Nghiên cứu mô phỏng và cải tiến thiết kế bó nhiên liệu lò phản ứng VVER 1000 v 320 sử dụng vi hạt gd2o3 bằng chương trình MVP TT TIENG ANH

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE HOÀNG THANH PHI HÙNG NUMERICAL CALCULATION AND IMPROVED DESIGN OF VVER-1000/V-320 FUEL ASSEMBLY WITHIN Gd2 O3 PARTICLE USING THE MVP CODE Major: Nuclear and Atomic Physics Code: 44 01 06 SUMMARY OF DOCTORAL DISSERTATION OF PHYSICS Hà Nội – 2021 The thesis has been completed at: Nuclear Training Center, Vietnam Atomic Energy Institute Supervisors: Assoc Prof Dr Tran Hoai Nam - Duy Tan University Dr Ho Manh Dung - Vietnam Atomic Energy Institute Referee 1: Referee 2: The dissertation has been defended against the Institute-level Doctoral Dissertation Defense of Nuclear Training Center, Vietnam Atomic Energy Institute at h., ., 202 The thesis can be found at: National Library of Vietnam Library of Nuclear Training Center OVERVIEW The VVER-1000 under study is made up of 163 hexagonal fuel assemblies of three different enrichments, i.e., 1.6%, 2.4%, and 3.6% The burnable poisons (BPs) are usually added in a number of fuel rods of several assemblies for controlling excess reactivity in the early burnup stage of the fresh fuel The excess reactivity is reduced and power distribution in the core is flattened to avoid a high power peaking factor at fresh fuel assemblies [3] Integral burnable absorber (IBA) is a common nonremovable BP design integrated in a fuel assembly or mixed homogeneously with UO2 fuel in several fuel rod designs of PWR and VVER reactor [4, 8, 13] Gadolinium oxide (Gd2 O3 ) is a common material used in LWRs burnable absorbers LWRs , because of the higher absorption crosssection of 155 Gd 157 Gd [1] In conventional design, an amount of Gd2 O3 within a few percent is mixed homogeneously with UO2 fuel in several fuel rods of a fuel assembly Since Gd2 O3 has a smaller thermal conductivity than that of UO2 , one of the disadvantages is that the additional content of Gd2 O3 leads to the decrease of the thermal conductivity of the fuel pellet [5] It was reported that the thermal conductivity of Gd2 O3 -dispersed UO2 fuel pellet is larger than that of (U,Gd)O2 solid solutions with the same Gd2 O3 content Iwasaki et al conducted experiments to investigate the effect of Gd2 O3 dispersion on the thermal conductivity [7] This means that the use of Gd2 O3 particles could improve the thermal conductivity of Gd2 O3 -dispersed fuel pellets effectively Due to these urgent requirements, I chose the thesis topic Numerical calculation and improved design of VVER-1000/V-320 fuel assembly within Gd2 O3 particle using the MVP code with my desire to contribute a small part in the field of numerical calculation reactor Purpose of this study: 1) To learn the neutronics feasibility of using Gd2 O3 particles in new design VVER1000/V-320 The motivation is that the use of Gd2O3 in form of micro-particles would increase the thermal conductivity of the Gd2O3 bearing fuel pellet UO2 + Gd2 O3 2) To learn the new fuel assembly design with BPPs should be carried out to controll excess reactivity, improve the pin-wise power distribution and reduce the PPF at the beginning of burnup (0–10 GWd/t) 3) To apply for design new assembly Gd2 O3 BPPs with low soluble boron content in the coolant and improved neutronics performance CHAPTER INTRODUCTION 1.1.Introduction to VVER type Hình 1.1: VVER-1000 system[6] Bảng 1.1: Main design parameters of the VVER-1000 reactor [15] Main design parameters VVER-1000 Type V-320 V-428 Thermal power, MWt 3000 3000 Pressure 1st round, MPa 15,7 15,7 Pressure 1nd round, MPa 6,27 6,27 Reactor coolant flow, m /h 84800 86000 Reactor outlet temperature, o C 320 321 Number of fuel assemblies, pcs 163 163 Number of CPS assemblies, pcs 61 121 Uranium loading, ton 80 80 Fuel enrichment in isotope 235 U, wt% 4,4 4,4 Lifetime (year) 30 40 is a series of pressurized water reactor designs originally developed in the Soviet Union, and now Russia, by OKB Gidropress from 1950s Power output ranges from 300 MWe to 1700 MWe with the latest Russian development of the design VVER power stations are used by Armenia, Bulgaria, China, Czech Republic, Finland, Hungary, India, Iran, Slovakia, Ukraine, and the Russian Federation The first VVER reactor (VVER-210) was put in operation in 1964 in Novovoronezh The first Units and were VVER-440, model 179 reactors in Novovoronezh, they started operation in 1971 and 1972, respectively Bảng 1.2: The versions and generation reactor VVER 1955–1975 Gen-I Type (Design) VVER-210 (VVER-1) (Rus) VVER-70 (VVER-2) (Germ) VVER-365 (VVER-3M) VVER-440 (V-179) VVER-440 (V-230) VVER-440 (V-270) 1966–2003 Gen-II Type (Design) VVER-1000 (V-187) (Rus) VVER-1000 (V-302) (Sounth Ukraine) VVER-1000 (V-338) (Rus, Ukraine) VVER-1000 (V-320) (Rus, Ukraine, Ukraine, Czech, Bulgaria) VVER-440 (V-213) (Ukraine, Poland, Hungari, Slovakia, Czech, Rus) 2000–2007 Gen-III Type (Design) VVER-1000 (V-392) (Rus) VVER-1000 (V-446) (Iran) VVER-1000 (V-392B) (Rus) VVER-1000 (V-412) (India) VVER-1000 (V-428) (China) VVER-640 (V-407) (Rus) VVER-1000 (V-466B) (Rus) 2007 – Now Gen-III+ Type (Design) VVER-1200 (V-392M) (Rus) VVER-1000 (V-491) (Rus) VVER-1500 (V-448) (Rus) VVER-640 (V-407) (Rus) VVER-1000 (V-466B) (Bulgaria) VVER-1200 (V-392 M) (China) Bảng 1.3: General properties of BP materials [14] Neutron absorber Main absorbing nuclide Main absorber content (wt%) Density (g/cm3 ) Neutron mean free path (µm)a Melting temp (o C) α - At thermal neutron energy 0,0253 eV B4 C 10 B 90 2,52 25 2350 CdO 113 Cd 1,22 8,15 101,6 1427 Sm2 O3 149 Sm 13,82 8,35 61,7 2325 Eu2 O3 151 Eu 47,8 7,3 87,8 2050 Gd2 O3 155 Gd, 157 Gd Dy2 O3 161 Dy, 164 Dy 14,8; 15,65 7,4 8,3 2350 18,91; 28,18 7,81 418,6 2340 Er2 O3 167 Er 22,95 8,64 2373,6 2355 HfO2 177 Hf 18,6 9,68 4164,6 2758 VVER-1000 version V-320, V-428 and V-392 was constructed from nuclear safety analysis, Evaluation and Lessons Learned by OKB Gidropress It is a advanced reactor that incorporates passive safety systems and simplified system designs, important design features of the Generation III+ (VVER-1200) [12] Table 1.2 listed some version VVER and evolution of VVER technology Figure 1.1 displays main system of VVER-1000 include: Reactor pressure vessel, Steam generator, Feedwater pump, Pressurizer, Feedwater pump, Table 1.1 showed the main design parameters of VVER-1000 V-320 and V-428 type 1.2.Reactivity 1.2.1.The infinite multiplication factor k∞ The infinite multiplication factor k∞ is the ratio of the neutrons produced by fission in one neutron generation to the number of neutrons lost through absorption in the preceding neutron generation neutron production from fission in one generation k∞ = (1.1) neutron absorption in the preceding generation k∞ = εpr ηf (1.2) Wher: ε is fast fission factor; pr is resonance escape probability; η is reproduction factor, f is thermal utilization factor 1.2.2.Reactivity This relationship represents the fractional change in neutron population per generation and is referred to as reactivity: k−1 ρ= (1.3) k From equation 1.3 it may be seen that ρ may be positive, zero, or negative, depending upon the value of k The larger the absolute value of reactivity in the reactor core, the further the reactor is from criticality It may be convenient to think of reactivity as a measure of a reactor’s departure from criticality 1.2.3.The reactivity coefficients Changes in the physical properties of the materials in the reactor will result in changes in the reactivity Reactivity coefficients are useful in quantifying the reactivity change that will occur due to the change in a physical property such as the temperature of the moderator or fuel The Moderator Temperature Coefficient - MTC is the change in reactivity per degree change in temperature Because different materials in the reactor have different reactivity changes with temperature and the various materials are at different temperatures during reactor operation The Fuel temperature coefficient - FTC or Doppler temperature coefficient is the change in reactivity per degree change in fuel temperature This coefficient is also called the "prompt" temperature coefficient because an increase in reactor power causes an immediate change in fuel temperature A negative fuel temperature coefficient is generally considered to be even more important than a negative moderator temperature coefficient because fuel temperature immediately increases following an increase in reactor power 1.3.General properties of BP materials Hình 1.2: Microscopic absorption cross-sections of the main absorbing nuclides in the thermal neutron energy range [14] Traditionally, boron and gadolinium have been used as BP materials to control reactivity for the long term Some other rare earth elements are applicable as BP in a nuclear reactor In the thermal neutron range, the BP materials such as Gd2 O3 , B4 C, CdO, Sm2 O3 , Eu2 O3 , Dy2 O3 , Er2 O3 and HfO2 [1] Figure 1.2) showed Microscopic absorption cross-sections of the main absorbing nuclides in the thermal neutron energy range Table 1.3 listed microscopic absorption cross-sections of the main absorbing nuclides in the thermal neutron energy range described above Bảng 1.4: The Isotopic compositions of natural gadolinium and the microscopic absorption cross-section at thermal neutron energy of 0,0253 eV (200 C) [2] Isotope Abundances (at%) 153 Gd 154 Gd 155 Gd 156 Gd 157 Gd 158 Gd 160 Gd 2,18 14,8 20,47 15,65 24,84 21,86 σa (b) 22,334 85 60,737 1,8 252,912 2,2 1,4 In conventional LWRs, that excess burnup reactivity is controlled using control rods, chemical shim, or a burnable poison: • Control rod: Insertion of control rods can reduce excess reactivity However, using control rods might provide local flux depression around the control rods Therefore, reduction of the control-rod-drive-mechanism maneuvering is desirable to simplify plant operation • Chemical shim: Known as a soluble poison, produces spatially uniform neutron absorption when it is dissolved in the water of pressurized water reactors (PWRs) The most common chemical shim in PWRs is boric acid Changing the density of the boric acid controls the excess burnup reactivity of the core The uniform distribution of chemical shim in the core minimizes control rod operation and provides a flatter flux distribution over the core than using only control rods because no region of depressed flux exists • Integrated burnable poison: IBAs are the most common type in which burnable absorbing materials are integrated in a fuel assembly The IBA is designed so that the reactivity of the fuel assembly remains relatively constant This is to avoid a peak of reactivity during burnup, and avoid the appearance of a power peak during burnup CHAPTER METHODOLOGY 2.1.Particle Transport equation 2.1.1.The neutron transport equation The particle behavior is described by the density n(r, v, t) of particles at the spatial position r = (x, y, z), the velocity v = (vx ,vy ,vz ) and time t Often used is the angular density n(, E, Ω, t) that has independent variables the particle energy E and the unit vector of the flight direction Ω instead of the particle velocity The degree of freedom for Ω is The particle behavior is described by the following differential-form transport equation (Boltzmann equation): ∂n (r, E, Ω, t) + v · ∇n (r, E, Ω, t) + (r, E) (r, E, Ω, t) = t ∂t (2.1) = ∫ dv ′ r, E ′ f r, E ′ , Ω′ → E, Ω r, E ′ , Ω′ , t + S (r, E, Ω, t) t where t is the total cross section; f (r, E ′ , Ω′ → E, Ω) is the transition probability for the total cross section; v (= |v|) the particle speed and S (r, E, Ω, t) is the particle source The transition probability is expressed by the probability fx for each reaction type x: t r, E ′ f r, E ′ , Ω′ → E, Ω = t r, E ′ fx r, E ′ , Ω′ → E, Ω (2.2) Defining the angular flux: (2.3) Φ (r, E, Ω, t) = (r, E, Ω, t) the actual calculation is based on the following equation:: ∂ϕ (r, E, Ω, t) + Ω∇ϕ (r, E, Ω, t) + (r, E) Φ (r, E, Ω, t) (2.4) t v ∂t Here only the reaction of particles with nucleus is taken into account and the interaction between the particles is ignored On the other hand, no discretization for space and time is required in the Monte Carlo method We obtain the integral-form transport equation from Eq 2.4: s Φ (r, E, Ω, t) = ∫0∞ dse−η(s) Q r − sΩ, E, Ω, t − , (2.5) v η (s) = ∫0∞ ds′ r − s′ Ω, E , (2.6) t Q (r, E, Ω, t) = ∫ dE ′ ∫ dΩ′ t (r, E) f r, E ′ , Ω′ → E, Ω Φ r, E ′ , Ω′ , t (2.7) +S (r, E, Ω, t) η (s) is the integral of a reaction cross section along the direction of the particle flight and is called the optical path length or the optical thickness; Q (r, E, Ω, t) is is the particle source including the scattering source In dimensional form, the collision density is described: Ψ (r, E, Ω, t) = ∫ dr′ |r−r′ | t (r, E) exp − ∫0 t (r − s r − r′ ds |r − r′ | ′ × r−r δ Ω |r−r ′| − |r − r′ |2 Q r, E ′ , Ω′ , t ′ ′ = ∫ dr′ t Where r′ = r − sΩ ; t′ = t − and collision kernel is C : s v (r, E) e−η(|r−r |) r−r δ Ω |r−r ′| − |r − r′ |2 Q r, E ′ , Ω′ , t (2.8) δ(x) is the Dirac delta function, transport kernel T ′ ′ T r, E, Ω, t, r′ = t (r, E) e−η(|r−r |) r−r δ Ω |r−r ′| − (2.9) |r − r′ |2 Cx r, E, Ω, E ′ , Ω′ C r, E, Ω, E ′ , Ω′ = (2.10) x C r, E, Ω, E ′ , Ω′ = x (r, E ′ ) fx (r, E ′ , Ω′ → E, Ω) ′ t (r, E ) (2.11) We define the transition kernel: K r, E, Ω; r′ , E ′ , Ω′ = T r, E, Ω; r′ C r′ , E, Ω; E ′ , Ω′ (2.12) The collision density and the solution is expressed by the Neumann series:: ∞ dΓ′ Km Γ; Γ′ S Γ′ Ψ (Γ) = (2.13) m=0 Where: K0 Γ; Γ′ = δ Γ − Γ′ ; K1 Γ; Γ′ = K Γ − Γ′ K2 Γ; Γ′ = ∫ dΓ1 K Γ − Γ′ K Γ1 ; Γ′ Ki Γ; Γ′ = ∫ dΓ1 ∫ dΓi−1 K (Γ − Γi−1 ) K (Γi−1 ; Γi−2 ) K Γ1 ; Γ′ (2.14) 2.1.2.Particle Transport with Monte Carlo Methods The ”pseudo”-particles walk around in the three-dimensional virtual space of a computer so that they obey the physical laws between particles and nucleus We can calculate physical quantities by scoring events of the particles The particle behavior is determined with random numbers so that it satisfies physical laws statistically This is called random walk The events in the random walk are as follows: • Generation of particles: Particles are generated with the probability density for the specified space, energy, time and the kinds of particles and then start random walk • Flight of particles: The energy of particles doesn’t change in the flight between collisions with a nucleus in space The distance from a collision to the next collision is sampled statistically with reaction cross sections of the material where the particles pass The probability density function of the distance is the transport kernel expressed by Eq 2.9: p(x)dx = t e− t x dx (2.15) 12 Bảng 2.2: Design parameters of the VVER-1000 fuel assembly Parameters Number of central tube Number of guide tube Number of fuel cell with Gd Number of UO2 fuel cell Fuel cell inner radius Fuel cell outer radius Central tube cell inner radius Central tube cell outer radius Guide tube cell inner radius Guide tube cell outer radius Pin pitch Fuel assembly pitch Fuel temperature Non-fuel temperature Enrichment 235 U Density Gd2 O3 Unit Rod Rod Rod Rod cm cm cm cm cm cm cm cm K K wt% g/cm3 Value 18 12 300 0,3860 0,4582 0,4800 0,5626 0,5450 0,6323 1,2750 23,6 575,0 1027,0 3,7 7,4 Hình 2.3: The k∞ curves as a function of burnup of the VVER-1000 fuel assembly with homogeneous mixture UO2 and Gd2 O3 using MVP, SRAC code and BM 13 Hình 2.4: The pin-wise power distribution in the VVER-1000 fuel assembly with 12 Gd2 O3 uniform distribution fuel rods using MVP and SRAC code Hình 2.5: The pin-wise power distribution in the VVER-1000 fuel assembly with 12 Gd2 O3 uniform distribution fuel rods using MVP and BM result 14 CHAPTER RESULTS AND DISCUSSION 3.1.The fuel assembly with 12 UO2 – Gd2 O3 fuel rods using Gd2 O3 particles 3.1.1.The infinite multiplication factor k∞ The purpose this research is obtaining the burnup reactivity curve approximately that of the homogeneous mixture of UO2 and Gd2 O3 In the design procedure, it is assumed that the same content of Gd2 O3 but in form of BPPs is added into the fuel pellet, i.e the packing fraction of 5%, as in the reference design [10] Figure 3.1a) Hình 3.1: The k∞ curves as a function of burnup of the VVER-1000 fuel assembly designed with 12 Gd2 O3 -dispersed fuel rods a) The k∞ curves in the burnup range of to 10 GWd/t The diameter of Gd2 O3 60 µm was determined b) The k∞ curves as a function of burnup within diameter of Gd2 O3 is 60 µm in the burnup range of to 40 GWd/t displays the effect of the BPP diameter on the reactivity k∞ curves of the assembly from the beginning of burnup up to 10 GWd/t The diameterwas investigated in the range of 40 – 100 µm Since the objective is to attain the k curve approximate the reference one, the diameter of 60 µm was determined The pin-wise power distribution and PPF of the new fuel assembly is evaluated Figure 3.1b) depicts the k∞ curve of the new fuel assembly with the optimal BPP design (the diameter of 60 µm and the packing fraction of 5%) Figure 3.2 displays the evolution of 155 Gd and 157 Gd densities during burnup in the two designs with BPPs and with homogeneous BP It can be seen that the two absorbing isotopes decrease approximately in the two designs, this again explains the approximation of the reactivity curves 3.1.2.The pin-wise power distribution of the fuel assembly Figure 3.3 and figure 3.4 depict the pin-wise power distributions of the new fuel assembly designed with BPPs at the burnup of GWd/t and 10 GWd/t, respectively The relative power distributions were shown in one sixth symmetrical geometry in comparison with that of the reference design The relative power densities of the two 15 Hình 3.2: the evolution of 155 Gd and 157 Gd densities during burnup in a fuel rod BPPs and with homogeneous mixture of UO2 – Gd2 O3 Hình 3.3: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 12 Gd2 O3 -dispersed fuel rods at GWd/t in comparison with the reference design The optimal Gd2 O3 parameters are 60 µm in diameter and the packing fraction of 5.0% Gd2 O3 -dispersed fuel rods at GWd/t increase from 0.366 to 0.407 (about 11%)Figure 3.3 11%) The power densities increase slightly within 0.8% at the fuel rods located in the center of the assembly The PPF at the peripheral rod decreases from of 1.167 to 1.156 (about 0.9%) The pin-wise power distribution of the new fuel assembly is slightly flattened by using Gd2 O3 micro-particles Figure 3.5 displays the PPF as a function of burnup of the new fuel assembly designed with Gd2 O3 particles 16 Hình 3.4: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 12 Gd2 O3 -dispersed fuel rods at 10 GWd/t in comparison with the reference design The optimal Gd2 O3 parameters are 60 µm in diameter and the packing fraction of 5.0% µm Hình 3.5: The pin power peaking factor as a function of burnup of the VVER-1000 fuel assembly with 12 UO2 – Gd2 O3 fuel rods compared with that of the reference one The power distribution is flat and the PPF is about 1,04 to 1,07 during burnup from to 40 GWd/t In the reference assembly with homogeneous Gd2 O3 , the PPF is greater in the early burnup stage 17 3.2.New assembly with 18 UO2 – Gd2 O3 fuel rods The fuel assembly design with BPPs should be carried out to improve the pinwise power distribution and reduce the PPF during burnup from to 10 GWd/t The calculations have been performed to optimize the number of Gd2 O3 -dispersed fuel rods and their distribution in the fuel assembly in order to decrease the PPF: The number of gadolinia bearing rods; The position of gadolinia bearing rods in fuel assembly; The packing fraction Gd2 O3 particle in fuel rod; Diameter Gd2 O3 particles 3.2.1.The distribution of Gd2 O3 -dispersed fuel rods Hình 3.6: The configurations of the newly designed VVER-1000 fuel assembly with 18 UO2 - Gd2 O3 fuel rods Two models of the fuel assembly were selected corresponding to different arrangement of 18 UO2 – Gd2 O3 fuel rods We can see that in the case of no gadolinia bearing rod, the power distribution is flat and the PPF is about 1,04 – 1,07 during burnup from to 40 GWd/t Because of the one sixth symmetrical geometry, the parametric survey of design has been conducted to determine the number of gadolinia bearing rod will be 18, 24, 30, We proposed two models of fuel assembly with 18 UO2 – Gd2 O3 fuel rods as figure 3.6 3.2.2.The parametric survey of new design with 18 UO2 –Gd2 O3 fuel rods In the optimization process, the total initial amount of Gd2 O3 loaded in the newly designed fuel assembly was constrained to be the same as that in the reference one Thus, the total amount of Gd2 O3 in 12 rods of the reference design is distributed equally to 18 rods in form of BPPs The packing fraction of BPPs in the fuel rods is determined as 3.33% When the same Gd2 O3 amount is distributed in 18 fuel rods, the burning rate of absorbing isotopes increases 18 µm µm µm µm Hình 3.7: The k∞ curves as a function of burnup of the VVER-1000 fuel assembly designed with 18 Gd2 O3 -dispersed fuel rods in Model µm µm Hình 3.8: The k∞ curves as a function of burnup of the VVER-1000 fuel assembly designed with 18 Gd2 O3 -dispersed fuel rods The optimization of the BPP diameter is 300 µm and packing fraction is 3,33% for both models 3.2.3.The infinite multiplication factor k∞ The same optimal diameter of the BPPs were obtained for both models Figure 3.8) depicts the k∞ curves of the two optimal cases as functions of burnup Comparing 19 with the reference design the k∞ curves of the new designs with 18 UO2 – Gd2 O3 fuel rods are almost the same 3.2.4.The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods Hình 3.9: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t (Model 1) The optimal BP parameters are 300 µm in diameter and the packing fraction of 3.33% Hình 3.10: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t (Model 2) The optimal BP parameters are 300 µm in diameter and the packing fraction of 3.33% 20 Figure 3.9 and figure 3.10 show the pin-wise power distributions of the newfuel assembly designed with 18 BPP rods in Model and Model 2, respectively It can be seen that flatter power distributions are obtained with the new designs in comparison with the reference one Using the Gd2 O3 fuel rods are used, they are arranged so that the Gd2 O3 is distributed more uniformly in the fuel assembly The BP amount in the center is reduced and that close to the peripheral positions increases The difference of pin power density is within 9.0% The PPFs appears at the burnup of fuel pins in both two models The values are 1.105 and 1.113 for Model and Model 2, respectively They was reduced by about 4,8% and 4,2% - as Figure 3.11 The results imply the possibility of using BPPs in the fuel rods for controlling burnup reactivity and flattening PPF of the VVER-1000 assembly Hình 3.11: The pin-wise power distributions of the newfuel assembly designed with 18 UO2 – Gd2 O3 fuel rods 3.3.New VVER-1000 fuel assembly designed with low soluble boron 3.3.1.The k∞ curves of fuel assembly with low soluble boron The BPP design has been performed for two cases corresponding to the reduction of soluble boron content to 50% and 0% The boron contents of 300 ppm and ppm, respectively Once the soluble boron contentis reduced, it is expected to attain a more negative MTC during the core lifetime, which is one of desirable safety parameters of fuel design Figure 3.12 displays the k∞ curves of the optimal cases in comparison with the reference design It can be seen that in the case of 50% boron content (300 ppm), the optimal diameter of 320 µm and the packing fraction of 5.5% were selected for both Model and Model The diameter and packing fraction selected for the case of boron free are 360 mmand 8.0%, respectively Comparing with the reference 21 design, the total Gd2 O3 amount in the assembly with the reference design, the total Gd2 O3 amount in the assembly is increased by factors of 1.65 and 2.40 for the designs with 50% boron content and 0% boron, respectively In the cases of 50% boron content and boron free the k∞ values of the fuel assembly at the later burnup stage, when the effect of BPPs has ended, are greater than that of the reference case by about 160 and 330 pcm during burnup range of 10 to 15 GWd/t, respectively µm µm µm Hình 3.12: The k∞ curves of fuel assembly VVER-1000 low soluble boron 3.3.2.The pin-wise power distribution in the new VVER-1000 fuel assembly with low soluble boron Figure 3.13, Figure 3.14 and Figure 3.15, Figure 3.16 display the pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t The pin-wise power distribution is decreased by 1,6 2,7% compared to the reference design 3.3.3.The pin power peaking factor in the new VVER-1000 fuel assembly with low soluble boron Figure 3.17 depicts the PPF as a function of burnup in the new fuel assemblies with low boron content The PPFs appear at the beginning of burnup and are smaller than that of the reference value (1.160) In the case of boron 50% (300 ppm) the PPF is 1.120 and 1.126 for Model and Model 2, respectively The values are smaller than the reference value by 3.5% and 2.9%, respectively In the case of boron free, the PPFs are 1.129 and 1.142 at the burnup of GWd/t for Model and Model 2, respectively This values are smaller than that of the reference design by about 2.7% and 1.6% The total compositions of fuel and BP not change much compared to the reference design In the design with low soluble boron to apply BPPs for a full core analysis, it should be carefully conducted 22 Hình 3.13: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t, 50% boron content (Model 1) Hình 3.14: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t, 0% boron content (Model 1) 3.4.The MTC of the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods with low soluble boron In the design with low soluble boron content or boron free, the MTC of the fuel assembly could be affected Figure 3.18 shows the MTC of various designs as a function 23 Hình 3.15: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t, 50% boron content (Model 2) of burnup In most cases the MTC tends to be more negative with the increase of burnup The tendency of more negative MTC with the increase of burnup is ascribed to the hardening of neutron spectrum and the buildup of plutonium and absorbing fission products When the moderator temperature increases, the thermal flux spectrum is hardened and shifts to resonance region Some fission products with large absorption resonance would make the MTC more negative The MTC values for all cases are within the range of -60,0 đến -32,5 pcm/K At the beginning of burnup, the MTC in the case of boron free is more negative than others by about 10% Hình 3.16: The pin-wise power distribution in the new VVER-1000 fuel assembly designed with 18 Gd2 O3 fuel rods at GWd/t, 0% boron content (Model 2) 24 µm µm µm µm Mơ hình Mơ hình Mơ hình Mơ hình Hình 3.17: The pin power peaking factor as a function of burnup of the new VVER1000 fuel assembly designed with 18 UO2 - Gd2 O3 fuel rods and low soluble boron contents Hình 3.18: The moderator temperature coefficients as a function of burnup of the new VVER-1000 fuel assembly designed with Gd2 O3 particles 25 CONCLUSION In this work, we have investigatied the neutronics feasibility of using Gd2 O3 particles in the UO2 fuel pellet of the VVER-1000/V320 fuel assembly with all aim 1) controlling excess reactivity in the early burnup stage, increasing the thermal conductivity of the fuel pellets, 2) decreasing the PPF, more uniform distribution of BPPs in thefuel assembly, 3) Applying BPPs to design new assembly with low soluble boron content, and the following conclusion can be drawn: The neutronics feasibility of using Gd2O3 particles in the UO2 fuel pellet of the VVER-1000/V320 fuel assembly: • The results show that with the same content of 5% in volume, Gd2 O3 particles with the diameter of 60 µm distributed in 12 rods, the reactivity curve of the new fuel assembly are approximate that of the traditional design • The power density at the fuel pin with Gd2 O3 particles increases by about 11% at the beginning of burnup At other fuel rods, the power densities decreases lightly within 0.9 % in the outer fuel region and increase within 0.8 % in the central region The pin power peak which appears at the periphery fuel rod decreases by 0,9% so với thiết kế truyền thống New design assembly with 18 UO2 - Gd2 O3 fuel rods • Reducing the PPF at the beginning of burnup (0–10 GWd/t), 18 Gd2 O3 fuel rods are arranged so that the Gd2 O3 is distributed more uniformly in the fuel assembly The total amount of Gd2 O3 in 12 rods of the reference design is distributed equally to 18 rods in form of BPPs Hence, the packing fraction of BPPs in the fuel rods is determined as 3,33% • Two models of fuel assembly with 18 BPP-dispersed fuel rods were selected for optimizing the BPP parameters and evaluating the neutronics performance The optimal diameter of 300 µm and the packing fraction of 3.33 % were determined for both two models The reactivity curves are obtained approximately that of the reference one, while the PPF can be decreased by about 4.8% and 4.2% in Model and Model 2,respectively New design with the fuel assembly with low soluble boron • the k∞ curves of the optimal cases in comparison with the reference design In the case of 50% boron content (300 ppm), the optimal diameter of 320 µm and the packing fraction of 5.5%, the case of boron free, the diameter of 360 µm and packing fraction of 8.0% were selected for both Model and Model • Comparing between the two models of the BPP-dispersed rod distribution, the k curves are approximate in the early burnup stage The PPF is decreased by 1.6% and 2.7% compared to the reference design 26 REFERENCES Tiếng Anh: [1] Marielle Asou and Jacques Porta (1997), “Prospects for poisoning reactor cores of the future”, Nuclear engineering and design, 168 (1-3), pp 261–270 [2] Mark B Chadwick et al (2011), “ENDF/B-VII nuclear data for science and technology: cross sections, covariances, fission product yields and decay data”, Nuclear data sheets, 112 (12), pp 2887–2996 [3] James J Duderstadt and Louis J Hamilton (1976), Nuclear reactor analysis, John Wiley and Sons, Inc ISBN 0-471-22363-8 [4] Kevin Hesketh et al (2020), “Burnable poison-doped fuel”, Comprehensive Nuclear Materials, 2, pp 106–124 [5] Kouta Iwasaki et al (2009), “Effect of Gd2 O3 Dispersion on the Thermal Conductivity of UO2 ”, Journal of nuclear science and technology, 46 (7), pp 673– 676 [6] M Jabbari et al (2015), “Power calculation of VVER-1000 reactor using a thermal method, applied to primary secondary circuits”, Annals of Nuclear Energy, 77, pp 129–132 [7] Iwasaki Kouta et al (2008), “Thermal conductivity of Gd2 O3 dispersed UO2 pellet”, Proceeding of International Conference Atalante [8] Martin Loveckỳ et al (2020), “Increasing efficiency of nuclear fuel using burnable absorbers”, Progress in Nuclear Energy, 118, p 103077 [9] Isao Murata, Takamasa Mori, and Masayuki Nakagawa (1996), “Continuous energy Monte Carlo calculations of randomly distributed spherical fuels in high-temperature gas-cooled reactors based on a statistical geometry model”, Nuclear science and engineering, 123 (1), pp 96–109 [10] Yasunobu Nagaya et al (2005), “MVP/GMVP version 3: general purpose Monte Carlo codes for neutron and photon transport calculations based on continuous energy and multigroup methods”, JAERI, 1348 [11] Ali Pazirandeh, Sahar Ghaseminejad, and Morteza Ghaseminejad (2011), “Effects of various spacer grid modeling on the neutronic parameters of the VVER-1000 reactor”, Annals of Nuclear Energy, 38 (9), pp 1978–1986 [12] AN Prytkov et al (2017), “Specific features of initial fuel load of the innovative power unit under AES-2006 project”, Nuclear Energy and Technology, (4), pp 307–312 [13] Riham Refeat (2015), “Optimum Erbium Isotopes Composition and Distribution for Power Flattening in Advanced PWR Fuel Assembly”, J Mater Sci Eng B, (3-4), p 85 [14] Hoai Nam Tran and Yasuyoshi Kato (2009), “An optimal loading principle of burnable poisons for an OTTO refueling scheme in Pebble Bed HTGR cores”, Nuclear engineering and design, 239 (11), pp 2357–2364 ... respectively Bảng 1.2: The versions and generation reactor VVER 1955–1975 Gen-I Type (Design) VVER- 210 (VVER- 1) (Rus) VVER- 70 (VVER- 2) (Germ) VVER- 365 (VVER- 3M) VVER- 440 (V- 179) VVER- 440 (V- 230) VVER- 440... VVER- 1000 (V- 428) (China) VVER- 640 (V- 407) (Rus) VVER- 1000 (V- 466B) (Rus) 2007 – Now Gen-III+ Type (Design) VVER- 1200 (V- 392M) (Rus) VVER- 1000 (V- 491) (Rus) VVER- 1500 (V- 448) (Rus) VVER- 640 (V- 407)... (V- 213) (Ukraine, Poland, Hungari, Slovakia, Czech, Rus) 2000–2007 Gen-III Type (Design) VVER- 1000 (V- 392) (Rus) VVER- 1000 (V- 446) (Iran) VVER- 1000 (V- 392B) (Rus) VVER- 1000 (V- 412) (India) VVER- 1000