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To develop and validate a versatile Monte Carlo (MC)-based dose calculation engine to support MC-based dose verification of treatment planning systems (TPSs) and quality assurance (QA) workflows in proton therapy. The GATE MC toolkit was used to simulate a fixed horizontal active scan-based proton beam delivery (SIEMENS IONTRIS). Within the nozzle, two primary and secondary dose monitors have been designed to enable the comparison of the accuracy of dose estimation from MC simulations with respect to physical QA measurements. The developed beam model was validated against a series of commissioning measurements using pinpoint chambers and 2D array ionization chambers (IC) in terms of lateral profiles and depth dose distributions. Furthermore, beam delivery module and treatment planning has been validated against the literature deploying various clinical test cases of the AAPM TG‐119 (c-shape phantom) and a prostate patient. MC simulations showed excellent agreement with measurements in the lateral depth-dose parameters and spread-out Bragg peak (SOBP) characteristics within a maximum relative error of 0.95 mm in range, 1.83% in entrance to peak ratio, 0.27% in mean point-to-point dose difference, and 0.32% in peak location. The mean relative absolute difference between MC simulations and measurements in terms of absorbed dose in the SOBP region was 0.93% ± 0.88%. Clinical phantom studies showed a good agreement compared to research TPS (relative error for TG-119 planning target volume PTV-D 95 ∼ 1.8%; and for prostate PTV-D 95 ∼ −0.6%). We successfully developed a MC model for the pencil beam scanning system, which appears reliable for dose verification of the TPS in combination with QA information, prior to patient treatment. [ABSTRACT FROM AUTHOR]

• Timely and correct identification of NPP transients could either prevent an accident or mitigate the consequences of an accident. • A hybrid deep learning technique is proposed for the online identification of nuclear power plant transients. • A CNN-LSTM network was used for the transient identification, which transformed the input matrices into vectors using a CNN and then LSTM layers predicted the probability of each transient by sequence processing. • The results were shown that the proposed technique performs better than common deep learning techniques in terms of accuracy, identification time, and computational cost. Identification of NPP transients plays an important role in the prevention of accidents and mitigation of their consequences. NPP parameters may follow different patterns during each transient. So the transients can be identified by monitoring the operating parameters. It has been shown in several studies that data-driven methods, especially deep learning approaches, have a desirable performance in NPP transient identification. A hybrid deep learning technique is proposed in the present paper, in which transient identification is done using a CNN-LSTM neural network. The training data set is taken from a VVER-1000 full-scope simulator and the most important operating parameters are determined by feature selection techniques. According to the results, the proposed technique has identified the NPP transients in a short time, with high accuracy, and with a reasonable computational cost. The effective performance of the technique makes it possible to use it as a practical tool for online transient identification. [ABSTRACT FROM AUTHOR]

• A novel sequential algorithm is developed for analyzing γ-ray spectra. • Whole spectral information are used to identify and quantify isotopes of a sample. • A sequence of spectra are produced for estimating a measured spectrum appropriately. • Both empirical and simulation studies are performed for testing the algorithm. • The identification procedure of developed algorithm is superior to the NNLS. A novel approach for analyzing complex gamma-ray spectra using a sequential algorithm is introduced. The developed Sequential Gamma-ray Spectrum Deconvolution (SGSD) algorithm produces a sequence of spectra converging to the best estimation of output spectrum of a gamma-ray detector. In each point of sequence, an isotope of unknown gamma-ray source is identified and the respective response of the detector to unknown source is reconstructed. Effectiveness of the developed algorithm is demonstrated by two empirical and simulation studies. In the case of empirical study, a number of recorded gamma-ray spectra related to a mixed gamma-ray source including different combinations of 5 isotopes (Co-60, Cs-137, Na-22, Eu-152 and Am-241) are analyzed using whole information of spectra. Furthermore, a number of simulated gamma-ray spectra related to a mixed gamma-ray source including different combinations of 30 isotopes are analyzed in simulation study. Both man-made and natural radioisotopes like Ba-133, Co-60, Ir-192, Cs-137, K-40, Th-232 series, U-238 series, Ac-227 series, etc. are used for Monte Carlo simulations. The numerical results of the SGSD algorithm are compared with those of the conventional Non-Negative Least Squares (NNLS) algorithm. Based on the results, the identification procedure of the SGSD algorithm has a remarkable superiority over the NNLS algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the neutron noise based on transport theory and diffusion noise theory using Green’s function technique is calculated. As the neutron noise is used for core diagnostic, surveillance and monitoring, calculation of neutron noise precisely can play an important role in monitoring and safety. We compare the accuracy of Green’s function based on transport and diffusion theory in order to survey the differences between these theories. In this study some deviation between results obtained two theories are observed, and the impact of dimensions, cross sections and frequency on the results investigated. [ABSTRACT FROM AUTHOR]

In the present study, the development of a neutron noise simulator, DYN-ACNEM, using the Average Current Nodal Expansion Method (ACNEM) in 2-G, 2-D hexagonal geometries is reported. In first stage, the static neutron calculation is performed. The neutron/adjoint flux distribution and corresponding eigen-values are calculated using the algorithm developed based on power iteration method by considering the coarse meshes. The results of the static calculation are validated against the well-known IAEA-2D benchmark problem. In the second stage, the dynamic calculation is performed in the frequency domain in which the dimension of the variable space of the noise equations is lower than the time dependent equations. Induced neutron/adjoint noise distribution due to the neutron noise source of type absorber of variable strength is calculated as well. Two different methods are used to validate the neutron noise calculation. The Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) as an important neutron noise source is investigated using ACNEM in this study. [ABSTRACT FROM AUTHOR]

• To determine the most important input parameters for NPP transient identification, the present paper has proposed a hybrid feature selection method. • Several filter methods are used to generate appropriate feature subsets by calculating the score of each feature. • A Long Short-Term Memory (LSTM) deep neural network is selected as the classifier to determine the best feature subset. • The Neighbourhood Components Analysis filter method has selected the best subset of features. • The effect of the number of used features on the accuracy of the model was investigated. Accidents that occur at NPPs must be correctly identified so quickly that mitigation actions can be taken in a timely manner. Depending on the type of transient, the operating parameters follow different patterns and it might be possible to identify the transient by monitoring these parameters. Due to the large number of parameters of an NPP, it is necessary to determine the parameters that play a vital role in transient identification. Data-driven methods have shown effective performance for NPP transient identification. To determine the most important input parameters for NPP transient identification, the present paper has utilized a hybrid feature selection method, in which feature subsets are created using several filter methods and then the best feature subset is determined by comparing the training results of a deep Long Short-Term Memory network. According to the results, the Neighbourhood Components Analysis method has selected the best subset of features. [ABSTRACT FROM AUTHOR]

A novel method is introduced which allows the higher order perturbative solution of a linear operator with a time variant coefficient. This method employs a form of raising and lowering operators which generate higher and lower order harmonics from a given harmonic. The analysis has been applied to the point kinetics equations with a monotone oscillatory reactivity to place bounds on the relative error of the linearization method frequently employed in the power reactor noise techniques. As a result, the maximum permissible reactivity amplitude for a given reactor as a function of frequency has been obtained such that regular power reactor noise methods remain accurate enough. Three benchmarks in subcritical and critical configurations show the accuracy of this method. [ABSTRACT FROM AUTHOR]

• 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]

In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value is calculated based on the 2G, 3D neutron diffusion theory. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of the neutron diffusion equation is performed based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured tetrahedron elements. Using power iteration method, neutron flux and corresponding eigen-value are obtained. The results are then benchmarked against the valid results for VVER-1000 (3D) benchmark problem. In the second stage, the neutron noise equation is solved using GFEM and Green’s function method for the absorber of variable strength noise source. Two procedures are used to validate the performed neutron noise calculation. The calculated neutron noise distributions are displayed in the different axial layers in the reactor core and its variation in axial direction is investigated. The main novelty of the present paper is the solution of the neutron noise equations in the three dimensional geometries using unstructured tetrahedron elements. [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]

Simulation, design and fabrication of a sealing enclosure is carried out for a NaI(Tl) 2″×2″ detector, to be used as in situ gamma radioactivity measurement system in marine environment. Effect of sealing enclosure on performance of the system in laboratory and marine environment (distinct tank with 10 m 3 volume) were studied using point sources. The marine volumetric efficiency for radiation with 1461 keV energy (from 40 K ) is measured with KCl volumetric liquid source diluted in distinct tank. The experimental and simulated efficiency values agreed well. Marine volumetric efficiency calibration curve is calculated for 60 keV to 1461 keV energy with Monte Carlo method. This curve indicates that efficiency increasing rapidly up to 140.5 keV but then drops exponentially. [ABSTRACT FROM AUTHOR]

Radiation transport techniques which are used in radiation detection systems comprise one of two categories namely probabilistic and deterministic. However, probabilistic methods are typically used in pulse height distribution simulation by recreating the behavior of each individual particle, the deterministic approach, which approximates the macroscopic behavior of particles by solution of Boltzmann transport equation, is being developed because of its potential advantages in computational efficiency for complex radiation detection problems. In current work linear transport equation is solved using two methods including collided components of the scalar flux algorithm which is applied by iterating on the scattering source and ANISN deterministic computer code. This approach is presented in one dimension with anisotropic scattering orders up to P8 and angular quadrature orders up to S16. Also, multi-group gamma cross-section library required for this numerical transport simulation is generated in a discrete appropriate form. Finally, photon pulse height distributions are indirectly calculated by deterministic methods that approvingly compare with those from Monte Carlo based codes namely MCNPX and FLUKA. [ABSTRACT FROM AUTHOR]

Many of the physical macroscopic quantities could be explained as the result of a collection of microscopic particles which act independent of each-other, in a linear fashion. Since the physical laws of the interaction of these particles with their surrounding medium are non-deterministic, one could think of these particles as the generators of a linear stochastic field. In this paper, we have introduced a derivation which has yielded an equation for the spatiotemporal correlations in such a field. The derivation is simple and extendable to include the behavior of many physical particles. A simple numerical algorithm has been devised to solve the obtained initial value integrodifferential equation and a computer program has been developed accordingly. The temporal correlations in four benchmark problems, i.e. a three dimensional one group fissile cube, two multi-region one group slabs and a two-group multi-region slab, have been obtained and compared with direct Monte Carlo simulations which show the accuracy of the method. Finally, these benchmarks show some possible applications of this formulation, e.g. generalizing the Rossi-alpha formula and extraction of the average neutron velocity in a steady-state reactor core. [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]

Evaluation of multigroup constants in reactor calculations depends on several parameters, the Dancoff factor amid them is used for calculation of the resonance integral as well as flux depression in the resonance region in the heterogeneous systems. This paper focuses on the computer program (MCDAN-3D) developed for calculation of the multigroup black and gray Dancoff factor in three dimensional geometry based on Monte Carlo and escape probability methods. The developed program is capable to calculate the Dancoff factor for an arbitrary arrangement of fuel rods with different cylindrical fuel dimensions and control rods with various lengths inserted in the reactor core. The initiative calculates the black and gray Dancoff factor versus generated neutron flux in cosine and constant shapes in axial fuel direction. The effects of clad and moderator are followed by studying of Dancoff factor’s sensitivity with variation of fuel arrangements and neutron’s energy group for CANDU37 and VVER1000 fuel assemblies. MCDAN-3D outcomes poses excellent agreement with the MCNPX code. The calculated Dancoff factors are then used for cell criticality calculations by the WIMS code. [ABSTRACT FROM AUTHOR]

Analysis of thermal–hydraulics fluctuations in pressurized water reactors (e.g., local and global temperature or density fluctuations, as well as primary and charging pumps fluctuations) has various applications in calculation or measurement of the core dynamical parameters (temperature or density reactivity coefficients) in addition to thermal–hydraulics surveillance and diagnostics. In this paper, the thermal–hydraulics fluctuations in PWRs are investigated. At first, the single-phase thermal–hydraulics noise equations (in the frequency domain) are originally derived, without any simplifying assumptions. The fluctuations of all the coolant parameters, as well as the radial distribution of the temperature fluctuations in the fuel, gap and cladding are taken into account. Then, the derived governing equations are discretized using the finite volume method (FVM). Based on the discretized equations and the proposed algorithm of solving, a single heated channel noise calculation code (SHC-Noise) is developed, by which the steady-state and fluctuating parameters of PWR fuel assemblies can be calculated. The noise sources include the inlet coolant temperature and velocity fluctuations, in addition to the power density noises. The developed SHC-Noise code is benchmarked in different cases and scenarios. Furthermore, to show the effects of the power feedbacks, the closed-loop calculations are performed by means of the point kinetics noise theory. Both the space- and frequency-dependence of the temperature fluctuations are analyzed in this work. [ABSTRACT FROM AUTHOR]

A space dependent model for the second moment of a stochastic field has been presented. The derivation procedure is simple and avoids non-physical assumptions for completeness. Moreover, a program has been developed which obtains the solutions to this equation in the three dimensional space. Two benchmarks, namely the fissile cube and the subcritical slab, show the accuracy of the results obtained using this method. [ABSTRACT FROM AUTHOR]

Neutron noise induced by propagating disturbances in VVER-type reactor core is addressed in this paper. The spatial discretization of the governing equations is based on the box-scheme finite difference method for triangular- z geometry. Using the derived equations, a 3-D 2-group neutron noise simulator (called TRIDYN-3) is developed for hexagonal-structured reactor core, by which the discrete form of both the forward and adjoint reactor dynamic transfer functions (in the frequency domain) can be calculated. In addition, both types of noise sources, namely point-like and traveling perturbations, can be modeled by TRIDYN-3. The results are then benchmarked in different cases. Considering the noise source as propagating perturbations of the macroscopic absorption cross sections, the induced neutron noise is calculated throughout the reactor core. For the first time, adjoint approach is applied and examined for modeling moving noise sources. Moreover, the space- and frequency-dependence of the propagation noise are investigated in this paper. [ABSTRACT FROM AUTHOR]

The evaluation of multigroup constants in reactor calculations depends on several parameters. One of these parameters is the Dancoff factor which is used for calculating the resonance integral and flux depression in the resonance region in heterogeneous systems. In the current paper, a computer program (MCDAN-3D) is developed for calculating three dimensional black and gray Dancoff coefficients, based on Monte Carlo, escape probability and neutron free flight methods. The developed program is capable to calculate the Dancoff factor for an arbitrary arrangement of fuel and moderator pebbles. Moreover this program can simulate fuels with homogeneous and heterogeneous compositions. It might generate the position of Triso particles in fuel pebbles randomly as well. It could calculate the black and gray Dancoff coefficients since fuel region might have different cross sections. Finally, the effects of clad and moderator are considered and the sensitivity of Dancoff factor with fuels arrangement variation, number of TRISO particles and neutron energy has been studied. [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: [•] The properties of Poisson distribution are exploited. [•] An Ito stochastic differential equation is obtained for a general stochastic system. [•] The formulation is applied to the point reactor. [•] Numerical results show the simplicity and accuracy of this method. [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]

Highlights: [•] Lagrange method is proposed for on-line reactivity calculation in nuclear reactors. [•] The need for nuclear power history or the Laplace transform is vanished. [•] The three- and five-point formulas are presented and examined in different benchmark cases. [•] Computational time-steps of up to 1s lead to highly reliable reactivity calculations. [•] The main advantage of the proposed approach is its stability and convergence in large time-step calculations. [Copyright &y& Elsevier]

Abstract: Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for IAEA-2D, BIBLIS-2D and IAEA-PWR benchmark problems. Convergence rate of GFEM in linear and quadratic approximations of the shape function are calculated and results are quantitatively compared. A sensitivity analysis of the calculations to the number and arrangement of elements has been performed. [Copyright &y& Elsevier]

Abstract: An improvement to the Direct Discrete Method (DDM), also known as the Cell Method, has been discussed. The improvement is based on a duality theorem between the primal and dual complexes. Also, the analog counterpart of the Integral operator has been derived in this paper. The multi-group neutron diffusion is then derived, directly in a discrete algebraic form, according to this procedure. A numerical example has shown that this method would yield a high order of convergence (approximately 4.6) if its parameters are adjusted suitably. Finally, the method is applied to the 2D IAEA benchmark problem, and has shown to yield accurate solutions with a reasonably low number of unknowns. [Copyright &y& Elsevier]

Abstract: The most general basis for approximating the transport equation has been studied. The application of the Gram–Schmidt procedure has been shown to unify the complete class of functions (polynomial type or non-polynomial type), applicable to this equation. The completeness of the series of functions is proved. A generalized version of the Fick''s law is introduced. It is shown that the spectrum of the transport equation obtained by this method agrees with the conventional methods of obtaining the spectrum. [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: Noise analysis techniques including Feynman-α (variance-to-mean) and Rossi-α (correlation) have been simulated by MCNP computer code to calculate the prompt neutron decay constant (α 0), effective delayed neutron fraction (βeff ) and neutron generation time (Λ) in a subcritical condition for the first operating core configuration of Tehran Research Reactor (TRR). The reactor core is considered to be in zero power (reactor power is less than 1W) in the entire simulation process. The effect of some key parameters such as detector efficiency, detector position and its dead time on the results of simulation has been discussed as well. The results of proposed method in the current study are validated against both the experimental data and the results of MTR_PC computer code. [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]

Abstract: Several parameters, one of which is the Dancoff Factor (DF), are used to calculate the resonance integral (RI) and reduced flux in the resonance region of heterogeneous systems as well as to accurately determine the group constants for criticality calculations. This paper is a report on the development of a program to calculate the DF correction factor using Monte Carlo method and collision probability definition in three-dimensional (3-D) geometries and with multi energy groups. Hence, the DF for any arbitrary arrangement of cylindrical and slab fuel elements is hereby calculated. The fuel elements are monitored and kept at equal levels, though different material compositions and formations are allowed rendering the materials either black or partially transparent. A separate investigation is carried out as to the effects of extension to 3-D geometry, energy group divisions, clad, coolant and moderator. The program is applied to calculate DF for slab fuels of a pool-type research reactor (PRR) containing 19 slab fuels and for cylindrical fuel element of CANFLEX fuel bundle with 43 cylindrical fuels elements. All calculations are performed in 3-D geometry and for six energy groups. The viability as well as the feasibility of the program is verified using the WIMSD computer code for the obtained 3-D and six-group DF for CANFLEX fuel bundle. [Copyright &y& Elsevier]

The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss'' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method. [Copyright &y& Elsevier]

• Transport Green function data is used for localization of a noise source. • Comparative study between inverse Green's function based on SN transport and diffusion is performed. • The impact of more accurate Green's function on the validation of the source localization is investigated. • The sensitivity of the localization results to the position and the number of detectors is investigated. In an attempt to explore the significance of transport theory in neutron noise, localization of a noise source by Green's function based on transport theory is investigated. There are considerable differences between Green's functions based on diffusion and transport, such as small dimensions, near edges, high heterogeneity medium and high-frequency source of perturbation. These differences are expected to significantly impact unfolding, reconstruction, and identification of the neutron noise source. Improvement in noise source unfolding methods is essential in terms of safety aspects and reactor performance enhancement. Since gaining the ability to monitor nuclear reactor based on noise diagnostics principle using few numbers of detectors is a challenging problem, more accurate methods of calculation of neutron noise can help reduce the detectors in number and sensitivity to location. This study revealed that inverse Green's function based on diffusion and transport is fundamentally different in concept. The inverse Green's function based on diffusion theory requires applying complicated reconstruction methods to gain more accurate results. This means that a large number of detectors must be used for noise source reconstruction. In contrast, in the case of inverse Green's function based on transport theory, each mesh's shape function is strongly correlated with the adjacent mesh. As a result, simple methods can be used to reconstruct the noise source. Therefore, the noise source can be identified and reconstructed with a smaller number of detectors in practical terms. [ABSTRACT FROM AUTHOR]

One of the well-known online monitoring techniques used for quality control of bulk samples is Prompt Gamma Neutron Activation Analysis (PGNAA). PGNAA suffers from the so-called matrix effect problems such as density, thickness and moisture content of the sample under study. In this work, an Artificial Neural Network (ANN) model is introduced to deal with these effects. The required spectra for training and testing the proposed ANN model are obtained by Monte Carlo simulation of the gamma-ray spectra recorded in a PGNAA online analyzer system used in cement factories. The gamma-ray spectra related to given set of density, thickness and moisture content are corrected channel-to-channel using the proposed ANN model. The corrected spectra are then compared against the standard spectra obtained for predefined standard density, thickness and moisture content. The improvement in Theil coefficient is larger than 70% for the tested spectra. • The PGNAA online monitoring technique suffers from the so-called matrix effect problems. • A commercial PGNAA online analyzer used in cement factories is simulated to investigate the matrix effects and correct them. • Artificial neural network is used for correcting the matrix effects in the Monte Carlo simulated spectra of analyzer. • Investigated matrix effects are density, thickness and moisture content of cement sample. • Quantitative and qualitative results indicate that the proposed ANN method is accurate. [ABSTRACT FROM AUTHOR]

• 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]

• The Code works based on Monte Carlo method using MCNPX code. • The restrictions of previous methods in transient analysis have been removed. • The Code is able to use either continuous or multi-group energy cross section libraries. • The Code is capable to simulate the systems with time-varying geometry and cross sections. • The Code is applied the effect of temperature on the cross section and density. Transient analysis which is vital in safety analysis requires a reliable calculation method. Most valid tools use diffusion theory with many approximations by now. However, the Monte Carlo method inherently overcomes these approximations and accurately calculates the parameters of a reactor. In this paper, a new time-dependent transport approach is described to simulate the nuclear reactor dynamic correctly using the MCNPX code. In this approach the fundamental parameters of a nuclear reactor like multiplication factor (K eff) and mean generation time (t G) are calculated using MCNPX code. They are then employed in the formulas to compute neutron population, proportional to K eff , during a generation time as well as precursors are decayed. Based on the approach, a dynamic Monte Carlo code namely DMCNP (Dynamical MCNPX code) is developed for a time-dependent simulation of particle tracking in an arbitrary geometry, considering the thermal-hydraulic feedbacks. The effects of temperature on cross section and density are applied at each time steps. Several test problems such as TWIGL, LMW, LRA and C5G7 are examined to assess the performance of the method. [ABSTRACT FROM AUTHOR]

A highly reliable tool for transient simulation is vital in the safety analysis of a nuclear reactor. Despite this fact most tools still use diffusion theory and point-kinetics that involve many approximation such as discretization in space, energy, angle and time. However, Monte Carlo method inherently overcomes these restrictions and provides an appropriate foundation to accurately calculate the parameters of a reactor. In this paper fundamental parameters like multiplication factor (K eff) and mean generation time (t G) are calculated using Monte Carlo method and then employed in transient analysis for computing the neutron population, proportional to K eff , during a generation time considering precursors decay. Based on this approach, a dynamic Monte Carlo code named MCSP (Monte Carlo dynamic Simulation of Particles tracking) is developed for both the steady state and time-dependent simulation of particle tracking in an arbitrary 3D geometry. MCSP is able to use either continuous or multi-group energy cross section libraries. To speed up the simulation, the MCSP was empowered with parallel processing as well. Several test problems such as C5G7, LMW and TWIGL are examined to assess the performance of the method. • Development of a 3D Computer code for safety analysis of a nuclear reactor. • The Code works based on Monte Carlo method. • The restrictions of previous methods in transient analysis have been removed. • The Code is able to use either continuous or multi-group energy cross section libraries. • The Code is capable to simulate the systems with time-varying geometry and cross sections. [ABSTRACT FROM AUTHOR]

Power reactor noise analysis is one of the most powerful tools in online monitoring and diagnostics of nuclear power reactors. Unfortunately, since such an analysis belongs to the non-linear “parametric excitation” realm, its theoretical aspects and relations have been mostly carried out after linearization. In this paper a general framework, i.e. the Ladder Expansion Method, is developed to convert such equations to a series of coupled linear equations, up to any desired accuracy. This method is then applied to the single mode random fluctuations of the absorption cross sections in a power reactor which is modelled by the multigroup diffusion equation with multiple delayed neutron groups. A system of coupled pseudo steady state diffusion equations has been derived as the result. The procedure of numerically solving such a system, using the Finite Element Method is described and the previously reported GFEM code, which is a Galerkin FEM based diffusion solver and Linear Power Reactor Noise analyzer for two dimensional geometries, has been generalized to accommodate the LEM to evaluate the higher order power reactor noise moments. Use of these moments in the Power Spectral Density of the flux and its derivatives, such as the detection rate, has shown that the value of the PSD at the main harmonic of the fluctuation deviates with the predictions of the conventional LPRN method. Moreover, the generation of super-harmonic modes in the PSD of the neutron flux distribution has been shown to follow naturally by using the developed LEM. Three numerical benchmarks show the correctness and accuracy of the developed method. Finally, the error introduced in the linearization process is quantified by comparing numerical results of the LPRN method with that of the LEM, and some of the general trends of this error have been identified. As a result, the expectation of validity of the linearization process in the “sufficiently small perturbation” region is confirmed. [ABSTRACT FROM AUTHOR]

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting functions in these two approaches would naturally lead to different values for the kinetic parameters. This paper mainly compares the outcome of these two approaches in calculating kinetic parameters for two main types of thermal critical lattices: Mixed Oxide (MOX) and Uranium Oxide (UOX) using ultrafine B N method. The results show that calculations which are based on using the forward weighted spectrum for generating the kinetic parameters underestimate prompt neutron generation time in both thermal lattices, while effective delayed neutron fraction is overestimated in UOX thermal lattice and underestimated in MOX one. [ABSTRACT FROM AUTHOR]