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• Model development to calculate the bowing effects of the FAs on power in VVER-1000. • The model is developed using the DRAGON and PARCS codes. • To verify the model, the bowed fuel geometry was simulated by MCNPX-2.7 code. • Power asymmetry depends on boric acid concentration, bowing size and direction. The Lateral deformation of Fuel Assembly (FA) under the operational conditions of the reactor cores is called FA bowing. This phenomenon is caused by factors such as thermal and hydraulic loads on FAs in the reactor core. It can lead to disturbances in the movement of control rods inside of FAs, cross-contact of FAs in refueling, and also changes in power distribution. Changing the distance between the fuels along the assemblies due to bowing, leads to non-uniform distribution of water (coolant) around the FAs and results in neutronic perturbation. In this research, by developing a calculation model for the bowed FAs of the VVER-1000 reactor, based on the distribution of water around FA at different heights. Macroscopic cross-sections are calculated by using the DRAGON cell calculation code and then the effect of bowing on the power distribution is calculated by using the PARCS core calculation code. To verify the model, the bowed FA geometry was simulated in MCNPX-2.7 Monte Carlo code. Results of DRAGON and MCNPX show the relative difference in all macroscopic cross-sections is less than 5%, except for scattering cross-sections (Σs,2), which is about 9%. Comparing the results with each other shows that the model to simulate the bowing effect of VVER-1000 reactor fuel has acceptable accuracy. Besides, for the central FA with C-shape bowing, the relative differences between the results of PARCS and MCNPX for thermal and fast flux are respectively less than 2% and 4%. Also, the effect of FA bowing in different states has been investigated. At last, results show the magnitude of power asymmetry depends on the size of the deformation of the FAs, bowing direction, and boric acid concentration. In addition, the effect of FAs bowing on power distribution and its resulting asymmetry is different during the cycle according to the concentration of boric acid. [ABSTRACT FROM AUTHOR]

Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient. [ABSTRACT FROM AUTHOR]

In normal operation conditions of nuclear power plants, the distribution of primary coolant between fuel channels would be considered almost uniform. When different number of Reactor Circulation Pumps (RCPs) are switched off, known as an abnormal condition, this uniform distribution is disturbed and different conditions occur for each channel depending on its position in the core. In this research, the normal and abnormal condition (with one or two tripped RCPs) for a VVER-1000/446 is investigated. For evaluation of the core neutronic calculations and thermal power distribution, USNRC's PARCS system code is employed. Then a thermal-hydraulics module was developed for performing the T/H calculation of the core zone. The input velocity of each channel in abnormal condition was calculated based on developed CFD model in downcomer and lower plenum of Reactor Pressure Vessel (RPV) by ANSYS-CFX. The results show that, in normal operation, the hot channel is related to the central fuel assembly of the reactor core with the highest relative power equal to 1.29 and total power of 23.74 MW. In this case, the minimum inlet velocity, the maximum coolant outlet velocity, and the maximum fuel temperature are 5.6 (m/s), 330.96 (°C), and 1345.8 (°C), respectively. In the cases of operation with one and two tripped RCPs, the hot channel is related to the fuel assemblies with the lowest inlet velocities. The lowest velocities are 0.32 m/s, 0.24 m/s, and 0.22 m/s respectively for the condition with one tripped pump, two tripped pumps placed oppositely, and two tripped pumps placed contiguously. The hot channel numbers in these cases are 158, 102, and 90, respectively. In these channel, the condition of outlet flow would be superheated, but the fuel temperature (1006.3, 1050.9, and 987.9) do not reach the maximum allowable margin. The study confirms the necessity of the coolant distribution consideration in OLCs as well as events that may disturb the symmetry of the coolant flow. It also showed that the lateral fuel assemblies are more at risk in this situation because of a significant reduction in coolant flow. Likewise, the investigations proved the safe continuation of the operation in PLOFA conditions with the preventive algorithm of the emergency protection system and without any need for immediate mitigation actions or operator intervention. [Display omitted] [ABSTRACT FROM AUTHOR]

Neutron noise induced by propagating thermal-hydraulic disturbances (propagation noise for short) in pressurized water reactors is investigated in this paper. A closed-loop neutron-kinetic/thermal-hydraulic noise simulator (named NOISIM) has been developed, with the capability of modeling the propagation noise in both Western-type and VVER-type pressurized water reactors. The neutron-kinetic/thermal-hydraulic noise equations are on the basis of the first-order perturbation theory. The spatial discretization among the neutron-kinetic noise equations is based on the box-scheme finite difference method (BSFDM) for rectangular-z, triangular-z and hexagonal-z geometries. Furthermore, the finite volume method (FVM) has been used for the discretization of the thermal-hydraulic noise equations, which comprises the fluctuations of all the coolant parameters, as well as the radial distribution of the temperature fluctuations in the fuel, gap and cladding. Based on the discretized governing equations and the proposed solving procedure, the closed-loop noise calculations have been performed (using NOISIM) for the case study of a typical VVER-1000 reactor core and the numerical results are presented and analyzed for different scenarios. The noise sources include the inlet coolant temperature and velocity fluctuations, in addition to the power density noises. Moreover, the space- and frequency-dependence of the propagation noise are studied in this paper. [ABSTRACT FROM AUTHOR]

Abstract: The present paper consists of two separate sections. In the first section, the neutron noise source is reconstructed using Artificial Neural Network (ANN) in a typical VVER-1000 reactor core. In the first stage of this section, the neutron noise calculations are performed based on Galerkin Finite Element Method (GFEM). To this end, two types of noise sources including absorber of variable strength and vibrating absorber are considered. As the results of noise calculations, the neutron noise is obtained in the location of detectors. In the second stage, the multilayer perception neural network is developed for reconstruction of the noise source. Complex neutron noises (real and imaginary parts) in the location of detectors are considered as the inputs of ANN. The developed artificial neural network consists of two hidden layers of type hyperbolic tangent sigmoid transfer function and a linear transfer function in the output layer. Noise source characteristics including strength, frequency and the location (X and Y coordinates) are identified with high accuracy. The developed hybrid method which comprises scanning method and multilayer perception neural network is employed for reconstruction of two coincidence noise sources. The number, type and location of noise source are exactly reconstructed using the hybrid method. The strength and frequency of noise source(s) are also identified with high accuracy using the developed method. A sensitivity analysis of the reconstructed noise source to some ANN parameters like the number of hidden layers, neurons in each hidden layer and the applied transfer functions is performed. Variation of accuracy of reconstructed noise source versus number of detectors and their arrangement in the reactor core are investigated as well. In the second section of present work, neutron flux variations (neutron noise) due to absorber of variable strength and vibrating absorber noise sources are studied in both frequency and time domains. Time dependency of neutron noise was obtained using inverse Fourier transform. [Copyright &y& Elsevier]

Highlights: [•] Scaling factors are calculated for the beginning of cycle (BOC) of VVER-1000 reactor using the direct and adjoint methods. [•] Space and energy dependent power density in core region is obtained from MCNP code. [•] Linearity assumption of relative detector response for small CBM is investigated. [•] It is shown that the direct method result is reliable for determining the CBM. [Copyright &y& Elsevier]

Abstract: In-core nuclear fuel management is one of the most important concerns in the design of nuclear reactors. Two main goals in core fuel loading pattern design optimization are maximizing the core effective multiplication factor in order to extract the maximum energy, and keeping the local power peaking factor lower than a predetermined value to maintain the fuel integrity. Because of the numerous possible patterns of fuel assemblies in the reactor core, finding the best configuration is so important and challenging. Different techniques for optimization of fuel loading pattern in the reactor core have been introduced by now. In this study, a software is programmed in C# language to find an order of the fuel loading pattern of a VVER-1000 reactor core using the perturbation theory. Our optimization method is based on minimizing the radial power peaking factor. The optimization process launches by considering an initial loading pattern and the specifications of the fuel assemblies which are given as the input of the software. The results on a typical VVER-1000 reactor reveal that the method could reach to a pattern with an allowed radial power peaking factor and increases the cycle length 1.1days, as well. [Copyright &y& Elsevier]

Abstract: In this paper, the development of a neutron noise simulator for hexagonal-structured reactor cores using both the forward and the adjoint methods is reported. The spatial discretisation of both 2-D 2-group static and dynamic equations is based on a developed box-scheme finite difference method for hexagonal mesh boxes. Using the power iteration method for the static calculations, the 2-group neutron flux and its adjoint with the corresponding eigenvalues are obtained by the developed static simulator. The results are then benchmarked against the well-known CITATION computer code. The dynamic calculations are performed in the frequency domain which leads to discarding of the time discretisation. Then, the developed 2-D 2-group neutron noise simulator calculates both the discretised forward and the adjoint reactor transfer function between a point source and its induced neutron noise, by assuming the neutron noise source as an “absorber of variable strength” type. The neutron noise induced by a “vibrating absorber” type of noise source may also be modeled using the calculated transfer function. The viability of the simulator is verified for different benchmark cases. [Copyright &y& Elsevier]

• The malfunction of boron injection system is one transients affecting the characteristics of cooling fluid. • A realistic approach based on the CFD and nodal expansion method is employed for simulation of this accident. • The utilization of CFD method depicted the boron heterogeneous distribution effects. • Due to the reduction of the absorber in a part of the reactor core DNBR is close to the critical value of 1. Nuclear power, as a low-carbon energy source, provides the steady and reliable electricity. In this power source, safe operation plays a significant role from the point of view of design and economic cost. While nuclear power plants are designed to be safe in their operation and safe in the event of any malfunction or accident, some accidents with considerable occurrence frequency should be considered to provide related safety system and operation. The malfunction of boron injection system is one of this accident affecting the chemical and neutronic characteristics of cooling fluid. The aim of this study is the simulation and analysis of the boron dilution accident as one of Design Basis Accident, by considering the heterogeneous distribution of boron. For this purpose, CFD methods were used for exact evaluation of the boron distribution in each fuel assembly. Also, cross-section correction module and core calculation module are respectively developed by a cell calculation code and nodal expansion method. These modules are employed to apply absorber effects including boron and control banks and calculate 3D relative power. The results reveal the effect of heterogeneous distribution of boron in reactor pressure vessel and non-uniform chemical characteristics of coolant across fuel channels. [ABSTRACT FROM AUTHOR]

• Development of a Computer code for safety analysis of a nuclear reactor. • The Code works based on nodal discretization using MCNPX code. • The restrictions of previous methods in transient analysis have been removed. • The Code is capable to simulate the systems with time-varying geometry and cross sections. • Independency of the method of the code to the node size. This paper proposes a new method for solving the time-dependent neutron transport equation based on nodal discretization using the MCNPX code. Most valid nodal codes are based on the diffusion theory with differences in approximating the leakage term until now. However, the Monte Carlo (MC) method is able to estimate transport parameters without approximations usual in diffusion method. Therefore, improving the nodal approach via the MC techniques can substantially reduce the errors caused by diffusion approximations. In the proposed method, the reactor core is divided into nodes of arbitrary dimensions, and all terms of the transport equation e.g. interaction rates and leakage ratio are estimated using MCNPX. They are then employed within the time-dependent neutron transport equation for each node independently to compute the neutron population. Based on this approach, a time-dependent code namely MCNP-NOD (MCNPX code based on a NODal discretization) was developed for solving time-dependent transport equation in an arbitrary geometry considering feed backs. The MCNP-NOD is able to simulate multi-group processes using appropriate libraries. Several test problems are examined to evaluate the method. [ABSTRACT FROM AUTHOR]

• A neutronic/thermal–hydraulic simulator has been developed based on coarse mesh methods to calculate AO for a Small Modular Reactor. • Average Current Nodal Expansion Method (ACNEM) and Single Heated Channel (SHC) method are considered as the neutronic and the TH simulator. • Macroscopic cross-sections were generated by cell calculation module corresponding to reactor operation conditions. • The results demonstrate that the AO variation remains in a safe and standard operating region for SMART reactor. Axial-Offset (AO), as an important operational parameter, should be monitored in the load-following procedure due to the safety limits related to xenon oscillation and axial peaking factor in a nuclear power plant. In this study, to calculate AO for a Small Modular Reactor, a neutronic/thermal–hydraulic simulator has been developed based on coarse mesh methods. In this simulator, the average current nodal expansion method and the single heated channel approach have been used for neutronic and thermal–hydraulic analysis, respectively. The developed simulator is verified by the IAEA-3D model and thermal–hydraulic benchmark model. As the iPWR small modular reactor case study, SMART reactor has been simulated, and the neutronic and thermal–hydraulic parameters have been calculated. For investigation of AO behavior during power changes, the regulating bank repositioning approach is employed, and the reactor core characteristics are estimated by a developed simulator. The results demonstrate that the AO variation remains in a safe and standard operating region for SMART reactor. [ABSTRACT FROM AUTHOR]