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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.

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.

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.

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 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.

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.

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.

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.

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 linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation for the angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is O (Δ 4 ) whereas that of diamond differencing is O (Δ 2 ). The positivity of the method is also stronger than that of diamond differencing. To accelerate the linear multiple balance method, we also describe an additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration scheme. It is demonstrated, via Fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius c ( c being the scattering ratio). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance with additive angular rebalance acceleration is effective and sufficiently efficient.

Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and arbitrarily distributed source for multi-layered slab problems are obtained by using the infinite medium Green's function (IMGF) and Placzek's lemma. In this approach, the infinite medium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transposed equation, and this infinite medium solution is related to the finite medium solution by Placzek's lemma. The resulting equation leads to an exact relation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and the interior inhomogeneous source for each slab. For heterogeneous problems having multi-layered slabs, the slabs are coupled through the interface angular fluxes. Since all derivations are performed analytically, the method gives exact solution with no truncation error. After the interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solution) in each slab is given straightforwardly in terms of the IMGF and the boundary angular fluxes.

A 1575 MWt transuranic (TRU) burner reactor core with a low sodium void worth has been developed by devising a pan-shaped active core design. The core consists of two types of fule subassemblies that differ in the height of the fueled regions. This strategy has allowed an extreme "pancaking" of the inner core region while the radial dimension increase is limited by placing longer fuels in the outer core region. The fuel cycle analysis has been performed in the equilibrium cycle consisting of external feed fuel with reprocessed typical PWR spent fuel and fissile makeup with recycled TRU elements. The neutronic performance characteristics obtained from the equilibrium cycle analysis show that it would work safely as well as economically as measured in terms of burnup reactivity swing peak power density Doppler coefficient TRU burning and sodium void worth. The core has relatively low double power peaks in both the inner and outer cores without enrichment zoning and this enables to make an active core volume smaller. The developed TRU burner core has been subjected to an extensive parametric study on the reprocessing schemes. Investigations are given for sodium void worth transmutation capability burnup reactivity swing and minor actinide (MA) contents. Through this series of study a variant of the TRU burner core that is aimed at preferentially burning MA has been determined. This MA burner core uses U-235 as well as the homogeneously recycled TRU elements. This MA burner core consumes 140 kg of MA per year without penalizing the sodium void reactivity observed in the TRU burner core. Finally the combined introduction of developed TRU and MA burner cores shows the functional effectiveness of reducing PWR discharged TRU inventory.

This paper applies the grey Dancoff factor calculated by Monte Carlo method to the criticality calculation for cluster fuel bundles. Dancoff factors for five symmetrically different pin positions of CANDU37 and CANFLEX fuel bundles in full three-dimensional geometry are calculated by Monte Carlo method. The concept of equivalent Dancoff factor is introduced to use the grey Dancoff factor in the resonance calculation based on equivalence theorem. The equivalent Dancoff factor which is based on the realistic model produces an exact fuel collision probability and can be used in the resonance calculation just as the black Dancoff factor. The infinite multiplication factors based on the black Dancoff factors calculated by collision probability or Monte Carlo method are overestimated by about 2 mk for normal condition and 4 mk for void condition of CANDU37 and CANFLEX fuel bundles in comparison with those based on the equivalent Dancoff factors.

This paper deals with the structure of public attitude towards nuclear power plants in Korea. Special emphasis is given to the issues of public acceptance in relation to perceived benefits, perceived risk, judged safety, and safety satisfaction. The national survey data of 1995 by the Korea Institute of Nuclear Safety is analyzed with a latent class model and logistic regression. The latent class model is used to construct benefit and risk factors. With these factors and safety-related variables, a public attitude model is developed by logistic regression which enables the relationships between national or local acceptance of nuclear power and explanatory variables to be quantified. The results show that the attitude structure is somewhat different by gender. Subjectively perceived risk is found to be the most influential factor for local acceptance. The odds of local acceptance with the best risk perception is about 16 times the odds with the worst perception for males and about 7.7 times for females. From the results of this analysis, it is clear that subjective satisfaction with nuclear safety is a more important factor for explaining public acceptance rather than judgment of it. These important findings should be reflected in the public acceptance improvement strategy for the nuclear power program.

A transport theory code CRX based on the method of characteristics with a general geometric tracking routine for rectangular and hexagonal geometrical problems is developed and tested for heterogeneous cell and assembly calculations. Since the method of characteristics uses the characteristic form of the Bolzmann transport equation, CRX has no practical limitations placed on the geometry of the problem and gives accurates solutions in strongly absorbing media. To relax the constraints of the existing characteristic transport calculation codes, a new treatment of the reflective condition is introduced. In this treatment, the external reflective boundary is discretized into small segments and the angular fluxes for rays along a segment are assumed to be uniform. Also, a new calculational procedure for condensation is devised to obtain an accurate energy spectrum of absorber cells: after the characteristic cell calculation, an SN transport calculation is performed for the assembly comprised of homogenized cells. The result is used to calculate group and angular octant dependent albedos on absorber cell boundaries. Then, the two-dimensional characteristic transport calculation with the albedo boundary conditions is performed again for absorber cells. Using the condensed group macroscopic cross sections, a two-dimensional characteristic transport calculation is performed for the heterogeneous assembly. To test the code, it is applied to several benchmark problems which consist of complex meshes and compared with other codes. The results show that the CRX code is very accurate.

Based on the spectral-Galerkin method and domain decomposition method, a novel coarse-mesh model (SGCM) has been developed for solving the two-dimensional multigroup neutron diffusion equations. In this study, the reactor domain is decomposed into subdomains (or course meshes). Within any individual subdomain, the neutron diffusion equations with the Robin boundary condition are first reformulated in a weak (variational) form, which is then solved by means of the Legendre-spectral method. As for interfacial coupling between subdomains, it is relaxed by an interfacial relation of discontinuity between incoming and outgoing partial currents if discontinuity factors are considered on subdomain interfaces. The resulting discretized system with block-sparse-structured matrix is solved by the block successive over-relaxation method (BSOR). The method was examined with two well-known PWR benchmark problems and a realistic reactor core. It turns out that the method can generate not only extremely accurate assemblywise average quantities, but also satisfactory smooth homogenized fluxes, and heterogeneous reconstructed pinwise fluxes, which results from the fact that all the formulations are derived in a variational form in which the admissible solution space consists of higher-order Legendre polynomials.

A new discrete ordinates nodal method is developed for the two-dimensional transport equation in hexagonal geometry. We solve the discrete ordinates equation analytically after the source term is projected and represented in high-order polynomials. This source projection analytic nodal discrete ordinates method (SPANDOM) is applied to two four-group fast reactor benchmark problems. Compared with the TWOHEX code, the numerical results indicate that the present method accurately predicts not only effective multiplication factor but also groupwise flux distributions.

To get the equivalent assemblywise flux-weighted constants (FWCs) for use in the coarse-mesh nodal analysis, the global/local iterative homogenization procedures, including the procedures based on variational principles, are developed in this study. The nodal expansion method is employed in the global core analysis and the fine-mesh finite difference method in the local assembly calculation. To achieve fast and stable convergence, the mixed boundary condition is imposed on the assembly surface in local assembly calculation, where we modulate the surface flux using the assemblywise fundamental mode eigenfunction. The results of numerical tests using the assemblywise FWCs are compared with the reference solutions for the PWR and BWR problems. In the PWR problems, there is no strong need for the global/local iterative homogenization. However, in the BWR problems, the iterative procedures we developed remarkably improve the accuracy of the assembly power distribution. Especially the surface flux should be modulated in the local calculation, when there exists high heterogeneity at the node surface as in BWR. The procedures based on the variational principles provide similar trend in accuracy to the direct iterative procedures.

Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are described in this paper: Method A based on expansion of a Lyapunov function and Method B based on expansion of any positive definite function. The methods are established on the stability definitions of Lyapunov itself. Method A provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most reactor systems are stiff. Method B requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for reactor systems that are stiff. These methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared.

To suppress the spatial xenon oscillations in a nuclear reactor, an implementable stabilization scheme is proposed based on the finite dimensional compensator theory in control theory for the distributed parameter systems. The method is applied to a one-dimensional reactor whose dynamics is governed by one-group diffusion equation with its associated iodine and xenon dynamics. The modal decomposition of the state variables enables us to use the pole assignment algorithms developed in finite dimensional systems to obtain the stabilizing compensator gains. This allows us to estimate the states of a reactor in a transient using output measurement data and arbitrary initial conditions, and control the states using the estimated values. The resulting compensator is tested by using model-based data for measurement output through numerical simulations. The results show that unstable spatial xenon oscillations initiated by perturbations can be controlled by the finite dimensional compensator.