Abstract | Proračuni izgaranja na referentnom nivou te na različitim nivoima snage u svrhu određivanja kvantitativnog utjecaja koncentracija 135Xe i 149Sm obavljeni su dvodimenzionalnim spektralnim programom FA2D. Nakon toga formirana je biblioteka korigiranih udarnih presjeka. Paralelno, kontrole radi, dio proračuna ponovljen je programima Polaris i TRITON. Unutar PARCS-a napravljene su preinake s ciljem omogućavanja korištenja korigiranih udarnih presjeka u ovisnosti o trenutnoj i povijesnoj vrijednosti (tokom izgaranja) relativne snage. Da bi se uvidio utjecaj korigiranih udarnih presjeka na reaktivnost (određivanje kritične koncentracije topivog bora) i aksijalnu raspodjelu snage napravljen je globalni trodimenzionalni proračun jezgre NE Krško pomoću dodatno modificiranog programa PARCS povezanog s termo-hidrauličkim programom COBRA-VIP. Dobivene su vrijednosti uspoređene s projektnim i mjerenim vrijednostima za 27. ciklus NE Krško i samo s projektnim vrijednostima za 28. i 29. ciklus. Također, napravljeni su proračuni s pogonskom promjenom snage relevantni za promjenu koncentracije i prostorne raspodjele ksenona i samarija. Utjecaj razmazivanja ekvidistantnih rešetki unutar moderatora zahtijevao je dodatne spektralne proračune. Ekvidistantne rešetke razmazane su na dva načina. U prvom slučaju šest ekvidistantnih rešetki razmazano je unutar 120? dugog centralnog dijela, a jedna rešetka razmazana je unutar 6? duge donje zone sa smanjenim obogaćenjem goriva. U drugom slučaju sedam rešetki razmazano je u sedam različitih aksijalnih regija dugih po 6?, s tim da je prva rešetka, kao i u prvom slučaju, razmazana u donjoj zoni smanjenog obogaćenja goriva. Homogenizirani udarni presjeci za aksijalne i radijalne reflektore napravljeni su programima FA2D, te, opet zbog kontrole, NEWT-om i Polarisom. Utjecaj promjene koncentracije čelika zbog prisustva bafflea unutar reflektorskog elementa na raspodjelu snage određen je na osnovi PARCS-ovih rezultata proračuna 29. ciklusa. Programom FRAPCON-3 dobiven je toplinski odziv za najopterećeniju gorivu šipku, pri čemu su povijest izgaranja i aksijalni profil snage dobiveni iz PARCS-a. Dobiveni rezultati uspoređeni su s odzivom toplinskog modela gorive šipke iz PARCS-a. Analiziran je i utjecaj promjene temperature goriva tokom odgora na rezultate proračuna dobivenih PARCS-om (promjena toplinskih svojstava goriva i zazora u ovisnosti o odgoru). Nakon formirane metodologije projektnog proračuna neutronskih i termo-hidrauličkih parametara jezgre tokom odgora, proračuni su ponovljeni za napredne IRIS i I2S-LWR reaktore. Iako su oba reaktora u stvarnosti bili samo projekti u kojima je FER učestvovao, njihova izvedba, veličina rešetke, nova vrsta goriva i materijala košuljice te predloženi sagorivi apsorberi daju odličnu mogućnost za testiranje predložene metodologije i usporedbu s rezultatima drugih učesnika u projektima koji koriste sofisticiranije alate za proračun. |

Abstract (english) | The improvement of the methodology for the neutronic and thermal-hydraulic calculations of traditional PWRs is subject of the dissertation. The methodology was applied to the calculations of NPP Krško and additionally to two advanced reactors, IRIS and I2S-LWR. The differences between obtained results and the referent calculation values for NPP Krško and both advanced reactors are within satisfying limits, leading to the conclusion that the proposed methodology can be used in the calculations of the advanced reactors with different types of fuel, cladding materials, burnable absorbers or fuel dimensions. In the introduction short overview of the neutronic steady state design calculation for LWR reactors is given. Usual two-steps approach is used. In the first step fine mesh 2D transport fuel assembly calculation is used for homogenization of cross section data, and then 3D neutron diffusion nodal calculation was performed. The problems related to the homogenization of diffusion constants were mentioned as well as mathematical basis of the diffusion nodal method. The separate chapter was devoted to the calculation of pin power reconstruction. The used methodology is based on modified PARCS code with addition of separate core thermal hydraulic model based on COBRA code. The cross section homogenization was performed using FER FA2D transport code using collision probability theory. The auxiliary codes were developed to post process FA2D data and prepare cross section library. Cross section model is similar to MSLB benchmark table format. Each cross section set is three dimensional matrix dependent on fuel temperature, moderator density and boron concentration. The burnup dependency is explicit forth variable. Additional correction factors and interpolation procedure were used for history correction (fuel temperature, moderator density and boron concentration). The consistent methodology responsible for organization of the calculation was presented. It starts with selection of material composition. The composition is determined with fuel type, the enrichment of the fuel, the type distribution and concentration of burnable absorber. For each selected material composition referent 2D transport depletion is performed for average thermal conditions and for reflected geometry. Additional branching calculations (boron concentration, coolant density, fuel temperature) were performed for automatically selected burnup points to get dependence of cross section data on local thermal hydraulic conditions for each burnup point. Typically, 4 points were used for coolant density and fuel temperature branches, and 3 points for boron concentration branches. For each property four-dimensional matrix was formed and stored in cross section library. Interpolation procedure used in nodal code is trilinear interpolation for TH variables and additional linear interpolation in burnup. All data needed for steady state and transient core calculation have explicit burnup dependence. The two-group pin power form factors are part of separate library and they have only burnup dependence. The corresponding libraries are prepared for rodded material compositions too. The property of the node in nodal calculation is result of linear interpolation using unrodded and rodded property and position of control rod tip as a weighting factor. In order to take into account history spectral effects, separate depletion transport calculations were performed for two extreme values (min and max) of each thermal hydraulic variable (coolant density, fuel temperature, and boron concentration). Eight obtained values together with referent value were used in tetrahedral interpolation to correct cross sections in any nodal code for spectral influence. The library of spectral corrections is separate library of the XS model. Taking into account mostly withdrawn control rods in PWR reactors the corrections are not applied to rodded cross sections to decrease calculation load (the model is general and that can be done if user wants). The history variables needed in correction procedure are calculated within nodal code using linear and exponential burnup weighting. Last part of the cross section model is related to storage of history data, for each fuel assembly, needed for realistic core design calculations in multi-cycle case. That is done in special file unique for each fuel assembly. Initially the file contains fuel assembly design data (geometry, enrichment, BA info, relation to material composition cross section library). After each depletion cycle the file is automatically updated with burnup axial distribution, power density distribution and distribution of history TH variables. Main idea of the thesis was to explore influence of the assumed constant power level (and corresponding Xe and Sm concentrations) during cross section homogenization in the transport code to the results obtained in 3D core depletion calculation. In order to do that additional transport calculations were performed, and new correction, as part of XS feedback calculation in nodal code, was proposed. For all material compositions used in the NPP Krško in the last three fuel cycles (27-29), additional calculations have been made for the depletion at different power levels (from 10%Pn to 150%Pn). The power level is related to the concentration of the two strongest neutron absorbers: 135Xe and 149Sm. It has been shown that both isotopes have a non-negligible history impact on all nuclear cross sections and parameters. Traditionally it is assumed that main influence is only related to the cross section for neutron thermal absorption. That influence is usually treated explicitly. The burnup calculation at different power levels has shown that 135Xe and 149Sm for low power density have an effect on the spectral ratio, the fission cross sections - thermal and fast, the xenon and samarium microscopic cross section for the absorption of thermal neutrons, the Xe fission yield and the fast absorption cross section (subtracted absorption contribution of xenon and samarium). For low power density, the maximum deviation of the cross section from the reference values is mostly experienced at the highest burnup, however some cross sections show a greater discrepancy than expected even for minimal burnup. For example, the fission cross section for fast neutrons deviates more than + 1% when power level (fission products concentration) was changed. The cross section for the neutron removal from fast group and the microscopic absorption cross section for fast neutrons are the only ones that show maximal deviation at low burnup. Although, the majority of the maximum cross sections deviations for the burnup at the low power have a negative sign, some of them change the sign of deviation. The burnup at the higher power does not show so pronounced effects like those at the lower power. The reason for that is that the maximum power, for which the calculations are made, was 1.5 times higher than the nominal, and the lowest power was ten times smaller than nominal. Additional reason is that dependence of xenon poisoning on power shows saturation. The base to establish correction library for the burnup dependent cross sections are the calculated deviations of the cross section from the reference values. The power is additional parameter used in interpolation. Previously calculated cross sections, based on reference burnup, selected local thermal hydraulic branching and historical corrections, are additionally corrected due to the history influence of xenon and samarium. The effect of fission product poisoning at the current power was taken into account through the 2-group absorption cross section only. The introduction of a new correction cross section library caused additional changes in PARCS code, as well as developing of some new auxiliary programs. That was done successfully. The impact of additional corrections to the results of the global 3D depletion calculation is demonstrated using 29th NPP Krško fuel cycle as an example. The differences between the uncorrected and corrected values of critical boric acid concentrations, the axial power offset, the axial and radial power distribution have been shown, as well as the differences between the uncorrected and corrected values and corresponding values in the official nuclear core design report, which were taken as the reference. The influence of power history correction is visible in all cases. The difference for the boric acid critical concentration is approximately 20 ppm, for axial power offset it is around 1%, and it is approximately 2-3% for other power distribution dependencies. Regarding the deviations of the obtained values from the reference value, they are in some cases reduced (especially towards the end of the cycle) and in some cases increased. Regarding the power distribution differences, generally the power has increased in the higher power density areas, central area of the core, and reduced toward the peripheral areas of the core, in the lower power density areas. Some inconsistencies in transport homogenization of fission yields and microscopic cross sections of Xe and Sm were noticed. These values are important due to their usage in 3D diffusion code to calculate Xe and Sm concentrations. That is why it is important to trace and explain those inconsistencies in homogenization process. That was outside scope of this thesis. The fuel rod thermal model in the thermal-hydraulic program COBRA has also been changed compared to the initial one. The influence of the three-dimensional burnup distribution (available from PARCS) on the fuel and cladding thermal conductivity was taken into account. That way it was possible to increase accuracy of fuel temperature prediction at core hot spots. The calculation of reflector constants is improved too. The presence of the steel core baffle is explicitly taken into account, while the rest of the reflector cell is filled with a mixture of steel and coolant at the core inlet temperature. The importance of reflector constants is visible in better prediction of radial power distribution at the periphery of the NPP Krško reactor. It has some influence on global core reactivity (critical boron concentration) too. The methodology was able to address pure steel reflectors used I2S-LWR and IRIS reactor concepts. The I2S-LWR reflector constants were determined with the EDH method for the steel portion of 91% by volume. The additional improvement of the calculation methodology is related to the modeling of spacer grids. That is especially important if stainless steel is used as spacer grid material (for example in I2S-LWR). The simplified approach is based on smearing of fuel assembly central spacer grids along central part of fuel assembly, in 2D transport calculation. That material composition is used in corresponding part of reactor core in 3D diffusion calculation. The detailed approach smears one spacer grids over 15.24 cm on the assembly height (6 in). That will result in increase of number of material compositions in homogenized neutron cross section library, but, in 3D diffusion code it is possible to address power depression close to the spacer grids. More detailed axial power distribution similar to the results obtained from plant in-core instrumentation can be calculated. The influence of these changes is the most obvious in predicting the critical boric acid concentrations and the axial power distribution. The development of neutronic core design calculation capability at FER was initially mentioned to be applied to NPP Krško. Later, due to participation in two advanced integral PWR reactor development projects, IRIS and I2S-LWR, methodology and calculation tools have improved to take into account their unique properties. Similar approach was followed in this thesis too. The initial development and testing were done for NPP Krško core and then the described methodology, except power history correction, was applied to calculation of IRIS and I2S-LWR, too. IRIS reactor has rather small reactor core and uses the fuel assemblies similar to standard Westinghouse 17x17 fuel, but integral absorber is Er mixed with fuel. The I2S-LWR core contains 121 fuel assemblies with active height of 365.76 cm which is typical value for standard 2-loop PWRs (like NPP Krško). The major difference compared to standard PWR is its almost 50% higher power rating. To accommodate such power increase, specific design features are introduced, such as 19×19 square pitch lattice, U3Si2 fuel and advanced stainless-steel cladding and grids. New design of fuel, high-conductivity silicide fuel and more robust stainless steel cladding allow a reasonable margin against fuel melting during hypothetical accidents. The initial first core design was prepared by Westinghouse and it uses 3 different fuel enrichment and axial variation of IFBA absorber length. Both reactor concepts were developed with steel reflector. The differences between results obtained using described methodology and reference results provided by Westinghouse, presented in the thesis, were in all cases within the margins normally used for core design calculations. The core design variations covered in the verification set (assembly grid: 16×16, 17×17, 19×19; fuel type: UO2, U3Si2; cladding and spacer grid material: ZIRLO and stainless steel (importance of homogenization); burnable absorbers: IFBA coating (both symmetric and asymmetric), Er mixed with fuel; reflector: classical, steel) guarantee general character of improvements and the methodology as a whole. In all cases, in addition to the neutronic core model, the thermal hydraulic part of the model based on COBRA subchannel code coupled to PARCS code, was used. That means that thermal hydraulics design data like DNBR and fuel center temperature were available too. It can be concluded that the understanding of the PWR core burnup calculation, the calculation methodology and accuracy have been enhanced due to this research. |