CHAPTER 1INTRODUCTION1.1 BACKGROUNDNuclear power is a successful power generation technology in the long run only if it haslower cost (both economical and social) than other competing technologies.
One of the promising approaches to lower the cost of nuclear power is by increasing the power density of the reactor core1.The last few years have marked a period of rethinking of nuclear reactor technology because of a changing economic environment reflecting stronger competition with other power sources coupled with aderegulation trend in the electric utility industry1. The new and highly competitive environment put all nuclear plants under increased pressure to significantly reduce total power cost. Therefore, reduction of total generation cost while maintaining excellent safety is a key challenge facing the nuclear industry today and in the future 1. One approach to improve the economy of both the operating and new plants is to increase their power density and extract more energy from a given system volume. One of the key components affecting the allowable power density in the nuclear island is the nuclear fuel.
In fact, the safety limits in a nuclear power plant are largely related to its fuel. Evolutionary improvements in fuel design and cladding quality allowed a remarkable reduction of failure rate, and fuel assembly design changes allowed both power increases and performance improvement at steady state and during accidents 1. Thermal hydraulic studies proposed two types of fuel design, which are: 1. Conventional solid cylindrical fuel rods.
2. Internally and externally cooled annular fuel rods.The proposed annular fuel departs from the traditional solid rod design by introducing internal cooling of each fuel pellet. The idea of annular fuel pellets is not new in reactor technology. In pressurized water reactors, annular fuel pellets are used in the short axial blankets of western PWRs and BWRs and in Russian VVER cores 2. Annular fuel with both internal and external cooling was also proposed for high temperature gas cooled reactors where a compact fuel element ofannular shape was conceived to be enclosed in an inner tube and an outer tube 2.
The annular fuel proposed in this thesis uses UN fuel and is intended for all core assemblies with the prime objective being to significantly increase core power density (up to 25%), while increasing or at least maintaining safety margins. The new internally and externally cooled Annular Fuel (AF) for a PWR has been proposed to substantially increase power density while retaining or improving safety margins. The geometry of this annular fuel is shown schematically in Figure 1.1, where the traditional solid fuel rod is also drawn for comparison. Figure1.
1. Schematic of (a) solid and(b) internally and externally cooled annular fuel (not to scale)The annular fuelrodsare of significantly larger diameter than the typical solid rods to accommodatean inner coolant channel allowing for sufficient coolant flow 1.If core power density is increased;there is some benefit from relatively smaller reactor vessel. In addition, the size of the containment can be kept the samesince the coolant enthalpy and primary coolant mass remain the same. A simplified assessmentof potential capital cost benefits for new PWR plant with higher power density core design canbe found in Ref 21.2 DESIGN LIMITS FOR PWRSIn a pressurized water reactor, water at high pressure (typically 15.
5 MPa) and moderate temperature (about 3150C) is circulated through the reactor vessel where it is heated by extracting the heat generated by nuclear reactions from the fuel. The hot water is pumped to thesteam generator where it transfers heat to the secondary coolant which boils at a pressure ofabout 7.0 MPa and drives the turbines coupled to the electricity generator. The initial pressurized water reactors for electricity power production were developed in the United States by theWestinghouse Electric Company. This is now the most widely used type of reactor.
More than230 units in more than 20 countries are in use to generate electrical power. The Westinghouse4-loop PWR (Seabrook) was chosen as the reference design for evaluation of the high powerdensity core designs in this thesis 1. Pressurized water reactors conventionally employ thin cylindrical rods with oxide fuel pelletsand metallic cladding. For these sealed fuel pins, thermal design limits have to beimposed to maintain the integrity of the clad, so that radioactive fission products are containedwithin the cladding.
In theory, these limits should all be expressed in terms of structural designparameters, e.g., strain and fatigue limits for both steady-state and transient operations. However, it is quite impractical to specify the limits in these terms because the behavior of materials in radiation and thermal environments in power reactors is very complex. So, the design limits forthe power reactors have been imposed directly on certain temperatures and heat fluxes 1.
1.2.1 Minimum Departure from Nucleate Boiling Ratio (MDNBR)The most limiting constraint on the thermal power output of a PWR is the minimum DNBR. The damage limits for the reference PWRs employing Minimum Departure from Nucleate Boiling Ratio (MDNBR) smaller than 1.
0. The departurefrom nucleate boiling is related to the critical heat flux phenomenon which results in a drasticreduction of the heat transfer capability of the two-phase coolant. For the fuel rods, reduction insurface heat transfer capability at normal bulk coolant temperature and clad heat flux causes theclad temperature to jump. Physically, a change in the liquid-vapor flow patterns at the heatedsurface causes the reduction to occur.
At PWR operating conditions, void fractions are low. Thehot fuel rod surface is normally cooled by nucleate boiling. Once the surface is totally coveredby vapor, the clad surface temperature will sharply increase.
In the low void fraction regime in aPWR core, the ratio of the critical heat flux divided by the operating surface heat flux is calleddeparture from nucleate boiling ratio (DNBR). The most limiting point that has the smallestmargin to critical heat flux phenomenon is the point that has the minimumdeparturefrom nucleate boiling ratio, thus the design limit is expressed in terms of MDNBR.In practice, in order to have adequate design margins, the MDNBR is required to be largerthan 1.0, typically 1.2 or 1.
3 depending on the correlation used for evaluating the critical heatflux 1.1.2.
2 The loss of coolant accident (LOCA)Another design limit may be derived from transient situations, specifically in the loss ofcoolant accident (LOCA). At normal operation conditions, the pressurized water in the corecools the rod surface so that the clad temperature is limited to a narrow band above the coolantsaturation temperature so that it is typically not necessary to employ a steady-state limit on cladtemperature. However, a significant limit on clad average temperature has to be employed for thetransient conditions like the LOCA. For this accident, a key limit is that the Zircaloy cladtemperature has to be below 1200oC to prevent extensive occurrence of self-heatingmetal and water chemical reactions 1.A small pressure drop in the core is helpful to having a larger portion ofthe flow directly into the core, and less flow bypassing the core, through the broken loop, to thecontainment.1.
2.3 Peaking Factors The core peaking factors are primary indices of the power distribution. In order to improve core performance, there is strong incentive to keep the core power as flat as possible by reducing the power peaking factors to a minimum. Specifically two commonlyused peaking factors are discussed: the total peaking factor and the maximum enthalpy rise factor 3. The total peaking (hot spot) factor is defined as This characterizes the total peaking including both the axial and the radial contributions.The limiting value is 2.
50 for a typical Westinghouse 4-loop PWR (also depending on the type of fuel) 4. Furthermore the hot spot factor can be decomposed into a nuclear factor and an engineering factor. The nuclear factor usually comes from neutronic core analysis, for example, using the CMS package by Studsvik.
The engineering factor typically includes a 4% margin for analysis uncertainties and 4% for manufacturing tolerances. Therefore, the typical design limit for the nuclear total peaking factor is 2.31. The maximum enthalpy rise (hot channel) factor is defined as This is needed for DNBR hot channel analysis.
The typical limit is 1.65 for a Westinghouse PWR 4. Applying the same 1.
08 engineering factor yields 1.53 for the nuclear hot channel factor limit. As noted above, one should be aware that these peaking limits are for specific fuel assembly designs. For example, increasing the number of grids and/or better mechanical design of the grids in the fuel assembly would improve the thermal hydraulic margins (and would increase peaking limits). Therefore, the design limits of peaking factors are supplied by the individual fuel vendors. Flexibility in these limits has provided large design space in core design and facilitated the implementation of low-leakage fuel management with high burnup and long cycles 4.
1.2.4 The fuel temperatureThe last thermal limit is on the fuel temperature. No melting is allowed in the fuel.
The most limiting point of the fuel temperature is at the centerline of the fuel pellet existing athot spot of the core, typically also where the linear heat generating rate is the largest. Themelting point of U02 is in the vicinity of 2840OC. The melting point is somewhat reduced by thepresence of PuO2 after significant burnup.Themelting point of UN is in the vicinity of 2850OC. The melting process for the oxide starts at a solidustemperature but is completed at a higher temperature called the liquidus point.
It is often assumed that, in LWRdesigns, the fuel temperature should be below the conservatively low value of 26000C 1.There are many other safety criteria for LWR fuel using UO2 and zircalloy cladding. A goodreview of them can be found in the review generated by Nuclear Energy Agency 5.
The design limits discussed above are the key limits for evaluating fuel geometries that canbetter achieve high power density.1.3 TRANSITION FROM THE SOLID FUEL ROD TO THE ANNULAR FUEL ROD The fuel weproposed is of annular shape and has both internal and external cooling, as shown in Figure 1.
1. To provide sufficient flow rate through the inner cooling channel, significantly larger rod size than the typical fuel rods of 17×17 PWR fuel arrays has to be employed. Therefore, for a fixed assembly size, the PWR fuel assembly has a smaller number of fuel rods.A transition from solid to annular geometry has two important implications that allow power density increases: (1) reduction of conduction path thickness, which improves margin from peak fuel temperature to melting and (2) increased heat transfer surface area (in spite of a reduction of the number of fuel rods), which improves the margin for Departure from Nucleate Boiling Ratio (DNBR) 6.The improved core can increase electricity production by one or both of the followingstrategies; increasing the number of fuel assemblies per core (which implies a redesign of thereactor vessel) and/or increasing the amount of power produced per assemblies6. Redesigning largecomponents like the reactor vessel is possible; however it could face manufacturing limits.
Advanced fuel designs, on the other hand, can be utilized with far less limitations. This thesis pursues the development of advanced fuel designs, i.e. the development of high-performanceannular geometries which can achieve higher power densities and hence, higher electricityoutput.1.4.
DESIRABLEFUEL DESIGNSThe previous section discussed the main thermal limits for LWR fuels. In order to design ahigh power density core, more issues have to be addressed includingdesirable features. This section will discuss thefeathers for achieving a high power density fuel 1.1.4.
1 Large Surface to Fuel VolumeIn a PWR, the coolant also acts as the moderator. From the neutronics point of view, the ratioofhydrogen to metal (H/M) has to be adequate for moderation of the neutrons. So it is importantto have good moderator/coolant-to-fuel volume ratio in the core design. Modern PWR designshave a coolant-to-fuel volume ratio of about 1.8 in the core. Once this ratio is fixed and total corevolume is pre-designed, the fuel volume and the coolant volume are decided 1.
For a given fuel volume, it is very desirable to have a large surface area since a large surfacearea will lead to low surface heat flux, as the average surface heat flux is the total core powerdivided by the total fuel surface area. The smaller the surface heat flux, the larger is DNBR sinceit is the ratio between the critical heat flux to the surface heat flux, and the critical heat flux isapproximately constant for a given flow velocity, pressure and temperature 1. So, it is desirable forhigh power density fuel design that the fuel surface-to-volume ratio be large.1.
4.2 Small Fuel ThicknessThe small fuel thickness leads to alow fuel temperature. Different fuel geometries have different characteristics of heat conduction.Heat is generated in the fuel and is transferred to the surface of the cladding through heatconduction where it is cooled by the flowing coolant. For a cylindrical fuel geometry, thecenter-line temperature of the fuel is solely determined by the linear generation rate while thediameter of the fuel rod has no effect on the center-line temperature or maximum fuel temperature 7.
The smaller the fuel rod diameter, the larger is thenumber of fuel rods that can be incorporated in a given volume for a fixed total core power 7. Thelinear heat generation rate of the fuel rod is smaller, so that the fuel centerline temperature issmaller. Therefore, the smaller the fuel rod diameter, the lower is the fuel temperature in a givencore. For an internally and externally cooled annular geometry fuel, the fuel ring is thin and fueltemperature is low 1. Therefore the average fuel temperature and the maximum fuel temperatureare low for a given power density.
The fuel temperature is one of the important aspects of high power density fuel sinceincreasing the power density of the fuel will increase the fuel temperature. As a thermal limit, thefuel temperature should not exceed the melting point, and a low fuel temperature will have alarge margin to fuel melting. A low fuel temperature is helpful to achievinghigh burnup. Since the major limit for high burnup is the fission gas release that will lead to fuelrod pressurization, low operating fuel temperature will be helpful in reducing fission gas releaseand achieving high burnup.
This will be beneficial for maintaining the same cycle length at highpower density 1.1.4.
3 Open Parallel ChannelsIt is very important to design the coolant channels to be open for mass, momentum andenergy exchange. In a nuclear reactor core, the radial power distribution is not uniform. Somechannels will receive larger than average power.
The channel that receives the largest power iscalled the hot channel, and usually this is where the minimum DNBR exists. The MDNBR in thehot channel is usually larger in an open core than that in a core that has isolated coolant flowchannels. 1.
5. OBJECTIVE OF THIS THESISThe primary objective of this thesis is to characterize and develop advanced high performance annular fuel design for PWRs,Using uraniumnitride fuel (UN) instead of uranium dioxide fuel (UO2). We usedfrom(12 x 12 to 14 x 14) internally and externallycooled annular fuel pin geometry. This allowed a significant increase of core power density and fuel cycle while maintaining safety margins. The proposed designs achieved low operating fuel temperatures and long fuel cycle. This objective was accomplished through twoprincipal tasks.
First, determination if an equivalent fuel cycle length could be achieved with uranium nitridefuel at an uprated power density as the nominal uranium dioxide fuel at 100% power densitywithout exceeding the current 5 weight percent licensing limit for fuel enrichment. The secondtask is a determination of what the relativedifference in reactivity swing was between the suggested annular uranium nitride (UN) and the17x17 solid reference uranium dioxide (UO2) fuel assemblies. 1.6.
ORGANIZATION OF THE THESIS This thesis is organized into five chapters. Chapter 1 (the current chapter) startsby looking at the background on the nuclear power followed by the design limits for PWRsthen the features for high power density fuel designs.Finally, the study objectivesand organization of the thesis.
Chapter 2gives a brief review of the previously completedwork on annular fuel for high power density reactor applications.Chapter 3starts witha short overview of the analysis tool MCNPX then the neutronic modeling and results by using uraniumnitride fuel (UN) instead of uranium dioxide fuel (UO2).Chapter 4 starts witha short overview of the analysis tool thermal hydraulic RELAP5 code then the thermal hydraulic parameters results.Chapter 5 includes the conclusions as well as recommendations and future works whichmay be a continuation of this study.
?CHAPTER 2LITERATURE REVIEW2.1. ANNULAR FUEL The U.S. Department of energy funded NERI (Nuclear Research Energy Initiative) program on development of the internally and externally cooled annular fuel for high power density pressurized water reactors PWRs. This new fuel was proposed by MIT to allow a substantial increase in power density (on the order of 30% or higher) while maintaining or improving safety margins.
A comprehensive study was performed by a team consisting of MIT (lead organization), Westinghouse Electric Corporation, Gamma Engineering Corporation, Framatome ANP (formerly Duke Engineering) and Atomic Energy of Canada Limited. The study involved the evaluation of the new fuel in terms of thermal hydraulic, neutronics, fuel performance including first scoping irradiation tests at the MIT reactor, fuel manufacturing and economics 2.The overall objective of the NERI project was to examine the potential for improving safety and economics of pressurized water reactors (PWRs) through a high-performance externally and internally cooled annular fuel. This has been pursued through the following tasks 2: 1.
Identify the most promising fuel assembly arrangement for PWRs to achieve a significant increase in power density of at least 30 percent; based to a large extent on the extensive PWR UO2 fuel database to minimize R&D development expenses and the risks associated with transition to a new fuel materials. Optimize the fuel for superior thermal hydraulic performance. Examine flow distribution, core pressure drop, departure from nucleate boiling ratio (DNBR), and resistance to parallel channel instabilities. 2.
Perform safety analyses, such as loss of coolant accident (LOCA) analyses, to confirm safety benefits for the optimum configuration identified in item (1). 3. Evaluate the neutronic fuel design to achieve high reactivity-limited burn-up and a refueling cycle comparable to current PWR practice to attain good economic features.
Confirm the acceptability of the coefficients for reactivity feedback and reactivity control. 4. Select fabrication processes to produce annular fuel elements with the required product characteristics, including fissile loading and high integrity cladding, which are capable of eventual scale-up into efficient production processes for economic and reliable fuel element performance. 5.
Evaluate the materials and mechanical performance of UO2 fuel forms obtained by production technologies different from current U.S. practices (e.
g., vibropacked fuel), and operating under new conditions (such as very low fuel temperature). Develop models for assessing fuel performance as well as for scoping irradiation tests performed at the research reactor of Massachusetts Institute of Technology (MIT). 2.
2. HISTORY OF NUCLEAR ANNULAR FUELThe proposed annular fuel departs from the traditional solid rod design by introducing internal cooling of each fuel pellet. The idea of annular fuel pellets is not new in reactor technology, although it has been usually applied within the solid cylindrical cladding. In pressurized water reactors, annular fuel pellets are used in the short axial blankets of western PWRs and BWRs and in Russian VVER cores, in which pellets employ a small (~10 vol %) central voided region to reduce the fuel centerline temperature. Annular fuel pellets were also proposed for axial power flattening without the need to vary enrichment by having annular pellets stacked in the fuel rod in such a way as to compensate for neutron flux variation along the core height through changes of the diameter of a central voided region in each pellet 8. All these annular pellets, either employed in or proposed for PWRs considered only a central voided region without internal cooling, where the benefit of reduced fuel centerline temperature was marginal and the more limiting minimum DNBR margin could not be appreciably affected.
In fact, in detailed neutron physics and economic evaluations, annular pins with voids were not found to offer fuel cost or uranium utilization benefits at extended burn-up 8. Annular fuel with both internal and external cooling was proposed for high temperature gas cooled reactors where a compact fuel element of annular shape was designed to be enclosed in an inner tube and an outer tube. The inner tube was made of graphite having a lower coefficient of shrinkage than the graphite of the outer tube under irradiation to attain good contact of both tubes at high fluencies 9. Annular fuel has also been evaluated in the framework of the Strategic Defense Initiative (SDI) for a Wire Core Reactor proposed by Rockwell where Tungsten-Rhenium clad UN fuel wires, 0.05 to 0.
25 cm in diameter, are shaped into a number of concentric annular fuel assemblies having alternating layers of fuel wires separated by tension-stressed un-fueled spacer wires to maintain fuel element spacing and facilitate propellant flow 10. This, as well as a number of similar concepts, remained as proposals without actual application or operational experience. Annular fuel cooled from both sides has been utilized in some research and special purpose reactors. For example, Atomic Energy of Canada Ltd (AECL) has developed an internally cooled oxide fuel element for use in the heavy water Maple X isotope production reactor in Canada. However, these “target”fuel elements operate at relatively low power density, and fuel endurance of only a few months is required 10. Also the dual purpose plutonium production N-reactor at Hanford site used 66cm-long tubular metallic uranium fuel that was placed in pressure tube coolant channels and effectively cooled from both the inside and outside.
Although this reactor generated electricity, its primary mission was focused on plutonium production and was run at low power density and at small burn-up 10. Most recently, Commissariat à l’EnergieAtomique (CEA) proposed advanced fuel assemblies with large fertile-free annular fuel rods containing plutonium surrounded by traditional UO2 solid rods 11. These fuel assemblies were evaluated for plutonium burning due to a softer local neutron spectrum and better capability of annular rods to accommodate higher power peaking.
The annular fuel proposed uses UO2 fuel and is intended for all core assemblies with the prime objective being to significantly increase core power density, while increasing or at least maintaining safety margins 11.Aprevious study assessed the thermal hydraulic and neutronics feasibility of a nitride fueled pressurized water reactor (PWR) breeder design. Because of the higher fuel density, the use of nitride fuel would be preferable to the traditional oxide fuel for a high conversion PWR design 12. Marc Caner and Edward T. Dugan in 1999 13 studied ThO2-UO2 annular pins for high burn-up fuels. The main purpose of this work was to investigate the use of annular fuel pins (particularly pins containing thorium dioxide) for high burn-up fuel. The following parameters were evaluated and compared between postulated mixed thorium-uranium dioxide standard and annular (9% void fraction) type fuel assemblies, as a function of burn-up: the infinite multiplication factor, the uranium and plutonium isotopic compositions, the fuel temperature coefficient of reactivity and the conversion ratio. They used the SCALE-4.3 code system. The calculation method consisted of obtaining actinide and fission product number densities as functions of assembly burn-up, by means of a 1-D transport calculation combined with a 0-D burn-up calculation. These number densities were then used in a 3-D Monte Carlo code for obtaining K-inf from two-dimensional-symmetry snapshots 13. In July 2003, Han and Chang 14 developed of a thermal-hydraulic analysis code forannular fuel assemblies.The code is capable of modeling both internally and externally cooled annular fuel pins. The coolant flow distribution in the annular fuel-based assemblies was adjusted by a pressure drop model allowingfor conditions such as non-equal velocity and non-saturated phases. The heat transfer fraction was determined by the ratio ofcross-sectional areas distinguished by the radius at which the first derivative of the temperature within the annular fuel equalszero. The code predictions have been compared with calculations from Korea Atomic Energy Research Institute (KAERI) andMIT. The heat transfer fraction difference between the code and RELAP was about 3.9%, and the Departure from Nucleate BoilingRatio (DNBR) prediction of the code agreed well with the MIT’s result in the region below 3 m 14. In July 2005, Hanaet.al15 developed a thermal hydraulic analysis codefor gas-cooled reactors with annular fuels, with a heat transfer model of a block element, which was solved implicitlywith the helium energy equation. Validation was carried out through comparison with both experimental and analytical results. At normal operation, the annular fuel showed 800 C lower peak temperatures than the solid fuel for the same powerin Japan’s high temperature engineering test reactor (HTTR), even though the pressure drop was higher in the annular fuel 15.In May 2008, Tak et.al 16 proposed a double-side-cooled annular fuelconcept for a prismatic type very high temperature gas-cooled reactor to solve the fuel temperature issue.Adetailed thermo-fluidanalysis using a computational fluid dynamics (CFD) code was carried out to investigate the thermo-fluidperformances of the proposed fuel design. The CFD results showed that the proposed design has superiorthermo-fluid characteristics to the existing prismatic fuel assembly designs 16.In June 2009, Korea Atomic Energy Research Institute (KAERI) pursued the development, including irradiation and testing, of annular fuel for Generation III Korean OPR-1000 reactor. The OPR-1000 reactorhas different dimensions of the fuel assembly, different fuel lattice (16×16 versus 17×17) and different operating conditions than the standard Westinghouse PWR considered in previous MIT analyses. Moreover, the fuel design was developed under the additional constraint of preserving control rod positions and a limited increase in the coolant flow rate. Thus, instead of proportionally increasing the flow rate, the core outlet temperature was kept constant while reducing the core inlet temperature by about 100 C. Also, the power uprate target was smaller than that strived for in the MIT design for the Westinghouse reactor. Therefore, this power up rate was aimed for the plant without major component modifications 25.KAERI developed a conceptual design of a 12×12 annular fuel assembly to achieve 20% power uprate while increasing DNBR margin and remaining compatible with current control rod positions 17.In 2010, C. H. Shin et.al 18estimated the thermal-hydraulic characteristics of annular fuel arrays for the highpower-density PWR. The 12×12, 14×14, and 16×16annular fuel arrays were suggested for reloading tooperating PWR reactors of OPR-1000.The pressure drop in the annular fuels was increaseddue to the increasing friction area. The pressure drop forthe 16×16 annular array is increased by 38%, eventhough the loss coefficient of the spacer was not strictlyadopted.The sensitivities of the outer channel are similar tosolid fuel, but the inner channel is sensitive to thepower density. Because the 12×12 arrays have a largerflow area in the inner channels, the sensitivity ofMDNBR at the inner channels was lower than otherarrays. In terms of the sensitivity, the 12×12 array was better 18.In August 2011, Faghihi et al 18 studied the shut-down margin (SDM) for the next generation VVER-1000 reactor including 13×13 hexagonal annular assemblies.They used MCNP-5 for manycases with different values of core burn-up at various core temperatures, and therefore their correspondingcoolant densities and boric acid concentrations. There was a substantial drop in SDM in the case ofannular fuel for the same power level 19.In November 2011,Shirvana et al 20 designed a compact integral medium size PWR to eliminate loss of coolant events,and reduce the number of large vessels of a nuclear power plant. They focused on how tofurther increase the power that can be derived from a given vessel volume. The example was applied to theInternational Reactor Innovative and Secure (IRIS), a medium size, light water reactor rated at 1000 MWt.The IRIS is an integral design containing all pumps and steam generators along with a traditional PWRcore inside the reactor vessel. IRIS was designed with 8 Once-Through Helically Coiled Steam Generators(OTHSG), located above the core, in an annular region between the riser and the pressure vessel wall 20.This work examined ideas to increase its power output in the same vessel size while maintaining orimproving the safety margins. The combination of Printed Circuit Heat Exchangers (PCHE) and internally and externally cooled Annular Fuel (IXAF) was proposed to implement such improvement in otherwise thereference IRIS design. Safety implications of such steam generator and fuel design changes for the samereactor size were examined, under both steady state and transients, using the RELAP5 and VIPRE codes. Itis found that the IRIS reactor power can be increased by 50% by using the PCHE and IXAF. The proposeddesign was found to be less expensive per unit electric power produced; these improvements and analysescan be applied to any integral reactor design 20.In December 2011,Shinet.al 21 assessed the thermal hydraulic performance of dual-cooled annular nuclearfuel for OPR-1000.An internally and externally cooled annular fuel was proposed for an advance PWR, which can enduresubstantial power uprating. KAERI is pursuing the development for a reloading of power uprated annularfuel for the operating PWR reactors of OPR-1000 20. The characteristics and verification of theMATRA-AF were described. The thermal hydraulic performance of a 12×12 annular fuel was calculated for themajor design parameters and its performance was compared against the reference 16×16 cylindrical fuelassembly. In particular, the enhancements of the thermal hydraulic performance of dual-cooled annularfuel were estimated for the 100% normal power reactor core. The purpose of this study was to estimate anormal power for OPR-1000 with dual-cooled annular fuel, and ultimately to assess the feasibility of120% core power. The parametric study was carried out for the fuel rod dimension, gap conductance,thermal diffusion coefficients, and pressure loss of the spacer grids. As a result of the analysis on thenominal power, annular fuel showed a sufficient margin available on DNB and fuel pellet temperature relative to cylindrical fuel 21.In March 2012, Kuridan and Al-Dukali 22 studied the neutronics of increased power density PWR core based on annular fuel rods using theMonte Carlo method. In this study, the design parameters of the annular fuel cell were investigated andverified using the Monte Carlo method. The annular design showed a comparableneutronics performance to the solid fuel design as the difference in the infinitemultiplication factor (K?) was far less than 1% and the difference from published work was within 1%. InMay 2012, Saidinezhad andHamieh 23 studied the 13×13 annular fuel assembly 1000 MWe PWR response to a reactivity excursion. A useful method was presented to predict, by simple means, the dynamic response of a large scale 13×13 annular fuel assembly 1000 MWe PWR to reactivity excursion. The method benefited from the newly provided tally by the MCNP5.1.60 to calculate the point reactor kinetics equation parameters. These parameters were then used as input to their developed code, KINETICS, to investigate the numerical solution of the point reactor kinetics equations with temperature feedback for a relatively large reactivity excursion within the core 23.In April 2013,Mozafari andFaghihi 24 investigated the design of annular fuels for a typical VVER-1000 core. Ordinary solid pins as well as annular pins were fullyinvestigated using MNCP5 code to find many neutronics parameters of the core. A comprehensive calculationhas been performed on the possible configurations of the annular fuel rods applicable to VVER-1000 type reactors. Many investigations were carried out to make under-moderated coreof the annular fuel pins, and then the pitch optimization was performed for each annular case to obtain the best configuration and dimension. Moreover, using the neutronic calculationsfor the selected annular cases, power peaking factors of the fuel assemblies and the heat flux ofhottest annular fuel rods were determined and based on the results, MDNBR calculation was carried outfor these hot annular fuel rods. The calculations showed that annular fuel rods have a sufficient marginavailable on MDNBR in both inner and outer surfaces relative to solid fuel. As the final result, an annularpin configuration, called annular-8, was proposed based on full neutronics investigations togetherwith MDNBR calculation 24.In November 2013, Zhaoa et al 25 studied pre-conceptual core design of supercritical light water reactor (SCWR) with annular fuel rods. The geometry of the annular fuel was optimized to achieve better performance for the SCWR. Based on the annular fuel assembly, an equilibrium core has been designed. The results showed that the equilibrium core satisfied all the objectives and design criteria. Annular fuel consisted of several concentric rings. Feed water flowed through the center and outside of the fuel to give both internal and external cooling. Thanks to this feature, the fuel center temperature and the cladding temperature was reduced and high power density was achieved. The water flowing through the center also provided moderation, so there was no need for extra water rods in the assembly. The power distribution was easily flattened by use of this design. The geometry of the annular fuel has been optimized to achieve better performance for the SCWR. There were 19 fuel pins in an assembly. Burnable poison was utilized to reduce the initial excess reactivity 25. The fuel reloading pattern and water flow scheme were optimized to achieve more uniform power distribution and lower cladding temperature. An equilibrium core has been designed and analyzed using three dimensional neutronics and thermal-hydraulics coupling calculations. The void reactivity, Doppler coefficient and cold shut down margin were calculated for safety consideration. The results showed that this concept is a promising design for the SCWR 25.In May 2014, Deokulea et.al 26 designed and analyzed of 19 pin annular fuel rod cluster for pressure tube type boiling water reactor. They found that the limitation on the power was not due to physics parameters but rather from the thermal hydraulics side. In order to increase power rating of the annular fuel cluster, keeping same pressure tube diameter, the pin diameter was increased, achieving larger inside flow area. However, this reduced the number of annular fuel rods. In spite of this, the power of the annular fuel cluster could be increased by 30% compared to the solid fuel rod cluster 26. This made the nineteen pin annular fuel rod cluster a suitable option to extract more power without any major changes in the existing design of the fuel. In April 2015, Rowinski et al 27 described an innovative annular fuel concept in details and showed that it was a promising technology in terms of safety aspects. Liquid metal cooled reactors were considered to burn used nuclear fuel from conventional nuclear power plants or processed weapon grade plutonium and therefore, higher safety standards must be assured. During the design process seven fuel assemblies with annular fuel elements were created 27. The investigation was conducted in case of both commonly used fuel lattices i.e. square and hexagonal; moreover effect of spacer grids was taken into considerations. Results showed that the annular fuel is superior in case of maximum fuel temperature, which is up to 757 oC lower than in default base design with use of spacer grids. The most promising designs were hexagonal lattice with 91 fuel elements and square lattice 18 x 18, where the maximum temperatures are 822oC and 732 oC, while pressure drop of 185 kPa and 128 kPa, respectively 27.The square lattice proved better performance according to their evaluation, Hence, use of the same or even smaller coolant pumps was possible in case of annular fuel elements. Moreover, the innovative fuel also allowed to over power reactor up to 110% of nominal power, while securing all safety limits 27.In July 2015, Rahmanet.al28 studied the hydraulic lift-off issues for application of high performance annular fuelsin pressurized water reactors. They took the 17×17 solid fuel design as the reference andthe hydraulic lift-off issue was investigatedfor proposed 12×12 and 13×13 annular fuel designs. Both the steady-state and start-up operatingconditions were evaluated. It is found that the hydraulic lift-off indeed was an issue for annular fueldesign which requires careful analysis. By comparison, the lift-off forces and hold-down forces requiredfor the externally and internally cooled annular fuels (13×13 and 12×12 arrays) were several timeslarger than that of the referenced solid fuel (17×17 array). Therefore, the hold-down mechanism forannular fuel needs to be carefully designed 28.In August 2015, Ansarifar andEbrahimian29 examined the design and neutronics of the Nano fluids applicationto VVER-1000 nuclear reactor with dual cooled annular fuel. Reactivitychange, radial and axial local power peaking factors (LPPF), and the consequence of nanoparticle depositionon fuel clad were investigated. As a result of changing the effective multiplication factor and PPF calculationsfor six types of nanoparticles which have been studied extensively for their heat transferproperties including Alumina, Aluminum, Copper oxide, Copper, Titania, and Zirconia with different volumefractions, it was concluded that at low concentration (0.03 volume fraction), Zirconia and Aluminaare the optimum nanoparticles for normal operation. The maximum radial and axial PPF were found to beinvariant to the type of nanofluid at low volume fractions. With an increase in nanoparticle depositionthickness on the outer and inner clad, a flux and Keff depression occurred and ZrO2 and Al2O3had thelowest rate of drop off 29.InMarch 2016, Deng et.al 30 simulated and studied the mechanisms that cause heat split, a specific phenomenon in dual-cooled annular fuelelements. It was found that thermal expansion, fuel densification, swelling,creep, relocation and fission gas release were the original parameters driving the development of heat split. The theoretical simulation on heat split was performedby FROBA-ANNULAR, which is a coupled thermal–mechanical analysis code for dual-cooled annularfuel elements. Key parameters at different burn-up stages, including gap size, gap conductance,temperature profile, coolant flux and heat flux were obtained. In November 2016,Zaidabadi et al 31 studied VVER-1000 nuclear reactorwith dual-cooled annular fuel using K–x SST Turbulence model. In addition,the amount of thermal power uprate in a VVER-1000 reactor using annular fuels is investigated.As one of the most importantresults of the analysis, annular fuel showed a sufficient margin available on DNB and fuel pellet temperaturerelative to cylindrical fuel. The margin amount accommodating a 129% power uprate seemed viable.?CHAPTER 3NEUTRONICS MODELING AND VALIDATIONIn this chapter we study the proposed annular fuel from a neutronic point of view.Section 3.1 describes the MCNPX code which used for the nuclear analyses.3.1. MCNPX CODEMCNPX is a Fortran90 (F90) general-purpose Monte Carlo radiation transport code for modeling the interaction of radiation with everything. MCNPX stands for Monte Carlo N -Particle eXtended. It extends the capabilities of MCNP4C3 to nearly all particles, nearly all energies, and to nearly all applications. MCNPX is fully three-dimensional and time dependent. It utilizes the latest nuclear cross section libraries and uses physics models for particle types and energies where tabular data are not available 32.MCNPX’s new capability of depletion is a linked process involving steady-state flux calculations in MCNPX and nuclide depletion calculations in CINDER90. The integration of CINDER90 into the MCNPX Monte Carlo radiation transport code provides a completely self-contained Monte Carlo–linked depletion capability in a single Monte Carlo code that is compatible with most nuclear criticality (KCODE) particle tracking features in MCNPX. MCNPX depletion tracks all necessary reaction rates and follows as many isotopes as cross-section data permit 32.The code is used to calculate the effective multiplication factor (Keff) and the fuel burnup of the reactor core. The new depletion capabilities of the code facilitate tracking of the changes in each fuel assembly’s composition for any reactor core under consideration 33.Figure 3.1. Shows Monte Carlo Flowchart NO YES YES NO YES NO YESFigure 3.1. Monte Carlo Flowchart 3.2. REFERENCE PWR CORE AND PARAMETERSTo evaluate the performance of the internally and externally cooled annular fuel, it is useful to select a reference current design against which to compare the new fuel. A typical Westinghouse 3411 MWth four loop PWR plant was selected as the base case for the thesis. Table 3.1 summarizes the design data of the reference PWR core. The data were provided by Duke Engineering and Services (formerly Yankee Atomic Electric Company) 34.Table 3.1.The operating parameters and characteristics of a typical Westinghouse 4-loop PWRParameters 4-loop PWR1. Plant Number of primary loops 4Reactor thermal power (MWth) 3411Total plant thermal efficiency(%) 34Plant electrical output 1150Power generated directly in coolant (%) 2.6Power generated in the fuel (%) 97.42. Core Core barrel inside diameter/outside diameter (m) 3.76/3.87Rated power density (kW/L) 104.5Core volume (m3) 32.6Effective core flow area (m2) 4.747Active heat transfer surface area (m2) 5546.3Average heat flux (kW/m2) 598.8Design axial enthalpy rise peaking factor (F?h) 1.65Allowable core total peaking factor (FQ) 2.53. Primary Coolant System pressure (MPa) 15.51Core inlet temperature (°C) 292.7Average temperature rise in reactor (°C) 33.4Total core flow rate (Mg/s) 18.63Effective core flow rate for heat removal (Mg/s) 17.7Average core inlet mass flux (kg/m2 .s) 3,7294. Fuel Rods Total number 50,952Fuel density (% of theoretical) 94Fuel pellet diameter (mm) 8.19Fuel rod diameter (mm) 9.5Cladding thickness (mm) 0.57Cladding material Zircaloy-4Active fuel height (m) 3.665. Fuel Assemblies Number of assemblies 193Number of heated rods per assembly 264Fuel rod pitch (mm) 12.6Fuel assembly pitch (mm) 215Number of grids per assembly 7Fuel assembly effective flow area (m2) 0.02458Location of first spacer grid above beginning of heated length (m) 0.3048Grid spacing (m) 0.508Grid type L-grid Number of control rod thimbles per assembly 24Number of instrument tubes 1Guide tube outer diameter (mm) 12.2436. Rod Cluster Control Assemblies Neutron absorbing material Ag-In-CdCladding material Type 304 SSCladding thickness (mm) 0.46Number of clusters Full/Part length 53/8Number of absorber rods per cluster 243.2.1. Fuel Assemblies and Core Loading The enriched uranium dioxide (UO2) pellets are clad in a corrosion-resistant zirconium metal alloy Zircaloy which is backfilled with helium to aid heat conduction and detect leakages as shown in figure 3.2. The finished fuel rods are grouped in fuel assemblies, called fuel bundles, which are then used to build the core of the reactor. The model chosen was that of a pressurized water reactor (PWR) in a17×17 assembly lattice of pins all of which have the same initial composition. The assembly contains 24 control rod guide tubes, some of which may contain annular burnable poison rods at various times during the assembly irradiation. A central instrumentation channel is also present.Figure.3.2 Schematic of solid fuel and associated coolant cell.The geometry was atypical Westinghouse PWR assembly and is shown in Figure 3.3. The lattice consisted of a 17×17 array with 24 guide types containing wateror burnable poison rods and 1 instrumentation tube. Figure 3.3. PWR lattice geometry. When present,the burnable poison rod locations are the same as the guide tubes. 43.3. MODEL VALIDATION3.3.1. Poison-Free Pin Cell modelling The pin cell model for a typical PWR solid fuel design in the case of poison-free, i.e., neither burnable poison nor soluble poison was considered. The multiplication factor (Kinf)variation of thepoison-free pin cellwith respect to burnup is shown in figure. 3.4.The model results and the benchmark data werethe same. Figure 3.4. The multiplication factor versus the burnup for a solid 17 x 17 poison-free pin cell3.3.2. Gadolinium-Poisoned Pin Cell modellingNormal Westinghouse PWRs utilize an Integrated Fuel Burnable Absorber (IFBA) (thin layer of B10coated onto the fuel pelletsurface) for their burnable poison. Other options for burnable poison include either Erbia or Gadolinum mixed homogenously with the fuel. The Gadolinum hasan absorption cross section two orders of magnitude larger than B10at thermal energies. Also,due to the significantly higher expense of Erbium and questions regarding whether or not theIFBA coating could be applied to the inner annulus, Gd was selected for the annular assemblies’burnable poison. The integral burnable absorber -gadolinium oxide (Gd2O3) was chosen in this work 34.Gadolinium consists of seven natural isotopes (Gd-152, Gd-154, Gd-155, Gd-156, Gd-157, Gd-158, and Gd-160). The two Gd isotopes, Gd-155 and Gd-157, have higher absorption cross sections of 61,000 and 254,000 barn, respectively, Gd-152 and Gd-159 have very low natural abundance ratios. Table 3.2 shows the natural abundances for gadolinium isotopes 35. Table 3.2 Gadolinium natural abundances ratiosymbol Mass of Atom (u) % AbundanceGd-152 151.919788 0.2Gd-154 153.920862 2.18Gd-155 154.922619 14.8Gd-156 155.92212 20.47Gd-157 156.923957 15.65Gd-158 157.924101 24.84Gd-160 159.927051 21.86The absorption cross section of each isotope over the energy spectrum is given in Figure 3.5 36. Figure 3.5 Neutron capture cross section of Gd isotopes versus energyThe calculations were performed for the 17 x17design with 5.0 w/o U-235 enrichment and 10.0 wt% Gd2O334. However because Gadolinium was known as a “black” absorber, it burnt out in layers. This caused a slight difficulty initially with MCNPX because the burnup region was being re-homogenized between each depletion time step. This problem was solved by separately defining 10 equi-volume cylinders within each poisoned fuel pin so that each “layer” could be treated independently. This significantly increased computation time however it was necessary in order to accurately capture the effect of the burnable poison.Kinf variation of Gd poison pin cell with respect to burnup is shown in Figure 3.6. there was a a littlevariation between model results and benchmark data because of the calculations were with two different codes. Figure 3.6The multiplication factor versus the burnup for a solid 17 x 17 Gd-poison pin cell.3.3.3. Solid Fuel Assembly The fuel assembly is the combination of the poison-free and poisoned pin cells. The assembly was a 17×17-lattice design consisting of 24 guide tubes and 264 fuel rods. The fuel enrichment was5.0 w/o. Figure 3.7. compares the multiplication factor as a function of the effective full power days for the benchmark data and the calculated results.We noticed that no agreement for the multiplication factor of the benchmark data and the calculated results for less than 600 days because of the reason which was presented in the previous section. Figure 3.7.Comparison of Kinffor typical assembly calculations.3.4. MODELING OF ANNULAR FUELTo identify the optimum dimensions of the annular fuel pin and the array size applicable to the reference PWR core, the overall dimensions of the new annular fuel assembly were assumed fixed equal to those of the reference 17×17 assembly with solid pins. A range of array sizes from 12×12 to14x14 were analyzed. The pin size was increased with decreasing array size. So, the pin linear heat rate and coolant flow rate per fuel rod was increased, for fixed total power. In order to perform this exploratory analysis of the design of the annular fuel assembly, the following assumptions were assumed: • Power peaking for the hot rod in the core is the same as for the reference Westinghouse PWR core (2.5 total, axial distributions – chopped cosine with peaking of 1.55). Analyses were performed at 18% overpower, to allow for transients 4. • Mass flow rate per fuel rod was taken equal to core-average flow rate per rod. • Thickness of both inner and outer cladding is identical and equal to the cladding thickness of a solid pin in the Westinghouse 17×17 array.Table 3.3 Dimensions (cm) of annular fuel elements of various arraysArray Dcii Dcio Dfi Dfo Dci Dco Pitch12x12 0.9533 1.0676 1.08 1.54 1.5524 1.6667 1.78913×13 0.8633 0.9776 0.99 1.41 1.4224 1.5367 1.65114×14 0.7533 0.8676 0.88 1.294 1.3064 1.4207 1.53317×17-ref. Solid pin – – 0.8255 0.8379 0.9522 1.263 Based on the above assumptions and restrictions, typical dimensions of fuel rods for each array size are listed in Table 3.3, where in the first subscript c and f stand for cladding and fuel, respectively; in the second subscript, i and o designate inner cladding and outer cladding, respectively, or inner diameter and outer diameter for the fuel ring; and the third subscript denotes the diameters of the cladding (i=inner, o=outer) 4. The layout of the fuel rods and guide tubes for 12×12 through 14×14 arrays is shown to scale in Figures 3.8 through 3.10 Figure 3.8 Fuel assembly in a 12×12 array Figure 3.9 Fuel assembly in a 13×13 array Figure 3.10 Fuel assembly in a 14×14 arrayFigure 3.11 shows selected key parameters characterizing important neutronics and thermal hydraulic performance as a function of array size. It can be observed that the total cooling surface is significantly higher than that for the solid fuel and becomes smaller with decreasing array size. Fuel and coolant volumes and fuel-to-moderator ratio are kept close to the value for the reference 17×17 assembly. Figure 3.11 Neutronics and thermal hydraulics parameters compared to 17×17 reference solid FuelA transition from solid to annular geometry has twoimportant implications that allow higher power density: 1. Reduction of the thickness of the heat conduction path, which improves the margin from peak fuel temperature to melting. 2. Increasing the heat transfer surface area (in spite of a reduction of the number of fuel rods), which enlarges the Departure from Nucleate Boiling Ratio (DNBR) margin. In addition to peak fuel temperature and DNBR limits, the fuel has to satisfy a number of other safetylimits and performance constraints. The internally and externally cooled annular fuel concept exhibits significantly lower fuel temperature than solid fuel, hence it is expected that fission gas release will be smaller, allowing for higher burn-up 37.Many different cases are investigated in order to reach a long fuel cycle and a high power.CASE A : uranium dioxide (UO2) annular fuel 100% powerTo evaluate the reactivity limited burn-up potential of annular fuel, burn-up calculations were performed using MCNPX on the pin cell level and compared to the reference solid fuel. The fuel was5.0 w/o enriched UO2 for the two cases. The results are shown in Figures 3.12 and 3.13. The annular fuel 13 x13 design achieved the same reactivity-limited burn-up as the solid pin as shown in figure 3.12. However, Figure 3.13 shows that the annular fuel design 13 x 13 fell short of energy generation compared to the solid fuel. This is attributed to the reduced fuel (heavy metal) loading. The additional layer of cladding reduces the available core fuel volume, which led to a 10% decrease in heavy metal loading. Therefore, the annular fuel needs higher fuel burn-up to support the same energy production compared to the reference solid fuel. This requires slightly higher fuel enrichment or use of other means to improve neutron economy. Note that I still assumed the same power level for both the annular fuel and the reference solid fuel 34. Figure 3.12Kinf versus burn-up for the annular fuel designs and solid fuel pin Figure 3.13.Comparison of Kinf versus EFPDs for annular and solid pinsFigure 3.14,Shows the multiplication factor versus EFPDs for Annular fuel assemblyUO2. Because of the reduced fuel loading, the fuel cycle in this case was less than of the solid case with 200 days, and we observed that Kinf was higher in the case of free poison fuel pin and decreased in the begin of the cycle with increasing the number of Gd poison fuel pins. Figure 3.14.The multiplication factor versus EFPD for Annular fuel assemblyUO2 CASE B : uranium dioxide (UO2) annular fuel 150% powerIf the annular fuel operates at higher power level, the burnup requirement will increase even more.To extract ~50% moreenergy per assembly requires a corresponding increase of enrichment. Hejzlaret. al., 2001showed that the enrichment would be 8.1% and 9.0% which above the 5 w/o licensing limit ofmost manufacturing plants, hence a transition to this annular high power density fuel would require changes in fuel manufacturing plants. However, if heavier uranium compounds can be considered, e.g., uranium nitride, or the number of reload assemblies can be increased, the fuel enrichment can be limited within 5 w/o34.Figure 3.15.Show the multiplication factor versus EFPDs for the uranium dioxide annular fuel for the case of 150% power. We observed that if we increased the power at the same enrichment, the fuel cycle decreased to 680 days. To maintain the same cycle we must increase the enrichment or replace the uranium dioxide (UO2) with uranium mononitride (UN). Figure 3.15.The multiplication factor versus EFPD forannular fuel assembly UO2 13 X 13 150% power CASE C :Uranium Mononitride (UN) annular fuel modelingUranium mononitride (UN) is the advanced nuclear fuel for fast reactors with respect to safety improvement and efficiency of reactors. Uranium mononitride is characterized by high concentration of uranium, high melting point and thermal conductivity, increased radiation resistance and good compatibility with structural materials 35.The basic properties of uranium mononitride are presented in Table 3.3Table 3.4. Physical and thermal properties of UO2 and UNProperties UO2 UNTheoretical density (g/cm3) 10.96 14.32HM atom density (g/cm3) 9.67 13.52Specific heat (J/Kg K) 270(at 200C0 ) 205(at 280C)Melting point (0C) 2800 2700Thermal conductivity (W/m K) 7.19 (at 2000C)3.35 (at 10000C) 4(at 2000C)20(at 10000C)Linear thermal expansion coefficient (10-6 K-1) 10.1(at 9400C) 9.4(at 10000C)Swelling rate(normalized to UO2) 1.00 0.80Fission gas release(normalized to UO2) 1.00 0.45As shown above in Table 3.4, UN has several beneficial attributes over U02.The higher theoretical and HM atom density allows the designer to pack in approximately 40% more uranium atoms in an equivalent volume. This attribute has tremendous implications for the development of advanced fuel designs since the integration of UN gives the enhanced ability to run the fuel assemblies hotter and longer than current U02 designs. UN also has a smaller linear expansion coefficient and swelling rate which helps with long term performance of the fuel. Furthermore, the fission gas release is also believed to be markedly less than that of UO2. Finally, one of the more unique attributes of UN is that the thermal conductivity of the material actually increases with increasing temperature. The opposite trend of the UO2 gives the UN fuel tremendous advantage in this respect 37. 3.5. RESULTS 3.5.1. The Pin Cell184.108.40.206. The Pin Cell With Poison FreeThe infinite multiplication factors versus Effective Full Power Days (EFPDs for the different array sizes are plotted in Figure 3.16. The Kinf differences were much larger for the annular fuel designs(UN) than the reference solid fuel and the annular fuel UO2as shown in figure 3.13. We noticed that in the cases of annular fuel design (UN), the fuel cycle was increased with decreasing array size. So the annular fuel design (12 x 12) is a better design compared to (13 x 13)and (14 x 14) arrays.Table 3.5 gives the cycle length for both solid and annular fuel pins at different cases. Figure 3.16. the multiplication factor versus EFPD for solid and Annular fuel 100% power Table 3.5.The cycle length for both solid and annular fuel pins in different cases.Pin Type array Fuel Type Cycles Length(Days)Solid Fuel 17 x 17 UO2 1200Annular Fuel 13 x 13 UO2 1050Annular Fuel 12 x 12 UN 1460Annular Fuel 13 x 13 UN 1400AnnularFuel 14 x 14 UN 13603.5.1.2. Gadolinium-Poisoned Pin CellFor the poisoned pin cell simulation the GdN was assumed to be uniformly mixed with the UN fuel in the pin. However because Gadolinium was known as a “black” absorber, it burntout in layers.Figure 3.17. shows the infinite multiplication factor versus burnup(GWd/t) for the UN GdN poisoned pin cell. The burnout of Gd was 30 GWd/t for the uranium nitride (UN) and 17.5 GWd/t for the uranium dioxide(UO2) as shown in figure 3.6. Figure 3.17. The multiplication factor versus burnup(GWd/t) for Annular poison pin (UN)3.5.2. Full Fuel Assembly220.127.116.11. Fuel assembly at 100% powerAs shown in figure 3.18. It can be seen that the value of the multiplication factor did not decrease sharply in the beginning of burning fuel, because of the effect of burnable poisons (GdN) in the fuel, which play a main role in controlling the positive high reactivity in fresh fuels. After a while, the value of the multiplication factorwas decreased smoothly as the fuel burnt 3.The value of the multiplication factorin MCNP-X code is obtained by considering all edge surfaces in the model as reflected surfaces, which `means that no neutron particles are lost, And all neutrons are absorbed in the media.Table 3.6. Gives the cycle length for both solid and annular fuel assemblies at different cases. As shown in figure 3.18 and table 3.6, It can be seen that the fuel cycle in all cases of the annular fuel with uranium nitride is longer than the fuel cycle in the cases of the uranium dioxide. Also, we can observe that the fuel cycle is better with decreasing the array size. Figure 3.18.The multiplication factor versus EFPD for the diferent assembliesat 100% power Table 3.6.The cycle length for both solid and annular fuel assembliesin different cases.AssemblyType Array Fuel Type Burnable Absorber Cycles Length(Days)Solid 17 x 17 UO2 Gd2O3 1200Annular 13 x 13 UO2 Gd2O2 1050Annular 12 x 12 UN GdN 1480Annular 13 x 13 UN GdN 1440Annular 14 x 14 UN GdN 14003.5.2.2. Fuel assembly at 125% powerWhen we increased the power from 100% to 125% as shown in figure 3.19, We noticed that the fuel cycle is equal to 1190,1150and 1110 days for the annular fuel assembly (12×12),(13×13) and(14×14) respectively with compared to 1200 days in the reference case of the solid fuel pin U02. So we can increase the power at the same cycle length by replacing the solid fuel uranium dioxide by the annular fuel uranime nitride.Table 3.7 gives the cycle length for both solid and annular fuel assemblies at different cases at 125 % power. Figure 3.19. The multiplication factor versus EFPD for Annular fuel UN 13 X 13 125% power densityTable 3.7.The cycle length for both reference solid and annular fuel assembliesin different cases at 125 % power.Assembly Type Array Fuel Type Burnable Absorber Cycles Length(Days)Solid(100% power) 17 x 17 UO2 Gd2O3 1200Annular(125%power) 12 x 12 UN GdN 1190Annular(125%power) 13 x 13 UN GdN 1150Annular(125%power) 14 x 14 UN GdN 1110It can be seen from figure 3.20 that the burnup of the uranium nitride fuel at the end of cycle was increased with decreasing array size.The annular fuel design (12 x12) is a better design compared to (13 x13) and (14 x 14). The 13 x13 design achieves the same reactivity-limited burnup as the solid pin, which verifies a larger conversion ratio compared to the solid fuel pin. Figure 3.20.The multiplication factor versus burnup for annular fuel (UN)3.5.3. Burnable poisonsFigure 3.21 shows the concentrations of gadolinium isotopes Gd-155, and Gd-157with the full power days during the depletion. It can be seen that sharp decrease in Gd-157 concentration. This was because of high neutron absorption cross section of it; it fully burned at 600 EFPDs. The concentration of Gd-155 decreased smoothly with increasing the full power days and fully burned out at 700 EFPDs. Figure 3.21Gadolinium isotopes concentrations in (atom/barn.cm) versus EFPDs for Annular fuel UN 3.5.4. Fission product poisonsTwo fission products, Xenon-135 and Samarium-149, have an impact onthe reactor design, operation and control. They have very large neutron absorptioncross sections and are produced in large quantities directly from the fission and produced indirectly from thedecay of the fission products.These isotopes are formed during reactor operation and are not present in the initial fuel composition. It is very important to take their evaluation into our account. XenonXe-135 is formed directly as a fission product with relatively high fission yield 0.3 % and in series of decays of 135Sb, 135Te, and 135I. In general, it is assumed that 135Xe is produced directly from 135I (6.6h) decay due to short half-life times of 135Sb (1.7s) and 135Te (19.2s). There are two processes, which remove 135Xe from the system. First, 135Xe decays to135Cs with half-life time 9.2 hr. Second, 135Xe burns out in neutron flux to non-absorbing 136Xe. The Xe-135 concentration is very sensitive to the concentration of its precursor 135I and the neutron flux, and thus to the power changes in the reactor core 38. In a system without burnable poison, the higher power is the higher 135Xe concentration.Figure 3.22 represents the accumulation rates of Xe135 in the four cases. The figures show that the buildup of isotope increases and reaches equilibrium in the early stages of the core cycle. In annular cases of uranium nitride, the equilibrium is reached at about 10 days but in the solid case of uranium dioxide, the equilibrium is reached at about 2 days. It can be seen that the consumption of 135Xe in the solid fuel is better than the annular fuel. Figure 3.22 The concentration of Xe-135 versus the effective full power daysSamariumSm-149 is characterized by the absorption cross section of 4.2E4 barns in the thermal energy range and its small quantities are produced in fission directly. It is a fission product daughter of 149Nd and 149Pm. One usually neglects 149Nd because of its short half-life time of 1.7 hr. The 149Pm with half-life time of 53 hr is the precursor of 149Sm with total fission product yield 1.2%. Unlike 135Xe, the 149Sm is a stable isotope and does not decay, so it has only one removal channel – burnout in neutron flux to 150Sm. After reactor shutdown, concentration of 149Sm increased because of its production from accumulated 149Pm 38. The absorption cross section of 149Sm is lower than for 135Xe. The 149Sm equilibrium concentration is independent of the neutron flux level but the time to reach equilibrium depends on neutron flux. In all cases, equilibrium is reached at about 20 days.Figure 3.22 and Figure 3.23 represent the accumulation rates of Xe135 and in thecore. The figures show that the buildup of both isotopes increases and reaches equilibrium in the early stages of the core cycle.Figure 3.23 represents the accumulation rates of Sm149 in the four cases. The figures show that the buildup of isotope increases and reaches equilibrium in the early stages of the core cycle. In annular cases of uranium nitride, the equilibrium is reached at about 100 days but in the solid case of uranium dioxide, the equilibrium is reached at about 40 days. It can be seen that the consumption of Sm149 in the solid fuel is better than the annular fuel Figure 3.23The concentration of 149Sm versus the effective full power days3.5.5. ActinidesPu-239The neutron capture on 238U forms 239Pu, which decays to 239Np. The decay of 239Np (half-life time 56 hr) leads to the formation of fissile 239Pu. The concentration of 239Np is proportional to the neutron flux and thus to the power level. The fuel losses due to 235U burnup are partly compensated by 239Pu breeding. The percentage change in 238U concentration is not significant due to its high concentration in the reactor core 38.Figures 3.24 shows the increase of the239Pu during the cycle length. The trends of plutonium accumulation in the reactor core are approximately the same for the three annular cases, while the solid fuel produces lower amount of plutonium(because of the high power density in the case of the annular fuel design). Thus the solid fuel can be considered to be more attractive from the safeguards point of view Figure 3.24 Build-up of Pu-239 versus the effective full power days?CHAPTER 4THERMAL HYDRAULIC MODELING AND VALIDATION4.1. INTRODUCTIONAs mentioned before, the annular fuel rod has two cooling surfaces: the outer cladding in contact with the coolant flowing in the outer channel and the inner cladding in contact with the coolant flowing in the inner channel. The larger cooling surface results in a significantly higher Departure from Nucleate Boiling (DNB) margin, and, with lower fuel temperatures, the annular fuel provides significant benefits in terms of a low peak cladding temperature following a Loss of Coolant Accident (LOCA) 6.Thermal hydraulic analysis is a critical part of annular fuel design since it determines the dimensions of the fuel that allow achievement of the power uprate within acceptable MDNBRmargins. Because the option space of the thermal hydraulic design is constrained by assemblydimensions and control rod guide tube positions, it is important to assure thermal hydraulicfeasibility with core neutronic design 6. Therefore, the effort in this chapter was focused on the verification and optimization of the annular fuel design within acceptable thermal hydraulic constraints, e.g., MDNBR should be no less than 1.3 4.2. THERMAL HYDRAULIC ANALYSIS TOOLSThe RELAP5 (Reactor Excursion and Leak Analysis Program-5) computer code is a light water reactor transient analysis code developed for the U.S. Nuclear Regulatory Commission (NRC) for use in rulemaking, licensing audit calculations, evaluation of operator guidelines, and as a basis for a nuclear plant analyzer. Specific applications of this capability have included simulations of transients in LWR systems, such as loss of coolant, anticipated transients without scram (ATWS), and operational transients such as loss of feedwater, loss of offsite power, station blackout, and turbine trip. RELAP5 is a highly generic code that, in addition to calculating the behavior of a reactor coolant system during a transient, can be used for simulation of a wide variety of hydraulic and thermal transients in both nuclear and nonnuclear systems involving steam-water non condensable solute fluid mixtures 39.4.3. THERMAL HYDRAULIC ANALYSIS OF REFERENC AND ANNULAR FUELSThe thermal operating conditions were assumed to be similar for the reference solid fuel and annular fuel at the same power level. If annular fuel design had a 25% power uprate, the coolant inlet temperature was assumed to be reduced to maintain the same core outlet temperature 6.The geometrical parameters of the reference solid and proposed annular fuel assemblies are given in Table 4.1.Fuel Assembly Solid Fuel Annular FuelRod array 17×17 12×12 13×13 14x14Fuel rods number 264 136 160 184Guide tube number 24 8 9 12Assembly pitch (mm) 215Rod pitch (mm) 12.64 17.91 16.53 15.35Fuel volume per assembly(cm3) 51529.632 47085.104 46331.448 47573.2RodInner clad inner diameter (cm) — 0.9533 0.8633 0.7533Inner clad outer diameter(cm) — 1.0676 0.9776 0.8676Fuel inner diameter (cm) — 1.08 0.99 0.88Fuel outer diameter (cm) 0.8255 1.54 1.41 1.294Outer clad inner diameter(cm) 0.8379 1.5524 1.4224 1.3064Outer clad outer diameter cm) 0.9522 1.6667 1.5367 1.4207Guide tube clad thickness(mm) 0.46Inner guide tube outer diameter (cm) 1.1323 1.552 1.42 1.3064Outer guide tube outer diameter (cm) 1.2243 1.6667 1.5367 1.4207Table 4-1: The geometric data of the reference solid and proposed annular fuel assembliesThe power distributions in the hot assembly from 12×12 to 14×14 configurations werecalculated by MCNPX. Figure 4.1 to figure 4.3 show the radial pin power distributions in the different hot fuel assemblies. The maximum radial peaking factor of the hot assemblies 12×12, 13×13 and 14×14 were 1.59, 1.57 and 1.55 respectively which were near that of the reference PWR (1.55). The Powers of the fuel assemblies of the core periphery wereadjusted to maintain correct normalization. Figure 4.4 shows the calculated power distributions for the fuel assembly in the 1/8th core. Figure 4.1. Pin power distribution in the hot fuel assembly 14×14 with 1/8 core symmetry Figure4.2. Pin power distribution in the hot fuel assembly 12×12 with 1/8 core symmetry Figure4.3.Pin power distribution in the hot fuel assembly 13×13 with 1/8 core symmetry The pin power normalized distribution in a modelof one-eighth assembly was calculated using MCNPX code under a reflective boundary and poisoncondition. The pin power distributions in the hot assemblies, shown in Figure 4.1, Figure 4.2 andFigure 4.3 wereobtained by multiplying the normalized pin power distribution by a factor that gives the samecore-wide maximum radial peaking factor as the reference solid fuel. Figure 4.4. Calculated different assemblies power distributions in the 1/8th core The axial power distribution was assumed to be a chopped cosine shape with apeaking factor of 1.55.For the annular fuel with 100 % power, the reactor core model was modified such that each fuel assembly channel was divided into two flow channels representing the inner and outer flow paths of the annular fuel. Thus, the core was modeled by 4 cooling channels (inner and outer for the hot and the average channels) (Figure 4.5). The outer channels employ junctions to allow for cross flow between the outer channels, while the inner channels were non-communicating 6. Flow areas of the annular fuel channels were weighted based on the geometric volume ratio. Figure 4.5 Core Nodalization for the annular fuel model The annular fuel rod was modeled by radially subdividing it into 12 rings which represent the inner cladding (2 rings), the inner gap (1 ring), the fuel pellet (5 rings), the outer gap (1 ring) and the outer cladding (2 rings). Convective heat transfer boundary conditions were imposed on both the inner and outer cladding surfaces. However, since the code did not have the capability to model dynamic gap conductance of two gaps, i.e., the inner and outer gaps in a fuel rod, the gap conductance of both the gaps were assumed equal and maintained constant in all analyses. It should be noted that the solid fuel model also incorporated the same constant gap conductance for consistent comparison between the two fuels 6. With these models, the steady state conditions were initialized and they were in good agreement with the desired conditions as shown in Table 4.2 Table 4.2 the steady state conditionsParameters Solid17 x 17 Annular fuel 100% Power Annular fuel 125% PowerCore Power (MWth) 3411 3411 4263Pressurizer Pressure (bar) 155.1 155.1 155.1Cold Leg Temperature(K) 566.67 566 566Effective Core Flow (kg/s) 17700 17700 221254.4. THERMAL HYDRAULIC RESULTS OF THE FUEL ROD MODEL Figure 4.6 shows the radial temperature profiles at the hot spot for the reference solid fuel rod.Figure 4.7 shows the radial temperature profiles at the location of the peak linear heat rate of fuel elements for each array size. As the number of fuel rods in the assembly decreases, the rod linear heat rate was increased for fixed assembly power, which results in a higher peak temperature. The higher peak temperature results from the thicker fuel rods of smaller assembly sizes. Reducing the number of rods results in a more pronounced peak fuel temperatures, however the values were still well below those for the solid fuel case. Also asubstantial increase in pin power (by 25%) was possible while peak fuel temperatureremained less than in the reference case. This key advantage stems from twofactors:1) The fuel thickness is reduced to about one half or more of its original value.2) Introduction of double sided cooling further renders the effective conduction thickness toalmost 25% of its original value 6.From figure 4.7, a is refer to the inner radius of the inner clad, b is the thickness of the inner clad, c is the thickness of the inner gap, d is the thickness of the fuel meat, e is the thickness of the outer gap and f is the thickness of the outer clad. Figure 4.6. The fuel temperature profiles at the hot spot for the solid fuel UO2 at 100% power. Figure 4.7 the fuel temperature profiles at the hot spot for the different annular fuels UN at 125% power.DNBR is one of the important and fundamental parameters innuclear safety issue of nuclear power plants that limits heatflux of core to prevent entering the film boiling region.Figure 4.8 to Figure 4.11 show the DNBR profile in hot channels for all cores. The values of DNBR that are greater than 10 were assumed to be 10. • For the reference PWR with solid fuel, the MDNBR was 1.57, which satisfied the 1.3 limit with margin. • For annular fuel model at 100% power, MDNBR of the inner hot channels were larger than 3.0 and that of the outer hot channels were larger than 1.7. • For annular fuel model at 125% power, MDNBR of the inner hot channels were larger than 2.6 and that of the outer hot channels were larger than 1.6. It can be observed that the different annular fuel designs had larger MDNBR than the conventional solid fuel design. The main reason was that the fuel surface of annular fuel is significantly larger due to internal cooling. Thus, at the same power level, annular fuel design has thermal hydraulic advantages because of the larger safety margin. Figure 4.8 DNBR versus the axial height in the solid fuel and the hot outer channels for different arrays at 100% power Figure 4.9 DNBR versus the axial height in the solid fuel and the hot inner channels for different arrays at 100% power Figure 4.10 DNBR versus the axial height hot outer channels for different arrays at 125% power Figure 4.11 DNBR versus the axial height hot inner channels for different arrays at 125% powerDifferent fuel array sizes were investigated to optimize MDNBR in the inner and outercoolant channels. The MDNBR results for the above three assembly sizes were shown in Figure 4.12. The array sizes of 12×12, 13×13 and 14×14 can satisfy the 1.30 MDNBR limit at 125% power density. Moreover, the MDNBR margin is comparable to that calculated for the reference Westinghouse 17×17 solid fuel (MDNBR of 1.57) at 100% power using the same assumptions and boundary conditions. The results shown in Figure 4.12 indicate that the 12×12 array is the optimumdesign because of the well balanced MDNBR (inner/outer=2.62/1.72) than for the 13×13 and 14×14 designs and the large safety margin for both the inner andouter channels.It should be noted that for14x14 annular fuel, MDNBR of the outer hot channel is much larger than that of the inner hot channel andthe highly imbalanced MDNBR suggests that this design is not well optimized. Figure 4.12 MDNBR in the inner and outer channels for different assembly designsFigure 4.13 and Figure 4.14 Show the surface heat flux profile in the hot channels for both (inner and outer channel) at 100%power and 125%power. the heat flux is smaller for annular fuel due to larger fuel surface area. Thehigher heat flux of the outer hot channels were partially responsible for lower MDNBR, compared tothe hot inner channels. Figure 4.13. Surface heat flux versus the axial height in hot channels (100% power) Figure 4.14. Surface heat flux versus the axial height in hot channels (125% power) From figure 4.15 to figure 4.17.The temperature profile along the axial height in hot solid fuel rod (100% power) and the annular fuel rod in the two cases 100 % power and 125 % power. It can be seen that the hot spot of theannular fuel rod of the different fuel assembly had a lower peak fuel temperature thana typical solid fuel rod of the 17×17. Also, it can be seen that the temperature of all structure of the fuel rod (fuel, gap and cladding) of the annular fuel at high power is lower than the temperature of the solid fuel. Also, it can be observed that the annular fuel rod (14×14) had a lower peak fuel temperature at the same power than the annular fuel rod (13×13) and (12×12), this was because the fuel thickness was decreased with increasing the array size. Figure 4.15. The temperature versus the axial height in hot solid fuel rod (100% power) Figure 4.16. The temperature versus the axial height in hot fuel rod (100% power) Figure 4.17. The temperature versus the axial height in the hot fuel rod (125% power)Figure 4.18 and figure 4.19 show the pressure drop at 100% power and 125 % power respectively. It can be observed that the pressure drop increased with increasing the number of rods in the assembly. This was due to the smaller hydraulic diameter of the coolant channels. In addition, forcing more flow into the small inner channel in an effort to improve DNBR margin, requires increasing form losses in the outer channel by modifying the grids. This contributes to a steeper rise of pressure drop for assembly sizes 14×14. Figure 4.18. Pressure drop in the channels for different fuel assemblies at 100% power Figure 4.19. Pressure drop in the channels for different fuel assemblies at 125% power The results of MDNBR calculation and the pressure drop on the core can be found in Table 4.3.Table 4.3 MDNBR and pressure drop values of the different casesFuel type Power MDNBR Average pressure drop(kpa) Outer Inner Solid fuel 17×17 100% 1.57 0.138Annular fuel 12×12 100% 2.01 3.085 0.117Annular fuel 13×13 100% 1.7 3.55 0.129Annular fuel 14×14 100% 1.95 4.14 0.149Annular fuel 12×12 125% 1.72 2.62 0.136Annular fuel 13×13 125% 1.43 3.00 0.156Annular fuel 14×14 125% 1.66 3.55 0.163Based on this simplified the thermal hydraulic analysis, the optimum configuration for the annular fuel appears to be a 12×12 array.It offers the highest DNBR margin, relatively small peak fuel temperature and small pressure drop.Figure 4.20 shows the coolant temperatures in the hot inner and outer channels for the different arrays.it can be seen that the coolant temperature of the inner and outer channels of the array(12×12) is similar, but in the arrays (13×13) and (14×14) the temperature of the outer channels is higher than the inner channels. So the design of (12×12) is better than the arrays (13×13) and (14×14). Figure 4.20 Coolant temperatures in the hot inner and outer channelsChapter 5CONCLUSION AND RECOMMENDATIONS5.1 CONCLUSIONThe main goal of this thesis was the design and the development of annular fuel rods for the present typical operating AP-1000 reactor core from a neutronic point of view by using MCNPX 2.7.0 Code.However some important thermal hydraulic calculations were considered during our work such as the pressure drop on the core, the surface heat flux, the fuel and the coolant temperatures and departure from nucleate boiling ratio by using RELAP5 code.In our work, we used the uranium nitride (UN) instead of the uranium dioxide (UO2) because of the higher theoretical density of (UN). The burn-up capability of the solid fuel was about the same as the annular design because of the same enrichment.It can be seen that it is possible to design an annular fuel core with uranium nitride fuel (UN) for the same power as the solid fuel with increasing the cycle length to more than 1400 days. Or we can design the annular fuel for 125% power density that maintains the same cycle length, and generates 25% more energy. More burnable poison is needed than for the reference solid fuel to limit the power peaking. The performance of the steady-state core and the reactivity feedback parameters were calculated. Even though the annular fuel core operates at lower fuel temperatures, the performance of steady-state and the reactivity feedback parameters were very similar to the reference solid fuel core. So, all the above design targets are satisfied. The steady state core performance was investigated, including the calculation of the cycle length, radial and axial power distribution, the fission product concentration and the power peaking factors.Thermal hydraulic analysis of the high power density annular fuel was carried out using RELAP5 to identify the most promising configuration for power uprate. The annular fuel designs feature fixed core flow rate, fixed core inlet temperature. Annular fuel exhibits much lower peak fuel temperature (more than 1600 °C) than a typical solid fuel rod at 125 % power. The results showed that the annular fuel design had larger MDNBR margin than the solid fuel for all different arrays of annular fuel at 100% power and 125% power except in the case of 13×13 at 125 % power was equal 1.43 tess than the reference solid fuel (1.57) but was larger than the 1.3 limit.The thermal-hydraulic characteristics about annular fuel array were estimated for the high power-density PWR. The 13 x 13 annular fuel arrays were suggested for reloading to operating PWR reactors of AP-1000. The maximum radial peaking factor of the annular fuel rod is 1.570 is near that of the reference PWR, 1.550. And the average radial peaking factor of the hot assembly for the annular fuel is 1.35, which is lower than that for the solid fuel.It can be observed that the annular fuel designs have larger MDNBR than thesolid fuel design. This is because of the fuel surface of annular fuel issignificantly larger due to internal cooling. Thus, at the same power level, the annular fuel design has thermal hydraulic advantages because of the larger safety margin. Also, the 12×12 array is the optimumdesign because of the well balanced MDNBR (inner/outer=2.62/1.72) than for the 13×13 and 14×14 designs, the pressure drop was the same as the reference solid fuel pressure drop and the coolant temperature of the inner and outer channels of the array(12×12) is similar.5.2 FUTURE WORKSEconomic analysis may be performed in the future to know the best high power densityfuel designs for lowering the cost of the nuclear power. This may involve different strategies forexisting power plants and future plants. The best fuel design will be identified by balancing thepower density uprate potential and the cost of manufacturing the fuel design.Next steps of neutronic analyses should be focused on the calculation of reactivity feedback and control, i.e. temperature coefficient, shutdown margin, etc. However, before these detailed neutronic analyses can be performed, it is important to first confirm the thermal hydraulic design of the annular fuel, or possibly reoptimize it to achieve the largest possible MDNBR margins.?REFERENCES1 Dandong Feng et al, “Innovative Fuel Designs for High Power Density PressurizedWater Reactor, “MIT Department of Nuclear Engineering,September 2005.2 Kazimi M. S. et al, “High Performance Fuel Design for Next Generation PWRs,” 1stAnnual Report, MIT-NFC-PR-048, MIT Department of Nuclear Engineering, August 2002. 3 ZhiwenXu et al,”Design Strategies for Optimizing High Burnup Fuel in Pressurized Water Reactors, “MIT Department of Nuclear Engineering, January 2003.4 Westinghouse, “Plutonium Disposition in Existing Pressurized Water Reactors,” DOE/SF/19683-6, San Francisco, California, June 1994.5 OECD, ORGANIZAITON FOR ECONOMIC CO-OPERATION AND DEVELOPMENT,”Nuclear Fuel Safety Criteria Technical Review,” Nuclear Energy Agency, 2001.6 Kazimi M. S. et al, “High Performance Fuel Design for Next Generation PWRs,” final Report, MIT-NFC-PR-082, MIT Department of Nuclear Engineering,January 2006.7 N. E. Todreas, M. S. Kazimi, Nuclear Systems I, Thermal Hydraulic Fundamentals, Hemisphere Publishing Corporation, 1990.8 MildrumC.M.,”Fuel Rod with Annular Nuclear Fuel Pellets Having Same U-235 Enrichment and different annulus sizes for graduated enrichment loading,” U.S. patent # 4687629 (1987)B. 9 Bujas R. G. “Annular Fuel Element for High-Temperature Reactors,” U.S. patent # 3928132, (1975).10 Marshall A.C. “A Review of Gas-Cooled Reactor Concepts for SDI Applications,” SAND87-0558, Sandia National Laboratory, Albuquerque, NM, August (1989).11 Porta J., B. Gastaldi, C. Aillaud-Krakoviak AND L. Buffe, “Advanced Plutonium Assembly (APA): Evolution of the Concept, Neutron, and Thermal-Mechanic Constraints”, ARWIF-2001, Chester UK, October 22-24, (2001).12 Nathan Andrews, KoroushShirvan,” Viability of uranium nitride fueled high-conversion PWR”, Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 6 March (2014).13 Marc Caner1, and Edward T. Dugan. “ThO2-UO2 annular pins for high burn-up fuels,” Department of Nuclear and Radiological Engineering, University of Florida, PO Box 118300, Gainesville,July 1999.14Kyu Hyun Han, and Soon Heung Chang, “Development of a thermal-hydraulic analysis code for annular fuel assemblies,” Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology,16 July 2003.15Kyu-Hyun Hanaand et.al. “Development of a thermal hydraulic analysis code for gas-cooled reactors with annular fuels,” Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology, and Advanced Reactor Development Division, Korea Atomic Energy Research Institute, P.O. Box 105,Republic of Korea, July 2005.16 Nam-Il Takaand et.al. “Thermo-fluid investigation on a double-side-cooled annular fuel for theprismatic very high temperature gas-cooled reactor,” Korea Atomic Energy Research Institute, and School of Mechanical and Aerospace Engineering, Seoul National University, South Korea, May 2008.17 Liang Zhang et al,”Evaluation of High Power Density Annular Fuel Application in the Korean OPR-1000 Reactor”Department of Nuclear Science and Engineering (MIT), June 2009.18 C. H. Shinet.al. “The Design of Annular Fuel Arrays for a High-Power-Density PWR,” Transactions of the Korean Nuclear Society Autumn MeetingGyeongju, Korea, Korea Atomic Energy Research Institute, P.O.Box 105, Yuseong, Daejeon, Korea, October 29-30, 2009. 19FarshadFaghihi, and S. Mohammad Mirvakili. “Shut-down margin study for the next generation VVER-1000 reactor including13×13 hexagonal annular assemblies,”Department of Nuclear Engineering, School of Mechanical Engineering, Shiraz University, Research Center for Radiation Protection, Shiraz University, Reactors and Accelerators Research and Development School, Nuclear Science and Technology Research Institute (NSTRI), Atomic Energy Organisation of Iran (AEOI),Tehran, Iran, August 2011. 20KoroushShirvana, PavelHejzlarb, andMujid S. Kazimia. “The design of a compact integral medium size PWR,”Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States, TerraPower, LLC, Bellevue, WA, United States,November 2011.21 Chang-Hwan Shin, and et.al.”Thermal hydraulic performance assessment of dual-cooled annular nuclearfuel for OPR-1000,” LWR Fuel Development Division, Korea Atomic Energy Research Institute, 989-111 Daedeok-Daero, Yuseong-Gu, Daejeon 305-353, Republic of Korea, December 2011.22Ramadan Muftahkuridan and sanamohamed al-dukali.”The neutronics of increased power density PWRcore based on annular fuel rods using the Monte Carlo method,” Nuclear Engineering Department, Faculty of Engineering,University of Tripoli, Libya,march 2012.23 M. Saidinezhad, and S.D. Hamieh. “A 13×13 annular fuel assembly 1000 MWe PWR response to a reactivity excursion,” Laboratoire de Physique Nucléaire, Lebanese University, Faculty of Sciences (I), Hadath, Beirut, Lebanon, May 2012.24 M. Amin Mozafari, and F. Faghihi. “Design of annular fuels for a typical VVER-1000 core: Neutronicinvestigation, pitch optimization and MDNBR calculation,”Department of Nuclear Engineering, School of Mechanical Engineering, and IranRadiation Research Center, Shiraz University, Shiraz 71936, Iran, April 2013.25ChuanqiZhaoa and et.al.”Pre-conceptual core design of SCWR with annular fuel rods,”YouqiZhengbaKey Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China, November 2013.26 A.P. Deokulea and et.al.”Design and analysis of 19 pin annular fuel rod clusterfor pressure tube type boiling water reactor,” Bhabha National Institute, and Bhabha Atomic Research Centre, Trombay 400 085, Mumbai, India, May 2014.27Marcin Karol Rowinski and et.al.”Innovative model of annular fuel design for lead-cooled fast reactors,” Energy Research Institute at NTU, Interdisciplinary Graduate School, EXQUISITUS, Centre for E-City, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore, and Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, April 2015.28 Mohammad MizanurRahmanand et.al. “Hydraulic lift-off issues for application of high performance annular fuelsin pressurized water reactors,” Nuclear Energy Division, Energy Institute, Atomic Energy Research Establishment, Ganakbari, Savar, Dhaka 1000, Bangladesh, Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, and EXQUISITUS, Centre for E-City, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore, July 2015.29 G.R. Ansarifar, and M. Ebrahimian. “Design and neutronic investigation of the Nano fluids applicationto VVER-1000 nuclear reactor with dual cooled annular fuel,” Department of Nuclear Engineering, Faculty of Advanced Sciences & Technologies, University of Isfahan, Iran, August 2015.30Yangbin Deng and et.al. “Mechanism study and theoretical simulation on heat split phenomenonin dual-cooled annular fuel element,” State Key Laboratory of Multiphase Flow in Power Engineering, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City and Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu, China, March 2016.31M. Zaidabadia, G.R. Ansarifar,M.H. Esteki,2016 “Thermal hydraulic analysis of VVER-1000 nuclear reactor with dual-cooled annular fuel using K–xSST Turbulence model,”.Annals of Nuclear Energy 101, 118–127 32Michael L. Fensin, John S. Hendricks, SamimAnghaie ?The Enhancementsand Testing for the MCNPX 2.6.0 Depletion Capability?, Nuclear Technology,Volume 170, pp.68-79, April 2010.33Miko?ajOettingen., ?Validation of fuel burnupmodelling with MCNP Monte Carlosystem using destructive assay data from Ohi-2 PWR, Supervisor Faculty of Physics andApplied Computer Science Doctoral thesis :Dr hab. in?. Jerzy Cetnar, AGH University ofScience and Technology, Faculty of Energy and Fuels Krakow, September 2013.34M.S. Kazimi, P. Hejzlar, et al., “High Performance Fuel Design For NextGeneration PWRs: Final Report,” January 2006.35 Thermophysical Properties of Materials for Nuclear Engineering: Tutorial forstudents of specialty «Nuclear Power Plants» / Edited by Prof. P.L. Kirillov. Second revisedand augmented edition. – Obninsk. 2006. – 182 PP.36 KAERI Online Plotter for MCNP and ENDF cross section data, http://atom.kaeri.re.kr/cgibin/endfplot.pl 37 Tyler S. E.,” Advanced Design Concepts for PWR and BWR High-Performance Annular Fuel Assemblies” Massachusetts Institute of Technology ,June 2006.38 Bo Feng et al., ” Steady-state fuel behavior modeling of nitride fuels in FRAPCON-EP” Center for Advanced Nuclear Energy Systems, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 24-215, Cambridge, MA 02139, USA,April 201239 V. H. Ransom, et al. RELAP5/MOD2 Code Manual, Volume 3: Developmental AssessmentProblems. EGG-TFM-7952.Idaho National Engineering Laboratory. December 1987.