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For the pressurized water reactors (PWRs) depletion analysis, the critical boron concentration (CBC) search is required. In the Monte Carlo (MC) simulation, the CBC can be estimated by the neutron balance approach, which is called as the inline CBC search method in this paper. This method is based on the fixed-point iteration, which results in a number of inactive cycles for the MC simulation. For the acceleration of the convergence and real variance reduction, the p-CMFD feedback is applied to the inline CBC search method. Furthermore, a rejection technique is introduced in the p-CMFD calculation to suppress the error propagation from the p-CMFD parameters to the p-CMFD solution. For a near critical system with zero boron concentration, the inline CBC search method may get in trouble with the negative boron concentration. To solve this problem, the extended particle-tracking algorithm is proposed and verified in a simplified toy problem. In realistic PWR test problems, the numerical results show that the proposed method accurately estimates the CBCs, while the p-CMFD feedback effectively reduces the number of inactive cycles. In conclusion, for the PWR depletion analysis, the continuous-energy MC simulation under the CBC condition can be efficiently performed by the inline CBC search method with the p-CMFD feedback.

This work presents a new consistent derivation of the multigroup transport equations from the original continuous-energy transport equation, achieving group-wise condensation equivalence. The derivation of the multigroup transport equations currently in use involves an important approximation in the total cross section. The homogeneity and isotropy restoration (HIRE) theory described in this paper removes the angle dependency in the group condensed total cross section of the multigroup transport equations. The HIRE theory also restores the homogeneity of each material region, and it frees us from the higher-order moment scattering cross sections. To preserve the reaction rate of the original continuous-energy transport equation, the partial current discontinuity factor (PCDF) is introduced, that is instrumental in the theory. The theory was tested on several pin-cell problems, and the numerical results show that the new multigroup transport equations successfully reproduced the properties of the original continuous-energy transport equation.

In the three-dimensional (3-D) continuous-energy whole-core reactor analysis, the partial current–based coarse mesh finite difference (p-CMFD) feedback was applied to the Monte Carlo (MC) k...

This paper identifies the cause of slow convergence for optically thick coarse mesh cells, when coarse mesh-based acceleration methods known in the literature are applied to the neutron transport criticality calculation. To overcome the limitation, this paper introduces two two-level iterative schemes to speed up coarse mesh-based acceleration, and they are applied to the partial current-based coarse mesh finite difference (p-CMFD) acceleration method. In the first scheme, a type of fine mesh finite difference (p-FMFD)- or intermediate mesh finite difference (p-IMFD)-based acceleration with a fixed fission source is augmented in a coarse mesh-based acceleration with power iteration. The second scheme applies global/local inner iterations in addition to the first scheme. Because p-CMFD is unconditionally stable and provides transport partial currents (instead of net current) on the interface between two coarse mesh cells, this enables the two schemes to speed up convergence even in optically thick ...

Two two-dimensional/one-dimensional (2-D/1-D) methods, fusion and hybrid, have been developed and reported in the literature to deal with three-dimensional (3-D) heterogeneous reactor problems and to avoid direct 3-D transport calculations. The 2-D/1-D fusion method transforms a 3-D transport problem into 2-D and 1-D transport problems that have a smaller computational burden than the original problem. The hybrid method uses an additional diffusion (or SP3) approximation in the axial direction to enhance the efficiency of the calculation.This paper presents and compares the stability and the accuracy of the two methods. To this end, a 2-D transport problem is considered by reducing one dimension in the radial direction, leading to 1-D/1-D fusion or hybrid method. Fourier stability analysis is used to study the stability and the convergence behaviors of the two methods. With respect to accuracy, the two methods are compared via numerical solutions on a typical 2-D reactor problem. The results indic...

The continuous-energy Monte Carlo (MC) method is gaining attention not only for nuclear reactor statics but also for transient analysis, as computing power increases with the use of massive paralle...

In Part I of this paper, the two-temperature homogenized model for the fully ceramic microencapsulated fuel, in which tristructural isotropic particles are randomly dispersed in a fine lattice stochastic structure, was discussed. In this model, the fuel-kernel and silicon carbide matrix temperatures are distinguished. Moreover, the obtained temperature profiles are more realistic than those obtained using other models. Using the temperature-dependent thermal conductivities of uranium nitride and the silicon carbide matrix, temperature-dependent homogenized parameters were obtained. In Part II of the paper, coupled with the COREDAX code, a reactor core loaded by fully ceramic microencapsulated fuel in which tristructural isotropic particles are randomly dispersed in the fine lattice stochastic structure is analyzed via a two-temperature homogenized model at steady and transient states. The results are compared with those from harmonic- and volumetric-average thermal conductivity models; i.e., we compare k eff eigenvalues, power distributions, and temperature profiles in the hottest single channel at a steady state. At transient states, we compare total power, average energy deposition, and maximum temperatures in the hottest single channel obtained by the different thermal analysis models. The different thermal analysis models and the availability of fuel-kernel temperatures in the two-temperature homogenized model for Doppler temperature feedback lead to significant differences.

As modern computing power grows, whole-core transport calculations become more viable with parallel computing architectures. Nonoverlapping local/global (NLG) iterative method has been recently developed for the whole-core transport calculation. The NLG iteration adopts the 2-D/1-D fusion transport kernel as the local solver, and the p-CMFD equation is used as the global wrapper. The NLG iteration is capable of solving 3-D transient heterogeneous problems, and it is naturally parallelizable. In this study, the computationally-expensive local problems in the NLG iteration are parallelized by MPI protocol, and the Predictor–Corrector Quasi-Static (PCQS) method is applied to the transient calculations to reduce the computing time further. The parallelized NLG iteration and the PCQS method have been implemented in an in-house code, CRX-2K. Several numerical problems are computed, and the numerical results reveal that the parallelized NLG iteration has high potential in the realistic whole-core transport calculation, and the computing time in the transient calculations can be reduced by the PCQS method if the reactivity behaves linearly in time for a given macro time-step size.

This paper presents an approach to the continuous-energy Monte Carlo (MC)-based neutronics-thermal/hydraulics-depletion (N-T/H-D) coupled whole-core calculation. To reduce the memory demand for the detailed depletion calculation, the fission and surface source (FSS) iteration method is applied to the domain decomposed MC criticality calculation. For each iteration (i.e., MC cycle), inline feedback calculations are performed for the stable MC-based coupling calculation, where the partial current-based finite difference (p-CMFD) method is embedded to accelerate the convergence of both the critical boron concentration (CBC) and the neutron source distributions. Then, the subpin-level depletion calculations are performed by the Chebyshev rational approximation method (CRAM). The proposed framework was implemented in the continuous-energy MC code, McBOX, developed at Korea Advanced Institute of Science and Technology (KAIST). The detailed depletion analysis on a typical pressurized water reactor problem shows the improved performance of the proposed framework in terms of memory and computing time.

We present a new method for whole-core Monte Carlo calculation using space domain decomposition to alleviate the excessive memory requirement due to massive tallies. The proposed method is called t...

The rotational plane slicing (RPS) method is proposed for 3-D whole-core neutron transport calculation. This method takes a view of the 3-D structure with a set of vertical planes that are obtained by slicing along the characteristic lines. In a 3-D structure with a simple axial configuration, the sliced planes consist of rectangular cells. Each sliced plane is then analyzed quite easily with a 2-D transport discrete ordinate solver. Several numerical tests are performed and the results indicate that the RPS method reproduces the reference solution with good accuracy.

As modern computing power grows, whole-core transport calculations become more viable. However, the computing time and memory requirement remain major burdens. As a candidate for whole-core transport calculation methods, nonoverlapping local/global (NLG) iteration has recently been developed. In this study, the NLG iteration method is extended to make it capable of transient calculations of 3-D heterogeneous problems. It is then implemented in an in-house code, CRX-2K. Transient NLG iteration uses the 2-D/1-D fusion method as a local transport kernel, with the transient p-CMFD equation adopted as a global wrapper. In addition, a neighboring spectral index (NSI) weighting method is suggested as a tool for correcting the rod cusping phenomenon for rod ejection problems. Four problems, including a 3-D heterogeneous problem, are computed. Numerical results show that the NLG iteration converges to the reference solution obtained by means of the whole-core p-CMFD acceleration, and the NSI weighting method is accurate to correct the rod cusping phenomenon. The NLG iteration in present implementation takes more computing times (still less than 2 times) than the whole-core p-CMFD acceleration, but has great potential in parallelization.

In this paper, we present two novel approaches to reactor core analysis: (1) whole-core fine-group deterministic transport calculations are accelerated by a partial-current-based coarse-mesh finite...

To improve the currently used simplified fast reactor analysis method for few-group condensation, a two-material coexisting ring model is proposed in this study. In the two-material coexisting ring model, the θ-direction homogenized model from the R–θ–Z geometry is solved, but the neutron flux for each material in the homogenized region is obtained separately. In the numerical results on simple 2-D fast reactor test problems, the newly proposed two-material coexisting ring model shows excellent neutron spectrum agreement with the reference, as compared to the conventional simplified model. In addition, the few-group calculation result shows better keff estimation when a two-material coexisting ring model is used for group condensation. Because relative errors on the neutron spectrum are much flattened when the newly proposed model is used, accurate few-group cross sections can be generated even if a small few-group structure is selected for condensation.

Fully ceramic microencapsulated (FCM) fuel, a type of accident-tolerant fuel (ATF), consists of TRISO particles randomly dispersed in a SiC matrix. In this study, for a thermal analysis of the FCM fuel with such a high heterogeneity, a two-temperature homogenized thermal-conductivity model was applied by the authors. This model provides separate temperatures for the fuel-kernels and the SiC matrix. It also provides more realistic temperature profiles than those of harmonic- and volumetric-average thermal conductivity models, which are used for thermal analysis of a fuel element in VHTRs having a composition similar to the FCM fuel, because such models are unable to provide the fuel-kernel and graphite matrix temperatures separately. In this study, coupled with a neutron diffusion model, a FCM fuel-loaded reactor core is analyzed via a two-temperature homogenized thermal-conductivity model at steady- and transient-states. The results are compared to those from harmonic- and volumetric-average thermal conductivity models, i.e., we compare k eff eigenvalues, power distributions, and temperature profiles in the hottest single-channel at steady-state. At transient-state, we compare total powers, reactivity, and maximum temperatures in the hottest single-channel obtained by the different thermal analysis models. The different thermal analysis models and the availability of fuel-kernel temperatures in the two-temperature homogenized thermal-conductivity model for Doppler temperature feedback cause significant differences as revealed by comparisons.

In this paper, the overlapping local/global (OLG) iteration method based on deterministic SN transport/p-CMFD calculations was extended to hexagonal core geometry. For this framework, a deterministic SN transport code and p-CMFD equation solver was implemented on triangular cell base. These two calculations are iteratively performed with proper boundary condition update until it reaches converged solution, which is then compared with the direct whole-core transport solution. Two variations from the original overlapping local/global iterative scheme are also introduced and tested: (1) zeroth local calculation of fixed-k problem type with initially guessed incoming angular flux and multiplication factor, and (2) local calculation with non-overlapping region (nonoverlapping local/global iteration). Several numerical test results show OLG system has been successfully implemented on hexagonal core geometry and its variations improve the computational efficiency.

The concept of a graphite-moderating rod-inserted sodium-cooled fast reactor (SFR) fuel assembly is proposed in this study to achieve a low sodium void reactivity coefficient. Using this concept, two types of SFR cores are analyzed; the proposed SFR type 1 core has new SFR fuel assemblies at the inner/mid core regions while the proposed SFR type 2 core has a B 4 C absorber sandwich in the middle of the active core region as well as new SFR fuel assemblies at the inner/mid core regions. For the proposed SFR core designs, neutronics and thermal-hydraulic analyses are performed using the DIF3D, REBUS3, and the MATRA-LMR codes. In the neutronics analysis, the sodium void reactivity coefficient is obtained in various void situations. The two types of proposed core designs reduce the sodium void reactivity coefficient by about 960–1030 pcm compared to the reference design. However, the TRU enrichment for the proposed SFR core designs is increased. In the thermal hydraulic analysis, the temperature distributions are calculated for the two types of proposed core designs and the mass flow rate is optimized to satisfy the design constraints for the highest power generating assembly. The results of this study indicate that the proposed SFR assembly design concept, which adopts graphite-moderating rods which are inserted into the fuel assembly, can feasibly minimize the sodium void reactivity coefficient. Single TRU enrichment and an identical fuel slug diameter throughout the SFR core are also achieved because the radial power peak can be flattened by varying the number of moderating rods in each core region.

The fully ceramic microencapsulated (FCM) fuel, one of the accident tolerant fuel (ATF) concepts, consists of TRISO particles randomly dispersed in SiC matrix. This high heterogeneity in compositions leads to difficulty in explicit thermal calculation of such a fuel. For thermal analysis of a fuel element of very high temperature reactors (VHTRs) which has a similar configuration to FCM fuel, two-temperature homogenized model was recently proposed by the authors. The model was developed using particle transport Monte Carlo method for heat conduction problems. It gives more realistic temperature profiles, and provides the fuel-kernel and graphite temperatures separately. In this paper, we apply the two-temperature homogenized model to three-dimensional single-channel thermal analysis of the FCM fuel element for steady- and transient-states using 2-D FEM/1-D FDM hybrid method. In the analyses, we assume that the power distribution is uniform in radial direction at steady-state and that in axial direction it is in the form of cosine function for simplicity. As transient scenarios, we consider (i) coolant inlet temperature transient, (ii) inlet mass flow rate transient, and (iii) power transient. The results of analyses are compared to those of conventional UO2 fuel having the same geometric dimension and operating conditions.

In current practice of nuclear reactor design analysis, the whole-core diffusion nodal method is used in which nodal parameters are provided by a single-assembly lattice physics calculation with th...

A new method of depletion calculation is introduced by decomposing nuclide concentration vector into two blocks (short-lived nuclide block and long-lived nuclide block). For short-lived nuclide block calculation, general Bateman solution of each short-lived nuclide is used. An “importance” concept is introduced for selecting important parents for producing a particular short-lived nuclide so that computational burden for Bateman solution calculation is reduced. Long-lived nuclide block is solved by the method of variation of parameters, in which matrix exponentials are calculated efficiently since the norm of long-lived nuclide block matrix is small. The two-block decomposition method is tested on UO2 PWR fuel depletion problems and compared to existing depletion methods, i.e., ORIGEN code and Krylov subspace methods. The numerical results show that the two-block decomposition method gives much more accurate results than those of the ORIGEN code for similar computing time. For similar accuracy computing time of the two-block decomposition method is ∼10 times less than that of the Krylov subspace method.

A new core design concept for multi-purpose research reactors is presented. New concept cores using material test reactor (MTR) type fuel are constructed with the edge trimmed in-core irradiation hole. Conventional research reactors have core configurations with a constant assembly pitch. Sizes of in-core irradiation holes are limited to a multiple size of fuel assembly. The new concept enables a core configuration to have different sizes of in-core irradiation holes using the same size of fuel assembly. Two types of cores for multi-purpose research reactors are constructed and the performance results using MCNP calculation are compared. The new compact core for utilizing mainly beam tubes has a larger in-core irradiation hole and gives higher thermal neutron flux at the hole. The maximum thermal flux at the reflector region is almost the same. The new large core for utilizing in-core irradiation holes has small and large holes, while the conventional core has holes of the same size. The small hole is useful for high fast neutron flux and the large hole is useful for high thermal neutron flux. Compared to the conventional cores, the new cores use a smaller fuel assembly, which leads to enhanced safety at a high coolant speed for high power density. Two types of fuel plates are required for the conventional cores, but only one type of fuel plate will do for the new cores. This new design concept gives us several advantages and will be very useful for core design of multi-purpose research reactors.

This article discusses selects of some outstanding problems in nuclear reactor analysis, with proposed approaches thereto and numerical test results, as follows: i) multi-group approximation in the transport equation, ii) homogenization based on isolated single-assembly calculation, and iii) critical spectrum in Monte Carlo depletion.

For stable operation of a power reactor, the power coefficient (PC) of the nuclear reactor should be less than or equal to zero. In the CANDU reactor loaded with the recovered uranium (RU) which has a uranium enrichment of ∼0.9 wt% U 235 , the PC is estimated to be clearly positive over a wide power range of interest, owing to the generic positive coolant temperature coefficient (CTC) and weak fuel temperature coefficient (FTC) in the CANDU reactor. In order to improve the PC of the CANDU reactor without seriously compromising the economy, introduction of the burnable poison (BP) has been proposed in this work and a physics study has been performed to find the optimal BP material and its optimal loading scheme for the CANDU reactor loaded with the CANFLEX-RU fuel. Four potential BPs (Dy, Er, Eu, and Hf) were evaluated to find the optimal BP and various loading options of the selected BP were evaluated to determine the optimal loading scheme of the BP. From the viewpoint of the achievable fuel discharge burnup, it was found that Er is evaluated to be the best BP and the BP should be loaded within the central two fuel rings because the BP loading on the inner ring is more effective for reducing the CTC. The discharge burnup of the Er-loaded CANFLEX-RU fuel was 38% higher than that of the standard natural uranium (NU) fuel. The fuel discharge burnup can be increased further if the fuel enrichment is increased. It is shown that the discharge burnup of 1.0 wt%-enriched uranium fuel is 1.7 times higher than that of the NU fuel. This study has shown that the use of the BP is feasible to render the PC of the CANDU reactor negative, even though the slight reduction of the fuel burnup is inevitable, and thus the reactor safety can be greatly improved by the use of the BP in the CANDU reactor.

The group condensation of the transport equation is studied in this paper so that the computational burden can be reduced. The group condensation procedure leads to equivalent total cross section that becomes angle dependent. The difficulty of angle dependency has been traditionally treated by consistent P or extended transport approximation in multigroup transport computation. However, in this study, the angle dependency of the total cross section is applied directly to the discrete ordinates equation, and the solution procedure is validated numerically on a test problem. In addition, an angle-collapsing concept is proposed for the purpose of further simplifying the group condensed problem. A local/global iteration framework is also described, in which fine-group discrete ordinates calculation is used in local problems while few-group angle collapsed transport calculation is used in the global problem, with excellent test results in the k eff and flux estimation.

The Monte Carlo method is widely used in neutron transport calculations, especially in complex geometry and continuous-energy problems. However, an extended application of the Monte Carlo method to large realistic eigenvalue problems remains a challenge due to its slow convergence and large fluctuations in the fission source distribution. In this paper, a deterministic partial current-based Coarse-Mesh Finite Difference (p-CMFD) method is proposed that achieves fast convergence in fission source distribution in Monte Carlo k-eigenvalue problems. In this method, the high-order Monte Carlo method provides homogenized and condensed cross section parameters while the low-order deterministic p-CMFD method provides anchoring of the fission source distribution. The proposed method is implemented in the MCNP5 code (version 1.30) and tested on realistic one- and two-dimensional heterogeneous continuous-energy large core problems, with encouraging results.

The Korean HCSB (helium cooled solid breeder) TBM (test blanket module) is proposed with its specific compositions of lithium ceramic, beryllium and graphite in pebble form. In the Korean HCSB TBM, the amount of beryllium is reduced and the reduction is replaced by graphite for a neutron reflector, while tritium breeding ratio (TBR) remains almost unchanged with relatively low Li6 enrichment of ∼40%. However, the previous Korean HCSB was designed based on the LOCAL assumption, in which the surroundings are assumed by the reflective boundary condition. In this research, we establish a simple GLOBAL neutronics model based on demo fusion reactor and perform neutronics analyses including depletion (transmutation) calculation during 100 EFPDs (effective full power days) using the modified MONTEBURNS code.

While the deterministic lattice physics/depletion codes use leakage-corrected critical spectrum (although approximate due to the B1 buckling search employed), Monte Carlo depletion codes currently in use do not have such a feature in spite of their heterogeneity and continuous-energy modeling capability. This paper describes an approach to Monte Carlo depletion with leakage-corrected critical spectrum derived from first principles. This is based on the concept of albedo eigenvalue treated as weight of the reflected neutron in Monte Carlo simulation.

The Monte Carlo method for solving heat conduction problems [1-3] is extended for non-constant temperature boundary conditions in this study. The new method can treat problems with any given non-constant boundary temperatures, including heat convection problems with non-constant fluid bulk temperature. A set of problems, particularly the heat transfer problem in a pebble fuel, is analyzed by this new method. In addition, a new method to reduce the statistical errors in kernel fuel regions is introduced when the Monte Carlo method is applied to a pebble fuel.

This paper describes Daubechies’ wavelet method (DWM) for the discretization of the angular variable in the neutron transport equation. Two special features are introduced: (a) the azimuthal angle ...

The Korean HCSB (Helium Cooled Solid Breeder) TBM (Test Blanket Module), whose breeding zone is composed of lithium ceramic, beryllium and graphite in pebble form, was designed based on LOCAL assumption. In this research, we establish a simple preliminary GLOBAL neutronics model for the Korean HCSB TBM and perform neutronics analyses including depletion (transmutation) calculation during 500EFPDs (Effective Full Power Days) using the modified MONTEBURNS code. The neutronics characteristics for D-D plasma phase are investigated in the preliminary GLOBAL neutronics model, and the results are compared with those of D-T plasma phase. Moreover, we also establish the A-lite based GLOBAL neutronics model for more reliable neutronics calculation, and the results are compared with each other.

This article provides selects of outstanding problems in computational neutron transport, with some suggested approaches thereto, as follows: i) ray effect in discrete ordinates method, ii) diffusion synthetic acceleration in strongly heterogeneous problems, iii) method of characteristics extension to three-dimensional geometry, iv) fission source and k eff convergence in Monte Carlo, v) depletion in Monte Carlo, vi) nuclear data evaluation, and vii) uncertainty estimation, including covariance data.

In a pebble-bed type very high temperature gas-cooled reactor (VHTGR), a typical fuel pebble consists of over ten thousand five-layer TRISO particles in a graphite-matrix. The high heterogeneity in composition leads to difficulty in explicit thermal calculation of pebble fuels. Thus, a homogenization model becomes essential. Currently, a simple volumetric-average thermal conductivity approach is used. However, this approach is non-conservative and underestimates the fuel temperature. In this paper, we describe a homogenization model that is not only easy to implement but also gives a more realistic temperature distribution in a fuel pebble, providing the fuel-kernel and graphite-matrix temperatures separately. Steady-state and transient thermal analyses are performed using the homogenization model, and the point kinetics model is then coupled with the homogenization model to incorporate fuel-kernel temperature feedback.

Improving over a previous study [1], this paper provides a Monte Carlo method for the heat conduction analysis of problems with complicated geometry (such as a pebble with dispersed fuel particles). The method is based on the theoretical results of asymptotic analysis of neutron transport equation. The improved method uses an appropriate boundary layer correction (with extrapolation thickness) and a scaling factor, rendering the problem more diffusive and thus obtaining a heat conduction solution. Monte Carlo results are obtained for the randomly distributed fuel particles of a pebble, providing realistic temperature distributions (showing the kernel and graphite-matrix temperatures distinctly). The volumetric analytic solution commonly used in the literature is shown to predict lower temperatures than those of the Monte Carlo results provided in this paper.

It is known that the test of the capability of tritium self-sufficiency and the extraction of high-grade heat using tritium breeding blanket concepts is one of the major ITER missions. This requires the development of test blanket modules based on a corresponding DEMO blanket design, despite the differences in operating conditions between DEMO and ITER. Two blanket concepts such as a Helium-Cooled Solid Breeder (HCSB) blanket and a Helium-Cooled Molten Lithium (HCML) blanket are being considered as Korean Test Blanket Module (TBM) for ITER with the aim for verifying the capability of the breeding blanket design and manufacturability. In this paper, the current status of the design and analysis for the HCSB TBM is described. The key features of the design include the use of graphite neutron reflectors to reduce the amount of beryllium multiplier. Major analyses have been executed in order to optimize the design. The results of nuclear and thermo-hydraulic analysis show that the design parameters and requirements are satisfied. Also, the safety analysis results show that the design of the TBM system is sufficient to endure several accident events.

In the blanket design in a D-T fusion power plant, the majority of the fusion energy is obtained from neutron kinetic energy. The tritium for maintaining the self-sustainable D-T fusion reaction is to be procured from the (n,t) reaction in the blanket. For this reason, neutronics analysis in the blanket design is indispensable. Especially for solid-type blanket design, neutronics analysis, including a depletion (transmutation) calculation, is required to calculate the neutron flux and tritium production rate more accurately. In eigenvalue problems for the fission reactor design, the MONTEBURNS code is widely used for depletion calculations. However, the fusion blanket design is a fixed source problem. In addition to this, the current version of the MONTEBURNS code does not include Be9(n,t)Li7 and Li7(n,n′t)α reactions. Thus, in this research, (1) the MONTEBURNS code will be modified to solve the fusion blanket problem, including Be9(n,t)Li7 and Li7(n,n′t)α reactions, and (2) a three-dimensional neutronics depletion analysis for a solid-type blanket for ITER will be performed using the modified MONTEBURNS code.

ITER Test Blanket Module (TBM) which will be the act-alike module corresponding to DEMO blanket is aimed to verify the capability of tritium self-sufficiency and the extraction of high heat using tritium breeding concepts for ITER missions. Conceptual design of Korea Helium-Cooled Solid Breeder (HCSB) TBM, one of two concepts that Korea has proposed, has been performed including performance analyses. In this paper, the results of preliminary safety analyses of Korea HCSB TBM are described. In-vessel, in-box and ex-vessel loss of coolant accidents are selected as three reference accidental scenarios for the TBM. Each scenario is modeled and computed by RELAP5/MOD3.2, developed for thermo-hydraulic transient simulation of light water reactor coolant systems. The results show the robustness of the design from the safety perspective.

A coarse-mesh nodal method in cylindrical (r,θ,z) geometry, e.g., of pebble bed reactors, based on the analytic function expansion nodal (AFEN) methodology, is described in this paper. Two unique features are (a) no use of transverse integration-allowing a nodal scheme in (r, 0, z) geometry-and (b) nodal solution expressed in terms of analytic basis functions-leading to high accuracy and readily available reconstruction of homogeneous flux distributions. Additional features of multigroup formulation, two methods of void region treatment, and coarse-group-rebalance acceleration are implemented in the TOPS code and tested on several benchmark problems, including the Organisation for Economic Co-operation and Development/Nuclear Energy Agency PBMR-400 Benchmark Problem. The TOPS results are in excellent agreement with those of the VENTURE code, using significantly less computer time.

As the nuclear reactor core becomes more complex, heterogeneous, and geometrically irregular, the method of characteristics (MOC) is gaining popularity in neutron transport calculations. However, the long computing times require good acceleration methods. In this paper, the concept of coarse-mesh angular dependent rebalance (CMADR) acceleration is described and applied to the MOC calculation in x-y geometry. The method is based on the angular-dependent rebalance factors defined on coarse-mesh cell boundaries. A coarse-mesh cell may consist of several fine-mesh cells that can be heterogeneous and of mixed geometries with irregular or unstructured mesh shapes. The CMADR acceleration is tested on several test problems, including problems with strong material heterogeneity, and the results show that CMADR is very effective in reducing the number of iterations and the computing times of MOC calculations.

In the conventional discrete ordinates approach, the scattering source is approximated as a truncated Legendre series. In case of highly anisotropic scattering problems (e.g., incident beam problems), the truncated Legendre scattering cross-sections give unphysical negative cross-sections in some values of μ (cosine of scattering angle). These unphysical artifacts cause negative scattering sources and negative angular fluxes. In addition to that, negative angular fluxes may cause wrong scalar flux as well. A new method to generate non-negative scattering cross-sections, which is very efficient and deterministic, is proposed in this paper. The main idea of this method is to make non-negative scattering cross-sections that produce equivalent scattering sources. This method does not have a practical limitation to generate non-negative scattering cross-sections because the calculations of the scattering sources are performed with the conventional truncated cross-section data provided from the standard processing codes. In the both neutron and the photon/electron coupled cases, an inadequate truncated Legendre order causes problems, e.g., inaccurate angular distribution of scattering for low order, oscillations of differential scattering cross-sections where cross-sections are small for high order expansions, and negative differential scattering cross-sections in some values of μ . In the neutron case, if the anisotropy is very high compared to the truncated Legendre order, inaccurate angular distributions of scattering occur especially in within-group scattering. Even if the truncated Legendre order is quite high to represent angular distribution of scattering in the photon/electron coupled case, it still causes oscillations where the cross-sections are small. The method in this paper achieves both an accurate angular distribution of scattering and non-negative scattering cross-sections for neutron and photon/electron coupled cases. The generated non-negative scattering cross-sections with the new method are compared to the conventional scattering cross-sections and tested in the transport calculations. The numerical results tested in the transport calculation give accurate results without unphysical negative angular fluxes.

A new Monte Carlo method for solving heat conduction problems is developed in this study. Differing from other Monte Carlo methods, it is a transport approximation to the heat diffusion process. The method is meshless and thus can treat problems with complicated geometry easily. To minimize the boundary effect, a scaling factor is introduced and its effect is analyzed. A set of problems, particularly the heat transfer in the fuel sphere of PBMR, is calculated by this method and the solutions are compared with those of an analytical approach.

The unique features of the analytic function expansion nodal (AFEN) method in hexagonal- z geometry are described. The COREDAX code implementing the AFEN method is verified testing on the VVER-440 benchmark problem and a “simplified” VVER-1000 benchmark problem. The COREDAX code then applied to the original VVER-1000 benchmark problem exercise 2 (HZP case and HP case) provides very good results in comparison with those of other benchmark participants.

The analytic function expansion nodal (AFEN) method in hexagonal-z geometry is described focusing on its unique features, including the use of node-interface flux moments. Multigroup extension based on matrix function theory and coarse group rebalance (CGR) acceleration are also described. The COREDAX code implementing the AFEN method is verified testing on the VVER-440 benchmark problem, a “simplified” VVER-1000 benchmark problem, and the SNR-300 benchmark problem.

The method of characteristics (MOC) code CRX solves the three-dimensional transport problem by the 2D/1D fusion method, in which MOC is used in radial 2D calculation and SN-like methods are used in axial 1D calculation. The CRX code was used to provide the solutions for the three-dimensional OECD benchmark problem C5G7 MOX and the results were submitted to OECD and documented in the OECD report. This paper provides a description of the 2D/1D fusion method for three-dimensional transport calculation and presents additional work implementing several improved features performed since the submittal of benchmark solutions, with comparison of the results.