroni modeling of a TRIGA reator is non-trivial. Several reports have disussed the effets different ross-setion libraries have on the predited multipliation fator alulated for TRIGA reators via Monte Carlo methods (Bess, Marshall, and Maddok, 2011; Snoj, Trkov, and Ravnik, 2007; Snoj, Zerovnik, and Trkov, 2011). The findings of these reports point to inauraies in the most reent zironium ross-setion libraries that only beome apparent in fuel types that use a large amount of zironium within the fuel meat, suh as TRIGA fuel rods (Snoj, Trkov, and Ravnik, 2007; Snoj, Zerovnik, and Trkov, 2011). The ENDF/B-VII.0 libraries typially predit higher k eff values for TRIGA benhmark models when ompared to both the ENDF/B-VI.6 and JEFF 3.1 neutron ross-setion libraries (Snoj, Zerovnik, and Trkov, 2011). Further analyses of the individual isotopes within the ENDF/B-VII.0 library, as well as tests using the S(α,β) data within eah library found that the ENDF/B-VII.0 S(α,β) data gave the greatest ontribution to the differene between the ENDF/B-VII.0, ENDF/B-VI.6 and JEFF 3.1 libraries (Snoj, Zerovnik, and Trkov, 2011). These differenes between ENDF/B-VII.0 and ENDF/B-VI.6 are many times the alulated standard deviation of the benhmark model (Snoj, Trkov, and Ravnik, 2007). More detailed experiments found that the ENDF/B-VII.0 libraries inrease the thermal neutron flux, leading to a larger multipliation fator (Snoj, Zerovnik, and Trkov, 2011). Unfortunately, 22

39 further experiments need to be done to determine the orret treatment for zironium within neutron ross setion libraries, and are outside the sope of this projet Reator Exursion and Leak Analysis Program The Reator Exursion and Leak Analysis Program (RELAP) is a omputational fluid dynamis (CFD) suite developed for the Nulear Regulatory Commission to provide a regulatory thermo-hydrauli ode for use in reator appliations (D'Auria and Galassi, 1998). RELAP uses a finite-differene algorithm to determine the thermo-hydrauli properties of a user-defined geometry, and has the apability to represent both steady state and transient onditions (D'Auria and Galassi, 1998). Unlike several more modern odes, RELAP uses a one-dimensional two-fluid model to represent a two-phase system omprised of water, possibly some non-ondensable omponents in the steam phase, or soluble omponents in the liquid phase (Ranson and Hiks, 1984). This allows the ode to represent omplex thermal-hydrauli systems (suh as nulear reator ooling systems) while being omputationally less intensive than a full three-dimensional model. A series of eight equations solve eight variables (pressure, phasi speifi internal energies (for both liquid and gas phases), vapor volume fation, phasi veloities (both liquid and gas), nonondensable quality, and boron density) within the thermal-hydrauli system (Information Systems Laboratories, In., 2010a). Geometry is provided to the ode as a string of numeri lines in a text file. Eah line of ode is referred to as a ard, while an entire input file is referred to as a dek (Informations Systems Laboratories, In., 2010b). RELAP has a number of pre-defined geometry types that an desribe the geometry of a system. Eah geometry represents a different hydrauli 23

40 omponent in a light-water reator s ooling system (Informations Systems Laboratories, In., 2010b). Speial hydrauli omponents, referred to as time dependent volumes, represent boundary onditions within the system as their hydrauli properties ( i.e. temperature, pressure, fluid veloity, et.) are user defined and not affeted by the RELAP omputation (Informations Systems Laboratories, In., 2010b). Solid omponents, suh as pipe walls and fuel rods, are represented as heat strutures (Informations Systems Laboratories, In., 2010b). Heat strutures use a one-dimensional heat-transfer approximation to represent heat flow through a solid medium. The heat struture an have either a retangular or a ylindrial geometry. A series of nodes represent the solid materials in a heat struture as seen in Figure 2.5. Aside from the nodes for a one-dimensional analysis, multiple sets of nodes an be onneted axially (although heat does not transfer from one set of nodes to another) to represent more omplex strutures (Figure 2.5) (Information Systems Laboratories, In., 2010a). Multiple axial nodes are required when onneting a single heat struture to multiple hydrauli omponents (suh as those in a pipe). Eah heat struture an only onnet to a single hydrauli Figure 2.5. Example of a heat struture in RELAP with 10 nodes in two different materials with non-uniform mesh lengths. 24

41 omponent, and multiple materials an be represented within a single heat struture as long as the thermal data (thermal ondutivity and volumetri heat apaity) for eah material is provided by the user (Figure 2.5) (Information Systems Laboratories, In., 2010a). RELAP allows for this thermal data to be input through tables, equations, or as a onstant value (Information Systems Laboratories, In., 2010a). RELAP alulates the temperature and heat flux at eah node of a heat struture. A heat generation term an also be applied to a node, or distributed throughout a heat struture to represent internal heat generation (suh as within a heating oil or fuel rod) (Information Systems Laboratories, In., 2010b). Every heat struture has two boundary onditions (Riemke, Davis, and Shultz, 2008). These an be set to hydrauli volumes (to represent an interfae between the heat struture and fluid), onstant power fluxes, onstant temperatures, insulated boundaries, or refleting boundaries (representing the enter of a ylinder) (Riemke, Davis, and Shultz, 2008). RELAP uses several onvergene riteria to determine if a model has onverged when running a steady-state problem (Information Systems Laboratories, In., 2010a). The steadystate ondition for RELAP monitors the hange in the thermodynami density, internal energy, and pressure to monitor the hange in the system as a whole (Information Systems Laboratories, In., 2010a). Thus, one these three variables reah a onstant value (with respet to time), the system has reahed steady state (Information Systems Laboratories, In., 2010a). Within the ode this is represented as (Information Systems Laboratories, In., 2010a): ( ( ) ) ( ) ( ) (2.7) 25

42 However, this funtion is not well behaved with respet to time, as large flutuations in the value of the derivative an our, making a diret measurement diffiult (Information Systems Laboratories, In., 2010 a). To ompensate, RELAP uses a fitting funtion that is well behaved and an be solved over a number of time steps to determine steady state (Information Systems Laboratories, In., 2010a): [( ( )) ] ( ) ( ) ( ) (2.8) 2.6. Program for the Analysis of Reator Transients The Program for the Analysis of Reator Transients (PARET-ANL) provides a simple but aurate model for reator transients through a ombined point-kinetis and thermalhydrauli model (Woodruff and Smith, 2001). PARET was initially designed to analyze the SPERT-III experiments (Woodruff, 1982), and has sine beome a general use thermal-hydrauli ode optimized for researh reators, espially those with plate-type fuel (Woodruff, 1984; Woodruff and Smith, 2001). Like RELAP, PARET uses one-dimensional approximations for the thermal-hydrauli alulations (Adoo et al., 2011). Unlike RELAP, PARET is not apable of modeling general thermal-hydrauli geometries, and instead models a reator ore and the oolant hannels within the ore (Adoo et al., 2011; Woodruff and Smith, 2001). PARET-ANL an urrently model a ore of 1 to 50 fuel hannels. This greatly simplifies input dek onstrution ompared to RELAP. 26

43 PARET uses a momentum-integrated model to solve for the fluid onditions in oolant hannels, based on the following governing equations (Adoo et al., 2011): (2.9) ( ) ( ) ( ) (2.10) (2.11) These equations examine the relationship between the average density ( ), mass flow rate (G) pressure (P), and heat soure in a unit volume (q) (Woodruff, 1982). Eah hannel is independent of the other hannels. A standard six-group point-kinetis model alulates the transient power generation within the simulated fuel elements (Woodruff and Smith, 2001). PARET represents solid volumes using a series of axial and radial nodes. PARET an model up to three materials within a fuel rod, representing the fuel, ladding and another material (e.g. gap gasses) (Woodruff and Smith, 2001). All node points are assumed to be in the enter of the region. Radial nodes are assumed to be of equal length starting from the enterline of the fuel element, and extending to the outer edge of the ladding (Woodruff and Smith, 2001). The user defines axial node lengths; these must onform to the total length of the rod one added together. Only 20 axial setions may be defined for any fuel element, and PARET only onsiders the ative axial length of a fuel rod (i.e. the length of the fuel) (Woodruff and Smith, 2001). 27

44 The next hapter desribes the neutronis model used in this projet, as well as the validation and analysis alulations performed by the MCNP model. 28

45 CHAPTER 3 NEUTRONICS ANALYSIS 3. This hapter looks at the neutroni analysis performed by this projet. The initial setions provide bakground information on the analysis and the GSTR reator. Following this is a detailed desription of the GSTR MCNP model, and the different ore layouts examined in the projet. The remainder of this hapter shows the results of the alulations performed by the MCNP models. This inludes both the validation work on the GSTR, and the neutroni analysis of the GSTR limiting ore Introdution The Geologial Survey TRIGA Reator (GSTR) is a 1 MW th Testing Researh Isotope General Atomis (TRIGA) Mark I reator loated at the Denver Federal Center in Lakewood Colorado. As part of the reliensing proess, the United States Nulear Regulatory Commission (NRC) requires an update to the reator s safety analysis report and tehnial speifiations to doument the urrent operating onditions of the reator. A Monte Carlo N-Partile (MCNP) (X-5 Monte Carlo Team, 2003a and 2003b) model of the reator provides the basis for the neutronis analysis needed to update the safety analysis report and tehnial speifiations. This analysis is broken into two stages. First, validating the MCNP model with data from the urrent GSTR ore. Then, evaluating a limiting ore to determine the ore s exess and shutdown reativity margins, reativity feedbak oeffiients, and power distribution. The next setion provides a detailed desription of the GSTR, followed by a desription of the MCNP model in Setion 3.3. Setion 3.4. desribes the validation of the model against the 29

46 urrent operating GSTR ore and Setion 3.5. presents the neutronis analysis onduted with the model for the limiting GSTR ore Desription of the Geologial Survey TRIGA Reator The reator ore of the Geologial Survey TRIGA Reator (GSTR) is ontained in a water-filled pool 2.13 meters wide and 7.62 meters deep. Figure 3.1 shows the reator ore of the GSTR. The reator ore is m in radius from the inside of the lazy susan and m tall with 126 fuel loations loated around a entral thimble (see Figure 3.1). These fuel loations are split into six onentri fuel rings labeled B through G. Four ontrol rods are lazy susan entral thimble external irridation tubes B-Ring C-Ring D-Ring E-Ring F-Ring G-Ring refletor ontrol rods m m m Figure 3.1. The GSTR ore, highlighting the refletor, ontrol rods, and fuel. 30

47 loated in the C and D-Rings of the ore (see Figure 3.1). A radial graphite refletor serves to limit radial neutron leakage (the fuel rods ontain inserts to limit axial leakage, see Figures 3.2a and 3.2b). The refletor also houses a lazy susan irradiation faility in a groove fixed within the graphite refletor, as shown in Figure 3.1. General Atomis developed several different TRIGA fuel rod onfigurations (Tomsio, 1986). Table 3.1 desribes the three fuel rod types onsidered in the GSTR reliensing analysis: one of whih is lad in aluminum (Figure 3.2a), and two of whih are lad in stainless steel (Figure 3.2b). All three types ontain a uranium-zironium hydride fuel enrihed to less than 20 wt.% U-235 (General Atomis, 2011). Both fuel rod types have a length of m (Tomsio, 1986). Early TRIGA fuel rods inluded disks of samarium to at as a burnable neutron absorber; however, General Atomis stopped manufaturing these elements after 1964 (Tomsio, 1986). The present analysis ignores the effets of the burnable absorber, as all of the fuel at the GSTR is old enough that the burnable absorber has been depleted. The aluminum-lad fuel rods are the oldest TRIGA reator fuel manufatured by General Atomis (Day, 2004). The fuel within an aluminum-lad rod ontains 8 wt.% uranium, and is m tall and m in outer diameter (Figure 3.2a). The GSTR still uses several aluminum-lad fuel rods, whih are limited to the F and G rings in response to onerns over the Table 3.1. GSTR fuel types. Fuel Type Enrihment (wt.%) Cladding Material Uranium in Fuel Meat (wt.%) 8 % aluminum lad < 20 aluminum 8 8.5% stainless steel lad < 20 stainless steel % stainless steel lad < 20 stainless steel 12 31

48 graphite top fitting graphite top fitting samarium trioxide dis m samarium trioxide dis 8.81 m m pin to pin fuel meat (3.607 m diameter) m m pin to pin fuel meat (3.632 m outer diameter) zironium plug (0.635 m diameter) m aluminum ladding (0.076 m thik, m outer diameter) m stainless steel ladding (0.051 m thik, m outer diameter) 8.81 m bottom fitting bottom fitting a) aluminum lad fuel b) stainless steel lad fuel Figure 3.2. Shematis of the TRIGA fuel types used in the GSTR. 32

49 lower melting temperature of aluminum (Day, 2004). The stainless-steel lad fuel rods within the GSTR are a mixture of 8.5 wt.% and 12 wt.% fuel. The fuel in all of the stainless steel lad fuel elements is 38.1 m long and 3.73 m in outer diameter (Figure 3.2b). A zironium plug is loated in the middle of the fuel meat, as a onsequene of the tehniques used in manufaturing the U/ZrH fuel (see Figure 3.2b) (Tomsio, 1986). The dimensions of TRIGA fuel pins are not onsistent and vary from reator to reator and bath to bath. The dimensions in Figures 3.2a and 3.2b represent a best estimate and form the basis for all of the fuel modeling efforts in this analysis. There are four ontrol rods within the GSTR (Figure 3.1). Three are fuel-followed borated graphite ontrol rods (Figure 3.3a), while the forth is a void-followed borated graphite pulse rod (Figure 3.3b). The rod drives above the reator raise the rods during normal operation. All four rods inorporate an eletro-magneti SCRAM feature. During a SCRAM, the eletromagnet that binds the ontrol rods to their drives deativates, allowing gravity to pull the rods bak into the ore. As part of the GSTR tehnial speifiations, the ore must shutdown (beome subritial) with three of the four rods inserted in order to allow for the possibility of a rod beoming stuk. The GSTR s fuel followed ontrol rods are referred to as the shim 1, shim 2, and regulating rods. These rods ontain a fuel element of similar dimensions to the stainless steel lad fuel elements (Figures 3.3b and 3.3) following the borated graphite, whih redues the impat of removing the ontrol rod on the ore flux profile. The final ontrol rod, the transient rod, is void followed, and uses an eletro-pneumati rod drive instead of the mehanial system used by the other three ontrol rods. This system an quikly ejet the transient rod from the ore to initiate a power pulse. Otherwise, the transient rod serves the same funtion as the 33

50 38.1 m graphite top of ore 38.1 m absorber 38.1 m fuel fuel 38.1 m graphite bottom of ore void a) fuel followed ontrol rod b) void followed ontrol rod ) fuel rod Figure 3.3. Diagram of the two ontrol rod types used in the GSTR, showing how the fuel and void followers line up to a regular fuel element. other three rods, exept that the pneumati drive is not as sensitive as the mehanial rod drives. The void follower redues the total reativity worth of the transient rod. Three primary experimental failities are available within the GSTR: the entral thimble loated, the lazy susan, and the external irradiation tubes (see Figure 3.1). Loated in the middle of the ore, the entral thimble provides a high-flux irradiation loation. Normally, the entral thimble is water filled, but an be evauated to provide a beam tube for radiography. The lazy susan sits outside of the ore in an insert plaed in the GSTR s graphite refletor (see Figure 34

51 3.1). A pneumati system allows the forty sample loations within the lazy susan to be remotely loaded and unloaded and a mehanial drive rotates the lazy susan around the ore. The GSTR urrently uses the lazy susan (originally designed for isotope prodution) for sample irradiation. The two external irradiation tubes sit outside of the refletor. A reator operator must manually insert samples into the tubes from outside of the reator tank by lowering or raising the sample into the reator by hand Desription of the GSTR Core Model Figures 3.4a and 3.4b provide radial and axial views of the reator ore model, respetively, and show all of the important aspets of the model s geometry. The model s geometri desription is based on blueprints and other arhival data from the GSTR. Within the model, the ore onsists of the fuel rods, the top and bottom grid plates, and the ontrol rods, surrounded by a graphite refletor (Figures 3.4a and 3.4b). The lazy susan is outside of the fuel within a groove set into the refletor (Figure 3.4b). To save modeling and omputation time, the lazy susan onsists of a uniform mixture of aluminum and air, roughly equal to the homogenized omposition of the atual lazy susan. Material definitions within the model are based on arhival reords from the GSTR that indiate the type and omposition of the different material regions in the GSTR. The stainless steel in the model is type 304L while the aluminum is alloy Within the model, the fuel and ontrol rods have uniform ompositions; the axial geometry of the ontrol rods is defined in more detail to better repliate experimental data (see Setion 3.4.). 35

52 lazy susan stainless steel lad fuel rods entral thimble ontrol rods void followed ontrol rod aluminum lad fuel rod b b a a aluminum lad fuel rod refletor fuel followed ontrol rod stainless steel lad fuel rod All dimensions in m a) radial view a-a b) axial view b-b Figure 3.4. Radial and axial views of the MCNP model of the GSTR ore in the urrent operating onfiguration. 36

53 Figure 10 shows the urrent operating ore layout of the GSTR. The layout ontains 125 fuel elements (inluding the fuel followers in the ontrol rods), with the ontrol rods loated in the C- and D-Rings of the reator. Twelve stainless steel lad fuel elements of 12 wt.% uranium are in the C- and D-Rings of the ore interspaed with 8.5 wt.% uranium stainless steel lad fuel elements. The F-Ring is omprised entirely of aluminum-lad fuel, while roughly half of the outermost G ring is aluminum-lad fuel. The remainder of the ore is filled with 8.5 wt.% stainless steel lad fuel (see Figure 10). The model runs with 1000 ative yles following 15 inative yles with 50,000 neutrons per yle. This provides an average 1σ unertainty of ~$0.01 based on a MCNP old 8.5 wt.% fuel old 12 wt.% fuel aluminum lad fuel ontrol rods m Figure 3.5. Fuel layout in the urrent GSTR operating ore. 37

54 alulated β eff of The reator model utilizes the ENDF/B-VII.0 libraries. All unertainties presented in this paper represent 3σ estimates. The makxsf utility, distributed with MCNP5, Doppler broadened the neutron library data and interpolated the S(α,β) temperature data where needed to onstrut the full power ore (see Setion ). All reativities in this hapter are given as: (3.1) The MCNP model alulates the effetive delayed neutron fration and neutron generation time using the adjoint-weighted point kinetis parameter alulation method available in release 1.60 of MCNP5 (Kiedrowski et al., 2012). The predited effetive delayed neutron fration and neutron generation time for the model are 7.28x10-3 ±9.0x10-5 and 4.28x10-5 ±2.1x10-7, respetively Fuel Depletion Analysis The GSTR staff uses an equation derived in-house and approved by the NRC to alulate the amount of uranium-235 onsumed in grams as a funtion of the amount of energy produed by the ore:. (3.2) To evaluate the amount of unranium-235 onsumed in eah fuel rod, a per-rod power fator (PF) adjustment hanges the equation to: (3.3) 38

55 An analytial approah estimated the effetive burnup of eah type of fuel in eah ring within the GSTR ore. While a omplete inventory history exists for all of the new fuel aquired by the GSTR, a omplete history is not available for the seond-hand fuel added to the reator over the reator s lifetime. This unertainty regarding fuel history makes it unlikely that a more detailed analysis using detailed burnup odes suh as MCNPX or ORIGEN (Pelowitz, 2008; Beddingfield and Swinhoe, 2004) would yield better results than the simple analytial approah desribed in this sub-setion. Currently, the GSTR ontains 125 fuel rods, inluding the fuel followers in three of the ontrol-rods. The MCNP model of the GSTR alulated peaking fators for fuel rods in the ore, averaged by fuel type and loation. For instane, in the C-Ring, the fuel rods ontaining 12 wt.% uranium and 8.5 wt.% uranium fuel were onsidered separately. With the peaking fators alulated, Equation 3.3 alulates the uranium onsumed in eah fuel type while a separate methodology (desribed below) alulated the amount of fission produts produed within the fuel. Based on the revised material definitions, MCNP realulated the peaking fators. If the newly alulated peaking fators differed from the previous ones, the burnup was realulated with the new peaking fators, whih in turn produed new fuel material definitions to alulate a new set of peaking fators. This proess ontinued until the peaking fators onverged, at whih point the fuel omposition was assumed to adequately represent the atual onditions within the ore. Figure 3.6 shows the omposition of an 8.5 wt.% E-ring fuel before and following 25 at.% depletion of uranium-235 using the above method. The fission produt yields from the 39

56 Fuel Content Fration 1x10 0 1x10-1 Fresh fuel Burned fuel 1x10-2 1x10-3 1x10-4 1x10-5 1x10-6 1x10-7 Figure 3.6. Composition of an 8.5 wt.% E-Ring fuel element before and after 25 atom % uranium 235 depletion. depleted uranium-235 atoms are alulated using tables released by the Los Alamos National Laboratory (England and Rider, 1994). The analyti depletion methodology onsiders the ten most frequent light and eleven most frequent heavy fission produts (plus samarium-149) of uranium-235 (see Table 3.2). Eah uranium-235 atom was replaed by a single heavy and a single light fission produt based on the yields in Table 3.2. Samarium-149 has a large neutron apture ross-setion and exists at equilibrium onentrations in any thermal reator (Lewis, 2008). To ompensate, the burnup methodology alters the yield of the heavy fission produts to ompensate for the equilibrium onentration of samarium-149, shown in Equation 3.4: 40

57 Table 3.2. Isotopes onsidered in the depletion analysis. Light Produts Heavy Produts Yield Yield Isotope (%) Isotope (%) Mo Xe Zr Ba Zr Cs Zr Cs Mo La T Xe Zr Ce Mo Cs Zr Nd Sr Pr Ce Sm (3.4) The yields of the remaining non-saturating nulides are renormalized suh that the total yield of eah group (heavy or light) is unity Desription of the Limiting Core A thorough analysis of the GSTR s limiting ore onfiguration is key to the reator s reliensing appliation. A limiting ore represents the most ompat ritial assembly available to the operators, and usually onsists entirely of fresh fuel. It is unlikely that the GSTR will be able to aquire a full ore of fresh fuel in the future, and thus, the limiting ore onsists of a ombination of fresh fuel and partially depleted fuel urrently in the GSTR inventory. The limiting ore provides a safety envelope for the operating onditions of the reator. The limiting ore must safely operate under federal guidelines, and will provide both the 41

58 regulators and the operators an upper bound on the aeptable operating onditions for the ore under the new liense. The limiting ore also provides a basis for several limits in the GSTR s tehnial speifiations. These inlude the limits on the ore s exess reativity, shutdown reativity, and transient rod worth, as well as a new limit on the minimum number of fuel elements in the reator ore. Three guidelines informed the seletion of the limiting ore for the GSTR reliensing analysis: a large power peak towards the ore enter resulting from fresh 12 wt.% uranium stainless steel lad fuel surrounded by depleted 8.5 wt.% stainless steel lad uranium fuel, a ore exess reativity lose to but not exeeding $7.00, and minimizing the number of fuel elements Control Rods Fresh 12 wt% fuel old 8.5 wt% fuel m empty rod positions Figure 3.7. Radial view of the GSTR limiting ore 42

59 able to meet the first set two onditions. Inreasing the peaking in the enter involves removing fissile material from the outside of the ore, whih lowers the overall reativity of the reator. Therefore, the limiting ore results in a highly peaked hot-rod, whih yields a higher risk of fuel damage to that element, as opposed to a less peaked, but more reative ore. To meet these riteria, an analysis of several ores ontaining from 80 to 110 elements found that a 110- element ore reahed a entral peak power of 22.2 kw, with a maximum exess reativity of $6.48. Figure 3.7 illustrates this ore, whih serves as the basis for the re-liensing analysis for the GSTR Full-Power Model While liensed to operate at 1 MW, the GSTR usually operates at a measured power loser to 915 kw in order to provide a margin of safety. For the reliensing analysis, the high power trip threshold of 1.1 MW provides a bounding ase for the GSTR. While the ore would never normally operate at this level, the high power trip would also not ativate until the GSTR exeeded the 1.1 MW limit, making it theoretially possible for the GSTR to operate for a signifiant time period lose to 1.1 MW before shutting down. Analyzing the thermal onditions of the ore at this power level provides ertainty that the GSTR has no redible safety onerns at the expeted operating power levels. Thus, the operating full power ore was modeled at 915 kw to math the normal operating onditions of the GSTR, while the limiting ore was evaluated at a power of 1.1 MW. Altering the material and ell definitions to represent the temperatures expeted when the reator is operating at full power allows MCNP to predit the neutroni parameters of the fullpower limiting ore. At full power, the fuel, the ladding, the water within the ore, and the strutural materials of the ore are at an elevated temperature ompared to operation at 5 W. A 43

60 ombination of hand-alulations, measurements from the GSTR, and preditions from the RELAP5 mod 3.3 model of the hot-rod hannel of the GSTR (Chapter 4) yielded an initial estimate of the operating onditions of the GSTR based on the reator power. Iteration between the MCNP and RELAP models of the GSTR refined these initial estimates to provide an aurate estimate of the reator s temperatures when the reator is operating at full power. The full power model divides the reator s fuel by loation and type. This limits the number of different materials in the ore model and makes the best use of the limited information available for the GSTR. This simplifiation reates nine fuel areas within the operating ore: one fuel definition for eah ring with a single fuel type (8.5 wt.% uranium stainless steel lad fuel in the B- and E-Rings, and 8 wt.% uranium aluminum lad fuel in the F-Ring), two definitions for the C- and D-Rings, (to aount for the 12 wt.% and 8.5 wt.% uranium stainless steel lad fuel in these rings), and two definitions for the G ring (for the stainless steel and aluminum lad fuel in this ring). Averaging fission power tally results aross eah fuel group gives an average power fator for that fuel group. Multiplying this number by the reator averaged rod power rod yields that group s average rod power. Comparing this to a RELAP alulation of the average fuel, ladding, and ore water temperature as a funtion of rod power provides a refined estimate of the reator s operating temperatures. Adjusting the MCNP model to aount these new temperatures improves the temperature estimates. Three iterations were suffiient to redue the hanges in the ore fuel temperatures to less than 1 K, well within the unertainty bounds of both the RELAP and MCNP models, and within the auray of the measurement apabilities of the GSTR. All MCNP runs used the predited rod ritial positions for that temperature exept when stated otherwise. Setion examines the ontrol rod ritial positions in detail. 44

61 Table 3.3 shows the final average rod powers, fuel average temperature, the predited and hannel oolant and ladding temperatures for eah fuel type in the urrent full power GSTR ore. The ladding and water temperatures are onsistent to within 9 K over the range of rod powers. As a result, all of the ladding temperatures in the model are set to an average value of 395 K. Similarly, the temperature of the strutural materials in the ore (i.e. the refletor, grid plates, et. al.) is set to 394 K, while the ore water is set to an average temperature of 315 K. The simplifiations redued the preproessing and memory demands of the model while still providing aeptable results Table 3.4 lists the average water, ladding and strutural material temperatures used in the final full power MCNP model of the urrent GSTR ore. Updating the model temperatures inludes hanges to the neutron library, TMP ard, and S(α,β) data (if appliable). The density of the water in the ore is also adjusted based on Table 3.3. Average alulated rod powers and fuel, ladding, and hannel water temperatures by type and ring for the urrent GSTR ore at full power. Fuel Ring Wt % uranium Clad material Rod Power (kw) T fuel(avg) (K) T lad (K) T oolant (K) B 8.5 Stainless Steel C 8.5 Stainless Steel C 12.0 Stainless Steel D 8.5 Stainless Steel D 12.0 Stainless Steel E 8.5 Stainless Steel F 8.0 Aluminum G 8.5 Stainless Steel G 8.0 Aluminum

62 temperature; however, the full power model does not alter the temperature of the water outside of the GSTR ore, nor does it alter the density of any materials within the model aside from the ore water. Table 3.5 lists the hanges made from the low-power to the high-power model. The ontrol rods are modeled independently of the fuel groups, and the fuel follower of eah rod is orreted to math the temperature of the 8.5 wt.% stainless steel lad fuel within that ring (exluding the transient rod, whih is void- followed). This is onservative as approximately half of the fuel follower is outside of the ore when the rod is in the ritial position. The same proedure alulated the temperatures in the full power limiting ore model, with the peak power Table 3.4. Average surutual material, ore water and ladding temperatures used in the model of the urrent GSTR ore at full power Component Mean Temperature (K) Strutural Materials 396 Water 317 Steel Cladding 396 Aluminum Cladding 393 Table 3.5. Changes between the low power and full power MCNP models of the urrent GSTR onfiguration. Low Power Model Value (5W) Full Power Model (915 kw) Fuel Temperature K set aording to Table 4 Fuel Cladding Temperature K set aording to Table 5 Core Water Temperature K 315 K Bulk Tank Water Temperature K K Control Rods K set to math 8.5 wt.% fuel of same ring All Core Strutural Materials K 394 K 46

63 set to 1.1 MW. Tables 3.6 and 3.7 list the alulated temperatures and those used in the limiting ore model. As expeted these temperatures are higher than the temperatures predited at 5W 3.4. Validation The neutroni haraterization of the GSTR requires that the MCNP model is validated against the urrent ore operating onditions, demonstrating the model s ability to represent the urrent onfiguration of the GSTR. This validation involved three tests: a ontrol-rod alibration based on experimentally derived ontrol rod worth urves from the GSTR, a ritial position and multipliation fator predition omparison, and a flux haraterization aross the GSTR ore Control Rod Calibration The ontrol rods in the GSTR inlude two rods installed when the reator was initially onstruted (transient rod and shim rod 2) and two rods installed in Deember of 1991 (the regulating rod and shim rod 1). Three of the rods (shim rod 1, shim rod 2 and the regulating rod) Table 3.6. Average alulated rod powers and fuel, ladding, and hannel water temperatures by type and ring for the limiting GSTR ore at full power. Fuel Ring Wt % uranium Clad material Rod Power (kw) T fuel(avg) (K) T lad (K) T oolant (K) B 12.0 Stainless Steel C 12.0 Stainless Steel D 8.5 Stainless Steel E 8.5 Stainless Steel F 8.5 Stainless Steel G 8.5 Stainless Steel Table 3.7. Average strutural material, ore water and ladding temperatures used in the limiting GSTR ore model at full power. Component Mean Temperature (K) Strutural Materials 396 Water 317 Stainless Steel Cladding

64 have fuel followers to mitigate the effet they have on the ore flux profile while the transient rod is void followed to limit the reativity added during pulses (Nulear Installation Safety Division, 2004b). The ritial positions of eah of the ontrol rods hange over time as a result of ore onfiguration hanges, fission produt buildup, and temperature hanges, making an estimation of eah rod s effetive burnup more ompliated than the similar evaluation for the fuel rods. Time onstraints, as well as a lak of omplete information on the ontrol rod operating history, resulted in the use of a geometri approximation to determine the ontrol rod worths for the GSTR model based on Oregon State University s TRIGA-reliensing effort (Reese, 2007). Experiments performed at the reator determined the urrent ontrol rod worths. Comparing the experimental ontrol rod worths to the model predited ontrol rod worths for fresh ontrol rods yielded an estimate of the amount of boron depletion in the ontrol rods. Reduing the radius of the ontrol rod region ontaining the borated graphite simulates this boron depletion. Pure graphite then simulates the depleted material, as seen in Figures 3.8a and 3.8b. However, a single axial segment (Figure 3.8b) did not aurately represent the effets of the axial neutron flux on the ontrol rod depletion, yielding aurate results only when the rod was fully inserted or removed. Breaking the depletion zone into four axial segments better represents the intermediate withdrawal stages. The total volume of depleted graphite within eah rod was redistributed between the four axial segments within that rod based on the peak-to-average neutron flux ratio alulated eah region with the rod in the ritial position (see Figure 3.8). This provided the spatial resolution needed to aurately represent the boron depletion in the modeled GSTR ontrol rods. 48

65 borated graphite graphite plug ontrol rod fuel rod graphite plug fuel rod depleted graphite ontrol rod 5 m (a) fresh ontrol rod (b) 1-segment depleted ontrol rod Figure 3.8. Example ross-setions of fresh and depleted GSTR ontrol rods. () 4-segmented depleted ontrol rod Figures show the experimental integral rod worths a funtion of rod position for axial depletion zones. Dividing the ontrol rods into four axial depletion zones, with the depletion weighted by the neutron flux in eah of the axial segments, improved the rod worth alulations for rods with high boron depletion (the transient and shim 1 rods, Figures 3.10 and 3.11, respetively). This method did not signifiantly alter the rod worth preditions for the rods with little or no boron depletion (the regulating and shim 2 rods, Figures 3.9 and 3.12, respetively). Table 3.8 details the alulated and measured total worths of eah ontrol rod, as well as the 49

66 Integral Rod Worth ($) Integral Rod Worth ($) adsorber segment 4 adsorber segments experimental data Rod Position Figure 3.9. Measured and alulated reativity worth urves for the regulating rod adsorber segment 4 adsorber segments experimental data Rod Position Figure Measured and alulated reativity worth urves for the transient rod. 50

67 Integral Rod Worth ($) Integral Rod Worth ($) adsorber segment 4 adsorber segments experimental data Rod Position Figure Measured and alulated reativity worth urves for shim rod adsorber segment 4 adsorber segments experimental data Rod Position Figure Measured and alulated reativity worth urves for shim rod 2. 51

68 Table 3.8. Control rod alibration results. Regulating Transient Shim 1 Shim 2 Value Rod Rod Rod Rod Final Volume 1 (m 3 ) Calulated Control Rod Worth ($) Measured Control Rod Worth ($) Differene ($) Initial volume is m 3 urrent absorber volumes in eah rod. The ombined predited rod worth for the ore is $0.30 less than the experimentally measured values. In the ase of the regulating rod, the rod worth predited by MCNP is less than the experimentally determined worth data. In this ase, reduing the fuel follower s estimated depletion added reativity worth to the ontrol rod. It is possible that the material used for the absorber is not onsistent between the older and newer ontrol rods. Unfortunately, the doumentation available at the GSTR only lists the material as borated graphite, with no detail on the speifi omposition of eah rod, providing no basis for further adjustment of the ontrol rods. The 3σ model unertainty is around $0.03 for eah rod with a similar level of unertainty in the experimental data from the GSTR. This indiates that the modeled ontrol rods adequately represent the physial ontrol rods Critial Control Rod Position The urrent model must be able to aurately predit the ritial ontrol rod positions for the urrent ore. This validation examined multipliation fator preditions with the ontrol rods at the measured ritial rod heights for both the low power (5 W), and full power (915 kw) ores. Subsequent orretions to the initial model brought the multipliation fator estimates to unity. 52

69 Calulated Multipliation Fator Reent researh indiates that the ENDF/B-VII.0 neutron ross-setion libraries an result in signifiant biases in MCNP TRIGA reator models (Snoj, Trkov, and Ravnik, 2007; Snoj, Zerovnik, and Trkov, 2011; Chadwik et al., 2011). Figure 3.13 presents multipliation fator preditions for the four ases presented in Table 3.9 that test the effet of different ombinations of neutron ross-setions and S(α,β) data from the ENDF/B-VII.0 and ENDF/B- VI.6 data libraries. The results indiate that the S(α,β) and neutron ross setion library hoie has an equal effet on the alulated multipliation fator for the GSTR model, with the B-VI.6 libraries lowering the alulated multipliation fator by ~ for eah set of data. While the Table 3.9. Test ases onsidered in Figure Test Case Cross Setion Library S(α,β) data Multipliation Fator σ Case 1 B-VII.0 B/VII Case 2 B-VI.6 B/VII Case 3 B-VII.0 B/VI Case 4 B-VI.6 B/VI Case 1 Case 2 Case 3 Case 4 Figure Multipliation fators alulated by the GSTR model using the ombinations of neutron libraries listed in Table

70 model appears more sensitive to the hoie of the S(α,β) library version, the differene between Case 2 and Case 3 is well within the unertainty of the MCNP alulations. In the GSTR model, the ENDF/B-VII.0 libraries (.70 and.10t) yield a higher predited multipliation fator than the ENDF/B-VI.6 libraries (.66 and.66t). These findings agree with existing studies (Snoj, Trkov, and Ravnik, 2007; Snoj, Zerovnik, and Trkov, 2011; Chadwik et al., 2011). While the ENDF/B-VII.0 libraries result in a positive bias to the multipliation fator predited by the GSTR model, three reasons ditate that the final model inludes the ENDF/B- VII.0 libraries. First, many of the fission produts needed for the depletion analysis do not exist in the ENDF/B-VI.6 library, requiring the ENDF/B-VII.0 libraries for the burned fuel material definitions. A hybrid model introdues new ompliations that outweigh the possible benefits of using the ENDF/B-VI.6 libraries exlusively. Seond, the ENDF/B-VII.0 libraries ontain data at multiple temperatures that make the alulation of the temperature reativity feedbak oeffiients easier and more aurate. Finally, sine the ENDF/B-VII.0 libraries ontain more reent data, and the bias they ause in TRIGA reator models is doumented, it is aeptable to use the most reent libraries while aknowledging the resulting biases. Table 3.10 lists the measured ontrol rod ritial positions and the resulting multipliation fator predited by the model with all of the ontrol rods at the measured ritial position. For the urrent ore, the modeled ontrol rods are withdrawn of m for the 5 W ase, and m for the 915 kw (full power) ase. The model aurately predits the ritiality of the 915 kw ase to within the statistial unertainty of MCNP and is within $0.06 of the expeted value for the 5 W ase. 54

71 Table Critial ontrol rod position verifiation data. Core Configuration (Operating Core) Measured Critial Rod Height (m, from bottom of ore) Multipliation Fator Differene from Critial ($) 3 σ Unertainty ($) 5 W kw For eah ase, the model slightly over-predits the multipliation fator, giving a more onservative result. In the GSTR, the ritial position atually hanges from day to day, as the reator s operating shedule varies. This allows fission produts that at as absorbers (suh as samarium and xenon) to build up in variable amounts within the reator. These fission produts alter the atual ritial position from day to day, and the modeled fuel omposition represents an average value for these fission produts. This leads to the atual ritial rod positions being slightly elevated from the modeled results; however, the total differene in rod position is less than 1 m, whih is aeptable for this analysis Flux Profile Validation of the MCNP model requires that the model aurately predit the neutron flux profile within the GSTR. The GSTR does not have the failities to take radial flux measurements, as the GSTR staff urrently only measure flux in the entral thimble and at the external irradiation failities. The validation attempts to reprodue the entral thimble flux data by omparing the point-to-average normalizations of GSTR experimental data with alulations from the MCNP model. To predit the flux, the MCNP model employs a series of FMESH tallies using reation rate multipliers (X-5 Monte Carlo Team, 2003b) to simulate the gold foil reations measured by the GSTR staff. The atual gold foils used in the experiments are approximately point detetors within the reator; however, as MCNP tallies represent an average flux over an area, and the 55

72 GSTR s measured flux is not highly variable, the FMESH tallies provide an aeptable approximation. Aside from simple flux tallies, MCNP an also alulate reation-rates (in units of reations/barn-m) for eah tally, by using ross-setion multipliers for seleted materials. To hange this to an approximation of ativation rate, the number of atoms in a given foil is multiplied by the alulated reation rate flux to predit the total ativation rate for the geometry. MCNP tally data must be denormalized to be meaningfully ompared to experimental data. For the present analysis, this denormalization onstant orresponds to the soure partile rate (SPR), whih is based on the reator power: (3.5) This provides the neutron prodution rate orresponding to the speified reator power. This onstant allows MCNP tallies to be onverted to fluxes or reation rates whih an be translated to a predited ativity. The alulations for ativity are as follows: ( ) ( ) (3.6) ( ) (3.7) Figure 3.14 ompares the foil ativities alulated by the MCNP model to measurements taken at the GSTR using irradiation foils in January The values are in rough agreement near the axial enter, but diverge below the axial enter starting at -5 m This is onsistent with 56

73 Ativity (MBq/g) the model having a more peaked flux profile ompared to the atual ore and may result from onsidering fuel depletion to be axially uniform. Figure 3.15 presents the point to average flux profile from an MCNP FMESH analysis of the entral thimble ompared to flux measurements taken at the GSTR using irradiation foils in January The alulated flux in the entral thimble from a trak length (F4) flux tally over the examined area is 4.51x10 13 n/m 2 s based on a soure partile rate of 7.49x10 16 n/s, while measurements of the thermal flux taken using gold foils at the same loation in the ore give a flux of 2.01x10 13 n/m 2 s. The higher MCNP result is expeted, as MCNP predits the total neutron flux, while the gold foil ativation primarily measures the thermal flux. Sine the entral-thimble of the reator produes no neutrons, and is a water-filled ylinder, it is expeted that the majority of the flux in this region is thermal. As shown in Figure 3.15, the flux profile GSTR foil measurement MCNP predition Distane from Axial Centerline (m) Figure Gold foil ativity following a one-hour ativation as predited by MCNP and measured by the GSTR staff. 57

74 Point-to-Average Flux Ratio GSTR foil measurement 0.50 Model predition Distane from Axial Centerline (m) Figure Point-to-average flux ratios in the GSTR entral thimble. evaluated by the model peaks ~5 m higher in the entral thimble than the profile measured in the atual ore. The predited flux profile is also less flat than the experimentally determined flux profile. Some of the differenes in shape may be due to the lak of axial fidelity in the modeled fuel and the averaging of fuel depletion over the entire element Reliensing Analysis The validated model analyzed the limiting ore to produe the values needed for the updated GSTR Safety Analysis Report (SAR). This analysis inluded determining the exess and shutdown reativity margins, determining the ritial ontrol rod positions, and determining the fuel temperature, ore water temperature, ore void and power reativity oeffiients Limiting Core Exess and Shutdown Reativity Margins The ore exess and shutdown margins (the reativity when the ontrol rods are fully withdrawn or inserted, respetively) are important for the limiting ore alulations. The 58

75 Table Exess and shutdown margins of the limiting ore. Limiting Core Configuration Multipliation Fator Differene from Critial ($) 3 σ Unertainty ($) 1.1 MW Exess MW Shutdown W Exess W Shutdown limiting ore model alulates both of these values during low power (5 W) and full power (1.1 MW) operation (see Table 3.11). These values indiate how muh impat the power reativity oeffiient has on the ore, and provide bounding limits for the updated GSTR safety analysis. The power reativity oeffiient is determined in Setion As shown in Table 3.11, the full power limiting ore has less exess reativity and a greater shutdown margin than the low power limiting ore as a onsequene of the negative temperature reativity feedbak from the fuel. This makes the low power (5 W) ase the limiting onfiguration from a ritiality safety standpoint, as at low power the ontrol rods provide less negative reativity margin for the reator Reator Power Distribution Calulating the power distribution within the model involves a series of fission power (F7) tallies that trak the fission energy produed in eah fuel element. The average of these values provides the average power value in the reator. Dividing the individual tally value for a fuel element by the average power value provides the power fator for that element. In the GSTR limiting ore, the power fators range from 0.46 to 2.29, with a power fator of approximately unity existing in the E-Ring fuel of the reator (with values ranging from 0.93 to 1.06). Multiplying a rod s power fator by the arithmeti average rod power (reator power 59

76 divided by the number of fuel elements, 9.73 kw per rod in the limiting GSTR ore) gives an approximate value for the power produed in that rod. Figure 3.16 shows the alulated power profile for the full power limiting ore, operating at the maximum allowed power of 1.1 MW. The GSTR limiting ore, as designed, is highly peaked with the G-Ring fuel elements eah produing between 4.6 and 4.9 kw, while the peak element in the B-Ring (loated slightly to the right and below the entral thimble in Figure 3.16) produes over four times that power (22.2 kw) at a peak to average power fator of The ore is largely symmetrial, with a bias around the peak rod loated in the B-Ring. This bias likely results from the ontrol rods, as the transient rod without a fuel follower has a greater impat on the ore power profile than the fuel-followed ontrol rods. Sine the fuel elements within eah ring are idential, the ontrol elements are largely responsible for the polar hanges in the power profile Reativity Calulations The urrent analysis examines the limiting ore at both low (5 W) and full (1.1 MW) power to alulate the fuel temperature, moderator temperature, and void oeffiients of reativity for the GSTR limiting ore. For the low power ase, any materials not altered to aount for the oeffiient being alulated are set to K. For the full power ase, the omponent temperatures within the reator have been inreased to represent the higher power output, as desribed in Setion The reativity alulations are ompliated by the 60

77 Reator Power: 1.1MW A 9.7 C 7.1 B 9.7 Transient Rod A Regulating Rod B Shim 1 Rod C Shim 2 Rod Figure Power profile for the GSTR limiting ore operating at 1.1 MW. 61