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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]

This article aims to simulate the sudden and fast pressure drop of VVER-1000 reactor core coolant, regarding acoustic phenomenon. It is used to acquire a more accurate method in order to simulate the various accidents of reactor core. Neutronic equations should be solved concurrently by means of DRAGON 4 and DONJON 4 coupling codes. The results of the developed package are compared with WIMS/CITATION and final safety analysis report of Bushehr VVER-1000 reactor (FSAR). Afterwards, time dependent thermal-hydraulic equations are answered by employing Single Heated Channel by Sectionalized Compressible Fluid method. Then, the obtained results were validated by the same transient simulation in a pressurized water reactor core. Then, thermal-hydraulic and neutronic modules are coupled concurrently by use of producing group constants regarding the thermal feedback effect. Results were compared to the mentioned transient simulation in RELAP5 computer code, which show that mass flux drop is sensed at the end of channel in several milliseconds which causes heat flux drop too. The thermal feedback resulted in production of some perturbations in the changes of these parameters. The achieved results for this very fast pressure drop represent accurate calculations of thermoneutronic parameters fast changes. [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 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]

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]

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]

An embedded time interval data acquisition system (DAS) is developed for zero power reactor (ZPR) noise experiments. The system is capable of measuring the correlation or probability distribution of a random process. The design is totally implemented on a single Field Programmable Gate Array (FPGA). The architecture is tested on different FPGA platforms with different speed grades and hardware resources. Generic experimental values for time resolution and inter-event dead time of the system are 2.22 ns and 6.67 ns respectively. The DAS can record around 48-bit x 790 kS/s utilizing its built-in fast memory. The system can measure very long time intervals due to its 48-bit timing structure design. As the architecture can work on a typical FPGA, this is a low cost experimental tool and needs little time to be established. In addition, revisions are easily possible through its reprogramming capability. The performance of the system is checked and verified experimentally. [ABSTRACT FROM AUTHOR]

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: [•] A sensitivity analysis of unfolding methods to different parameters is done. [•] ISM is proposed to reconstruct the noise source of type vibrating absorber. [•] Four algorithms are used to solve the system of equations in the inversion method. [•] The neutron noise due to a new defined noise source (ILFAIP) is calculated. [•] We find that the scanning method is a reliable algorithm for source reconstruction. [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: In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The dynamic calculations are performed in the frequency domain which leads to reducing the dimension of the variable space of the noise equations. The forward/adjoint noise in two energy group is obtained 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 is also obtained from the calculated adjoint Green''s function. Comparison of the calculated neutron noise at zero frequency with the results of static calculation, and utilizing the results of adjoint noise calculations are two different procedures to validate the neutron noise calculations. [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]

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]

In this paper, a simpler approach compared to the existing approaches is developed to analyze nuclear reactor dynamics based on the explicit Monte Carlo method. A new population control method is also introduced to prevent neutron population growth and consequent computer memory shortages, which also increases simulation speed. The scheme is applied for time-dependent particle tracking in three-dimensional arbitrary geometries in the presence of feedbacks through a code named MCSP-Explicit. Changes in material density, as well as geometry dimensions, are also considered during simulation. MCSP-Explicit can be run with either continuous or multigroup data libraries, and it is further boosted by parallel processing to speed up simulations. A number of benchmark problems are studied at the end to evaluate the performance of the proposed approach in various situations. [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]

In this paper an approach based on system identification is used for fault detection in a nuclear reactor. A continuous-time Extended Kalman Filter (EKF) is presented, which allows the parameters of the nonlinear system to be estimated. Also a fault tolerant control system is designed for the nuclear reactor during power changes operation. The proposed controller is an adaptive critic-based neuro-fuzzy controller. Performance of the controller in terms of transient response and robustness against failures is very good and considerable. [ABSTRACT FROM AUTHOR]

• The development of the SD-HACNEM neutron noise simulator. • Use of high-order flux expansion in order to simulate ILOFAIP neutron noise. • Use of nodes in the dimensions of a fuel assembly of Western nuclear reactors. • Use of fourth-degree polynomials in discretization of diffusion equations. In this study, the SD-HACNEM (Sharif Dynamic - High order Average Current Nodal Expansion Method) neutron noise simulator in two energy groups using a second-order flux expansion method for two-dimensional rectangular X Y-geometry has been developed. In the first step, the calculations were performed for the steady state and results of ACNEM (Average Current Nodal Expansion Method) and HACNEM (High order Average Current Nodal Expansion Method) were examined and compared. To solve the problem, the power iteration algorithm has been used to calculate the distribution of neutron flux and neutron multiplication factor by considering the coarse-mesh (each fuel assembly one node). To validate the steady state calculations, the results were compared with the western nuclear reactor BIBLIS-2D (reference model). In the next step, dynamic calculations were performed in the frequency domain. For this purpose, after discretizing the neutron noise equations by the high-order average current nodal expansion method (NEM), a neutron noise source of absorber with variable strength was simulated. The results were verified by performing simulation at zero frequency and adjoint calculations. Then, the distribution of neutron noise for Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) is obtained. The numerical results showed that the use of HACNEM compared with ACNEM, without reducing the size of the meshes in neutron noise simulation, presented more accurate. [ABSTRACT FROM AUTHOR]